Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A comprehensive examination of procedures for testing the significance of a correlation matrix and its… Fouladi, Rachel Tanya 1991

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1991_A8 F67_5.pdf [ 30.44MB ]
Metadata
JSON: 831-1.0098755.json
JSON-LD: 831-1.0098755-ld.json
RDF/XML (Pretty): 831-1.0098755-rdf.xml
RDF/JSON: 831-1.0098755-rdf.json
Turtle: 831-1.0098755-turtle.txt
N-Triples: 831-1.0098755-rdf-ntriples.txt
Original Record: 831-1.0098755-source.json
Full Text
831-1.0098755-fulltext.txt
Citation
831-1.0098755.ris

Full Text

A COMPREHENSIVE EXAMINATION OF PROCEDURES FOR TESTING THE SIGNIFICANCE OF A CORRELATION MATRIX AND ITS ELEMENTS by RACHEL TANYA FOULADI B.A., The University of British Columbia, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER'S OF ARTS in THE FACULTY OF GRADUATE STUDIES Department of Psychology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1991 © Rachel Tanya Fouladi, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Psychology The University of British Columbia Vancouver, Canada Date September, 1991 DE-6 (2/88) ii ABSTRACT Correlational techniques are important tools in multivariate behavioural and social science exploratory research. A wide array of procedures have been proposed for testing (a) whether any of the variables are related, and (b) which variables are related. In the current study, the performance of the procedures currently available for testing these distinct questions is assessed on the primary Neyman-Pearson criterion for an optimal test. According to this criterion, an optimal procedure is the most powerful procedure that controls experimentwise Type I error rate at or below the nominal level. The findings of the first part of this study addressing how to test complete multivariate independence suggest that the statistic traditionally used (QBA) is not the optimal test, and that one of several recently derived statistics (QSE> QSA> QF) should be used. Computational efficiency of the procedures is also considered with the resulting recommendation of the use of QSA- The second part of this study addresses how to test which variables are correlated; the findings suggest the use of a multi-stage order statistics approach with z-tests (CF). The conditions necessary to ensure maximal power when addressing these questions are also considered. iii T A B L E O F C O N T E N T S ABSTRACT ii T A B L E OF CONTENTS iii LIST OF TABLES .' vii LIST OF FIGURES xvii ACKNOWLEDGEMENTS xviii GENERAL INTRODUCTION l Correlational Techniques 2 PART I TESTING WHETHER ALL THE CORRELATIONS ARE ZERO 6 1. Introduction 6 1.1 Likelihood ratio criterion based tests 7 Modifications in the multiplier 9 Box 1949 9 Box 1949, Bartlett 1950 10 Modifications in the root 11 Lawley 1940 11 Modifications in the multiplier and root 11 Bartlett 1950 11 1.2 Quadratic form tests derived from asymptotic normal theory 12 iv Tests based on the asymptotic normal distribution of correlations 13 Browne 1977 13 Tests based on the normalizing property of the Fisher transform 14 Steiger 1980, Burt 1954 14 Steiger and Fouladi 1991a, 1991b 16 1.3 Summary of LR and NT based tests 20 1.4 Other tests of multivariate independence 21 An exact test: Mathai and Katiyar 1979 21 A normal approximation: Mudholkar, Trivedi, and Lin 1982 21 Test on rmax 22 A sum of independent chi-squares: Steiger and Fouladi 1991c 22 1.5 Overview of simulation studies of tests of multivariate independence 23 1.6 Current state of affairs : 26 2. Methods 26 Procedures for generation of sample correlation matrices 26 Simulation experiments 28 Measures of experimentwise Type I error rate control 30 3. Results 30 When P is equal to I 30 When P is not equal to 1 32 4. Conclusions 33 PART II IDENTIFYING WHICH CORRELATIONS ARE NON-ZERO 34 1. Introduction 34 1.1 Simultaneous test procedures 35 t-tests at nominal alpha 35 Reduced alpha t-test procedures: Bonferroni (RB), Dunn-Sidak(RD) 37 1.2 Sequential test procedures 39 Procedures using t-tests 42 V Multi-stage reduced alpha: Bonferroni, Dunn-Sidak 42 Procedures using order statistics theory 45 Silver 1988 47 Fouladi . 49 Steiger 55 1.3 Overview of papers on the topic of tests on correlations 56 1.4 Current state of affairs 57 2. Methods 59 Procedure for generation of sample correlation matrices 59 Simulation experiments 60 Measures of performance 61 3. Results 63 P equal to 1 65 No preliminary test of the null hypothesis 65 With a preliminary test of omnibus hypothesis 66 P not equal to 1 66 With no preliminary test of the omnibus hypothesis 66 With a preliminary test of the null hypothesis 67 Detection theory measures of performance 67 Examining experimentwise Type I error control and Tp 68 3. Conclusions 68 G E N E R A L D I S C U S S I O N 7 0 1. A discussion of the results of this study in the context of prior research 70 1.1 Experimentwise Type I error control 70 Considering the tests of the omnibus null hypothesis 71 Considering tests of the elements of a correlation matrix 72 1.2 Power issues 73 1.3 Important design issues 74 2. Extensions and suggestions for future study 75 2.1 Tests of alternative null hypotheses 75 vi Generalizations of the omnibus tests 75 Generalization of the tests on individual correlations 77 2.2 Extension to non-normal data 77 3. Final note 78 BIBLIOGRAPHY 81 APPENDICES 88 Appendix A Extensions of Hotelling's approximations obtained by Steiger and Fouladi (1991a) 89 Appendix B The configuration of population matrices 95 Appendix C Setting the story straight 97 TABLES 98 FIGURES 182 LIST OF TABLES Table 1 99 The relationship between the number of variables, p, and the number of pairwise correlations, vp, in a matrix Table 2 99 Asymptotic chi-square tests of complete independence with vp degrees of freedom Table 3 99 Summary table of reviews of tests of LR and NT tests of multivariate independence Table 4 100 Table of sample sizes, N, for sample correlation matrices generated under P of order p and specified N:p ratios Table 5.1 101 Table of empirical Type I error rates for tests of complete multivariate independence at a = .05 Table 5.2 101 Table of empirical Type I error rates for tests of complete multivariate independence at a = .01 Table 6.1 102 Chi-square goodness of fit values for tests of complete multivariate independence at a = .05 under a true null hypothesis, df = 1, X2i,.05 = 3-84, X2i,.01 = 6-64, X2i,.001 = 10-83; X2i5,.ooi = 37.70 Table 6.2 102 Chi-square goodness of fit values for tests of complete multivariate independence at a = .01 under a true null hypothesis viii Table 7.1.1.1 103 Empirical power of tests of complete multivariate independence at a = .05, p = 5, mNz = .1 Table 7.1.1.2 104 Empirical power of tests of complete multivariate independence at oc = .05, p = 5, mNz = .3 Table 7.1.1.3 105 Empirical power of tests of complete multivariate independence at a = .05, p = 5, mNz = .5 Table 7.1.2.1 106 Empirical power of tests of complete multivariate independence at a = .05, p = 10, mNz = .1 Table 7.1.2.2 107 Empirical power of tests of complete multivariate independence at a = .05, p = 10, mNz = .3 Table 7.1.2.3 108 Empirical power of tests of complete multivariate independence at a = .05, p = 10, mNz = .5 Table 7.2.1.1 109 Empirical power of tests of complete multivariate independence at a = .01, p = 5 mNz = .1 Table 7.2.1.2 110 Empirical power of tests of complete multivariate independence at a = .01, p = 5 mNz = .3 Table 7.2.1.3 I l l Empirical power of tests of complete multivariate independence at a = .01, p = 5 mNz = .5 Table 7.2.2.1 112 Empirical power of tests of complete multivariate independence at a = .01, p = 10, mNz =. 1 ix Table 7.2.2.2 113 Empirical power of tests of complete multivariate independence at a = .01, p = 10, mNz = .3 Table 7.2.2.3 114 Empirical power of tests of complete multivariate independence at a = .01, p = 10, mNz = .5 Table 8 115 Experimentwise Type I error rate for testing the correlations between p uncorrelated variables at the nominal level a c = .05 under the assumption of independent tests: a E X =l - ( l -<x c)Vp Table 9 116 Table of critical values that an observed value must exceed for each procedure to test the significance of the pairwise correlations from a matrix of order p = 5 Table 10.1.1.1 117 Table of empirical results for tests of correlations with no preliminary omnibus test when P = I, p = 5 Table 10.1.1.2 118 Table of empirical results for tests of correlations with no preliminary omnibus test when P = I, p = 10 Table 10.1.2.1 119 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P = I, p = 5 Table 10.1.2.2 120 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P = I, p = 10 Table 10.2.1.1.1.1 121 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .1, pNz = .2 Table 10.2.1.1.1.2 122 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .1, pNz = .4 X Table 10.2.1.1.1.3 123 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .1, pNz = .6 Table 10.2.1.1.1.4 124 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .1, pNz = .8 Table 10.2.1.1.2.1 125 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .3, pNz = .2 Table 10.2.1.1.2.2 126 Table of empirical results for tests of correlations with no preliminary omnibus test when P I, p = 5, mNz = .3, pNz = .4 Table 10.2.1.1.2.3 127 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .3, pNz = .6 Table 10.2.1.1.2.4 128 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .3, pNz = .8 Table 10.2.1.1.3.1 129 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .5, pNz = .2 Table 10.2.1.1.3.2.. 130 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .5, pNz = .4 Table 10.2.1.1.3.3 131 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .5, pNz = .6 Table 10.2.1.1.3.4 132 Table of empirical results for tests of correlations with no preliminary omnibus test when P 561, p = 5, mNz = .5, pNz = .8 xi Table 10.2.1.2.1.1 133 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .1, pNz = .2 Table 10.2.1.2.1.2 134 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .1, pNz = .4 Table 10.2.1.2.1.3 135 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .1, pNz = .6 Table 10.2.1.2.1.4 136 Table of empirical results for tests of correlations with no preliminary omnibus test when P* I, p = 10, mNz = .1, pNz = .8 Table 10.2.1.2.2.1 137 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .3, pNz = .2 Table 10.2.1.2.2.2 138 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .3, pNz = .4 Table 10.2.1.2.2.3 139 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .3, pNz = .6 Table 10.2.1.2.2.4 140 Table of empirical results for tests of correlations with no preliminary omnibus test when P 561, p = 10, mNz = .3, pNz = .8 Table 10.2.1.2.3.1 141 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .5, pNz = .2 Table 10.2.1.2.3.2 142 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .5, pNz = .4 Table 10.2.1.2.3.3 143 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .5, pNz = .6 Table 10.2.1.2.3.4 144 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 10, mNz = .5, pNz = .8 Table 10.2.2.1.1.1 145 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .2 Table 10.2.2.1.1.2 146 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .4 Table 10.2.2.1.1.3 147 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .6 Table 10.2.2.1.1.2 148 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .8 Table 10.2.2.1.2.1 149 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .2 Table 10.2.2.1.2.2 150 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .4 Table 10.2.2.1.2.3 151 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .6 Table 10.2.2.1.2.4 152 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .8 xiii Table 10.2.2.1.3.1 153 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .2 Table 10.2.2.1.3.2 154 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .4 Table 10.2.2.1.3.3 155 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .6 Table 10.2.2.1.3.4 156 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .8 Table 10.2.2.2.1.1 157 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz = .2 Table 10.2.2.2.1.2 158 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz = .4 Table 10.2.2.2.1.3 159 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz = .6 Table 10.2.2.2.1.4 160 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz = .8 Table 10.2.2.2.2.1 161 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .3, pNz = .2 Table 10.2.2.2.2.2 162 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .3, pNz = .4 Table 10.2.2.2.2.3 163 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P I, p = 10, mNz = .3, pNz = .6 Table 10.2.2.2.2.4 164 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .3, pNz = .8 Table 10.2.2.2.3.1 165 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .2 Table 10.2.2.2.3.2 166 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .4 Table 10.2.2.2.3.3 167 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .6 Table 10.2.2.2.3.4... 168 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .8 Table 11.1 169 dEX for tests on correlations when P = I, across N:p x O x p (8crit .05 = .00427, 5crit .01 = .00562, 5crit .001 = .00717) Table 11.2 170 SEX for tests on correlations with no preliminary omnibus test when P * I, p = 5 across N:p x mNz x pNz (5crit .05 = .00427, Scrit .01 = .00562, Scrit .001 = .00717) Table 11.3 171 SEX for tests on correlations with a preliminary omnibus test when P * I, p = 5 across N:p x mNz x pNz (Scrit .05 = .00427, Scrit .01 = .00562, Scrit .001 = .00717) XV Table 11.4 172 SEX for tests on correlations with no preliminary omnibus test when P * I, p = 10 across N:p x mNz x pNz (Scrit .05 = .00427, Scrit .01 = .00562, 5crit .001 = .00717) Table 11.5 173 SEX for tests on correlations with a preliminary omnibus test when P * I, p = 10 across N:p x mNz x pNz (Scrit .05 = .00427, Scrit .01 = .00562, Scrit .001 = .00717) Table 12.1 174 Table of parametric measure of sensitivity obtained for tests of correlations with no preliminary omnibus test when P * L p=5, N:p x mNz x pNz Table 12.2 175 Table of parametric measure of sensitivity obtained for tests of correlations with a preliminary omnibus test when P * I, p = 5,N:px mNz x pNz Table 12.3 176 Table of parametric measure of sensitivity obtained for tests of correlations with no preliminary omnibus test when P * I, p = 10, N:p x mNz x pNz Table 12.4 177 Table of parametric measure of sensitivity obtained for tests of correlations with a preliminary omnibus test when P * I, p = 10, N:p x mNz x pNz Table 13.1 178 Table of parametric measure of criterion obtained for tests of correlations with no preliminary omnibus test when P* I, p = 5, N:p x mNz x pNz Table 13.2 179 Table of parametric measures of criterion obtained for tests of correlations with a prelimary omnibus test when P* I, p = 5, N:p x mNz x pNz Table 13.3 180 Table of parametric measures of criterion obtained for tests of correlations with no preliminary omnibus test when P* I, p = 10, N:p x mNz x pNz Table 13.4 Table of parametric measures of criterion obtained for tests of correlations with a preliminary omnibus test when I, p = 10, N:p x mNz x pNz xvii LIST OF FIGURES Figure 1 183 Empirical experimentwise Type I error rate for each procedure controlling ct^ x a t o r below the nominal level, O = y, p = 10, mNz = .3 for N:p = 2 and 20 Figure 2 184 Empirical experimentwise Type I error rate for CF when the omnibus null hypothesis is false, O = y, p = 10, mNz = .3 Figure 3 185 Empirical hit rate for CF when the omnibus null hypothesis is false, O = y, p = 10, mNz = .3 xviii ACKNOWLEDGEMENTS A few years of effort and consideration have gone into the completion of this project. Without the inspiration, guidance, and encouragement of Professor James H. Steiger, this study would never have been completed. I would like to thank Dr. Steiger for being available for continual interface. If I had not been able to get in touch with my supervisor and discuss my work, many problems would have taken exponentially longer to resolve. I would also like to thank Dr. Steiger's family for fielding many phone-calls and relaying accurate messages. I sincerely thank the members of my committee. Professors Steiger, Hakstian, and Wiggins have helped me bring this study to a finish. Their time, input, consideration, and support are deeply and lastingly appreciated. I thank my family for the love and support they have given me throughout my as yet short life. They have always encouraged me to continue and succeed in my studies. Without their love and support, this endeavor could not have been a reality. I wish to thank my father and mother for helping me construct an environment in which I could work with optimal efficiency. I would like to thank my partner for being so caring and supportive, but, especially for being such a good cook. I thank everyone who has contributed to this thesis. Without everybody's support, this thesis would not have been finished on time. The love and consideration that I enjoy has made this all worthwhile. 1 G E N E R A L I N T R O D U C T I O N Correlational methods are becoming increasingly popular in the behavioural and social sciences. A primary reason for this trend is the growing recognition of the legitimacy of correlational and quasi-experimental research. Numerous conditions can limit a researcher's ability to conduct experimental studies. Experimental research is often not feasible because the variables of interest can not be manipulated; this can be because of (a) the intrinsic nature of the variables or (b) ethical considerations. Alternative methods are required under these circumstances; correlational studies can be appropriate when constraints such as these apply. Correlational techniques are also useful in exploratory studies. Many researchers gather observational data for one or more occasions on several quantitative variables and then attempt to uncover important relations among the variables with exploratory data analysis. A variety of questions may be of concern to the researcher. But, the first question to be addressed is often "Given the sample data, are any of the variables related in the population?" If this is answered affirmatively, the next question becomes "Which variables are related?" Procedures that enable the researcher to answer these questions accurately are extremely important. The availability of appropriate statistical techniques is essential when the interest of the researcher is to explore the relationships between variables. 2 Correlational Techniques A variety of procedures have been proposed and used in the analysis of correlational data. Since the early 1900's, many authors have studied the sampling distribution of the correlation coefficient r based on a sample of size N drawn from a bivariate normal distribution with population correlation coefficient p. The exact sampling distribution of the sample correlation coefficient was first derived by Fisher (1915). He later proposed (Fisher, 1921) the normalizing and variance stabilizing transformation which is approximated by a normal distribution with mean z(p) and variance 1/(N - 3), for use in a significance test of the null hypothesis for a single correlation, where p is the bivariate correlation in the population. Other kinds of approximations to the distribution of r have been suggested (Sankaran, 1958; Ruben, 1966; Kraemer, 1973; Samiuddin, 1970; Konishi, 1978). Recent studies on transformations of the correlation coefficient in the presence of outliers and mixed distributions have indicated that in general, of currently available statistics, the Fisher z and the Samiuddin ts, H0:p = 0 vs. {r-pylN-2 are the transformations of choice for the test of a single correlation (Srivastava & Lee, 1983, 1984). 3 When p is equal to 0, ts is distributed exactly as Student's / with N - 2 degrees of freedom; when p is not equal to 0, t$ is approximately Student's t with N - 2 degrees of freedom (Samiuddin, 1970). Kraemer (1973) considered a more general formula; t$ is a particular case of her equation. Thus, either z, 2 or F i 2 (since fj2 equals F) transformations can be used for a significance test of a single bivariate correlation. However, when a researcher collects data on more than two quantitative variables for a single sample and the correlations between these variables are of interest to the researcher, the performance of individual significance tests on each of the correlations is not advisable. As Larzelere and Mulaik (1977) indicated, the performance of a large number of significance tests on correlations is analogous to the fallacy of multiple /-tests on means that was pointed out by Fisher (1925). In the same way that the experimentwise Type I error rate increases with the number of tests performed on a group of means, the probability of making at least one false rejection increases with multiple tests on a group of correlations. It is now common practice to take precautions when conducting tests on multiple means. Similar protection is just as important when tests on several correlations are performed. When data are collected on p variables (p > 2), the number of non-repeating pairwise correlations is pip - l)/2. Thus, the number of correlations that may be of interest, vp, increases rapidly as p increases. In a significant proportion of correlational studies, especially ones that are exploratory, the researcher is often concerned with examining all non-repeating pairwise correlations; hence, in many studies, vp equals pip - l)/2. Table 1 shows the relationship between p and the number of pairwise correlations for several common values of p. Given the sheer number of pairwise correlations under increasing p and keeping in mind the problem of inflated experimentwise Type I error rate 4 with multiple tests, it is obvious that the question of how the researcher should proceed in testing whether the p variables are significantly correlated is very important. Indeed, how to test whether the vp, where vp = p(p - l)/2, correlations between p variables on a single sample of size N are significantly different from zero and to simultaneously control experimentwise error rates has been a question of concern for the better part of this century and continues to be so. For some of the same reasons why the analysis of variance is commonly used as an omnibus test on means, overall tests on the correlation matrix have been examined as one way of obtaining experimentwise Type I error rate protection when testing the simultaneous hypothesis that all the correlations are zero. These overall tests address the first exploratory question of whether any of the correlations are non-zero in the population. These tests, however, do not address the second exploratory question of which correlations are non-zero in the population. Another category of tests is necessary to answer the latter question. In the present study, the procedures available to answer these two distinct questions concerning significance tests on correlation matrices and their elements are reviewed. In Part I, the question of how to test the null hypothesis of complete multivariate independence is examined; section 1 consists of a comprehensive review of the statistics available for this test; section 2 details the method of the Monte Carlo simulation experiment conducted to examine the performance of the statistics currently available; sections 3 and 4 describe some of results of this examination. In Part II, the question of how to test which correlations are significantly different from zero is examined; section 1 consists of a review of some of the procedures available to address this question; section 2 details the method of the Monte Carlo simulation experiment conducted to examine the performance of these procedures; sections 3 and 4 describe some of results of this examination of how to test which correlations are significant. Parts I and II are followed by a general discussion of the results 5 of the current study in the context of previous research; in a final note, tentative recommendations are made on how to proceed in testing the significance of a correlation matrix and its elements. 6 P A R T I TESTING WHETHER ALL THE CORRELATIONS ARE ZERO 1. Introduction Let R = {r,y} be a pxp sample correlation matrix based on N vectors of observations from a multivariate normal distribution with population correlation matrix P = {p,y}. There are several procedures to test the hypothesis that all of the correlations between p variables are zero, i.e., H0: = 0, V i *j vs Hy. pij *0, for at least one p,y, i*j , or expressed in equivalent matrix terms, H0:V = 1 vs. / / i : P * I , where I is the identity matrix. The procedures discussed in this section all test the null hypothesis of complete multivariate independence. The procedures vary substantially in accuracy and ease of computation. Most are seldom if ever described in textbooks. These procedures may be conceptualized in several different ways. Some procedures are exact, or very close to it, but are very difficult to compute. Others are based on asymptotic approximations and are somewhat less accurate. 7 One class of tests is based on the likelihood ratio criterion. Another class of tests is based on asymptotic normal theory for correlations and their differentiable functions; these tests are in general much easier to compute but have not yet become popular. Historically, the procedures that have been used to test the null hypothesis of multivariate independence have been of a general class of likelihood ratio tests. Under the assumption thatNobservation vectors xt,...,x# have been drawn independently from the p-dimensional multinomial population Np(u,Z), where £ is nonsingular, then the maximized value in the parameter space of the distribution is 1.1 Likelihood ratio criterion based tests 1 (N exp --j-tr X ( x I " X X X I ~ X ) ^ 1 Under the null hypothesis, the maximized likelihood of the sample is The Wilks (1935) generalized likelihood criterion is the ratio A — — , L(Q) which by substitution equals ,N/2 (OyGp) Wilks's lambda has the simplified form A = | R | W 2 , where |R| is the determinant of the positive semi-definite sample correlation matrix of p variables. Neyman and Pearson (1928, 1931) showed that under the null hypothesis, the following function of the generalized likelihood ratio criterion, Q' = -2 In A , is a large-sample chi-square distribution with vp degrees of freedom. The Neyman-Pearson likelihood ratio method in conjunction with Wilks's lambda results the following relationship, Q' = A/(-ln|R|) , where Q' may be used to obtain a decision rule in a test of multivariate independence. Unfortunately, the distribution of this likelihood ratio statistic departs rather significantly from a chi-square distribution at small samples. Many authors have indicated that this should be considered a large sample test and is too inaccurate for small samples (e.g., Morrison, 1976). There have been numerous attempts to deal with this problem. 9 The modifications to the likelihood ratio test that have been proposed have varied along two dimensions. (1) Changes in the multiplier, N, have been suggested in order to improve the performance of the statistic. (2) Changes in the root, - ln|R|, have also been put forth. In general, the changes in the root that have been suggested have the desirable property of increased ease of computation since calculating the determinant of a correlation matrix can be quite tedious. Modifications in the multiplier Box 1949 The use of the likelihood ratio statistic was modified in an approach discussed by Box (1949). In the modified approach, U is a function of X, U = X2'N , and W is a function of U, w = r/N-D/2 In a similar development as the derivation of Q, Q is obtained, g=2(- lnW) , which in terms of U is Q=(N-l)(-lnU) . Substitution of U yields G=(tf-l)(-ln|R|) , where Q is asymptotically distributed as a chi-square with vp degrees of freedom. 10 Box 1949, Bartlett 1950 Box (1949) extended an approach adopted by Bartlett (1937, 1938) in which, from the moments of a more sufficient form of the likelihood test of multivariate independence, he developed a scale factor which is related to sample size. He suggested the use of the 2p+5 multiplying factor, m = l - , with Q and indicated that the product of m and Q is distributed asymptotically in TV as a chi-square with vp degrees of freedom. Thus, the use of mQ, where mQ = m(N-l)(-\n\R\) = (^- l -^)(- ln |R|) , is suggested as an asymptotic test for multivariate independence. In order to improve the performance of the likelihood ratio test at small samples, Bartlett (1950, 1954) suggested the use of this modified test statistic. Bartlett indicated that improved approximation to the limiting distribution may be achieved by adopting the above modification in the multiplier (Box, 1949; Bartlett, 1950,1954). Although Box suggested this modification to the likelihood ratio test, Bartlett is often credited with this statistic. This statistic is commonly referred to as "Bartlett's test". Thus, in keeping with convention, the notation, Qg^, is adopted to refer to this statistic. 11 Modifications in the root Lawley 1940 Lawley (1940) showed through a multiple MacLaurin expansion that -ln|R| is approximately equal to rij . Hence, the test of multivariate independence that develops from Lawley's result is the following quadratic form statistic, where Qi is asymptotically distributed as a chi-square with vp degrees of freedom. Modifications in the multiplier and root Bartlett 1950 Bartlett (1950) suggested that a more appropriate version of Lawley's (1940) test is a statistic that includes the MacLaurin approximation and the multiplying coefficient proposed by Box and Bartlett; the resulting quadratic form statistic is where, as before, QJJ^ is asymptotically distributed as a chi-square with vp degrees of freedom. This test capitalizes on the modification proposed by Lawley and produces a computationally simpler variant than Bartlett's test. Morrison has indicated that this approximation is best for small correlations, and that for a large sample size, the decision should be the same as that obtained from the determinental formula (Morrison, 1976). Even 12 though it was Bartlett who suggested the modifications, the resulting statistic is commonly attributed to Lawley. 1.2 Quadratic form tests derived from asymptotic normal theory Steiger and Browne (1984) presented a general class of tests based on asymptotic theory for the distribution of elements of a correlation matrix and their functions. Asymptotic theory is available for the joint distribution of correlation coefficients under an assumption of multivariate normality (Hsu, 1949; Olkin & Siotani, 1976; Pearson & Filon, 1898), and without this assumption (Hsu, 1949; Steiger & Hakstian, 1982; Steiger & Browne, 1984). Available asymptotic theory for simple correlation coefficients and functions of a correlation matrix and some useful asymptotic theory of testing linear hypotheses can be applied to obtain simplified tests of the hypothesis of multivariate independence. Let x be apxl random vector variate with expected value \x, covariance matrix X, and population correlation matrix P. Let p be a v^ xl vector of unique off-diagonal elements of P. Let r be the corresponding random vector of elements of the sample correlation matrix R, based on a sample size of N on x. Define r* = (N- \)W(r - p). r* has an asymptotic multivariate normal distribution with mean vector 0, and variance-covariance matrix *¥*, where the elements of VF* are given by ¥ *jkjm = I [(p jl ~ P jkPkl ){Pkm ~ PklPlm ) + (pjm-P jlPlm ){Pkl ~ PkjP jl) +{P jl ~ PimPml )(pkm ~ PkjPjm ) + {pjm-P jkPkm ){Pkl ~ PkmPml)] (Pearson & Filon, 1898). The large sample distribution of r is hence, approximately multivariate normal with mean vector p and variance-covariance matrix ¥ = VF*//V. 13 Tests based on the asymptotic normal distribution of correlations Browne 1977 Browne (1977) described a very general procedure for testing pattern hypotheses on correlations. Steiger and Browne (1984) showed that pattern hypotheses can be expressed as linear hypotheses on p of the form H0: Mp = h , where M is a specified gxvp matrix of rank g, and h is a specified gxl vector. If ¥ * is any consistent estimate of x¥*, then the asymptotic distribution under HQ of the statistic, Q* = (N-l)(Mr-h)'(MvP*M)~1(Mr-h) , is chi-square with g degrees of freedom. While in general, M and h can have arbitrarily chosen elements, in the case of a test of multivariate independence: g equals vp, M is the identity matrix, and h is the null vector. The resulting test statistic, 2 * = (/V-l)r/xF*~1r , is asymptotically distributed as a chi-square with vp degrees of freedom. Under the assumption that *F* is the identity matrix, ¥ * is taken to be I. Where in general r is asymptotically N^p,*?), under the null hypothesis, r is approximately Np(0,D) where D is [1/0V- 1)]I. Thus, (N- l)!/2r is asymptotically Np(0,I) and (N- l^r'iN- V)ll2r is asymptotically distributed as a chi-square. Therefore, the test statistic, 14 Q* = (N-l)r'r , is distributed asymptotically as a chi-square with vp degrees of freedom. Let this special case be referred to as QBR. The derivation of this statistic as presented by Browne (1977) is by the method of generalized least squares which is asymptotically equivalent to methods of maximum likelihood but computationally more efficient. For the special case of concern, testing the null hypothesis that all the correlations are zero, the method of generalized least squares results in the same test suggested by Lawley's MacLaurin series expansion of - lnjRj, QL. Thus, for a test of complete multivariate independence, note that QBR = Q^. Tests based on the normalizing property of the Fisher transform Steiger 1980, Burt 1954 Steiger (1980a) showed how to modify Browne's general procedure by use of asymptotic theory for monotonic, differentiable functions of a correlation coefficient. Let f(r) be a qxl vector of functions of the elements of r, differentiable at r = p. Then (N-l)!/2(f(r) - f(p)) has an asymptotic distribution which is multivariate normal with mean vector 0, and variance-covariance matrix P*, where Y* = A,X¥*A and A' = ^/^\ r_^-Let z r be a VpXl vector of Fisher transforms of the elements of r, where z r = {z,y}. Straightforward application of the multivariate delta theorem (Olkin & Siotani, 1964) yields the result that zr, with A' = ^ /^.\r_^, has an asymptotic distribution which is multivariate normal with mean Zp and variance-covariance matrix T*/(N - 3), where T* has typical elements given by 15 Y j k M (i-p^ Xi-A) (Dunn & Clark, 1969). Capitalizing on the normalizing and variance stabilizing effect of the Fisher transform, Steiger (1980a) presented the derivation of an alternative statistic. In the case of the Fisher transform, he obtained the quadratic form Q* = (N-3)z; f * _ 1 z r . Under the null hypothesis and the assumption that VP* is I, (N- 3)1 / 2zr has an asymptotic distribution which is multivariate normal with mean vector 0 and variance-covariance matrix I. As a special case of the general test proposed by Steiger, one obtains for a test of the hypothesis of multivariate independence. Q^j is asymptotically distributed as a chi-square with vp degrees of freedom. In the back pages of a factor analysis paper recently cited in Reddon (1987), Cyril Burt (1952) proposed a statistic without proof to be used for tests of residual correlations after extraction of factors. Taking this statistic and considering it under the condition of extracting no factors, one obtains a test, QB\J, that the correlation matrix has only unique factors, i.e., represents p uncorrected variates. The special case of this asymptotic chi-square test statistic is equivalent to the test of multivariate independence, Q^j, described by Steiger (1980a, 1980b). QBJJ equals Q^j with vp degrees of freedom. 16 The theoretical justification of the statistic as discussed by Steiger is that, since the Fisher transforms of the correlations are more nearly normally distributed than the correlations, the square of the normalized Fisher z/y will be more nearly chi-square distributed and so will their sum. For this statistic, Steiger uses the approximation to the inverse of the variance of the Fisher transforms, N - 3, suggested by Hotelling (1953). Steiger and Fouladi 1991a, 1991b Generations of psychometricians have believed the commonly used approximate value of the variance of the Fisher transforms, (N- 3)_1, to be accurate enough for practical use. However, analysis and simulation studies have indicated that this is not quite the case (Konishi, 1978; Steiger & Fouladi, 1991a). The results of the examination of the quality of the approximation suggest that a test using known theory for the moments of the Fisher transform and the squared Fisher transform will likely result in improved performance. Konishi (1978) citing Johnson and Kotz (1970) indicated that the variance and the mean of the Fisher transform may be approximated by z(p)+p/2n+p(p+p2)/8/z2 and {l+(4— p 2)/2«+(22-6p 2-3p 2)/6« 2}/«, respectively where n equals A7 - 1. When p equals zero, the mean is zero and the variance is {l+4/2«+22/6«2}/n. Unfortunately, this approximation is not accurate enough for use in practical application (Steiger & Fouladi, 1991a). Steiger and Fouladi (1991a) derived exact expressions for the cumulants and moments of the Fisher transform and the squared Fisher transform when p = 0. They suggested that use of these results may produce significant improvements in the performance of tests of pattern hypotheses on correlation matrices. A test of multivariate independence, Q$£, results from some of these exact expressions. Let K"2 and /Qj be the second and fourth cumulants of the Fisher transform, 17 K - 4 = & A r — N even , 12 2 2^2 odd , K * 3^4 \r — N even , 120 4 7T 1 2 ^ odd , where W-4 2 1 , - 1 < y ;=1 N-3 N even 2 1 T — r iv* odd A (2/-iy From the second and fourth cumulants of the Fisher transform, the first and second cumulants of the squared Fisher transform were obtained, where K1(Z2) = K2(Z) , K2(Z2) = K4(Z) + 2K2(Z) The mean and variance of the squared Fisher transform are thus, and Li\(z2) = K2(z) , H'2(Z2) = K4(Z) + 2K2(Z) + K22(Z) Ideally, as a chi-square with one degree of freedom, (N - 3)z2 should have a mean of one and a variance of two. However, for small samples, the mean and variance of (N - 3)z2 18 deviate non-trivially from these values. The effect of this deviation becomes more severe when more correlations are tested. If the actual mean and variance of a squared Fisher transform are known, then a single z2 may be corrected, by a linear transformation, so that its mean and variance are precisely correct. If one assumes the vp Zy2 values are essentially independent, then both the mean and variance of Q^mny also be corrected. The current mean of Qgj is (N - 3)vpK2; the desired mean is vp. The current variance of Q$T (assuming independence of zy's) is (N -3)2vp(K4 + 2K"2>; the desired variance is 2vp. QSE corrects the mean and variance of Q^j with the following linear transformation, where the multiplicative and additive correction constants based on the exact results for the first two moments of the squared Fisher transforms are In the limit, under increasing sample size, m$£ approaches one and a$E approaches zero. Hence, Q$£ is asymptotically distributed as a chi-square with vp degrees of freedom. Steiger and Fouladi suggested that use of the correction constants will likely result in improved small sample performance. However, for greater computational ease, the use of series approximations is preferable to the exact expressions given above. QSE = mSEQsT + aSE ' and aSE = vp l-msE(N- 3)K[(Z2) 19 In a classic paper in the annals of correlational statistics, Hotelling (1953) derived series expansion formulae for moments of the correlation coefficient, and moments of the Fisher transformation about its mean. Unfortunately, these formulae are not accurate enough to be used in place of the exact formulae (Steiger & Fouladi, 1991b). Steiger and Fouladi (1991b) extended Hotelling's series expansion formulae. Analytic expansion of the approximations to the moments yields several more terms. The expanded approximations for the first-four moments of the Fisher transform and the lambda's are included in Appendix A. Monte Carlo simulation experiments have shown that these results are a significant improvement over approximations that are in current use and are accurate to a high level of precision (Steiger & Fouladi, 1991b). The corrections to the series approximations for the first two moments of the squared Fisher transforms when p = 0 are given below. Defining v,- = E[(z(r))'], we have 1 v2 (N-\) 1 + + (N-l) 3(N-])2 6 127 10 ^ + — + + (N-l)3 15(N-1) 4 (N-l) 5 J 1 (N-l)2 , 14 46 3+ —-; + (N-l) (N-l)2 124 4247 ^ (N-IY 15(N-IT Hence, the series approximations for the mean and variance of the squared Fisher transforms are and V4 - Vj2, respectively. QSA corrects the mean and variance of QgT with a linear transformation using the above series approximations. Specifically, is given by QsA = mSAQsT + aSA > where the multiplicative constant is 20 2 ™5A = and the additive constant is aSA = v /,[l-m S4(^-3)v 2] • In the limit, under increasing sample size, approaches one and a$A approaches zero. Hence, Q$A is asymptotically distributed as a chi-square with vp degrees of freedom. All of the statistics based on the generalized likelihood criterion and asymptotic normal theory for testing complete independence among p variables are asymptotic chi-square statistics with vp degrees of freedom. For each of these statistics, the test of the null hypothesis, P = I, rejects when the observed value exceeds X2vP,l-a • The LR and NT tests of multivariate independence reviewed in this paper vary along two dimensions: (a) the multiplier, (b) the root. These tests are tabled by multiplier and root in Table 2. The standard likelihood ratio criterion, based on the natural logarithm of the observed correlation matrix, gives an overall test procedure. However, the statistics from the class of tests derived from the standard likelihood ratio criterion necessitate certain considerations. (1) The observed correlation matrix is singular if the number of variables,/?, is greater than or equal to N, the sample size. The determinant of a correlation matrix that is singular is not defined. Thus, the tests utilizing the determinant can only be used when N is greater than p. (2) The likelihood ratio statistic and modifications using - lnJR| as a root have been derived as asymptotic tests. Further caution with respect to the use of the test comes from 1.3 Summary of LR and NT based tests 21 the results of Monte Carlo simulations indicating that the statistic is not a good approximation to a chi-square unless N is large. Studies have indicated that the various modifications have different sample size requirements. Asymptotic normal theory tests are easier to compute than likelihood ratio based tests. However, results obtained in Monte Carlo simulation studies on normal theory tests currently available show that these statistics do not perform as well as expected under certain conditions. Steiger and Fouladi have suggested that the recently derived Q^E and Q$A result in improved performance. 1.4 Other tests of multivariate independence In recent years, other classes of tests have been proposed. For various reasons, these tests have remained more or less unknown. An exact test: Mathai and Katiyar 1979 In an important but often overlooked paper, Mathai and Katiyar (1979) derived an exact test of the hypothesis of multivariate independence. The mathematical and computational aspects of the work of Mathai and Katiyar are quite complicated. The test is extremely difficult to describe, and just as difficult to calculate. Computer software is essential for the performance of the test. This software is not currently being distributed in a form that is accessible to the general research community. A normal approximation: Mudholkar, Trivedi, and Lin 1982 Mudholkar, Trivedi, and Lin (1982) proposed a normal approximation to test the null hypothesis. The computations of this procedure, though rather complicated, are less so than those of Mathai and Katiyar (1979). This procedure and the approximation are reportedly 22 quite accurate. However, test results with large sample sizes or matrices have not been published. The approximation has not been used widely in practice, although the authors have stated that they can provide a FORTRAN program to perform the necessary computations. Test on r m a x Conceptually equivalent to the test of the hypothesis that all the correlations are zero is the test that the largest correlation is zero. One technique involves ordering the observed correlations, then comparing r m a x = maxl ) to a distribution of order statistics from the half-normal distribution. Moran (1980) considered an another method and examined the asymptotic approximation of a test on the largest correlation to the likelihood ratio statistic. In general, these approaches have not received much attention for use as alternative omnibus test procedures. A sum of independent chi-squares: Steiger and Fouladi 1991c Various studies have indicated that correlations between p independent variates are pairwise uncorrected (Cameron & Eagleson, 1985; Geisser & Mantel, 1962) and are asymptotically totally independent and jointly normally distributed (Cameron & Eagleson, 1985). Monte Carlo studies have confirmed that under the null hypothesis, the squared Fisher transforms are essentially uncorrelated (Steiger & Fouladi, 1991c). These results suggest the possibility of a test using the distribution of the sum of several independent functions. 23 Several well-known statistics are available for a test of the hypothesis p = 0. As discussed earlier, a z-test, f-test, or F-test can be used to test the significance of a bivariate correlation. The F-test of this null hypothesis for a single correlation is given by the square of the Student's t statistic, i.e., F(r) = (/V-2) < r2 ^ 1-r 2 where, when p = 0, F(r) is distributed as an F with one and N- 2 degrees of freedom. Let O(F) be the cumulative probability distribution function for F. The following function, X(r) = -21n(l-<D(F(/-)) , is exactly distributed as a chi-square with two degrees of freedom (see, e.g., Hedges & Olkin). For each correlation, asymptotically independent chi-square statistics may be computed from the probability level of each corresponding F statistic. The sum of these vp approximately independent chi-squares gives the statistic where Qp is asymptotically distributed as a chi-square with 2vp = pip - 1) degrees of freedom. It follows that Qp can be used as a test of multivariate independence. 1.5 Overview of simulation studies of tests of multivariate independence The statistic most frequently used for tests of multivariate independence is QBA- However, as has been shown, a number of alternative procedures are available. To date, one of the best and certainly one of the easiest to use is £>sr- Steiger (1980a) demonstrated that this statistic 24 controls Type I error better than QBA at small-to-moderate sample sizes. This result was confirmed by Wilson and Martin (1983), Reddon (1987), Silver and Dunlap (Silver, 1988; Silver & Dunlap, 1989). The importance of examining whether tests on several correlations control experimentwise error rates is gaining increasing recognition. There have been several papers in recent years that have purported to have examined this issue. The quality of these papers has been less than optimal (Wilson & Martin, 1983; Reddon, 1987; Silver & Dunlap, 1989), however. The studies comparing the performance of tests of multivariate independence have been compromised for a variety of reasons: (1) inadequate number of Monte Carlo replications, (2) unrepresentative sampling of the parameter space and the class of hypotheses of interest, (3) limited scope, and (4) theoretical inaccuracies. Table 3 is a summary table of reviews of LR and NT tests of multivariate independence. In the most recently published examination of the question of how to test the significance of correlation matrices, Silver and Dunlap (1989) considered Brien's (1984) application of an analysis of variance approach to tests of equal correlations in a correlation matrix for a possible test of multivariate independence. Brien proposed a procedure for examining linear hypotheses on correlations. One special case of his test is a "grand mean" test (in the ANOVA sense) that the mean of all the correlations is zero. This statistic is 2^ (N-3) QAN where is asymptotically distributed as a chi-square with one degree of freedom. In the original paper, Brien (1984) suggested that a test of significance of the grand mean component is equivalent to a test of the hypothesis of independence under the assumption 25 of equal correlations. Silver and Dunlap failed to note this essential assumption in their statement that a test for the grand mean tests the null hypothesis that P = I versus the alternative P * I. The failure to acknowledge the requisite assumption is a major oversight. But, most importantly, this is not an assumption that is generally made or justifiable when testing complete multivariate independence. In general, Brien's statistic is a test that the grand mean of the correlations is zero, not that all the correlations are zero. A test of the hypothesis that the mean of a set of numbers is zero is not equivalent to a test that all the numbers in a set are zero. Thus, contrary to what Silver and Dunlap stated, (?AW *s n o t a valid test of multivariate independence. Silver and Dunlap performed a Monte Carlo comparison of QBA> QST> QAN> QBR procedures and concluded that QA/V ftad the best overall performance. However, their Monte Carlo populations involved only non-negative correlations! In general, researchers designing Monte Carlo studies have not employed negative correlations. Analysis of the Brien statistic proposed by Silver and Dunlap as a general test of multivariate independence indicates that the chi-square value is sensitive to signs of the correlations. Given this fact, the exclusion of negative values from the range of population correlation coefficients is a serious oversight. This problem is a classic example of what happens when the Monte Carlo examination of the parameter space is non-representative and this non-representativeness is unjustified. In general, when designing Monte Carlo simulation experiments, it is advisable to make some attempt to evaluate the performance of the statistics under conditions that are representative of the parameter space and the class of hypotheses of interest. This is a very complex and important issue. When the conditions are not representative, this non-representativeness must be justified. 1.6 Current state of affairs As has been shown, when observations are independent and identically distributed multivariate normal random variables and the measure of association is the Pearson product moment correlation, there are a wide variety of procedures available for testing the degree of relationship. Since the Mathai and Katiyar exact procedure and the Mudholkar, Trivedi, and Lin normal approximation technique are effectively unavailable, in general they have not been included in Monte Carlo examinations of tests of multivariate independence. Similarly, they are not the subject of the present study. To date, Monte Carlo simulations of available tests show that Q^j has the best overall performance; however, the relative performance of the recently derived statistics, Q$£, Q$A, and Qp, is as yet unconfirmed. The present study is a comprehensive comparison of the performance of the currently available and the recently derived statistics. 2, Methods In the present paper, a Monte Carlo simulation experiment was conducted in order to compare the experimentwise error rate control of tests of complete multivariate independence. A FORTRAN program was written for this set of experiments. The program uses several subroutines from a library of statistical modules implemented by James H. Steiger and Rachel T. Fouladi. Procedures for generation of samnle correlation matrices Several techniques for the generation of sample correlation matrices are available. One way to obtain sample correlation matrices is to generate samples of random variables from a multivariate normal distribution with a specified population correlation matrix and then 27 calculate the sample correlation matrices in the usual manner. In general, a considerable amount of computation is involved in this procedure. This is particularly salient when samples are large since this procedure requires the generation of Np normal variates. Given the computational intensity of this technique to generate sample correlation matrices, the use of a more economical procedure is advised. Browne (1968) described an alternative procedure to generate sample correlation matrices that is not as computationally intensive as the standard procedure. Let T be a lower triangular matrix of order p, whose non-zero elements are independently distributed variates of the following form: tjj is distributed as chi with (N- /) degrees of freedom, tjj is distributed as N(0,1) (i > J), tjj equals 0 (i < j). Random matrix H, where H = T T 1 , is distributed as Wishart distribution with covariance matrix Ip and N- 1 degrees of freedom (Odell & Feiveson, 1966). The approach described by Browne capitalizes on the fact that random matrices H can be used to construct random matrices, A, distributed as Wishart distributions with covariance matrix X and N- \ degrees of freedom. Since £ is positive definite or semi-definite, there is a matrix O such that Z equals 00*. For computational simplicity, O is chosen to be lower triangular with positive diagonal elements computed using the square root method of triangulating a matrix (Dwyer, 1945). Then A = OHO' = (OT)(OT)f. Let S = A/N and R = (Diag A)"1/2A(Diag A) - 1 / 2 . The resulting S and R are distributed as the maximum likelihood estimates of X and P, based on samples of N observations from a p variate normal distribution with population covariance matrix, E, and correlation matrix, P. 28 Using these results, the Browne procedure for obtaining a random correlation matrix directly, without generating a random sample from the multivariate normal distribution, reduces the number of random variables to be generated from Np random normal deviates to vp random normal deviates and p variates from chi distributions. In contrast with the standard method, there is also a considerable reduction in the computation involved in calculating the correlation matrix using the Browne method. In preliminary runs, it was verified that the fast method (Browne, 1968) produced similar results to the slower standard technique based on generating independent normal observations. Independent normal observations for the standard procedure were generated using the Kinderman-Ramage (1976) procedure using mixture distributions (Kennedy & Gentie, 1980). The Kinderman-Ramage technique uses a decomposition of the half-normal into a triangular density, three nearly linear densities, and a tail region. Simulation experiments For the main body of the study, the matrices were generated using the fast method. For the examination of Type I error control, sample correlation matrices were generated from population correlation matrix P where P was equal to I; that is, the sample matrices were generated under the condition of a true null hypothesis that all of the bivariate correlations are zero in the population. P was varied along one dimension: order pip = 5, 10, 15). For the examination of Type II error control, sample correlation matrices were generated from population correlation matrix P where P was not equal to I; that is, the sample matrices were generated under the condition of a false null hypothesis. P was varied along several dimensions: (a) order p ip = 5, 10), (b) proportion of non-null correlations ipNz = .2, .4, .6, .8), (c) magnitude of non-null correlations (mNz = .1, .3, .5), and (d) configuration, 29 M, of the pattern of non-zero correlations (U = upper submatrix, R = random location). The magnitude of the non-null correlations was selected on the basis of maintaining a positive definite P; non-null correlations in increments of .1 greater than .5 for the proportion of non-null correlations selected yield non-positive definite matrices. The locations for the non-zero correlations were determined according to the configuration of P. For matrices with configuration U, the upper submatrix was filled with V j , where V i = pNz(vp), non-zero correlations of a specific magnitude. For matrices with configuration R, V/ non-zero correlations of a specific magnitude were located randomly according to locations generated using a uniform random number generator. The configurations of the random pattern matrices for varying proportions of non-zero correlations generated through this procedure are shown in Appendix B. Sample correlation matrices were generated at various sample sizes for specific ratios of sample size to number of variables (N:p = 2, 4, 10, 20, 40). Table 4 shows the sample sizes at which correlation matrices of order p were sampled. For each sample correlation matrix, the test statistic for each test of multivariate independence (QBA, QL=BR> QlA^ QST> QsE' QSA> QF) w a s calculated; the percentile point of the observed value was computed and the decisions for the hypothesis tests at the nominal levels .05 and .01 were recorded. Under each condition, experiments for tests under a true null hypothesis were replicated 100,000 times; experiments for tests under a false null hypothesis were replicated 10,000 times. The number of rejections was tabulated and transformed into proportion rejected. The experiment-wise Type I error rates for each statistic, that is, the proportion of false rejections yielded for each omnibus test statistic in 100,000 replications under each factorial condition where P equals I, were assessed. Similarly, type II error rates, that is, one minus the proportion of true 30 rejections yielded for each omnibus test statistic in 10,000 replications under each factorial condition where P equals I, were also assessed. Measures of experimentwise Type I error rate control Chi-square goodness of fit values based on a normal approximation to the binomial were computed for each statistic in each condition. The chi-square statistic used was 9 (a;-a)2 where a, is the empirical estimate of Type I error and R is the number of replications. 3. Results The empirical results for the performance of the tests of complete multivariate independence QBA> QL=B& QLA' QST' QSE' QSA> a n d QF presented in this section. When, P js equal to I Empirical Type I error rate performance of each test of complete multivariate independence was assessed with 100,000 replications under p (5,10, 15) x N:p (2,4,10, 20, 40) x a (.05, .01) factorial conditions. Table 5 gives the empirical experimentwise Type I error performance of the statistics under these factorial conditions. Chi-square goodness of fit values for experimentwise Type I error performance were computed for each p x N:p x a factorial cell for each omnibus statistic. These values are given in Table 6. 31 Tables 5 and 6 also show the overall pattern for the actual experimentwise Type I error rates of each statistic. The results indicate that the experimentwise Type I error rates for Q B R and Qm are consistently at or below the nominal level. Q B R is conservative for small and moderate-to-large ratios of sample size to number of variables; Q B R performs at the nominal level for extremely large N:p ratios. In general, Q^A is conservative for all levels of N:p ratio tested. The tabled results show that the Type I error rate performance of QBA is at the nominal level across most conditions. QBA does not perform at the nominal level for sample matrices generated at small N:p ratios. Under these conditions, QBA does not control the experimentwise Type I error rate at or below the nominal level; QBA is consistently liberal for small N:p. The results show that actual experimentwise Type I error rate for Qgj exceeds the nominal level for small ratios of sample size to number of variables. Q$j performs at the nominal level for moderate and large N:p. Q$E performs at the nominal level across most conditions. For a nominal alpha equal to .05, the experimentwise Type I error rate of the statistic is at the nominal level except when N:p is at the smallest level. For a nominal alpha equal to .01, the experimentwise Type I error rate of the statistic is at the nominal level except when N:p is at the two smallest levels. The pattern of Type I error performance of <2s£ is the same for and Qp. Overall, the analyses show a similar pattern across all levels of a and all levels of p. This consistent pattern is the following where (a) Q B R and QJJ^ are extremely conservative, (b) Q-BA-> Q-ST' QSE> QSA> QF control experimentwise Type I error loosely at the nominal level when N:p exceeds two, and (c) QBA is more liberal that Q$p, Q$A, and Qp at small N:p. 32 Given the overall results, it can be said that, in general, the tests Qgp, QSA> a n d QF satisfy the Neyman-Pearson criterion of an optimal test with a caveat that these statistics are liberal for N:p less than or equal to two. When p is not equal to I Empirical performance of QBA, QL=BR, QIA, QST> QSE> QSA> a n d QF w a s assessed with 10,000 replications under p (5,10) x N:p (2,4,10,20, 40) x a (.05, .01) x pNz (.2, .4, .6, .8) x mNz (.1, .3, .5) x M (U, R) factorial conditions. The empirical power of the statistics as tests of complete multivariate independence under these factorial conditions is given in Table 7. These tables show that the overall pattern of results is generally the same for matrices P with matrix configurations U and R. There is, however, some differential performance between the performance of QBA at these levels. The tables show that power is very weak for tests of matrices with small proportions and low magnitudes of non-zero correlations. Within each table, the results show that power increases as the ratio of N to p increases; as the proportion of non-zero correlations, pNz, increases, the power of each statistic increases. As the magnitude of the non-zero correlations, mNz, increases, the power of each statistic increases. Comparison between results of tests performed on matrices of different order shows that power increases as the order of the matrix increases. The results show that Qr^ and QBR are the least powerful statistics for tests of multivariate independence. £>S£ a n a " QSA h a v e t n e s a m e power and tend to be more powerful than Qp as mNz departs increasingly from zero. Qp tends to be more powerful than QBA. Exceptions to this overall pattern are evidenced when the N:p ratio is low. The tables show that when N:p 33 equals two, QgA is sometimes more powerful than Qp, QgA, or Q$p. The results show that Qgj- is more powerful than all of the procedures. 4, Conclusions The results of Part I of the current study show that of currendy available omnibus statistics for testing complete multivariate independence, Qp, Q$A, and Q$p have the best overall performance in terms of Type I error control. Of these recently derived statistics, Q$A and Q$E are the most powerful. Thus, Q$A and Q$p are the optimal procedures in terms of the Neyman-Pearson definition. The empirical results further suggest that if an experimenter suspects that the non-zero correlations in the population are few and small, then as large an N:p ratio as possible should be used since this will increase the power for tests under weak power conditions. 34 PART II IDENTIFYING WHICH CORRELATIONS ARE NON-ZERO 1, Introduction Testing the null hypothesis of complete multivariate independence is a primary test in social science correlational research. Rejecting this hypothesis suggests that in the population, some of the p variables are likely correlated. Depending on how the researcher has selected the variables, the question of interest varies. But, beyond examining the structure of a correlation matrix, a main question a researcher may ask is: which of the correlations are significantly different from zero; that is, which of the p variables are significantly correlated. The omnibus test does not answer this question. Like the omnibus ANOVA test procedure, the test of multivariate independence is an overall test. The overall test on the correlation matrix indicates whether there is any dependency among the variables. Just as follow-up test procedures have been suggested and are routinely conducted in the context of tests on means, similar follow-up procedures can be conducted when testing correlations. In the following, let v0 be the number of zero correlations in the set of vp bivariate population correlation coefficients. Let v{ be the number of non-zero population coefficients, thus, v, = v„ - v0. 35 A variety of procedures have been proposed for use in testing which correlations are non-zero. The test statistics traditionally used for significance tests of correlations have been t-tests or z-tests using the Fisher transforms of the correlations. Recently, however, the use of order statistics has also been proposed for this purpose. In the following, we examine the use of these statistics applied in simultaneous and sequential test procedures. 1.1 Simultaneous test procedures Tests of single bivariate correlations have been examined in the presence of outliers and mixed distributions. Research on the performance of these statistics has shown that overall the Student's f-test is the preferred procedure (Konishi, 1978; Srivastava & Lee, 1983, 1984). In order to test which of several correlations are non-zero, individual tests of the form H0i: P / = 0 vs. are performed on each sample correlation r,-, i = l...vp. One dimension on which r-tests vary is the level at which the correlations are tested. /-tests at nominal alpha One approach to test which vp elements in a correlation matrix are non-zero is to test each correlation r,-, / = l...vp at some typical nominal level, such as .05. The /-test of each correlation rejects the corresponding null hypothesis when 1 1 l-^-,N-2 2 where ac is the nominal level at which each correlation is tested. 36 The main problem with testing each correlation at the nominal level is elevated experimentwise Type I error rate, which in the context of testing "which correlations are significantly different from zero" is the probability of falsely rejecting at least one correlation in the set of correlations under examination. The probability of making at least one Type I error on the set of vp correlations is aEX ~ ^ (at * e a s t o n e TyPe I e r r o r m vptests) = 1 - Pr(no Type I errors in vp tests) = 1 - Pr(no Type I errors in v0 and Vj tests) = 1 - Pr(no Type I errors in v0 tests) . When all the Mests are independent, the experimentwise Type I error rate is vo c*EX = l-YlQ-<Xci)> i"=l and if each comparison is tested at a common level, i.e., acl =ac, V /, then the experimentwise Type I error rate is aEX=l-(l-ac)v° . Table 8 shows the experimentwise Type I error rate for testing the correlations between p uncorrected variables (i.e., vp = v0) at the nominal level, ac = .05, under the assumption of independent tests. The elevated experimentwise Type I error rate that results from testing each correlation at a nominal level typically employed in individual tests is a serious problem. This procedure of testing each correlation at the nominal level violates the convention of conducting test procedures that satisfy the Neyman-Pearson criterion. According to this decision theory criterion, an optimal test is defined as the least conservative procedure that controls the 37 overall experimentwise Type I error rate at or below the nominal level. In spite of the inflated experimentwise Type I error rate, multiple tests at the nominal level are in fact conducted quite frequently. As specified by the Neyman-Pearson decision theory definition of an optimal test, an important criterion in assessing the quality of a test is whether a procedure maintains the experimentwise Type I error rate at the nominal level. Since conducting a set of f-tests at the nominal level does not satisfy this criterion, alternative procedures to control the actual experimentwise Type I error rate at or below the nominal level have been considered. Reduced alpha /-test procedures: Bonferroni (RB), Dunn-Sidak (RD) One familiar test procedure to identify which correlations are significant is to test each correlation at a single reduced level. Typically, the reduced level is at the Bonferroni level or the Dunn-Sidak level. This is in order to ensure that the experimentwise Type I error rate is controlled at or below the nominal level. It is known that the probability of a Type I error for the set of vp /-tests is never greater than the sum of the per comparison Type I error rates acj, since the probability of making at least one Type I error is a E X = Pr U Type I error on comparison,-v VP = 2 Pr(Type I error on comparison/) /=i - Pr(Type I error on two or more comparisons) VP = ^occi - Pr(Type I error on two or more comparisons) 38 Thus, the sum of the probability of making a Type I error on each comparison is the upper limit of the probability of making at least one Type I error in the family of correlations; i.e., i If each comparison is conducted at the same level acj where aci = ccc, Vz, then the probability of at least one Type I error for the set is never greater than vpac; i.e., aEX<vpac . In order to control the experimentwise Type I error rate at or below the nominal level, a, the Bonferroni level, acB, may be used for each comparison, where a acB=— ' VP A test using a reduced Bonferroni level rejects when 2 The Dunn-Sidak level specified by the Dunn-Sidak inequality may also be taken for each comparison in order to control the experimentwise Type I error rate at or below the nominal level. The Dunn-Sidak per comparison level is acj), where a c D =l-( l -a) l /vp . A test using a reduced Dunn-Sidak level rejects when 2 Traditionally, the Bonferroni level is used due to greater computational simplicity even though tests at the reduced Dunn-Sidak level yield an experimentwise error rate close to the 39 desired level. However, since the Dunn-Sidak inequality is based on the assumption of independence, non-zero covariance between the correlations may result in experimentwise Type I error rates that exceed the nominal level (Larzelere & Mulaik, 1977); however, Hochberg and Tamhane have suggested that tests at the Bonferroni and the Dunn-Sidak levels control experimentwise alpha at the nominal level strongly (Hochberg & Tamhane, 1987). 1.2 Sequential test procedures Sequential test procedures have been proposed for use in testing which correlations are zero. Most of these procedures use a step-down testing approach. A step-down procedure begins by testing the overall intersection hypothesis, HQ= f] //o/,and then steps down through the iel hierarchy of implied hypotheses. If any hypothesis is not rejected, then all of its implied hypotheses are retained without further tests; thus, a hypothesis is tested if and only if all of its implying hypotheses are rejected. Typically a step-down procedure uses a non-increasing sequence of critical constants for successive steps of testing (Hochberg & Tamhane, 1987, p. 53). Step-down procedures are generally more powerful than the corresponding single-step procedures. Marcus, Peritz, and Gabriel (1976) proposed a general method for constructing step-down test procedures. This method is referred to as the closure method. Hochberg and Tamhane have referred to procedures resulting from the closure method as closed testing procedures. Let {///(l ^ / ^  vp)J be a finite family of hypotheses on scalar or vector parametric functions. The closure of this family is formed by taking all nonempty intersections Hp= fl Hj for P c jl,2,...,vp}. If an a-level test of each hypothesis Hp is available, then 40 the closed testing procedure rejects any hypothesis HP if and only if HQ is rejected by its associated or-level test for all Q • P. Hochberg and Tamhane described a proof by Marcus, Peritz, and Gabriel showing that a closed testing procedure strongly controls the Type I experimentwise error rate. The proof follows below. Proof. (Marcus, Peritz & Gabriel, 1976; Hochberg & Tamhane, 1987). Let {//,-,/ e P} be any collection of true null hypotheses and let Hp= f] Hj where P is some unknown subset of {1,2,...,vp}. If P is empty, then there can be no Type I error, so let P be nonempty. Let A be the event that at least one true /// is rejected and B be the event that Hp is rejected. The closed testing procedure rejects a true /// if and only if all hypotheses implying //,-, in particular Hp, are tested at level or and are rejected, and the test of /// is also significant at level or. So A = A n B and thus under Hp, a E X = PrM} = PrlAnfl} = PT{B}PT{A\B} < a. This inequality follows since Pr{B} = or when HP is true. Because the above expression holds under any Hp, the experimentwise Type I error is strongly controlled at level or. A major drawback of the closed testing procedure is the feasibility of testing all of the Hi hypotheses. The number of tests in a closed testing procedure increases exponentially with the number of elements being tested. Therefore, a shortcut version of the closed testing procedure is advocated. According to Hochberg and Tamhane, a shortcut version of the closed testing procedure was formally proposed by Holm (1979) who labeled it a sequentially rejective procedure; however, it was also independently proposed earlier in special contexts by Hartley (1955), Williams (1971), and Naik (1975). Consider a closed testing procedure that uses union-41 intersection statistics for testing all intersection hypotheses {//,-,/ e P] (that is, the test statistic for every intersection hypothesis Hp is derived from those for the Hjs by the union intersection method). Such a closed testing procedure can be applied in a shortcut manner. Union-intersection tests have the property that whenever any intersection hypothesis Hp is rejected, at least one of the Hjs implied by Hp is rejected. Therefore, in order to make a rejection decision on any H[, it is not necessary to test all Hp containing that ///; one simply needs to test only ///. However, it is essential that the shortcut procedure be conducted in a step-down manner by ordering and then testing the Hjs. This procedure ensures that a hypothesis is automatically retained if any intersection hypothesis implying that hypothesis is retained; this is referred to as the coherence condition. If the union-intersection related test statistics for Hp are of the form ZP = maxig/> Z, (which is the case if the rejection regions for the individual Hjs are of the form Z/ > Q, then the coherence requirement can be ensured if the Hjs are tested in the order of the magnitudes of the corresponding test statistics Z/'s from the largest to the smallest. Thus, the hypothesis corresponding to the largest Z/ is tested first. (Note that testing this hypothesis is equivalent to testing the overall intersection hypothesis.) If it is rejected, then any intersection hypothesis containing that hypothesis will clearly be rejected and therefore that hypothesis can be set aside as being rejected without further tests. Next, the hypothesis corresponding to the second largest Z/ is tested. This procedure is continued until some Z/ is found to be not significant. At that point, all the hypotheses whose test statistic values are less than or equal to the current Z; are automatically retained. Suppose that at some step in the procedure, the hypotheses ///, / e P, remain to be tested. Then an a-level test is obtained by comparing the test statistic Zp = max,-6/> Z,- against the upper point of its distribution under Hp = f] Hj. ieP 42 According to Hochberg and Tamhane, the short-cut procedure controls the experimentwise Type I error rate at the nominal level or if the individual tests at different steps are of level or. They suggested that this relationship between experimentwise Type I error and the nominal level at which the individual tests are conducted holds rigorously when the tests are independent; however, when the tests are not independent, they speculated that this relationship may not hold. Procedures using t-tests Multi-stage reduced alpha: Bonferroni, Dunn-Sidak A multi-stage reduced alpha level test procedure for tests on correlations was proposed by Larzelere and Mulaik (1977). The sequence of tests recommended by Larzelere and Mulaik constitutes a sequentially rejective closed testing procedure. The procedure consists of a series of tests on the correlations. According to Larzelere and Mulaik, at each stage of this procedure, all of the correlations which have not been declared significant are tested at the reduced alpha level determined by the number of correlations to be tested at that stage; i.e., /// (1 < / < vp) is tested at the con-esponding reduced level. The multi-stage procedure begins by testing all of the correlations at the strict reduced level and continues in a step-down manner until there are no rejections at a particular stage. Larzelere and Mulaik suggested using sequentially determined Bonferroni reduced alpha levels for each of the tests. The recommended procedure is described by the following sequence of tests. In this algorithm, vp is the number of correlations being tested; k is the number of correlations rejected. At the start of the procedure, none of the correlations have been tested and therefore the number of rejections, k, is zero. At each stage /, for / = l...vp, test each correlation at the two-tailed acBi level, where acBi = ccl(vp - k). Let be the 43 number of rejections made during each stage. If k( is greater than zero, increment k by k( and proceed to the next stage testing the remaining correlations at the updated level; if k[ equals zero then do not proceed to the next stage. At the ith stage, this algorithm rejects a test when 2 An equivalent procedure and more simple to describe is a sequential stepped-down test on sorted correlations; the idea behind the procedure is the same as for Holm's (1979) sequentially rejective Bonferroni procedure. The absolute values of the observed correlations are sorted. The largest of the sorted values is tested at the two-tailed a/vp level, the second largest is tested at the two-tailed cc/(vp - 1) level, the third largest is tested at the two-tailed a/(vp- 2), the ith largest is tested at the two-tailed ac#; level, where CCCBJ = oc/(vp - i + 1), and so on until one of the correlations fails to reject. In general, this algorithm rejects the /th test when 2 The following shows the equivalence of the two algorithms described above. If at stage 1, k[ correlations are rejected at the ajvp level, then those k\ correlations are the largest of the vp correlations and would have been tested at the a/vp, cd(yp - 1 ) , a l ( y p - k\+Y) levels. If these correlations are rejected at the ajvp level, then it follows directly that they are also rejected at the ajvp, aj(yp - 1 ) , a l ( v p - £]+l) levels. Following this rationale, the equivalence of the two algorithms extends to stage 2 and so on. It is clear that the multi-stage reduced alpha procedure constitutes a closed testing procedure. The multi-stage reduced alpha procedure can also be implemented using tests at 44 sequentially determined Dunn-Sidak alpha levels. Using the second algorithm, the Dunn-Sidak alpha level for the /th test is a c D i = \-(\-a) p The ith test rejects when \ t i \ > \ CCcDi • 2 Hochberg and Tamhane suggested that the experimentwise Type I error rate is strongly controlled for this procedure using either the sequentially determined Bonferroni or Dunn-Sidak alpha levels. Larzelere and Mulaik suggested, however, that the dependency structure of the correlations may drive the actual experimentwise alpha level above the nominal level when the sequentially determined Dunn-Sidak levels are used. Until recently in the social sciences, these multi-stage procedures had not received much attention. It is interesting to consider some of the reasons why the multi-stage procedure is gaining renewed examination (Crosbie, 1985; Silver, 1988). One factor that plays a major role in determining whether a procedure is used or not is feasibility. In general, it is simply not feasible to conduct a multi-stage test procedure by hand since / reference tables with detailed increments in probability levels are not currently available. However, with computers and accurate ^ -routines, critical values for any ccc can be obtained. Crosbie (1985) implemented a Pascal program to execute the multi-stage procedure. The program is not widely available, nor has its accuracy yet been evaluated externally. Crosbie used a four-term approximation due to Zelen and Severo (1964) instead of Peiser's (1943) t-approximation which was used by Larzelere and Mulaik. More accurate t routines are currently available. Hence, Crosbie's program is probably not as accurate as it could be. 45 Silver (1988) attempted to examine the error control of the multi-stage procedure. Silver conducted a Monte Carlo simulation; however, his assessment of the performance of the procedure was compromised by his failure to examine the techniques under a representative choice of parameters. Procedures using order statistics theory In this section, the application of order statistics theory to tests on correlations is considered. This results in an alternative class of procedures for identifying which correlations are significant. Suppose thatXi, X^Xv, are v independent observations, each with common cumulative distribution function F(x). If the observations are rearranged in ascending order of magnitude and written as such thatX(i) corresponds to the smallest observation, and so on, then is called the ith order statistic. Alternative notation for order statistics is sometimes employed where X\:v < X2:v ^ . . Xv. v . In this notation, X ; : v are the order statistics in random samples of size v drawn from a continuous population having F(x) for its cumulative distribution function. Because the notation X^ is less informative than Xi:v since the symbol Y , : v includes information on the total number of ordered observations, the latter notation will be employed. The distributions of order statistics are generally very hard to describe. Unlike statistics which are based on symmetric functions of the observations, order statistics do not lend themselves to simple study. They have the distinctive property that if an ordinary random 46 sample of values is rearranged as order statistics, the values of the order statistics are no longer independent nor identically distributed even though the original observations were independently identically distributed (Kendall & Stewart, 1969). The distribution of each order statistic depends on: (1) the rank of the observation, (2) the number of observations, and (3) the parent distribution. In what follows, we will use F / : vXx) (/ = 1... v) to denote the cumulative distribution function of the ith order statistic Xi:v. Effective application of order statistics techniques usually requires adequate computer software or extensive reference tables since each ranked observation has its own distribution. Few approximations have been implemented and reference tables are not widely available. Undeterred by their generally complex nature, several authors have considered the application of some of the concepts of order statistics to tests on correlations (e.g., Stavig & Acock, 1976; Moran, 1980). These examinations have had virtually no impact on practice in the field. Stavig and Acock (1976) introduced a technique to test a set of correlations called the rank adjusted method; this testing procedure is based on a normal approximation to the distribution of order statistics. The validity of their approach is questionable, however (Larzelere & Mulaik, 1977; Silver, 1988). Moran (1980) examined the distribution of the largest element of a set of correlation coefficients. He made several suggestions for the use of a test of the largest correlation. However, he did not extend any suggestions for use in a test of several correlations. More recently, several authors have reexamined the use of order statistics for testing the individual elements in a correlation matrix. 47 Silver 1988 Silver (1988) proposed a sequential procedure for testing which correlations are non-zero using an order statistics approach. In this procedure, the absolute values of the standardized Fisher transforms of the observed correlations,V/V - 3jz,| , i = l...vp, are ordered. The largest observation, XVp- VpJ is compared to the critical value corresponding to the largest of vp ordered half-normal observations, ZVp:Vp where ZVp.Vp = £ such that FVp. V p(Q = 1 - a. The second largest observation,XVp_i:Vp, is compared to the critical value, ZVp_\.Vp, corresponding to the second largest of vp ordered observations, where ZVp_i:Vp = £ such that FVp_i:Vp{£) = 1 - a. The third largest observation, XVp_2:Vp, is compared to the critical value, ZVp_2:Vp where ZVp_2:Vp= £ such that FVp_2:Vp(Q = 1 - or, and so on. In Silver's procedure, the null hypothesis that a correlation is zero in the population is rejected at the a level if the order statistic corresponding to the absolute value of the standardized Fisher transform of the observed correlation, XVp_j- Vp, exceeds the critical value ZVp_i:Vp, i.e., X v p - i : v p > Z v p - i : v p • Silver proposed two ways to apply the sequentially determined tests. The first procedure involves comparing all of the correlations with their respective critical values; let this procedure be referred to as OR. The second procedure involves conducting the procedure in a step-down manner, i.e., when an observation fails to reject, stop and declare all subsequent observations as having failed to reject; let this procedure be referred to as OS. Silver conducted a Monte Carlo experiment to examine the performance of these procedures. On the basis of his result, he stated that his order statistics procedure is too conservative when assessing correlations via the step-down method, OS, and suggested the use of the OR procedure for tests on correlations, 48 Silver stated that the procedures were implemented using the half-normal distribution as an approximation of the order statistic distributions to obtain the critical values of each order statistic. The adequacy of the approximation and the theoretical basis of the use of order statistics proposed by Silver are questionable, however. The problems with Silver's proposal include: 1) A problem of coherence: OR vs OS. Analysis of the procedures shows that the OR procedure sometimes leads to rejections on observations when larger ones have failed to be rejected; thus, OR is not a coherent procedure. Intuitively, it does not make sense to state that a correlation is significant if larger correlations have not been rejected. Unlike OR, the step-down approach, OS, is consistent on this dimension and is therefore a coherent procedure. 2) A problem with reference distributions. The reference distributions for the ith of vp observations with cumulative distribution functions F , : V p are the correct ones to use under complete multivariate independence. These distributions are derived under the assumption that the vp observations have been independently sampled from the same distribution. Thus, the use of the reference distributions is asymptotically appropriate under a true null hypothesis. However, in general, one does not know the configuration of the population matrix. The critical values for Silver's procedure to test individual correlations are based on the assumption that all the null hypotheses are true. This assumption is retained even after some of the null hypotheses have been rejected. If the omnibus null hypothesis is false, the observations do not all have the same distribution, nor are they (even asymptotically) independent. Hence, under a false null hypothesis, the use of the reference distributions suggested by Silver for testing the vp ordered observations is not justified. 49 Let the population correlation matrix be P where P is not equal to I; thus, v0 does not equal vp. Let r0,-, for i = l...v0, denote the v0 observed correlations corresponding to the correlations that are zero in the population, and r1,-, for i = l...v lt denote the v, observed correlations corresponding to the correlations that are non-zero in the population. Let X°J:VQ denote the tth ordered observation corresponding to the v0 zero population correlations, and X1j.v denote the ith ordered observation corresponding to the v2 non-zero population correlations. Under the procedure proposed by Silver, the ordered observations for r0,-, / = l...v0 with v0 not equal to vp, are not compared to the appropriate critical values. For instance, if X0VQ.VQ is the;'th of vp order statistic for the complete set of observations, i.e., Xj.v , the order statistic is not compared to the critical value corresponding to the largest of v0, Z V q . V o , but is compared to the critical value corresponding to the jth of vp, Zj;;v . The appropriate critical values are never less than and, indeed, are usually greater than the critical values specified by Silver's procedure. Hence, it is likely that use of this procedure results in an excessive number of false rejections. Fouladi A coherent step-down order statistics closed testing procedure for testing the significance of vp ordered values of observations using appropriate ordered statistics reference distributions entails the following steps. First, test the largest value, XVp. Vp, against the critical value corresponding to the largest of vp observations, ZVp:Vp where ZVp.Vp - t\ such that Fyp:yp(0 = 1 - or. If the test fails to yield a rejection the test procedure stops; otherwise, test the next observation. To test the second largest of the vp observations, compare the observed value against the critical value corresponding to the largest of (v^  - 1) observations where ZVp_ i:vp_\ = £ such that Fvp-l:Vp-l(Q = 1 - Of- If the second test fails to yield a rejection, the test procedure stops; otherwise, test the next observation, and so on. 50 In general, the test of the ith largest of the vp observations is a comparison of the observed value against the critical value corresponding to the largest of (vp - /+1), where ZVp_i+i:Vp_ i+l = £ such that FVp_i+i: vp_,+i(0 = 1 - a- Th e t e s t procedure continues in a step-down manner until one of the tests fails to reject. The logic of this procedure comes directly from the theory justifying the closed testing procedure and order statistics theory. A primary assumption of order statistics theory is that the original un-ordered values are independent observations drawn from the same population. Consider vp non-negative observations. At the start of the procedure, one has these vp non-negative observations. In order to test the intersection hypothesis that all vp observations are zero and from the same population, it is standard to test the equivalent hypothesis that the largest observation is zero. To test the largest observation, the observed value is compared against the critical value from the reference distribution for the largest of vp. If one rejects the hypothesis that the largest one is zero in the population, then one is simultaneously rejecting the hypothesis that all of the observations are zero. After rejecting the hypothesis that the largest of vp observations, XVp-Vp, is zero, then V observations, where v' = iyp - 1), remain to be tested. If one can no longer state that all of the observations are from the hypothesized distribution given a rejection of the largest of vp observations, the following steps must be taken in order to ensure a valid test. To test whether the remaining v' correlations are significantly different from zero, the largest of the v' observations (which is the same observation as the second largest of the original vp observations) is tested against the critical value from the appropriate reference distribution; the reference distribution for this test is the distribution for the largest of V observations, Fy':v'(;c). The procedure continues in a step-down sequential manner testing each observation against the corresponding reference distribution until one of the tests fails to reject. 51 In general, for a test of the /th observation of the original vp observations, the reference distribution is the distribution for the largest of v', Fv'-y(x) where v'=vp-i + \. Unlike the procedure proposed by Silver, this procedure relies only on the use of the reference distributions corresponding to the extremes of an ordered set. Where Fi:v(x) (/ 1...V) denotes the cumulative distribution function of the /th order statistic Xi:VJ the cumulative distribution function of the largest order statistic Xv v is given by Fv:v(x) = Pi{Xv:v<x) (v \ = Pr f](Xi<x) \i=l Since a primary assumption of order statistics is that the original un-ordered observations are independent, the cumulative distribution function can be expressed as i=l = f[F(x) 1=1 = [F(x)]v . To test the largest of an ordered set at the nominal level, Fv(Xv:v) = [(F(x)]v = l-cc . Thus, F(x) = (l-a)l/v . Under the assumption of independent observations, this step-down order statistics procedure satisfies the conditions of a closed method testing procedure described in Hochberg and Tamhane. The tests meet the condition of coherence and since in the sequence of tests the 52 largest observation of the remaining set is tested at the nominal level (i.e., each intersection hypothesis is tested at the nominal level), according to the Marcus, Peritz, and Gabriel proof, the experimentwise Type I error rate should be controlled at or below the nominal level. This step-down order statistics procedure may be applied in the context of tests on correlations. It is well known that correlations and their Fisher transforms are asymptotically normally distributed. Under the null hypothesis, the standardized Fisher transforms are very nearly distributed as a standard normal and the squared standardized Fisher transforms are very nearly distributed as chi-square with one degree of freedom. If all vp correlations are not zero, then the observations are not all from the same distribution since the distribution of a transform of a correlation coefficient is a function of p. Thus, a procedure for testing correlations requires sequentially determined reference distributions for extremes. To test the significance of a set of correlations, the above order statistics procedure can be applied to the ordered squared standardized Fisher transforms of the correlations. Since the parent population of the ordered observations is approximately chi-square with one degree of freedom, the critical values for the largest of v observations may be generated by an accurate inverse chi-square distribution function. Similarly, the above order statistics procedure can be applied to test the significance of a set of correlations using the ordered f2 transformations of the correlations. Since the parent population of the ordered observations is approximately F with one and N - 2 degrees of freedom, the critical values for the largest of v observations may be generated by an accurate inverse F distribution function. Since extensive tables of chi-square and F distributions are not widely available, the order statistics procedure using tests on the squared standardized Fisher transforms or on the 53 squared t's cannot be conducted by hand. The order statistics procedure on chi-square observations can be conducted with an accurate inverse chi-square distribution program. Similarly, the order statistics procedure on observations distributed as F's can also be conducted with an accurate inverse F distribution program. An equivalent procedure that does not require computer software and for which tables are widely available involves tests on the ordered absolute values of the standardized Fisher transforms of the sample correlations. A one-tail test of a chi-square observation at the nominal level is the same as a two-tail test of a standard normal observation. If the observations are not restricted to being non-negative, a test of the intersection hypothesis is expressed in terms of the extremes of the observations. The test of the intersection hypothesis that all the observations are zero, is, in order statistics terms, a test of the intersection hypothesis that the extremes of the order statistics are zero. A test of the hypothesis that the extremes of the order statistics are zero rejects when the largest ordered observation is greater than Zv v and the smallest ordered observation is less than Z\.\. Thus, the experimentwise Type I error rate of this test is aEX = Pr(X1:v <Zl:vnXv:v > Zv:v) = 1 -Pr(X 1 : v > Z 1 : v nX v : v < Zv:v) = l -Pr(Z 1 : v ^X / <Z v : v Vi) . For normally distributed observations, the critical value Zj.^is non-positive and the critical value Zyyis non-negative; the critical values also have equal absolute values, i.e., Zj.y = —Zv:v . Therefore, 54 aEX=l-Pr<\Xi\<Zv.v Vi) . Since the unordered observations are assumed to be independent, the experimentwise Type I error rate can be expressed as v a£ X = l - I l P r ( W ^ Z v : v ) i=l = l-[Pr(|X /|<Zv:v)]V The above yields Pr(\Xi\<Zv:v) = {\-aEX) l/v and since Pr(lX/|<Zv:v) = l-2(l-F(Z v : v)) , the cumulative probability for the critical value Zy-yis l/v i - ( i - q C T ) 2 Reference to tables for the standard normal gives the critical value Zvv for each test for a specified experimentwise Type I error rate. Let Qr^ be the inverse distribution function of the standard normal. The critical values Zy-y, where Z v : v = 0> -1 1 -l - ( l - a ) l/v 5 5 can be computed for each v, for vfrom vp to 1, as necessary. Each intersection hypothesis rejects at the nominal level a when Xv-v>z i-(l -g)" v • 2 Thus, a direct relationship between this sequential step-down testing of the extremes of ordered standardized Fisher transforms of a set of correlations and a sequentially rejective closed Dunn-Sidak testing procedure using z-tests is made. Indeed, the two procedures are exactly equivalent. This is a relationship that is not clarified in the popular literature. This test procedure is easily implemented with use of an accurate inverse normal distribution function. As stated above, however, a primary assumption of order statistics is that the observations are independent. Once one rejects a hypothesis ///, one can no longer state that the correlations are asymptotically independent. Thus, this procedure may not control experimentwise Type I error rate at or below the nominal level. Steiger An alternative to sequentially testing the intersection hypothesis that v, v=vp...l, observations are all zero by use of order statistics is testing the hypotheses using the asymptotic chi-square statistic proposed by Steiger (1980a, 1980b). The improved series general approximation formula for the mean and variance of the squared Fisher transforms (Steiger & Fouladi, 1991b) may be applied to this approach yielding the general formula: QsA=mSAQsT+aSA . where aSA=v[l-mSA(N-3)v2], 56 of which the test for complete multivariate independence is a special case since v is restricted to vp. Testing each hypothesis at the nominal level in a sequential step-down will yield a powerful test procedure, but since this chi-square statistic may reject a hypothesis without rejecting all of its implying hypotheses the error rate experimentwise will not be controlled at or below the nominal level. 1.3 Overview of papers on the topic of tests on correlations Few papers have been published on the topic of tests on correlations. The papers that have appeared in journals have generally suggested rather loosely that a problem of excessive family-wise Type I error rates exists with testing each correlation at the nominal level (e.g., Collis & Rosenblood, 1985). It has also been stated that conducting tests on each correlation at the reduced alpha level will constrain family-wise Type I error rate below the nominal level. Larzelere and Mulaik (1977) described the multi-stage reduced alpha procedure and on the basis of results in Larzelere's unpublished masters' thesis suggested that it would be more powerful than the reduced-alpha procedure and would constrain family-wise Type I error rates at or below the nominal level. Several published papers have been written suggesting the use of the multi-stage reduced alpha procedure, but none of these has included Monte Carlo simulation results (Collis & Rosenblood, 1985; Crosbie, 1986). Silver's unpublished dissertation (1988) included a simulation study comparing the error rates of certain tests on correlations. The comparison of a procedure using approximations to order statistics and the multi-stage Bonferroni procedure yielded results showing that the approximate order statistics approach suggested by Silver was more powerful than Larzelere's multi-stage Bonferroni procedure and maintained Type I error rates below the 57 nominal level. However, the procedures were examined under conditions that are not representative of the population parameter space. The population matrices were either identity or non-identity such that all of the off-diagonal elements were equal to a specified non-zero value. Consideration of the order statistics approach, as discussed above, suggests that the family-wise Type I error rates may be sensitive to the proportion of non-zero correlations in the population matrix and use of the procedure proposed by Silver may be inappropriate. Silver (1988) also proposed to examine the utility of conducting a preliminary test of complete multivariate independence prior to follow-up procedures testing individual correlations. He concluded that "testing the global hypothesis P = I is a moot point in examining individual correlations in a matrix" (p. 39). Since he used an incorrect omnibus test, and failed to examine a representative set of parameters, further examination of this issue is necessary. 1.4 Current state of affairs The issue of maintaining control of experimentwise Type I error is of primary importance. The necessity of making this clear is quite salient. As students of the social sciences proceed through their graduate training, many are exposed to a cookbook method of performing statistical techniques without understanding the theoretical relevance of what they are learning. The performance of an ANOVA prior to follow-up Mests on means has been ritualized, but an appreciation of the theoretical issues is missing. Without this understanding, students are unable to extend what they have learned to novel situations. Thus, many do not appreciate why it is necessary to ensure experimentwise error rate protection in the context of correlations. This is reflected in the surplus of papers that report significance at the nominal level for individual correlations. However, it is not appropriate to conduct tests at reduced alpha level in certain situations either; researchers not 58 understanding the issues will conduct experiments with a large number of correlations, thereby, running excessively conservative tests. Most of the alternative procedures for testing which correlations are significant have not appeared in the popular literature. One reason may be that most of these procedures cannot be conducted by hand because complete reference tables are not available. As more textbooks incorporate statistical software tutorial examples, these procedures may be implemented increasingly. Current statistical software packages do not include the follow-up procedures for tests on correlations that have been discussed in this paper. Some of the statistical packages include an option for printing the p-levels of each correlation. But, there has been no instruction as to how to proceed with the p-levels. At best an almost arbitrary decision is made to consider all correlations with p-levels less than a specified value to be significant. Under such circumstances, a researcher has no idea what the experimentwise Type I error rate might be. To date, few Monte Carlo simulation studies have adequately examined the relative performance of the procedures for identifying which correlations are significantly different from zero. The present study is a preliminary comprehensive comparison of the performance of the procedures currently under discussion. In what follows we will signify < the various procedures with the following notation, NT: procedure with f-tests at the nominal level, MB: sequential step-down testing of //,• (i = l...Vp) using the multi-stage Bonferroni procedure, RB: procedure with f-tests at the reduced Bonferroni level, MD: sequential step-down testing of //,• (/ = 1... vp) using the multi-stage Dunn-Sidak procedure, 59 RD: procedure with /-tests at the reduced Dunn-Sidak level, OR: Silver order statistics approach (not step-down), OS: Silver order statistics approach (step-down), OF: sequential step-down testing of (i = l...vp) using the Fouladi order statistics approach with critical values generated by Silver and Dunlap's routine, CF: sequential step-down testing of H{ (i = l...vp) using the Fouladi order statistics approach with critical values generated by an inverse normal distribution function, CS: sequential testing of //,• (i = 1...vp) using Q$A, and examine their performance as tests of individual correlations both with and without a preliminary test of the overall null hypothesis. 2. Methods In the present paper, a Monte Carlo simulation experiment was conducted in order to compare the error rate control, sensitivity, and bias of procedures (NT, MB, RB, MD, RD, OR, OS, OF, CF, and CS) for testing which elements in a correlation matrix are different from zero in the population. A FORTRAN program was written utilizing a variety of Applied Statistics algorithms and subroutines from a library of statistical subroutines implemented by James H. Steiger and Rachel T. Fouladi. Procedure for generation of sample correlation matrices Sample correlation matrices from multivariate normal distribution with specified population correlation matrices were generated using the Browne procedure (1968). 60 Simulation experiments. For the examination of Type I error control, sample correlation matrices were generated from a population correlation matrix P where P was equal to I; that is, the sample matrices were generated under the condition of a true null hypothesis that all of the bivariate correlations are zero in the population. For the examination of Type I and Type II error control when all of the correlations are not zero in the population, sample correlation matrices were generated from a positive definite population correlation matrix P, where P was not equal to I; that is, the sample matrices were generated under the condition of a false null hypothesis. P was varied along several dimensions: (a) order p (p = 5,10), (b) proportion of non-null correlations (pNz = .2, .4, .6, .8), and (c) magnitude of non-null correlations (mNz =.1, .3, .5). The magnitude of the non-null correlations were selected on the basis of maintaining a positive definite P; non-null correlations in increments of .1 greater than .5 for the proportion of non-null correlations selected yield non-positive definite matrices. Procedures for testing which correlations are significant were conducted under two conditions: (a) after rejection of the hypothesis of complete multivariate independence, and (b) with no prior test of the hypothesis of complete multivariate independence. The statistic QSA w a s used to test the hypothesis P = I; Q$A was selected to test the omnibus hypothesis because of its control of experimentwise Type I error at or below the nominal level across all conditions and its power. For each sample correlation matrix, the procedures for testing which correlations are significant (NT, MB, RB, MD, RD, OR, OS, OF, CF, and CS) were conducted as necessary; the number of rejections, the number of false positives, the number of true positives, the number of false negatives, the number of true negatives, and whether a Type I error was committed were recorded for each procedure. 61 Each experiment was replicated 10,000 times at specific ratios of sample size to number of variables (N:p = 2,4, 10,20,40). Under each condition, the Type I experimentwise error rates, that is the proportion of 10,000 replications in which at least one r0 was falsely declared significant, were computed. The mean number of rejections, false positives, true positives (and therefore false negatives, true negatives) were calculated and transformed into proportions; the standard deviations for each of these proportions were also computed. Under each condition, the observed difference between empirical and nominal experimentwise Type I error, SEx = AEX ~ A-> w a s compared with the critical difference, £ c ri t, derived from a non-null consistent chi-square statistic; i.e., where a is the nominal experimentwise Type I error rate and R is the number of replications. From this information, whether a procedure satisfied the primary condition of the Neyman-Pearson criterion of controlling experimentwise Type I error rate at or below the nominal level was assessed. Additional descriptive measures of performance based on signal detection theory were also computed on each procedure. Detection theory measures of performance were included as possible additional useful information on which to base a recommendation of a procedure for "detecting" which correlations are non-zero in the population. Detection theory is commonly used to evaluate the performance of a detector of signals in noise. The popular Measures of performance 62 detection theory measures of performance are based on the assumption of Gaussian signals embedded in Gaussian noise; the signals and noise are further assumed to have equal variance. If one considers non-zero population correlations to be signals and zero population correlations to be noise, then procedures to test which correlations are non-zero can be conceptualized as detectors. Since a vector of correlation coefficients is asymptotically multinomial though the assumption of homoscedasticity does not necessarily hold, detection theory measures can be considered suggestive of the relative performance of the test procedures as detectors of non-zero population correlations (signals) from zero population correlations (noise). From mean hit and mean false alarm proportions, Tp and Fp, measures of sensitivity and criterion (or bias) were computed. Let <J>_1 be the inverse distribution function of the standard normal. Parametric measures of sensitivity and bias are d' and p\ where Since the standard assumptions of detection theory do not necessarily hold, nonparametric measures of sensitivity A', cr=Qr\\-Fp)-QT\\-Tp) , and f(<tT\\-Tp);0,\) 0 = -4—; 1 | (Tp-Fp)(\ + Tp-Fp) 2 4Tp(\-Fp) and criterion B", Tp(\-Tp)-Fp{\-Fp) Tp(\-Tp) + Fp(\-Fp) 1 63 were also computed (Coren, Porac, & Ward, 1984, p. 26). The ranges for the measures of sensitivity (from zero sensitivity to perfect performance) are (a) non-negative for d', and (b) .5 to 1 for A'. The ranges for the measures of criterion are (a) non-negative for p\ and (b) -1 to 1 for B". Lax criterion (bias toward rejecting) is indicated by values of /3 less than 1 or values of B" less than zero. Stringent criterion (bias toward not rejecting) is indicated by values of j3 greater than 1 or values of B" greater than zero. The relative performance of each procedure was considered. Keeping with conventional criteria, the procedure with the greatest experimentwise Type I error rate at or below the nominal level and the highest hit rate was declared to be optimal. 3. Results Table 9 gives the critical r's that an observed value must exceed for each of the procedures that examine the individual correlations directly; the critical chi-square values that each Q $ A must exceed for CS is also included in this list. This table shows the following relationship between the rejection values for each procedure for which a critical /• can be computed directly RB<RD<MB<MD<CF,OF<OS<OR<NT. This relationship is reflected in the measures of performance for the procedures with "critical r's". The relative performance of CS, however, cannot be deduced from this table. Empirical measures of performance were obtained for procedures NT, MB, RB, MD, RD, OR, OS, OF, CF, and CS. Empirical performance was assessed with 10,000 replications under p (5, 10) x N:p (2,4,10,20,40) x pNz (.2, .4, .6, .8) x mNz (.1, .3, .5) x O (n = with 64 no omnibus test, y = with a preliminary omnibus test at a = .05) factorial conditions. The complete set of empirical measures AEX = empirical experimentwise Type I error, i.e., the proportion of 10,000 simulation experiments on which at least one Type I error was made, Rej = the mean proportion of vp correlations rejected in 10,000 replications, Fp = the mean proportion of v0 r° correlations rejected in 10,000 replications, Fn = the mean proportion of v, r1 correlations that failed to be rejected in 10,000 replications, Tp = the mean proportion of v, r1 correlations rejected in 10,000 replications, Tn = the mean proportion of v0 r° correlations that failed to be rejected, sRej - the standard deviation of Rej sFp/Tn = the standard deviation of Fp and Tn, sFn/Tp = the standard deviation of Fn and Tp, d' = a parametric detection theory measure of sensitivity, = a parametric detection theory measure of criterion, A' = a nonparametric measure of sensitivity, B" = a nonparametric measure of criterion, are included in Table 10. Some of the primary measures of performance d', p) are presented in this section. The tabled results show the equivalence of two methods to generate critical values for Fouladi's step-down order statistics approach. The performance of OF and CF is essentially identical. Thus, Silver's routine to generate critical values of order statistics distributions is valid for testing extremes of observations with a half-normal parent distribution.- The overall validity of Silver's approximation is, however, not known. In the following, reference will 65 only be made to CF, Fouladi's step-down order statistics approach using the inverse normal distribution function to generate critical values. CS was included in the simulation study to demonstrate the importance of satisfying the conditions of a closed testing procedure in order to control experimentwise Type I error at or below the nominal level. The empirical results show that, indeed, the shortcut version of a procedure using the normal theory statistic Q$A as a test of the intersection hypotheses does not control actual experimentwise Type I error. Because CS was included to demonstrate the importance of satisfying the requisite conditions of a closed testing procedure, the results will not be discussed further. In the following, the results obtained in the examination of procedures that have been proposed to be useful in identifying which correlations are significant are reviewed. P equal to I Table 11.1 gives the difference between the empirical experimentwise Type I error performance of the test procedures and the nominal Type I error rate of the test procedures when all the correlations are zero in the population, i.e., P is the identity matrix. Using a non-null consistent chi-square statistic based on 10,000 replications, critical values <5crjt for the difference o^, where 8Ex = &EX ~ A> w e r e obtained. 8CTlt 95 = .00427, 8CTlt 01 = .00562, and 5 c r i t .ooi = .00717. No preliminary test of the null hypothesis The results show that when no preliminary omnibus test is conducted, the experimentwise Type I error rate is controlled at or below the nominal level by MB and RB. Experimentwise Type I error is not always controlled at or below the nominal level across all conditions when P is the identity matrix by RD, MD, OS, and CF; these procedures fail 66 to control actual a when N:p is low. Experimentwise Type I error is never controlled at or below the nominal level for OR and NT. With a preliminary test of omnibus hypothesis The results show that when a preliminary omnibus test is conducted, the experimentwise Type I error rate is controlled at or below the nominal level for all procedures except NT and OR when N:p is small or moderate. P not equal to I Tables 11.2-5 give the difference between the empirical experimentwise Type I error performance and the nominal Type I error rate of the test procedures when not all the population correlation coefficients are zero, i.e., P is not an identity matrix. Using a non-null consistent chi-square statistic based on 10,000 replications, critical values <5crit for the difference 8Ex, where 8EX = ccEx - &, were obtained. 8CIlt 0 5 = .00427, 8CTlt 0 1 = .00562, Scrit . 0 0 1 =-00717. With no preliminary test of the omnibus hypothesis The results show that across all levels of N:p, pNz, mNz, and p, when no preliminary omnibus test is conducted and P does not equal I, the experimentwise Type I error rate is controlled at or below the nominal level for MB and RB, MD and RD, and CF; in contrast, procedures OS, OR, and NT do not control experimentwise Type I error rate at or below the nominal level. However, when N:p equals 2 and pNz equals .2, CF does not control actual experimentwise Type I error rate at or below the nominal level. 67 The overall results show that of the procedures that have overall control of experimentwise Type I error, RB and RD are the most conservative, MB and MD are the second most conservative procedures, and CF is the least conservative procedure. With a preliminary test of the null hypothesis The results show that across all levels of N:p, pNz, mNz, and p when a preliminary omnibus test is conducted, the experimentwise Type I error rate is controlled at or below the nominal level for MB and RB, MD and RD, and CF; procedures OS, OR, and NT do not control experimentwise Type I error rate at or below the nominal level. The overall results indicate that of the procedures that control experimentwise Type I error at or below the nominal level (RB, RD, MB, MD, and CF), the strictly reduced alpha level procedures RB and RD are the most conservative, the sequentially determined reduced alpha level procedures MB and MD are the second most conservative procedures, and CF is the least conservative procedure. Figure 1 illustrates this consistent pattern among the procedures that control of experimentwise Type I error. The expeiimentwise Type I error of CF is shown to be consistently greater than that of MD, MB, RD, and RB; though, as N:p increases, the difference between the level of performance of MB, MD, and CF decreases. Detection theory measures of performance. Parametric measures of sensitivity and criterion are included in Tables 12 and 13. Comparison of the sensitivity of the procedures indicates that MB, RB, MD, RD, and CF are more sensitive than NT, OR, and OS. Comparison of measures of criterion indicates that RB, RD, MB, and MD have stricter criteria than CF which in turn has much more stringent criterion than NT, OR, and OS; NT, OR, and OS are, in fact, often quite lax. 68 Comparison between the measures of performance of these procedures when (a) an omnibus test is not conducted and (b) the overall test is conducted, shows that, in general, the procedures are more sensitive when the omnibus test is not conducted. The procedures have comparable bias under both conditions. A problem with using these detection theory measures to indicate which test is optimal is suggested in the tabled results. The results show that measures of sensitivity gain when experimentwise Type I error rate is too low. Examining experimentwise Type I error control and To In general, a procedure is considered optimal if the procedure has the highest hit rate (Tp) of the procedures controlling experimentwise Type I error. Of the procedures that control empirical alpha at or below the nominal level (RB, RD, MB, MD, and CF), CF consistently has the highest hit rate. According to this objective of maximizing hit rate under the constraint that experimentwise Type I error be controlled, CF is defined as the optimal procedure. 3. Conclusions The empirical results provide evidence that multiple tests (each at the nominal level) on a set of correlations does not control experimentwise Type I error. Further evidence showed that none of the procedures recommended by Silver control experimentwise alpha at or below the nominal level. Thus, none of these procedures should be used in the context of identifying which correlations are significant. 69 Reduced-level tests have generally been considered to be the only available testing procedure that controls empirical alpha at or below the nominal level. This procedure, however, tends to be conservative, particularly for moderate-to-large con-elation matrices. The alternative multi-stage reduced alpha procedures perform much better than the corresponding single level reduced alpha tests especially for moderate-to-large N:p (see Figure 1 for example). The results of the current study show, however, that the sequential step-down order statistics procedure (CF) outperforms the other multi-stage procedures. The results show that of the test procedures examined, the sequential step-down order statistics approach CF strictly satisfies the Neyman-Pearson criterion of an optimal test when conducted in conjunction with a preliminary omnibus test on a correlation matrix of order p, p > 2. When the researcher has a priori knowledge that P does not equal I, the results of the current study suggest that CF can be conducted without a preliminary omnibus test. Detection theory measures showed that the sensitivity of CF is very weak for tests of matrices with low magnitudes of non-zero correlations. Figure 3 illustrates the hit rate of the procedure for N:p x pNz when mNz = .3. This figure shows the importance of having adequate sample size to obtain acceptable power. To ensure optimal detection of non-zero correlations, a researcher should have as large an N:p as possible. 70 GENERAL DISCUSSION Correlational studies constitute a significant portion of behavioural and social science research. The primary role of inferential statistics in social science methodology is reflected in the fact that most papers include at least one significance test. As has been shown in the preceding sections of this paper, a wide array of correlational procedures can be used for testing the exploratory questions (a) whether any of the variables under examination are related in the population and (b) which correlations are non-zero in the population. The present study examined the relative performance of the procedures for these two questions. In this final section, the general results of this study in the context of prior research are reviewed. The importance of design issues in Monte Carlo research is considered. Possible application of the recendy derived procedures to tests other than the ones addressed in this study is also suggested. 1. A discussion of the results of this studv in the context of prior research U Experimentwise Type \ error control A primary criterion for the evaluation of a statistic is experimentwise Type I error control. Many papers in statistics and in the behavioural and social sciences are devoted to discussing the general importance of experimentwise Type I error control. The primary purpose of this study was to evaluate the performance of significance tests on a correlation matrix and its elements on this dimension. 71 Considering the tests of the omnibus null hypothesis Traditionally, the statistic used for a test of complete multivariate independence is from the class of likelihood ratio tests. This statistic is Bartlett's modified likelihood ratio test, Q B A . Q B A has been used because, of the likelihood ratio tests, it has the best control for experimentwise Type I error. However, the results of several Monte Carlo simulation studies have shown that Q B A does not control experimentwise Type I error rate at or below the nominal level when the ratio of sample size to the order of the matrix being tested, N:p, \ is small. The current study examined the experimentwise Type I error rate of several statistics from the class of likelihood ratio tests: QBR, QU^, and Q B A . This study confirms that, indeed, of the likelihood ratio statistics examined, Q B A (1) has the best experimentwise Type I error rate control, (2) does not control alpha at the nominal level for small N:p, and (3) controls alpha tightly at the nominal level for adequate N:p. Alternative statistics are available for the test of the omnibus null hypothesis. Steiger's (1980) normal theory statistic, Q$j, has repeatedly been shown to have better control of experimentwise Type I error. In spite of these assessments, this statistic has not been widely used. Recent analytic results suggest, however, that the popular approximation of the variance of the Fisher transforms used in Q$j is not optimally accurate. The results of this study show that normal theory statistics proposed by Steiger and Fouladi (1991a, 1991b), incorporating the exact variance of the squared Fisher transforms (Q$E) o r a more accurate approximation of the variance (QSA)> D o m result in even better control of experimentwise Type I error. Steiger and Fouladi's Qp also controls the experimentwise Type I error rate at the same level as QSE and QSA. 72 The results of the Monte Carlo simulation studies suggest that for overall optimal control of experimentwise Type I error, Q$E, Q$A, or QF should be used. However, QBA can be used if N:p is moderate-to-large. Considering tests of the elements of a correlation matrix Several procedures have been suggested for testing the significance of the elements of a correlation matrix. However, few valid and decisive recommendations have been made on how to proceed in the context of testing several correlations. This study showed that Mests at the nominal level, the procedures proposed by Silver, OS and OR, and sequential application of Q$A (CS) do not control experimentwise alpha at the nominal level. These procedures should not be used. The results of the present study showed that the remaining procedures including tests at stricdy reduced alpha levels (RB and RD), tests at sequentially determined alpha levels (MB and MD), and step-down testing of the extremes (CF), all control experimentwise Type I error rates at or below the nominal level. Of these procedures, CF is the optimal test. Overall, the use of CF is recommended for testing which con-elations are significant. The results show that this procedure can be used both with and without a preliminary test of the omnibus null hypothesis when N:p is moderate-to-large. When N:p is small, however, a preliminary omnibus test is recommended. If the omnibus test rejects, proceed to conduct follow-up CF testing; otherwise, declare all individual correlations not significantly different from zero. A preliminary omnibus test is required because the results obtained showed that when P equals I, experimentwise Type I error rate is conuolled for CF if a preceding omnibus test is conducted, but not if no preliminary omnibus test is conducted. 1.2 Power issues Overall, the results of the current study show that experimentwise power is low when the magnitude and proportion of non-zero correlations in the population are small. Power is also a function of sample size. In order to ensure maximal power under relatively low power conditions, it is recommended that a researcher have as large a sample size as possible when examining either exploratory question. Previous studies comparing the power of Q^j and Q B A have consistently shown Q$j to be more powerful; the current study confirms this result. However, since Q$j does not control Type I error as well as its derivative statistics Q^E and Q $ A , it cannot be recommended as a general test of complete multivariate independence. Of the omnibus tests that control experimentwise Type I error best, Q$E and Q $ A are shown to be more powerful than the others. Since the experimentwise Type I error rate for CF is always controlled at or below the nominal level for moderate-to-large N:p, both with and without a preliminary omnibus test, and since the procedure has greater power when conducted without a preliminary omnibus test, if the researcher is not primarily interested in the overall structure of the correlation matrix but is primarily interested in identifying which pairs of variables are significantly correlated, the following strategy is recommended. If N:p is small, conduct a preliminary overall test and proceed to follow-up CF testing should the omnibus hypothesis reject; if N:p is moderate or large, conduct tests of the individual correlations using CF without a preliminary omnibus test. 74 1.3 Important design issues. In this study, the procedures were examined under a variety of conditions. The conditions were selected in order to try to have as representative a sampling of the parameter space as possible. Even though Browne's procedure was used to generate sample con-elation matrices, the computational time factor of simulating many replications meant that matrices of smaller order than sometimes seen in behavioral correlational research were investigated. The major trends manifested in these data were consistent, and the results obtained probably generalize to matrices of larger order. In general, Monte Carlo simulation studies have only examined the performance of tests under conditions when (a) P is equal to I or (b) P is equal to A, where A is the correlation matrix with all off-diagonal correlations non-zero and equal in magnitude. In the present study, the performance of the test procedures was examined under additional conditions. These additional conditions were included because analysis showed (a) alternative configurations would yield different results for one omnibus test procedure, QBA-> A N D (°) some of the follow-up procedures are differentially sensitive to differing proportions of non-zero correlations. The empirical results showed differences on both (a) and (b). The results of this study confirm the importance of examining the parameter space prior to designing and running the Monte Carlo simulation experiments. Silver and Dunlap (Silver, 1988; Silver & Dunlap, 1989) failed to run their experiments under conditions to which some of their procedures were sensitive. Hence, the results of their studies do not accurately represent the general relative performance between the statistics they examined. The serious consequence of failing to conduct a study under representative conditions is exemplified by the fact that, contrary to their conclusions, the cuirent study shows that the procedures 75 recommended by them do not control experimentwise Type I error rate at or below the nominal level. The present study did not include an examination of the performance of the statistics under the condition when the non-identity population correlation matrix has a range of non-zero correlations. However, the major trends in the results of this study were very consistent across all magnitudes of non-zero correlations tested; these results probably generalize quite well. 2. Extensions and suggestions for future study In this study, the performance of several statistics was examined in the context of testing the simplest form of a null hypothesis on data collected from a multivariate normal population. Tests of significance of all of the correlations in a matrix were examined. Several of the procedures examined in this study can be extended to tests of alternative null hypotheses. 2.1 Tests of alternative null hypotheses Generalizations of the omnibus tests Steiger and Browne (1984) provide a general procedure for comparing correlation coefficients. The procedure allows a wide variety of computationally efficient significance tests. Their results indicate that asymptotic tests for any linear hypothesis can be expressed with differentiable monotonic functions of p, where f(r) is gxl vector of functions of the elements of r, differentiable at r = p, such that (A7 - l^CfCr) - f(p)) has an asymptotic ryo, T*). For tests of linear hypotheses of the form 76 HQ\ Mzr = h , where the vector of transforms is vpxl vector zr, and M is a specified gxvp matrix of rank g, and h is a specified gxl vector, if t * is any consistent estimate of P*, then according to their development, the asymptotic distribution under HQ of the statistic, g* = (N-3)(M^-h) (Mf*M)~ (Mz.-h) , is chi-square with g degrees of freedom. The results in Steiger (1980a) and Steiger and Browne (1984) suggest that this normal theory statistic can be extended to test any linear combination hypothesis. Similarly, Q$E and QSA can be used to test linear hypotheses by applying their respective linear transforms toQ*. Hence, the normal theory statistics Q$E and Q$A can be extended to tests of pattern matrices in the same way that QST is extended to tests of pattern matrices in Steiger (1980a). Q$E and QSA can be applied to tests of any set or subset of elements from an intercorrelation matrix or an intracorrelation matrix. Thus, with the recenUy derived normal theory procedures, QgE and Q$A, (a) the significance of any linear combination of a set of correlations can be tested, (b) pattern hypotheses for a set of correlations can be tested, and (c) tests between sets of correlations can be tested. The statistic QF can be applied to tests of any set or subset of intercorrelations or intracorrelations. Steiger (1980a) showed that the relative performance of the general statistic is consistent across tests of several alternative pattern hypotheses. It is likely that Q$E and Q$A as transforms of this general statistic will perform similarly. 77 However, the current study did not examine the performance of the recently derived statistics for any of the tests described above. Any recommendation for the use of these tests under these conditions should be accompanied by Monte Carlo simulation results. Generalization of the tests on individual correlations In the current study, the performance of the sequential step-down implementation of an order statistics approach to testing extremes (CF) was examined where the observations of interest were all pairwise correlations in matrix of order p. However, it is important not to forget that this closed testing procedure applies to any set of independent identically distributed observations. Thus, in the context of tests on correlations, the significance of the elements from any set or subset of an intercorrelation or intracorrelation matrix can be tested. This sequential step-down procedure (CF) can also be extended to tests of contrasts between the elements of two or more sets or subsets of correlation matrices. It is likely that the sequential step-down procedure can be applied freely in this context as long as the observations (contrasts or transformed contrasts) are independently and identically distributed with a known parent distribution. In this case, the observed statistics for a test of the contrast are ordered and the extremes are tested. 2.2 Extension to non-normal data Steiger and Hakstian (1982) demonstrated that although a vector of correlation coefficients remains asymptotically multinomial under non-normal parents, the asymptotic variance-covariance structure of the correlation coefficients changes, with non-normality (from the Pearson-Filon values), as a function of the moments of the parent distribution. They suggested that quadratic form test statistics that rely on the Pearson-Filon formula for 78 estimation of the variance-covariance structure of the correlations may be distributed quite differently from corresponding statistics in the multinomial case. Their results showed that normal theory tests retain their correct asymptotic distributions under non-normal parent distributions when the correlations are all equal to zero. However, when sample size is small-to-moderate, Steiger and Hakstian emphasized that a normal theory test should be approached with caution. Given the results in Steiger and Hakstian, Q S E and Q$A are probably somewhat robust as tests under non-normal conditions. However, before a recommendation can be made for use of a statistic as a test when the assumption of normality is violated, a Monte Carlo simulation experiment under a variety of non-normal conditions must be conducted. 3. Final note Several statistics were examined in the current study. Deciding which procedure is most suitable for a significance test involves considering a myriad of dimensions. Convention dictates, however, that first and foremost is the issue of experimentwise Type I error control. The primary purpose of this study was to determine the relative performance of several procedures on this dimension. Of the statistics currently available for testing the hypothesis of multivariate independence with multinomial data, normal theory statistics Q$£ and Q$A, and the statistic Qp had the best overall performance. However, the results also showed that even though these statistics perform better than QgA for small sample size, Q^ QSA> a n ( * QF a r e s u u " "asymptotic in N". Furthermore, the results show that for adequate N:p, QgA has tighter control over experimentwise Type I error than Q$E, Q$A, and Qp. This is because, unlike Q$E, Q$A, and Qp, QBA is not based on the assumption of asymptotic independence (p increasing) of 79 correlations under a true null hypothesis. Thus, Q$g, Q$A, and Qp are also "asymptotic in p". In general, the use of Q$£ or Q$A is suggested for optimal Type I error control and power; however, if testing requires "exact" control of experimentwise Type I error and N:p is adequate, then QBA should be used. If testing requires precise control of experimentwise Type I error and N:p is not moderate-to-large, then an exact test of complete multivariate independence should be conducted (e.g., Mathai & Katiyar, 1979). Even though independence of correlations was assumed for the order statistics closed testing procedure CF, dependency among correlations did not appear to detract from the performance of this procedure recommended for testing which correlations are significant. The current study has shown that the order statistics closed testing procedure CF is the optimal test procedure for testing individual correlations. However, further analysis of the issue of non-independence is recommended. Unfortunately, optimality is not the only factor that affects whether a test procedure will be widely employed. Other factors also determine whether a researcher uses a procedure. (1) The researcher must be aware of a procedure before he or she can use it. (2) The experimenter must be able to perform the required computations. Indeed, knowing which procedure is best is not enough. To be useful, a procedure must be computable by hand, trivially programmable, or implemented in pre-packaged software. For most social scientists, the primary sources of such awareness are (a) the general statistical training received in graduate school, (b) procedures given in common "advanced" texts, and (c) procedures implemented in best-selling general purpose computer packages. However, many useful procedures of value are not contained in or mentioned by any of these sources; in addition, many classic books and computer programs implement procedures which are either erroneous or suboptimal. 80 At present, the recently derived and here recommended statistics for a test of overall independence and for the significance test of the individual correlations are not available in popular statistical packages, nor are they in any statistical reference book. But perhaps, in spite of this, the results of this comprehensive examination of procedures for testing the significance of correlation matrices and their elements will become known and the recommended statistics will be applied widely and effectively. 81 BIBLIOGRAPHY Bartlett, M.S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society, Ser. A, 30, 327. Bartlett, M.S. (1938). Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society, 34, 33-40. Bartlett, M.S. (1950). Tests of significance in factor analysis. British Journal of Psychology, Statistical Section, 3,77-85. Bartlett, M.S. (1954). A note on multiplying factors for various Chi-squared approximations. Journal of the Royal Statistical Society, Ser. B, 16, 296-298. Box, G.E.P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36, 317-346. Brien, C.J., Venables, W.N., & Mayo, O. (1984). An analysis of correlation matrices: Equal correlations. Biometrika, 71,545-554. Browne, M.W. (1968). A comparison of factor analytic techniques. Psychometrika, 33, 267-334. Browne, M.W. (1974). Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 8,1-24. Browne, M.W. (1977). The analysis of patterned correlation matrices by generalized least squares. British Journal of Mathematical and Statistical Psychology, 30, 113-124. Burt, C. (1952). Tests of significance in factor analysis. British Journal of Psychology, 5, 109-133. Cameron, M.A., Eagleson, G.K. (1985). A new procedure for assessing large sets of correlations. Australian Journal of Statistics, 27, 84-95. 82 Choi, S.C., & Wette, R. (?). Test of hypotheses on non-independent correlation coefficients. Biometrische Zeitschrift, 14,178-183. Collis, B.A., & Rosenblood, L.K. (1985). The problem of inflated significance when testing individual correlations from a correlation matrix. Journal for Research in Mathematics Education, 16,52-55. Coren, S., Porac D., & Ward, L.M. (1984). Sensation and perception (2nd ed.). Orlando, FL: Academic Press, Inc. Coren, S., & Ward, L.M. (1989). Sensation and perception (3rd ed.). Orlando, FL: Harcourt Brace Jovanovich, Inc. Crosbie, J. (1986). A Pascal program to perform the Bonferroni multistage multiple-correlation procedure. Behavior Research Methods, Instruments, & Computers, 18, 327-329. David, H.A. (1970). Order statistics. New York: Wiley. Dunn, O.J., & Clark, V. (1969). Correlation coefficients measured on the same individuals. Journal of American Statistical Association, 64, 366-377. Dwyer, P.S. (1945). The square root method and its use in correlation and regression. Journal of the American Statistical Association, 40,493-503. Dziuban, CD., & Shirkey, E.C. (1974a). On the psychometric assessment of correlation matrices. American Educational Research Journal, 11,211-216. Dziuban, CD., & Shirkey, E.C. (1974b). When is a correlation matrix suitable for factor analysis? Some decision rules. Psychological Bulletin, 81, 358-361. Elston, R.C. (1975). On the correlation between correlations. Biometrika, 62, 133-140. Fisher, R.A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507-521. Fisher, R.A. (1921). On the "probable error" of a coefficient of correlation deduced from a small sample. Metron, 1,1-32. Fisher, R.A. (1925). Statistical methods for research workers. Edinburgh: Oliver & Boyd. 83 Fouladi, R.T., & Steiger, J.H. (1991). A general sequentially rejective step-down closed testing procedure based on order statistics theory: Theory and Applications. Manuscript in preparation. Geisser, S., & Mantel, N. (1962). Pairwise independence of jointly dependent valuables. Annals of Mathematical Statistics, 33,290-291. Govindarajulu, Z. & Hubacker, N.W., (1964). Percentiles of order statistics in samples from uniform, normal, chi (1 d.f.) and Weibull populations. Reports of Statistical Application Research, Union of Japanese Scientists and Engineers, 11, 64-90. Gupta, A.K., & Rathie, P.N. (1983). On the distribution of the determinant of sample correlation matrix from multivariate Gaussian population. Metron, 61,43-56. Hartley, H.O. (1955). Some recent developments in analysis of variance. Communications in Pure and Applied Mathematics, 8,47-72. Hochberg, Y., & Tamhane, A.C. (1987). Multiple comparison procedures. New York: Wiley. Hotelling, H. (1953). New light on the correlation coefficient and its transforms. Journal of the Royal Statistical Society, Ser. B, 15,193-232. Hsu, P.S. (1949). The limiting distribution of functions of sample means and application to testing hypotheses. Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability, 359-402. Johnson, N.L., & Kotz, S. (1970). Distributions in statistics: Continuous univariate distributions, Vol. 2. Boston: Houghton Mifflin. Kaiser, H.F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 27,179-182. Kendall, M.G., & Stuart, A. (1967). The advanced theory of statistics. New York: Hafner. Kennedy, W.J. Jr., & Gentle, J.E. (1980). Statistical computing. New York: Marcel Dekker, Inc. 84 Kinderman, A. J., & Ramage, J.G. (1976). Computer generation of normal random variables. Journal of the American Statistical Association, 71, 893-896. Knapp, T.R., & Swoyer, V.H. (1967). Some empirical results concerning the power of Bartlett's test of the significance of a correlation matrix. American Educational Research Journal, 4,13-17. Konishi, S. (1978). An approximation to the distribution of the sample correlation coefficient. Biometrika, 65, 654-666. Konishi, S. (1981). Normalizing transformations of some statistics in multivariate analysis. Biometrika, 68, 647-651. Kraemer, H.C. (1973). Improved approximation to the non-null distribution of the correlation coefficient. Journal of the American Statistical Association, 68, 1004-1008. Larzelere, R.E. (1975). An empirical investigation of three procedures for multiple significance tests of intercorrelations. Unpublished master's thesis. Georgia Institute of Technology. Larzelere, R.E., & Mulaik, S.A. (1977). Single-sample tests for many correlations. Psychological Bulletin, 84,557-569. Lawley, D.N. (1940). The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, Section A, 60, 64-82. Lee, Y.S. (1972). Some results on the distribution of Wilks's likelihood-ratio criterion. Biometrika, 59, 649-664. Marcus, R., Peritz, E., & Gabriel, K.R. (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika, 63, 655-660. Mathai, A.M., & Katiyar, R. S. (1979). Exact percentage points for testing independence. Biometrika, 66, 353-356. Moran, P.A.P. (1980). Testing the largest of a set of correlation coefficients. Australian Journal of Statistics, 22,289-297. Morrison, D. F. (1976). Multivariate statistical methods. New York: McGraw-Hill. 85 Mudholkar, G.S., Trivedi, M.C., & Lin, CT. (1982). An approximation to the distribution of the likelihood ratio statistic for testing complete independence. Technometrics, 24, 139-143. Naik, U.D. (1975). Some selection rules for comparing p processes with a standard. Communications in Statistics, Ser. A, 4, 519-535. Neyman, J., & Pearson, E.S. (1928). On the use and interpretation of certain test criteria for the purposes of statistical inference. Biometrika, 20A, 175,263. Neyman, J., & Pearson, E.S. (1931). On the problem of k samples. Bull. Acad. Polon. Sci. (Bull int. Acad Cracovie, A), 3, 460. Odell, P.L., & Feiveson, A.H. (1966). A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association, 61, 199-203. Olkin, I., & Siotani, M. (1976). Asymptotic distribution of functions of a correlation matrix. Technical Report No. 6, Laboratory for Quantitative Research in Education. Stanford University, 1964. In S. Ideka (Ed.) Essays in Probability and Statistics. Tokyo: Shinko Tsusho. Pearson, E.S., & Hartley, H.O. (1972). Biometrika tables for statisticians (2nd ed.). London, England: Cambridge University Press. Pearson, K., & Filon, L.N.G. (1898). Mathematical contributions to the theory of evolution: IV. On the probable error of frequency constants and on the influence of random selection of variation and correlation. Philosophical Transactions of the Royal Society of London, Ser. A. 191,229-311. Pillai, K.C.S., & Gupta, A.K. (1969). On the exact distribution of Wilks's criterion. Biometrika, 56,109-118. Reddon, J.R. (1987). Fisher's tanh-1 transformation of the correlation coefficient and a test for complete independence in a multivariate normal population. Journal of Educational Statistics, 12,294-300. Reddon, J.R., Jackson, D.N., & Schopflocher, D. (1985). Distribution of the determinant of the sample correlation coefficient: Monte Carlo type one error rates. Journal of Educational Statistics, 10, 384-388. 86 Ruben, H. (1966). some new results on the distribution of the sample correlation coefficient. Journal of the Royal Statistical Society, Ser. B, 28, 513-525. Samiuddin, M. (1970). On a test for an assigned value of con-elation in a bivariate normal distribution. Biometrika, 57, 461-464. Sarhan, A.E., & Greenberg, B.G. (1962). Contributions to order statistics. New York: Wiley. Selin, I. (1965). Detection theory. Princeton, NJ: Princeton University Press. Silver, N.C. (1988). Type I errors and power of tests of correlations in a matrix. Doctoral dissertation, Tulane University, 1988. U.M.I. Dissertation Information Service (Order Number 8817301) Ann Arbor, MI. Silver, N.C., & Dunlap, W.P. (1989). A monte carlo study of testing the significance of correlation matrices. Educational and Psychological Measurement, 49, 563-569. Srivastava, M.S., & Lee, G.C. (1983). On the choice of transformations of the correlation coefficient with or without an outlier. Communications in Statistics: Theory and Methods, 12,2533-2547. Srivastava, M.S., & Lee, G.C. (1984). On the distribution of the correlation coefficient when sampling from a mixture of two bivariate normal densities: Robustness and the effect of outliers. The Canadian Journal of Statistics, 12,119-133. Stavig, G.R., & Acock, A.C. (1976). Evaluating the degree of dependence for a set of correlations. Psychological Bulletin, 83,236-241. Steiger, J.H. (1980a). Testing pattern hypotheses on con-elation matrices: Alternative statistics and some empirical results. Multivariate Behavioral Research, 15, 335-352. Steiger, J.H. (1980b). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 57,245-251. Steiger, J.H., & Browne, M.W. (1984). The comparison of interdependent correlations between optimal linear composites. Psychometrika, 49, 11-24. Steiger, J.H., & Fouladi, R.T. (1991a). Squaring the Fisher transform: Some theoretical considerations. Manuscript in preparation. 87 Steiger, J.H., & Fouladi, R.T. (1991b). Asymptotic normal theory chi-square tests on correlation matrices. Manuscript in preparation. Steiger, J.H., & Fouladi, R.T. (1991c). Asymptotic tests of multivariate independence based on the sum of independent chi-squares. Manuscript in preparation. Steiger, J.H., & Hakstian, A.R. (1982). The asymptotic distribution of elements of a correlation matrix: Theory and application. British Journal of Mathematical and Statistical Psychology, 35,208-215. Tippet, L.H.C. (1925). On the extreme individuals and the range of samples taken from a normal population. Biometrika, 17,364-387. Wilks, S.S. (1935). On the independence of k sets of normally distributed statistical variables. Econometrica, 3,309-326. Williams, D.A. (1971). A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103-117. Wilson, G.A., & Martin, S.A. (1983). An empirical comparison of two methods for testing the significance of a correlation matrix. Educational and Psychological Measurement, 43,11-14. 88 APPENDICES 89 Appendix A Extensions of Hotelling's approximations obtained bv Steiger and Fouladi (1991a) la. V!. Vi = N-l p | 5p + p> | llp + 2pj+3p~ 1^2 ' 8(JV-1) ' 16(N-1)2 83p + 13p3-27p5 + 75p7 128(A/-1)3 143p+20p3 + 138p5-780p7+735p9 + 256(A/-1)4 | 625p +113p3 - 990p5 + 14250p7 - 33075p9 +19845p* 1 ^  1024(/V-1)5 lb. v2. v 2 = N-l 8-p" [88-9p^-9p 4 4(/V-l) 24(iV-l)2 384-19p2+2p4-75p6 64(/V-l)3 | 16256 -225p2 - 375p4 + 8025p6 -11025p8 1920(N-1)4 [ 5120 + 113p2 + 20p4 - 7194p6 + 26460p8 -19845p10 ^ 512(/V-1)5 90 lc. V3. V3 N-l 3p 39p + 6 p 3 2(N-1) + S(N-lf ( 362p + 4 5 p 3 + 6 3 p 5 3 2 ( N - 1 ) 3 ( 2809p + 2 9 6 p 3 - 3 2 7 p 5 - H 1 7 0 p 7 12S(N-1)4 ( 47461p + 5 7 2 0 p 3 + 1 1 1 9 0 p 5 - 7 3 3 5 0 p 7 + 77175p 1280(7V-1) 5 9^  Id. v4. v 4 = N-l 3 ( 2 8 - 3 p ^ I J A ' - I ) 2 ( t f - l ) 2 7 3 6 - 8 4 p 2 - 5 1 p 4 1 6 ( N - 1 ) 3 3 1 7 4 4 - 3 0 1 6 p 2 - 8 6 4 p 4 - 3 4 8 0 p 6  + 2 5 6 ( / V - l ) 4 [ 543616 - 4 1 3 1 0 p 2 - 1 7 5 9 5 p 4 + 8 7 3 0 0 p 6 - 1 6 5 3 7 5 p 8 1 9 2 0 ( A / - 1 ) 5 91 p p-9p 3 ( p + 42p3-75p5 2 8(W-1) 16(/V-1)2 | -5p-657p3 + 3825p5-3675p7 ^ ( i V - l ) 3 -23p + 2580p3 + 3621 Op5 + 91140p7 - 59535p9  + 256(A/-1)4 t 53p - 20817p3 + 623250p5 - 3079650p7 + 4862025p9 - 2401245P11 1024(W-1)5 23p2 -97p2 + 309p4 + 4(N-l) + S(N-l)2 ( 1541p2-15210p4+20901p6 64(W-1)3 -6121p2+142851p4-509067p6 + 431985p8 92 2c. % 1 (N-iy ( 15p+123p^L798p3 2 8(/V-l) [ -978p + 19449p3-40311p5 32(7V-1)2 | 7809p - 364308p3 +1953909p5 - 221661 Op7 128(N-1)3 -31305p + 3125790p3 - 32698Q80p5 + 89257770p7 - 67864095p  + 256(N-1)4 2d. 1 XA — n T (N-l)2 [ -12 + 237pz ^ + 2(JV-1) | 192-11484p2+39789p4 16(N-1)2 | -768 + 107391p2 - 961884p4 + 1529325p6 32(N-1)3 [ 6144 - 1842030p2 + 32147595p4 - 122970780p6 + 120297375p8 ^ 128(A/-1)4 2e . X5 . X5=-1 (N-l)' fl35p ( 3255p-22605p3 V 2 8(/V-l) -60810p-H090470p3 -2603445p5 32(/V-l)2 | 1042725p-36421425p3 + 209106600p5 -272870100p7 ^ 128(N-1)4 • 93 A*=-(N-l)' 15 + -360 + 7515p^ 4(N-l) 6720 - 3 6 1 8 9 0 p 2 + 1440945p 4 1 6 ( N - 1 ) 2 | 1800 + 12078225p 2 - 1 1 5 6 2 9 7 5 0 p 4 + 2 1 1 3 1 4 0 6 0 p 6 ^ 6 4 ( / V - l ) 3 2g. A ^ 2h. Ag. 2 i . A9. 2j. A 10-A 7 = 1 ' l 3 6 5 p ( N - l ) 4 I 2 8 ( N - 1 ) | -2188830p + 41926185p 3 - 1 1 4 9 6 1 1 4 0 p 5 ^  3 2 ( / V - l ) 2 1 105+• -1260 + 30135pJ (N-l) 84000 - 4 8 2 8 7 4 0 p 2 + 2 2 0 7 2 3 6 5 p 4 ^  8(7V - 1 ) 2 Ao — • (N-lf 16065p | 1286145p-11760525p 2 S(N-l) 3 A A 1 0 =• ( N - l ) 5 945 + --75600+ 2074275p 4 ( / V - l ) 2 A 2(iV-l) 6 95 Appendix B The configuration of population matrices A. When p = 5 pNz A/ = U M = R 1.0 1.0 .x 1.0 .0 1.0 .2 .x .0 1.0 .0 .0 1.0 .0 .0 .0 1.0 .x .0 .0 1.0 .0 .0 .0 .0 1.0 .0 .x .0 .0 1.0 1.0 1.0 .x 1.0 .x 1.0 .4 .x .x 1.0 .0 .0 1.0 .x .0 .0 1.0 .x .0 .0 1.0 .0 .0 .0 .0 1.0 .0 .x .x .0 1.0 1.0 1.0 .x 1.0 .x 1.0 .6 .x .x 1.0 .x .x 1.0 .x .x .x 1.0 .0 .x .x 1.0 .0 .0 .0 .0 1.0 .0 .0 .x .0 1.0 1.0 1.0 .x 1.0 .x 1.0 .8 .x .x 1.0 .x .x 1.0 .x .x .x 1.0 .x .x .x 1.0 .0 .0 .0 .0 1.0 .0 .x .0 .x 1.0 96 2. When p = 10 pNz M = U M = R 1.0 1.0 .X 1.0 .0 1.0 .X .X 1.0 .0 .0 1.0 .X .X .X 1.0 .X .0 .0 1.0 .2 .X .X .X .0 1.0 .X .0 .0 .X 1.0 .0 .0 .0 .0 .0 1.0 .0 .0 .0 .0 .0 1.0 .0 .0 .0 .0 .0 .0 1.0 .0 .0 .0 .0 .X .X 1.0 .0 .0 .0 .0 .0 .0 .0 1.0 .0 .X .0 .0 .0 .0 .0 1.0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .0 .0 .0 .X .0 .0 .X .0 1.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .X .0 .0 .0 .0 .0 .0 .0 .0 1.0 1.0 1.0 .X 1.0 .0 1.0 .X .X 1.0 .X .0 1.0 .X . X .X 1.0 .0 .X .0 1.0 .4 .X .X .X .X 1.0 .X .0 .0 .0 1.0 .X .X .X .X .X 1.0 .X .0 .X .0 .X 1.0 .X .X .X .0 .0 .0 1.0 .0 .X .X .X .0 .X 1.0 .0 .0 .0 .0 .0 .0 .0 1.0 .X .0 .0 .0 .0 .X .X 1.0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .X .0 .0 .X .0 .0 .0 .0 1.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .0 .0 .X .X .0 .X .0 .0 .0 1.0 • 1.0 1.0 .X 1.0 .0 1.0 .X .X 1.0 .0 .X 1.0 .X .X .X 1.0 .0 .X .0 1.0 .6 .X .X .X .X 1.0 .X .X .0 .0 1.0 .X .X .X .X .X 1.0 .X .0 .X .0 .X 1.0 .X .X .X .X .X .X 1.0 .0 .0 .X .0 .X .X 1.0 .X .X . X .X .X • X .0 1.0 .X .X .X .X .X .X .X 1.0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .X .X .0 .0 .X .0 .0 .0 1.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .X .X .0 .0 .X .X .X .X .X 1.0 1.0 1.0 .X 1.0 .X 1.0 .X .X 1.0 .X .X 1.0 .X .X ' .X 1.0 .X .X .X 1.0 .8 .X .X .X .X 1.0 .X .0 .X .X 1.0 .X .X .X .X .X 1.0 .X .X .X .X .X 1.0 • .X .X .X .X .X .X 1.0 .0 .X .X .X .X .0 1.0 .X .X .X .X .X .X .X 1.0 .X .X .0 .X .0 .X .X 1.0 .X .X .X .X .X .X .X .X 1.0 .X .X .X .X .X .0 .X .0 1.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1.0 .0 .X .X .0 .X .X .X .X .X 1.0 Appendix C Setting the storv straight Several statistics were examined in this study. In this paper, I have tried to delineate the relationship between these statistics as accurately as possible. The results that I have referenced here have for the most part come directly from my reading of the original sources. I have avoided the primary referencing of secondary sources as much as possible. A comparison of the results in primary sources with the results in secondary sources produced some esoteric findings. I would like to set the story straight in this section. 1) Lawley's statistic is commonly described as equalling Qy^. However, the original Lawley test is QE. QIA is the statistic resulting from substitution of Bartlett's multiplier for QBA to Ql suggested by Bartlett (1950). The results of the current study show that (2LA performs worse than QE. Thus, a disservice is being rendered to Lawley by crediting him with a statistic that performs worse than his own statistic. 2) Wilks's result in the original paper has the multiplier N - 1, some sources have the result described as having the multiplier N. This error is likely attributable to the inconsistent notation for sample size and sample size minus 1. In the first part of Wilks's paper, sample size is defined as n; half way through the paper, Wilks's changes notation and lets n equal sample size minus 1. Wilks's result appears after he changes notation. The confusion is further enhanced by the subsequent example where for computational considerations, n equals sample size. 98 TABLES 99 T A B L E S Table 1 The relationship between the number of variables,/?, and the number of pairwise correlations, V p , in a matrix p 2 5 10 15 20 100 1 10 45 105 190 4950 Table 2 Asymptotic chi-square tests of complete independence with vp degrees of freedom Multiplier N N- 1 N- 1 -(2p+5)/6 N-3 MSE MSA Root -lnlRI Q Q QBA ZSrii2 QL=QBR QLA QST=QBU QSE QSA Table 3 Summary table of reviews of tests of LR and NT tests of multivariate independence # replications in a typical condition conditions representative of parameter space scope theoretical inaccuracies Steiger (1980a) 10000 Q vs. Q B A vs. QSTVS- QBR-Wilson & Martin (1983) 20 QBA v s - QST Reddon (1987) 2500 QBA v s - QST Silver & Dunlap (1990) 10000 NO QBA™. (2srvs-QBR v s - QAN YES 100 Table 4 of sample sizes, N, for sample correlation matrices generated under P of order p and specified N:p ratios 2 4 N:p 10 20 40 5 10 20 50 100 200 P io 20 40 100 200 400 15 30 60 150 300 600 1 0 1 Table 5.1 Table of empirical Type I error rates for tests of complete multivariate independence at a = .05 p N:p a QBA QST QSE QLA QBR QF QSA 5 2 .05 .05847 .05718 .05109 .00210 .02998 .05206 .05128 5 4 .05 .05084 .05369 .05065 .01491 .03924 .05037 .05065 5 10 .05 .04983 .05021 .04862 .03179 .04393 .04864 .04862 5 20 .05 .04897 .05061 .04992 .04052 .04756 .04950 .04992 5 40 .05 .05152 .05195 .05168 .04726 .05053 .05190 .05168 10 2 .05 .06668 .05574 .05232 .00102 .04103 .05255 .05232 10 4 .05 .05233 .05315 .05142 .01067 .04559 .05160 .05142 10 10 .05 .05000 .05171 .05085 .02933 .04803 .05062 .05085 10 20 .05 .04999 .05059 .05020 .03833 .04903 .05041 .05020 10 40 .05 .05041 .05059 .05041 .04443 .04976 .05084 .05041 15 2 .05 .07403 .05537 .05290 .00024 .04455 .05266 .05290 15 4 .05 .05312 .05189 .05054 .00590 .04629 .05090 .05054 15 10 .05 .04991 .05046 .05001 .02452 .04820 .04989 .05001 15 20 .05 .05022 .05138 .05114 .03600 .05026 .05098 .05114 15 40 .05 .05087 .05145 .05126 .04360 .05093 .05131 .05126 Table 5.2 Table of empirical Type I error rates for tests of complete multivariate independence at a = .01. P N:p a QBA QST QSE QLA QBR QF QSA 5 2 .01 .01304 .01712 .01450 .00010 .00501 .01356 .01459 5 4 .01 .01021 .01375 .01230 .00178 .00666 .01184 .01230 5 10 .01 .00954 .01067 .01017 .00506 .00782 .01010 .01017 5 20 .01 .01010 .01068 .01054 .00745 .00929 .01037 .01054 5 40 .01 .01036 .01069 .01058 .00889 .00978 .01079 .01058 10 2 .01 .01569 .01504 .01345 .00007 .00777 .01324 .01345 10 4 .01 .01055 .01218 .01152 .00142 .00865 .01154 .01152 10 10 .01 .01031 .01127 .01106 .00529 .00996 .01078 .01106 10 20 .01 .01000 .01027 .01016 .00714 .00962 .01015 .01016 10 40 .01 .00986 .01017 .01012 .00814 .00988 .01007 .01012 15 2 .01 .01712 .01327 .01214 .00001 .00847 .01213 .01214 15 4 .01 .01018 .01077 .01028 .00058 .00855 .01028 .01028 15 10 .01 .00990 .01070 .01047 .00382 .00978 .01037 .01047 15 20 .01 .01072 .01090 .01083 .00714 .01040 .01093 .01083 15 40 .01 .01036 .01068 .01063 .00839 .01045 .01037 .01063 Table 6.1 Chi-square goodness of fit values for tests of complete multivariate independence at a .05 under a true null hypothesis, df = 1, %2iv05 = 3.84, X*1,M - 6-64, X21,.001 = 10.83 X215,.001 = 37.70 p N:p a QBA QST QSE QLA QBR QF QSA 5 2 .05 130.32 95.63 2.45 109487.54 1378.21 8.60 3.37 5 4 .05 1.46 26.80 0.88 8383.26 307.10 0.29 0.88 5 10 .05 0.06 0.09 4.12 1077.36 87.73 4.00 4.12 5 20 .05 2.28 0.77 0.01 231.16 13.14 0.53 0.01 5 40 .05 4.73 7.72 5.76 16.67 0.59 7.34 5.76 10 2 .05 447.06 62.60 10.86 235440.19 204.49 13.06 10.86 10 4 .05 10.95 19.72 4.13 14653.53 44.70 5.23 4.13 10 10 .05 0.00 5.96 1.50 1500.71 8.49 0.80 1.50 10 20 .05 0.00 0.72 0.08 369.47 2.02 0.35 0.08 10 40 .05 0.35 0.72 0.35 73.08 0.12 1.46 0.35 15 2 .05 842.37 55.13 16.79 1031938.33 69.78 14.18 16.79 15 4 .05 19.35 7.26 0.61 33158.52 31.18 1.68 0.61 15 10 .05 0.02 0.44 0.00 2714.31 7.06 0.03 0.00 15 20 .05 0.10 3.91 2.68 564.78 0.14 1.99 2.68 15 40 .05 1.57 4.31 3.26 98.23 1.79 3.53 3.26 .05 1460.61 291.79 53.48 1439797.14 2156.54 63.05 54.39 Table 6.2 Chi-square goodness of fit values for tests of complete multivariate independence at a .01 under a true null hypothesis p N:p a QBA QST QSE QLA QBR QF QSA 5 2 .01 71.81 301.27 141.71 98019.80 499.51 94.75 146.54 5 4 .01 0.44 103.70 43.54 3802.75 168.62 28.94 43.54 5 10 .01 2.24 4.25 0.29 484.74 61.25 0.10 0.29 5 20 .01 0.10 4.38 2.80 87.94 5.48 1.33 2.80 5 40 .01 1.26 4.50 3.21 13.98 0.50 5.85 3.21 10 2 .01 209.64 171.47 89.70 140874.00 64.50 80.35 89.70 10 4 .01 2.90 39.50 20.29 5191.63 21.25 20.79 20.29 10 10 .01 0.94 14.47 10.27 421.59 0.02 5.71 10.27 10 20 .01 0.00 0.72 0.25 115.38 1.52 0.22 0.25 10 40 .01 0.20 0.29 0.14 42.85 0.15 0.05 0.14 15 2 .01 301.27 81.66 38.19 998010.98 27.87 37.86 38.19 15 4 .01 0.32 5.57 0.77 15308.26 24.80 0.77 0.77 15 10 .01 0.10 4.63 2.13 1003.63 0.50 1.33 2.13 15 20 .01 4.89 7.51 6.43 115.38 1.55 8.00 6.43 15 40 .01 1.26 4.38 3.77 31.16 1.96 1.33 3.77 .01 597.37 748.30 363.51 1263524.07 879.49 287.39 368.33 103 Table 7.1.1.1 Empirical power of tests of complete multivariate independence at a = .05, p = 5, mNz = .1 P N.p M pNz a QBA QST QSE QLA QBR QF QSA 5 2 U .2 .05 .0616 .0629 .0578 .0024 .0345 .0558 .0580 5 2 R .2 .05 .0638 .0627 .0565 .0026 .0354 .0585 .0567 5 4 U .2 .05 .0609 .0658 .0609 .0172 .0467 .0614 .0609 5 4 R .2 .05 .0622 .0648 .0617 .0182 .0514 .0627 .0617 5 10 U .2 .05 .0760 .0793 .0778 .0542 .0709 .0782 .0778 5 10 R .2 .05 .0757 .0799 .0788 .0541 .0726 .0776 .0788 5 20 U .2 .05 .1201 .1222 .1211 .1026 .1172 .1180 .1211 5 20 R .2 .05 .1160 .1159 ' .1149 .0986 .1110 .1140 .1149 5 40 U .2 .05 .2181 .2200 .2189 .2052 .2143 .2059 .2189 5 40 R .2 .05 .2116 .2144 .2129 .2003 .2096 .2056 .2129 5 2 U .4 .05 .0664 .0680 .0623 .0028 .0376 .0612 .0624 5 2 R .4 .05 .0665 .0679 .0607 .0023 .0387 .0609 .0610 5 4 U .4 .05 .0710 .0793 .0740 .0234 .0583 .0772 .0740 5 4 R .4 .05 .0708 .0756 .0719 .0241 .0585 .0716 .0719 5 10 U .4 .05 .1090 .1174 .1159 .0853 .1081 .1149 .1159 5 10 R .4 .05 .1144 .1155 .1124 .0818 .1051 .1124 .1124 5 20 U .4 .05 .2033 .2151 .2134 .1892 .2077 .2122 .2134 5 20 R .4 .05 .2009 .2022 .2006 .1758 .1938 .1968 .2006 5 40 U .4 .05 .4155 .4342 .4327 .4161 .4282 .4259 .4327 5 40 R .4 .05 .4429 .4404 .4395 .4241 .4356 .4356 .4395 5 2 U .6 .05 .0680 .0707 .0661 .0030 .0403 .0655 .0661 5 2 R .6 .05 .0683 .0714 .0659 .0030 .0409 .0653 .0659 5 4 U .6 .05 .0810 .0949 .0903 .0311 .0730 .0919 .0903 5 4 R .6 .05 .0801 .0897 .0848 .0295 .0666 .0857 .0848 5 10 U .6 .05 .1359 .1603 .1575 .1190 .1481 .1574 .1575 5 10 R .6 .05 .1469 .1569 .1544 .1158 .1434 .1534 .1544 5 20 U .6 .05 .2788 .3170 .3144 .2894 .3086 .3171 .3144 5 20 R .6 .05 .2942 .3119 .3098 .2838 .3038 .3126 .3098 5 40 U .6 .05 .5718 .6154 .6145 .6005 .6108 .6178 .6145 5 40 R .6 .05 .6149 .6308 .6299 .6140 .6262 .6286 .6299 5 2 U .8 .05 .0743 .0760 .0679 .0039 .0433 .0696 .0681 5 2 R .8 .05 .0722 .0754 .0686 .0035 .0443 .0666 .0688 5 4 U .8 .05 .0935 .1052 .1011 .0394 .0835 .1030 .1011 5 4 R .8 .05 .0947 .1083 .1039 .0405 .0884 .1045 .1039 5 10 U .8 .05 .1768 .2033 .1998 .1596 .1904 .2010 .1998 5 10 R .8 .05 .1758 .2034 .2006 .1586 .1912 .2027 .2006 5 20 U .8 .05 .3730 .4122 .4101 .3806 .4043 .4180 .4101 5 20 R .8 .05 .3762 .4150 .4125 .3842 .4077 .4174 .4125 5 40 U .8 .05 .7317 .7617 .7612 .7494 .7588 .7688 .7612 5 40 R .8 .05 .7323 .7631 .7619 .7506 .7606 .7722 .7619 104 Table 7.1.1.2 Empirical power of tests of complete multivariate independence at a = .05, p = 5, mNz - .3 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 5 2 U .2 .05 .0929 .1012 .0929 .0057 .0583 .0933 .0930 5 2 R .2 .05 .0962 .1040 .0951 .0059 .0622 .0957 .0954 5 4 U .2 .05 .1788 .1875 .1804 .0727 .1475 .1761 .1804 5 4 R .2 .05 .1676 .1830 .1760 .0733 .1421 .1707 .1760 5 10 U .2 .05 .4986 .4830 .4791 .3857 .4463 .4395 .4791 5 10 R .2 .05 .4787 .4931 .4889 .4020 .4572 .4526 .4889 5 20 U .2 .05 .8868 .8723 .8705 .8475 .8618 .8398 .8705 5 20 R .2 .05 .8619 .8644 .8633 .8352 .8536 .8305 .8633 5 40 U .2 .05 .9985 .9979 .9979 .9973 .9976 .9963 .9979 5 40 R .2 .05 .9969 .9975 .9975 .9965 .9971 .9947 .9975 5 2 U .4 .05 .1337 .1638 .1500 .0136 .1056' .1524 .1506 5 2 R .4 .05 .1479 .1592 .1480 .0112 .1004 .1508 .1482 5 4 U .4 .05 .3215 .3609 .3505 .1942 .3119 .3483 .3505 5 4 R .4 .05 .3714 .3599 .3472 .1754 .2989 .3386 .3472 5 10 U .4 .05 .8102 .8241 .8213 .7716 .8083 .8119 .8213 5 10 R .4 .05 .8890 .8635 .8610 .8126 .8510 .8529 .8610 5 20 U .4 .05 .9924 .9936 .9934 .9911 .9930 .9927 .9934 5 20 R .4 .05 .9990 .9983 .9983 .9978 .9983 .9981 .9983 5 40 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .6 .05 .1588 .2437 .2276 .0381 .1802 .2407 .2276 5 2 R .6 .05 .1907 .2311 .2147 .0280 .1605 .2244 .2151 5 4 U .6 .05 .3903 .4932 .4866 .3433 .4634 .4958 .4866 5 4 R .6 .05 .4899 .5140 .5027 .3312 .4701 .5092 .5027 5 10 U .6 .05 .8663 .9098 .9088 .8872 .9046 .9112 .9088 5 10 R .6 .05 .9576 .9563 .9557 .9370 .9517 .9566 .9557 5 20 U .6 .05 .9968 .9984 .9984 .9981 .9983 .9984 .9984 5 20 R .6 .05 .9999 .9998 .9998 .9998 .9998 1.0000 .9998 5 40 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .8 .05 .2198 .3020 .2861 .0576 .2357 .3022 .2870 5 2 R .8 .05 .2192 .3063 .2889 .0595 .2369 .3057 .2894 5 4 U .8 .05 .5549 .6203 .6115 .4653 .5892 .6248 .6115 5 4 R .8 .05 .5550 .6214 .6113 .4635 .5917 .6275 .6113 5 10 U .8 .05 .9721 .9771 .9764 .9686 .9757 .9791 .9764 5 10 R .8 .05 .9758 .9804 .9802 .9743 .9792 .9824 .9802 5 20 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 105 Table 7.1.1.3 Empirical power of tests of complete multivariate independence at a = .05, p = 5, mNz = .5 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 5 2 U .2 .05 .2330 .2348 .2169 .0179 .1374 .2092 .2173 5 2 R .2 .05 .2011 .2393 .2239 .0189 .1437 .2132 .2247 5 4 U .2 .05 .6522 .5683 .5563 .2862 .4562 .5079 .5563 5 4 R .2 .05 .5305 .5679 .5578 .2900 .4604 .5075 .5578 5 10 U .2 .05 .9957 .9896 .9893 .9768 .9852 .9804 .9893 5 10 R .2 .05 .9743 .9776 .9767 .9610 .9711 .9655 .9767 5 20 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .4 .05 .4249 .4602 .4414 .0751 .3484 .4427 .4416 5 2 R .4 .05 .6407 .4741 .4519 .0680 .3302 .4433 .4528 5 4 U .4 .05 .9007 .8885 .8834 .7384 .8551 .8761 .8834 5 4 R .4 .05 .9930 .9329 .9276 .7765 .9019 .9179 .9276 5 10 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 10 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .6 .05 .4337 .6045 .5866 .2539 .5460 .6069 .5878 5 2 R .6 .05 .7678 .6454 .6260 .2016 .5530 .6384 .6264 5 4 U .6 .05 .8533 .9202 .9176 .8566 .9106 .9210 .9176 5 4 R .6 .05 .9988 .9873 .9861 .9431 .9838 .9883 .9861 5 10 U .6 .05 .9993 .9998 .9998 .9997 .9998 .9998 .9998 5 10 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .8 .05 .7445 .7419 .7278 .3697 .6934 .7518 .7280 5 2 R .8 .05 .7431 .7427 .7275 .3749 .6905 .7502 .7282 5 4 U .8 .05 .9942 .9863 .9858 .9645 .9849 .9881 .9858 5 4 R .8 .05 .9961 .9873 .9863 .9666 .9860 .9887 .9863 5 10 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 10 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 106 Table 7.1.2.1 Empirical power of tests of complete multivariate independence at a = .05, p - 10, mNz =. 1 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 10 2 U .2 .05 .0866 .0841 .0794 .0031 .0633 .0814 .0794 10 2 R .2 .05 .0860 .0848 .0799 .0026 .0632 .0795 .0799 10 4 U .2 .05 .0930 .1097 .1066 .0295 .0967 .1070 .1066 10 4 R .2 .05 .0954 .1036 .1014 .0272 .0907 .1027 .1014 10 10 U .2 .05 .1981 .2345 .2332 .1686 .2262 .2298 .2332 10 10 R .2 .05 .2222 .2340 .2323 .1654 .2242 .2250 .2323 10 20 U .2 .05 .4349 .4991 .4971 .4527 .4912 .4789 .4971 10 20 R .2 .05 .4965 .5081 .5067 .4623 .5010 .4925 .5067 10 40 U .2 .05 .8368 .8769 .8768 .8672 .8757 .8604 .8768 10 40 R .2 .05 .9034 .9039 .9035 .8930 .9022 .8878 .9035 10 2 U .4 .05 .1052 .1162 .1094 .0057 .0911 .1108 .1094 10 2 R .4 .05 .1084 .1120 .1059 .0047 .0879 .1057 .1059 10 4 U .4 .05 .1459 .1938 .1900 .0722 .1770 .1913 .1900 10 4 R .4 .05 .1630 .1860 .1829 .0639 .1669 .1802 .1829 10 10 U .4 .05 .3945 .4834 .4810 .4049 .4741 .4818 .4810 10 10 R .4 .05 .4680 .4966 .4943 .4009 .4853 .4895 .4943 10 20 U .4 .05 .7822 .8506 .8502 .8261 .8482 .8467 .8502 10 20 R .4 .05 .8761 .8872 .8867 .8671 .8843 .8841 .8867 10 40 U .4 .05 .9935 .9971 .9971 .9967 .9970 .9973 .9971 10 40 R .4 .05 .9992 .9992 .9992 .9991 .9992 .9993 .9992 10 2 U .6 .05 .1217 .1530 .1472 .0103 .1257 .1499 .1473 10 2 R .6 .05 .1278 .1470 .1413 .0099 .1194 .1435 .1413 10 4 U .6 .05 .1933 .2830 .2780 .1319 .2646 .2808 .2780 10 4 R .6 .05 .2182 .2811 .2759 .1229 .2600 .2756 .2759 10 10 U .6 .05 .5529 .6800 .6782 .6095 .6739 .6830 .6782 10 10 R .6 .05 .6383 .7002 .6984 .6279 .6925 .7004 .6984 10 20 U .6 05 .9199 .9604 .9602 .9508 .9594 .9614 .9602 10 20 R .6 .05 .9697 .9802 .9800 .9735 .9796 .9806 .9800 10 40 U .6 .05 .9998 .9999 .9999 .9999 .9999 .9999 .9999 10 40 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .8 .05 .1366 .1939 .1872 .0212 .1646 .1903 .1872 10 2 R .8 .05 .1476 .1852 .1793 .0175 .1553 .1808 .1793 10 4 U .8 .05 .2414 .3703 .3645 .2005 .3518 .3709 .3645 10 4 R .8 .05 .2815 .3695 .3630 .1952 .3479 .3694 .3630 10 10 U .8 .05 .6774 .8062 .8050 .7560 .8018 .8112 .8050 10 10 R .8 .05 .7630 .8320 .8308 .7794 .8284 .8378 .8308 10 20 U .8 .05 .9718 .9892 .9892 .9867 .9891 .9904 .9892 10 20 R .8 .05 .9915 .9960 .9960 .9943 .9958 .9962 .9960 10 40 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 107 Table 7.1.2.2 Empirical power of tests of complete multivariate independence at a= ,05yp = 10, mNz - .3 p N:p M pNz a QUA QST QSE QlA QBR QF QSA\ 10 2 U .2 .05 .2941 .4108 .4013 .0764 .3616 .3963 .40131 10 2 R .2 .05 .4175 .4174 .4066 .0529 .3545 .3943 .4066 10 4 U .2 .05 .6595 .7690 .7656 .5901 .7484 .7523 .7656 10 4 R .2 .05 .8808 .8456 .8422 .6229 .8184 .8179 .8422 10 10 U .2 .05 .9953 .9978 .9977 .9956 .9976 .9962 .9977 10 10 R .2 .05 1.0000 .9999 .9999 .9999 .9999 .9999 .9999 10 20 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .4 .05 .5205 .7003 .6921 .3069 .6655 .6944 .6921 10 2 R .4 .05 .8161 .7712 .7612 .2738 .7272 .7584 .7612 10 4 U .4 .05 .9266 .9674 .9661 .9122 .9639 .9662 .9661 10 4 R .4 .05 .9994 .9980 .9979 .9840 .9976 .9980 .9979 10 10 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .6 .05 .6307 .8252 .8210 .5309 .8059 .8261 .8210 10 2 R .6 .05 .8975 .8985 .8931 .5626 .8812 .8987 .8931 10 4 U .6 .05 .9661 .9910 .9908 .9754 .9899 .9907 .9908 10 4 R .6 .05 .9998 .9991 .9991 .9967 .9991 .9995 .9991 10 10 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .6 05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .8 .05 .6898 .8861 .8819 .6789 .8758 .8875 .8819 10 2 R .8 .05 .9602 .9475 .9450 .7233 .9421 .9520 .9450 10 4 U .8 .05 .9795 .9961 .9959 .9915 .9960 .9965 .9959 10 4 R .8 .05 1.0000 1.0000 1.0000 .9995 1.0000 1.0000 1.0000 10 10 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 108 Table 7.1.2.3 Empirical power of tests of complete multivariate independence at a = .05, p = 10, mNz = .5 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 10 2 U .2 .05 .8536 .9014 .8970 .5438 .8684 .8835 .8970 10 2 R .2 .05 .9961 .8526 .8446 .2862 .7583 .7974 .8446 10 4 U .2 .05 .9998 .9993 .9993 .9958 .9992 .9989 .9993 10 4 R .2 .05 1.0000 .9999 .9999 .9931 .9996 .9993 .9999 10 10 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .2 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .4 .05 .9989 .9906 .9896 .9227 .9885 .9910 .9896 10 2 R .4 .05 .9599 .9156 .9108 .4757 .8844 .9034 .9108 10 4 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .4 .05 1.0000 1.0000 1.0000 .9993 1.0000 1.0000 1.0000 10 10 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .4 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .6 .05 .9939 .9974 .9974 .9731 .9969 .9974 .9974 10 2 R .6 .05 1.0000 .9983 .9981 .9472 .9977 .9983 .9981 10 4 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .6 05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .6 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.00000 10 2 U .8 .05 .9804 .9981 .9981 .9871 .9976 .9981 .9981 10 2 R .8 .05 1.0000 .9985 .9984 .9657 .9981 .9983 .9984 10 4 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .05 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 109 Table 7.2.1.1 Empirical power of tests of complete multivariate independence at a = .01, p = 5, mNz = .1 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 5 2 U .2 .01 .0137 .0173 .0148 .0001 .0062 .0149 .0149 5 2 R .2 .01 .0131 .0192 .0161 .0000 .0055 .0163 .0163 5 4 U .2 .01 .0120 .0156 .0136 .0025 .0080 .0140 .0136 5 4 R .2 .01 .0136 .0178 .0152 .0032 .0088 .0149 .0152 5 10 U .2 .01 .0175 .0210 .0202 .0113 .0159 .0184 .0202 5 10 R .2 .01 .0171 .0207 .0201 .0113 .0163 .0203 .0201 5 20 U .2 .01 .0336 .0382 .0379 .0290 .0345 .0366 .0379 5 20 R .2 .01 .0325 .0354 .0347 .0264 .0313 .0325 .0347 5 40 U .2 .01 .0735 .0753 .0747 .0668 .0712 .0706 .0747 5 40 R .2 .01 .0761 .0785 .0776 .0689 .0736 .0727 .0776 5 2 U .4 .01 .0143 .0202 .0174 .0002 .0067 .0182 .0175 5 2 R .4 .01 .0144 .0205 .0179 .0002 .0061 .0168 .0180 5 4 U .4 .01 .0159 .0210 .0189 .0048 .0112 .0186 .0189 5 4 R .4 .01 .0162 .0215 .0192 .0043 .0112 .0191 .0192 5 10 U .4 .01 .0308 .0373 .0355 .0220 .0303 .0360 .0355 5 10 R .4 .01 .0293 .0351 .0343 .0199 .0286 .0337 .0343 5 20 U .4 .01 .0728 .0831 .0821 .0668 .0770 .0816 .0821 5 20 R .4 .01 .0704 .0703 .0690 .0568 .0640 .0686 .0690 5 40 U .4 .01 .2011 .2201 .2188 .2034 .2124 .2118 .2188 5 40 R .4 .01 .2159 .2154 .2144 .1986 .2095 .2094 .2144 5 2 U .6 .01 .0159 .0242 .0204 .0002 .0074 .0205 .0206 5 2 R .6 .01 .0158 .0222 .0187 .0003 .0074 .0188 .0187 5 4 U .6 .01 .0199 .0290 .0266 .0063 .0174 .0270 .0266 5 4 R .6 .01 .0199 .0267 .0242 .0054 .0160 .0242 .0242 5 10 U .6 .01 .0440 .0606 .0592 .0399 .0520 .0614 .0592 5 10 R .6 .01 .0440 .0558 .0543 .0337 .0462 .0547 .0543 5 20 U .6 .01 .1162 .1502 .1489 .1283 .1420 .1515 .1489 5 20 R .6 .01 .1203 .1405 .1388 .1186 .1327 .1422 .1388 5 40 U .6 .01 .3393 .3978 .3962 .3781 .3892 .4025 .3962 5 40 R .6 .01 .3747 .4011 .3996 .3826 .3944 .4073 .3996 5 2 U .8 .01 .0165 .0268 .0219 .0004 .0089 .0223 .0222 5 2 R .8 .01 .0170 .0272 .0224 .0005 .0077 .0230 .0226 5 4 U .8 .01 .0240 .0363 .0342 .0092 .0226 .0334 .0342 5 4 R .8 .01 .0242 .0356 .0331 .0090 .0223 .0334 .0331 5 10 U .8 .01 .0613 .0839 .0819 .0533 .0716 .0835 .0819 5 10 R .8 .01 .0634 .0850 .0829 .0552 .0732 .0846 .0829 5 20 U .8 .01 .1813 .2234 .2211 .1934 .2133 .2272 .2211 5 20 R .8 .01 .1825 .2199 .2177 .1933 .2101 .2251 .2177 5 40 U .8 .01 .5071 .5580 .5567 .5394 .5519 .5692 .5567 5 40 R .8 .01 .5132 .5623 .5609 .5444 .5572 .5748 .5609 110 Table 72.12 Empirical power of tests of complete multivariate independence at a = .01, p - 5, mNz = .3 p N:p M pNz a QBA QST QSE QLA QBR QF QSA 5 2 u .2 .01 .0232 .0361 .0296 .0005 .0115 .0305 .0297 5 2 R .2 .01 .0240 .0350 .0307 .0004 .0122 .0307 .0308 5 4 U .2 .01 .0550 .0707 .0653 .0121 .0394 .0613 .0654 5 4 R .2 .01 .0544 .0717 .0666 .0165 .0425 .0637 .0666 5 10 U .2 .01 .2631 .2538 .2484 .1673 .2097 .2195 .2484 5 10 R .2 .01 .2400 .2608 .2561 .1684 .2113 .2208 .2561 5 20 U .2 .01 .7255 .6999 .6968 .6333 .6644 .6341 .6968 5 20 R .2 .01 .6727 .6823 .6795 .6248 .6528 .6219 .6795 5 40 U .2 .01 .9893 .9865 .9865 .9840 .9855 .9760 .9865 5 40 R .2 .01 .9845 .9848 .9848 .9814 .9832 .9749 .9848 5 2 U .4 .01 .0372 .0677 .0602 .0018 .0263 .0591 .0604 5 2 R .4 .01 .0420 .0612 .0525 .0015 .0230 .0522 .0527 5 4 U .4 .01 .1342 .1848 .1764 .0631 .1300 .1725 .1764 5 4 R .4 .01 .1520 .1665 .1580 .0494 .1097 .1520 .1580 5 10 U .4 .01 .5936 .6358 .6303 .5369 .5965 .6159 .6303 5 10 R .4 .01 .7167 .6743 .6684 .5658 .6323 .6490 .6684 5 20 U .4 .01 .9691 .9721 .9717 .9637 .9690 .9672 .9717 5 20 R .4 .01 .9931 .9893 .9892 .9847 .9873 .9866 .9892 5 40 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 . .9999 1.0000 5 40 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .6 .01 .0487 .1167 .1051 .0068 .0606 .1111 .1052 5 2 R .6 .01 .0564 .1074 .0960 .0045 .0468 .0971 .0960 5 4 U .6 .01 .1919 .3213 .3126 .1716 .2680 .3203 .3126 5 4 R .6 .01 .2521 .3104 .2991 .1387 .2405 .3039 .2992 5 10 U .6 .01 .7069 .8109 .8068 .7609 .7935 .8142 .8068 5 10 R .6 .01 .8674 .8669 .8636 .8145 .8525 .8687 .8636 5 20 U .6 .01 .9871 .9935 .9934 .9918 .9932 .9939 .9934 5 20 R .6 .01 .9991 .9990 .9990 .9987 .9990 .9991 .9990 5 40 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .8 .01 .0765 .1588 .1416 .0139 .0898 .1515 .1418 5 2 R .8 .01 .0750 .1587 .1455 .0135 .0919 .1569 .1458 5 4 U .8 .01 .3193 .4353 .4231 .2604 .3779 .4394 .4231 5 4 R .8 .01 .3240 .4311 .4188 .2613 .3773 .4377 .4189 5 10 U .8 .01 .9136 .9365 .9347 .9110 .9278 .9401 .9347 5 10 R .8 .01 .9160 .9372 .9351 .9103 .9300 .9438 .9351 5 20 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .8 .01 .9999 .9999 .9999 .9999 .9999 1.0000 .9999 5 40 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 I l l Table 7.2.1.3 Empirical power of tests of complete multivariate independence at or = .01, p = 5, mNz = .5 p N:p M pNz or QBA QST QSE QLA QBR QF QSA 5 2 U .2 .01 .0718 .1003 .0882 .0016 .0340 .0817 .0886 5 2 R .2 .01 .0645 .1034 .0878 .0026 .0359 .0825 .0882 5 4 U .2 .01 .3751 .3263 .3118 .0913 .1920 .2661 .3118 5 4 R .2 .01 .2795 .3300 .3166 .0921 .1936 .2717 .3166 5 10 U .2 .01 .9769 .9452 .9431 .8736 .9103 .9031 .9431 5 10 R .2 .01 .9141 .9235 .9219 .8472 .8859 .8766 .9219 5 20 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .2 .01 .9997 .9998 .9998 .9996 .9998 .9994 .9998 5 40 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .4 .01 .1821 .2711 .2498 .0142 .1283 .2417 .2500 .5 2 R .4 .01 .3359 .2543 .2331 .0112 .1175 .2218 .2334 5 4 U .4 .01 .7418 .7351 .7220 .4565 .6332 .7035 .7220 5 4 R .4 .01 .9606 .7813 .7647 .4424 .6468 .7336 .7647 5 10 U .4 .01 .9997 .9995 .9994 .9987 .9992 .9994 .9994 5 10 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .6 .01 .2046 .4455 .4255 .0822 .3334 .4435 .4260 5 2 R .6 .01 .4958 .4394 .4154 .0550 .2861 .4195 .4159 5 4 U .6 .01 .6969 .8417 .8371 .7205 .8120 .8438 .8371 5 4 R .6 .01 .9905 .9307 .9244 .7829 .8976 .9307 .9244 5 10 U .6 .01 .9969 .9993 .9991 .9986 .9990 .9993 .9991 5 10 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 2 U .8 .01 .4916 .5799 .5534 .1588 .4595 .5810 .5542 5 2 R .8 .01 .4940 .5794 .5565 .1619 .4665 .5812 .5572 5 4 U .8 .01 .9785 .9549 .9522 .8920 .9409 .9580 .9522 5 4 R .8 .01 .9791 .9574 .9538 .8941 .9442 .9613 .9538 5 10 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 10 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 20 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5 40 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 112 Table 7.2.2.1 Empirical power of tests of complete multivariate independence at a= .01, p = 10, mNz = .1 p N:p M pNz a QBA QST QSE QlA QRR QF QSA\ 10 2 U .2 .01 .0220 .0280 .0255 .0002 .0148 .0248 .0255 10 2 R .2 .01 .0232 .0260 .0242 .0002 .0152 .0239 .0242 10 4 U .2 .01 .0229 .0331 .0317 .0054 .0255 .0311 .0317 10 4 R .2 .01 .0220 .0301 .0289 .0043 .0224 .0277 .02«9 10 10 U .2 .01 .0733 .1001 .0982 .0629 .0922 .0946 .0982 10 10 R .2 .01 .0792 .0908 .0894 .0528 .0812 .0834 .0894 10 20 U .2 .01 .2203 .2867 .2859 .2479 .2800 .2718 .2859 10 20 R .2 .01 .2659 .2784 .2774 .2379 .2698 .2601 .2774 10 40 U .2 .01 .6500 .7280 .7272 .7067 .7233 .6975 .7272 10 40 R .2 .01 .7518 .7560 .7555 .7332 .7510 .7211 .7555 10 2 U .4 .01 .0273 .0412 .0385 .0007 .0260 .0392 .0385 10 2 R .4 .01 .0292 .0373 .0352 .0003 .0235 .0340 .0352 10 4 U .4 .01 .0430 .0778 .0743 .0196 .0645 .0752 .0743 10 4 R .4 .01 .0481 .0697 .0666 .0144 .0544 .0661 .0666 10 10 U .4 .01 .1867 .2858 .2832 .2103 .2729 .2814 .2832 10 10 R .4 .01 .2316 .2645 .2615 .1923 .2518 .2625 .2615 10 20 U .4 .01 .5808 .6992 .6979 .6583 .6925 .6925 .6979 10 20 R .4 .01 .7051 .7325 .7313 .6921 .7267 .7238 .7313 10 40 U .4 .01 .9714 .9859 .9858 .9842 .9854 .9846 .9858 10 40 R .4 .01 .9942 .9943 .9943 .9935 .9942 .9941 .9943 10 2 U .6 .01 .0343 .0608 .0558 .0024 .0413 .0593 .0558 10 2 R .6 .01 .0357 .0565 .0531 .0019 .0371 .0540 .0531 10 4 U .6 .01 .0657 .1392 .1340 .0513 .1186 .1378 .1340 10 4 R .6 .01 .0775 .1304 .1264 .0412 .1110 .1276 .1264 10 10 U .6 .01 .3222 .4873 .4846 .4069 .4751 .4900 .4846 10 10 R .6 .01 .3948 .4976 .4928 .4060 .4828 . .4983 .4928 10 20 U .6 .01 .8027 .8969 .8965 .8795 .8949 .8988 .8965 10 20 R .6 .01 .8962 .9304 .9300 .9144 .9292 .9320 .9300 10 40 U .6 .01 .9983 .9996 .9996 .9996 .9996 .9996 .9996 10 40 R .6 .01 .9997 .9998 .9998 .9998 .9998 .9998 .9998 10 2 U .8 .01 .0426 .0906 .0849 .0058 .0656 .0858 .0849 10 2 R .8 .01 .0449 .0820 .0767 .0047 .0600 .0801 .0767 10 4 U .8 .01 .0928 .2066 .2021 .0909 .1862 .2077 .2021 10 4 R .8 .01 .1116 .2016 .1967 .0802 .1802 .2019 .1967 10 10 U .8 .01 .4525 .6579 .6546 .5825 .6472 .6642 .6546 10 10 R .8 .01 .5492 .6776 .6749 .5957 .6667 .6832 .6749 10 20 U .8 .01 .9111 .9673 .9667 .9598 .9661 .9701 .9667 10 20 R .8 .01 .9669 .9829 .9828 .9778 .9826 .9838 .9828 10 40 U .8 .01 .9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .01 .9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 113 Table 7.2.2.2 Empirical power of tests of complete multivariate independence at a = .01, p = 10, mNz = .3. p N:p M pNz a QBA QST QSE QlA QBR QF QSA\ 10 2 U .2 .01 .1158 .2424 .2316 .0246 .1842 .2210 .2316] 10 2 R .2 .01 .1912 .2235 .2128 .0131 .1540 .1989 .2129 10 4 U .2 .01 .4253 .6142 .6077 .3794 .5683 .5829 .6077 10 4 R .2 .01 .7015 .6584 .6499 .3593 .5965 .6113 .6499 10 10 U .2 .01 .9803 .9906 .9902 .9832 .9884 .9862 .9902 10 10 R .2 .01 .9998 .9996 .9996 .9991 .9996 .9995 .9996 10 20 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .4 .01 .2878 .5414 .5278 .1647 .4793 .5331 .52781 10 2 R .4 .01 .5936 .5769 .5600 .1146 .4924 .5562 .5602 10 4 U .4 .01 .8106 .9166 .9144 .8175 .9049 .9122 .9144 10 4 R .4 .01 .9970 .9852 .9849 .9185 .9804 .9841 .9849 10 10 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .6 .01 .4054 .7153 .7070 .3779 .6801 .7178 .7070 10 2 R .6 .01 .7363 .7865 .7745 .3633 .7417 .7852 .7746 10 4 U .6 .01 .9035 .9763 .9752 .9422 .9731 .9769 .9752 10 4 R .6 .01 .9991 .9967 .9967 .9868 .9963 .9973 .9967 10 10 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U \6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .8 .01 .4819 .8150 .8101 .5464 .7887 .8188 .8101 10 2 R .8 .01 .8652 .8776 .8706 .5606 .8531 .8839 .8706 10 4 U .8 .01 .9341 .9915 .9914 .9785 .9904 .9920 .9914 10 4 R .8 .01 1.0000 .9994 .9994 .9967 .9993 .9996 .9994 10 10 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000J 114 Table 7.2.2.3 Empirical power of tests of complete multivariate independence at a = .01,/? = 10, mNz = .5 p N:p M pNz a QRA QST QSE QlA QBR QF QSA 10 2 U .2 .01 .6711 .7993 .7917 .3260 .7314 .7657 .7917 10 2 R .2 .01 .9682 .6744 .6607 .1096 .5168 .5987 .6607 10 4 U .2 .01 .9979 .9964 .9961 .9790 .9944 .9938 .9961 10 4 R .2 .01 1.0000 .9977 .9975 .9482 .9907 .9918 .9975 10 10 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .2 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .4 .01 .9911 .9748 .9735 .8352 .9665 .9741 .9735 10 2 R .4 .01 .8480 .7845 .7738 .2577 .7035 .7586 .7739 10 4 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .4 .01 1.0000 .9996 .9996 .9928 .9989 .9991 .9996 10 10 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .4 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .6 .01 .9757 .9909 .9906 .9461 .9884 .9915 .9906 10 2 R .6 .01 1.0000 .9920 .9913 .8616 .9859 .9896 .9913 10 4 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .6 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 2 U .8 .01 .9426 .9955 .9954 .9748 .9950 .9961 .9954 10 2 R .8 .01 1.0000 .9927 .9917 .9005 .9905 .9934 .9917 10 4 U .8 .01 .9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 4 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 10 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 20 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 U .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10 40 R .8 .01 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 115 Table 8 Experimentwise Type I error rate for testing the correlations between p uncorrected variables at the nominal level ac = .05 under the assumption of independent tests: aEX -i - ( i-ai . ) v p 2 5 10 15 20 100 VP 1 10 45 105 190 4950 aEX .0500 .4013 .9006 .9954 .9999 1.000 Table 9 Table of critical values that an observed value must exceed for each procedure to test the significance of the pairwise correlations from a matrix of order p-5 i N.p rNT pMB rMB pMD rMD rOR/OS rOF tCF xCS 1 2 .6319 .0250 .6319 .0250 .6319 .1242 .6296 .6296 3.8415 2 2 .6319 .0125 .6973 .0127 .6962 .1926 .6886 .6886 5.9915 3 2 .6319 .0083 .7294 .0085 .7281 .2534 .7175 .7175 7.8147 4 2 .6319 .0063 .7499 .0064 .7486 .3119 .7359 .7359 9.4877 5 2 .6319 .0050 .7646 .0051 .7633 .3704 .7491 .7491 11.0705 6 2 .6319 .0042 .7759 .0043 .7746 .4310 .7592 .7592 12.5916 7 2 .6319 .0036 .7850 .0037 .7837 .4961 .7674 .7674 14.0671 8 2 .6319 .0031 .7926 .0032 .7913 .5692 .7742 .7742 15.5073 9 2 .6319 .0028 .7990 .0028 .7978 .6580 .7800 .7800 16.9190 10 2 .6319 .0025 .8046 .0026 .8034 .7850 .7850 .7850 18.3070 1 4 .4438 .0250 .4438 .0250 .4438 .0800 .4425 .4425 3.8415 2 4 .4438 .0125 .4993 .0127 .4984 .1245 .4948 .4948 5.9915 3 4 .4438 .0083 5282 .0085 .5270 .1647 .5220 .5220 7.8147 4 4 .4438 .0063 5473 .0064 .5461 .2041 5400 .5400 9.4877 5 4 .4438 .0050 .5614 .0051 .5602 .2445 .5532 5532 11.0705 6 4 .4438 .0042 5725 .0043 .5713 .2876 .5636 5636 12.5916 7 4 .4438 .0036 .5816 .0037 .5804 .3356 .5721 .5721 14.0671 8 4 .4438 .0031 5893 .0032 .5880 .3925 .5793 .5793 15.5073 9 4 .4438 .0028 5959 .0028 .5947 .4672 .5855 .5855 16.9190 10 4 .4438 .0025 .6018 .0026 .6005 .5909 5909 .5909 18.3070 1 10 .2787 .0250 .2787 .0250 .2787 .0481 .2783 .2783 3.8415 2 10 .2787 .0125 .3168 .0127 .3161 .0751 .3151 .3151 5.9915 3 10 .2787 .0083 .3371 .0085 .3363 .0996 .3349 .3349 7.8147 4 10 .2787 .0063 .3508 .0064 .3499 .1239 .3482 .3482 9.4877 5 10 2787 .0050 .3610 .0051 .3601 .1490 .3581 .3581 11.0705 6 10 .2787 .0042 .3692 .0043 .3682 .1761 .3660 .3660 12.5916 7 10 .2787 .0036 .3759 .0037 .3749 , .2069 .3725 .3725 14.0671 8 10 .2787 .0031 .3816 .0032 .3806 .2444 .3780 .3780 15.5073 9 10 .2787 .0028 .3866 .0028 .3856 .2955 .3828 .3828 16.9190 10 10 .2787 .0025 .3909 .0026 .3900 .3871 .3871 .3871 18.3070 1 20 .1966 .0250 .1966 .0250 .1966 .0335 .1964 .1964 3.8415 2 20 .1966 .0125 .2241 .0127 .2236 .0523 .2233 .2233 5.9915 3 20 .1966 .0083 .2389 .0085 .2383 .0695 .2378 .2378 7.8147 4 20 .1966 .0063 .2490 .0064 .2483 .0864 .2477 .2477 9.4877 5 20 .1966 .0050 .2565 .0051 .2558 .1041 .2551 .2551 11.0705 6 20 .1966 .0042 .2625 .0043 .2618 .1232 .2610 .2610 12.5916 7 20 .1966 .0036 .2675 .0037 .2668 .1451 .2659 .2659 14.0671 8 20 .1966 .0031 .2717 .0032 .2710 .1719 .2700 .2700 15.5073 9 20 .1966 .0028 .2754 .0028 .2747 .2089 .2736 .2736 16.9190 10 20 .1966 .0025 .2786 .0026 .2779 .2768 .2768 .2768 18.3070 1 40 .1388 .0250 .1388 .0250 .1388 .0235 .1387 .1387 3.8415 2 40 .1388 .0125 .1585 .0127 .1581 .0367 .1580 .1580 5.9915 3 40 .1388 .0083 .1691 .0085 .1687 .0488 .1685 .1685 7.8147 4 40 .1388 .0063 .1763 .0064 .1759 .0607 .1756 .1756 9.4877 5 40 .1388 .0050 .1818 .0051 .1813 .0732 .1810 .1810 11.0705 6 40 .1388 .0042 .1861 .0043 .1856 .0867 .1853 .1853 12.5916 7 40 .1388 .0036 .1897 .0037 .1892 .1022 .1888 .1888 14.0671 8 40 .1388 .0031 .1927 .0032 .1922 .1212 .1919 .1919 15.5073 9 40 .1388 .0028 .1954 .0028 .1949 .1477 .1945 .1945 16.9190 10 40 .1388 .0025 .1978 .0026 .1973 .1969 .1969 .1969 18.3070 Table 10.1.1.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P = I, p = 5 N:p OEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp NT 2 .4112 .05058 .05058 1.00000 .00000 .94942 .06888 .06888 .00000 MB 2 .0507 .00519 .005191.00000 .00000 .99481 .02272 .02272 .00000 RB 2 .0507 .00516 .005161.00000 .00000 .99484 .02253 .02253 .00000 MD 2 .0525 .00537 .00537 1.00000 .00000 .99463 .02307 .02307 .00000 RD 2 .0525 .00536 .005361.00000 .00000 .99464 .02301 .02301 .00000 OR 2 .2290 .04967 .04967 1.00000 .00000 .95033 .12347 .12347 .00000 OS 2 .0737 .01132 .011321.00000 .00000 .98868 .05636 .05636 .00000 OF 2 .0737 .00756 .00756 1.00000 .00000 .99244 .02722 .02722 .00000 CF 2 .0737 .00756 .00756 1.00000 .00000 .99244 .02722 .02722 .00000 CS 2 .0542 .00652 .00652 1.00000 .00000 .99348 .02986 .02986 .00000 NT 4 .4078 .05052 .05052 1.00000 .00000 .94948 .06907 .06907 .00000 MB 4 .0480 .00490 .00490 1.00000 ,00000 .99510 .02205 .02205 .00000 RB 4 .0480 .00488 .00488 1.00000 .00000 .99512 .02191 .02191 .00000 MD 4 .0492 .00503 .00503 1.00000 .00000 .99497 .02236 .02236 .00000 RD 4 .0492 .00500 .005001.00000 .00000 .99500 .02216 .02216 .00000 OR 4 .2329 .05040 .05040 1.00000 .00000 .94960 .12010 .12010 .00000 OS 4 .0597 .00924 .00924 1.00000 .00000 .99076 .04851 .04851 .00000 OF 4 .0597 .00613 .00613 1.00000 .00000 .99387 .02465 .02465 .00000 CF 4 .0597 .00613 .00613 1.00000 .00000 .99387 .02465 .02465 .00000 CS 4 .0532 .00603 .006031.00000 .00000 .99397 .02714 .02714 .00000 NT 10 .3993 .05011 .050111.00000 .00000 .94989 .06959 .06959 .00000 MB 10 .0460 .00474 .00474 1.00000 .00000 .99526 .02194 .02194 .00000 RB 10 .0460 .00471 .00471 1.00000 .00000 .99529 .02170 .02170 .00000 MD 10 .0469 .00483 .00483 1.00000 .00000 .99517 .02213 .02213 .00000 RD 10 .0469 .00480 .00480 1.00000 .00000 .99520 .02189 .02189 .00000 OR 10 .2318 .04996 .04996 1.00000 .00000 .95004 .11798 .11798 .00000 OS 10 .0496 .00822 .008221.00000 .00000 .99178 .04710 .04710 .00000 OF 10 .0496 .00513 .00513 1.00000 .00000 .99487 .02286 .02286 .00000 CF 10 .0496 .00513 .00513 1.00000 .00000 .99487 .02286 .02286 .00000 CS 10 .0491 .00557 .00557 1.00000 .00000 .99443 .02585 .02585 .00000 NT 20 .3949 .04923 .04923 1.00000 .00000 .95077 .06883 .06883 .00000 MB 20 .0475 .00489 .00489 1.00000 .00000 .99511 .02221 .02221 .00000 RB 20 .0475 .00486 .00486 1.00000 .00000 .99514 .02201 .02201 .00000 MD 20 .0483 .00498 .00498 1.00000 .00000 .99502 .02243 .02243 .00000 RD 20 .0483 .00494 .00494 1.00000 .00000 .99506 .02217 .02217 .00000 OR 20 .2337 .04910 .04910 1.00000 .00000 .95090 .11688 .11688 .00000 OS 20 .0502 .00840 .00840 1.00000 .00000 .99160 .04823 .04823 .00000 OF 20 .0502 .00519 .005191.00000 .00000 .99481 .02294 .02294 .00000 CF 20 .0502 .00519 .00519 1.00000 .00000 .99481 .02294 .02294 .00000 CS 20 .0507 .00568 .00568 1.00000 .00000 .99432 .02588 .02588 .00000 NT 40 .4077 .05056 .05056 1.00000 .00000 .94944 .06889 .06889 .00000 MB 40 .0488 .00502 .00502 1.00000 .00000 .99498 .02247 .02247 .00000 RB 40 .0488 .00499 .00499 1.00000 .00000 .99501 .02227 .02227 .00000 MD 40 .0501 .00516 .005161.00000 .00000 .99484 .02279 .02279 .00000 RD 40 .0501 .00512 .005121.00000 .00000 .99488 .02254 .02254 .00000 OR 40 .2355 .05050 .05050 1.00000 .00000 .94950 .11897 .11897 .00000 OS 40 .0509 .00814 .008141.00000 .00000 .99186 .04517 .04517 .00000 OF 40 .0509 .00524 .00524 1.00000 .00000 .99476 .02295 .02295 .00000 CF 40 .0509 .00524 .00524 1.00000 .00000 .99476 .02295 .02295 .00000 CS 40 .0486 .00537 .00537 1.00000 .00000 .99463 .02486 .02486 .00000 Table 10.1.1.2 Table of empirical results for tests of correlations with no preliminary omnibus when P = 1,/? = 10 N:p OEX Rej Fp Fn Tp Tn s:Rej s.FpTn s:FnTp NT 2 .9044 .05038 .05038 1.00000 .00000 .94962 .03295 .03295 .00000 MB 2 .0496 .00113 .001131.00000 .00000 .99887 .00500 .00500 .00000 RB 2 .0496 .00113 .001131.00000 .00000 .99887 .00500 .00500 .00000 MD 2 .0507 .00115 .001151.00000 .00000 .99885 .00506 .00506 .00000 RD 2 .0507 .00115 .001151.00000 .00000 .99885 .00504 .00504 .00000 OR 2 .3841 .04816 .04816 1.00000 .00000 .95184 .10950 .10950 .00000 OS 2 .0711 .00300 .003001.00000 .00000 .99700 .01901 .01901 .00000 OF 2 .0711 .00163 .001631.00000 .00000 .99837 .00600 .00600 .00000 CF 2 .0711 .00163 .00163 1.00000 .00000 .99837 .00600 .00600 .00000 CS 2 .0550 .00170 .00170 1.00000 .00000 .99830 .00819 .00819 .00000 NT 4 .9042 .04972 .04972 1.00000 .00000 .95028 .03232 .03232 .00000 MB 4 .0485 .00110 .001101.00000 .00000 .99890 .00489 .00489 .00000 RB 4 .0485 .00110 .001101.00000 .00000 .99890 .00489 .00489 .00000 MD 4 .0498 .00112 .001121.00000 .00000 .99888 .00495 .00495 .00000 RD 4 .0498 .00112 .001121.00000 .00000 .99888 .00495 .00495 .00000 OR 4 .3854 .04987 .04987 1.00000 .00000 .95013 .10880 .10880 .00000 OS 4 .0591 .00222 .00222 1.00000 .00000 .99778 .01424 .01424 .00000 OF 4 .0591 .00134 .00134 1.00000 .00000 .99866 .00541 .00541 .00000 CF 4 .0591 .00134 .00134 1.00000 .00000 .99866 .00541 .00541 .00000 CS 4 .0478 .00137 .00137 1.00000 .00000 .99863 .00691 .00691 .00000 NT 10 .9035 .05025 .05025 1.00000 .00000 .94975 .03287 .03287 .00000 MB 10 .0474 .00108 .00108 1.00000 .00000 .99892 .00489 .00489 .00000 RB 10 .0474 .00108 .00108 1.00000 .00000 .99892 .00487 .00487 .00000 MD 10 .0487 .00111 .00111 1.00000 .00000 .99889 .00496 .00496 .00000 RD 10 .0487 .00111 .00111 1.00000 .00000 .99889 .00495 .00495 .00000 OR 10 .3884 .05073 .05073 1.00000 .00000 .94927 .11112 .11112 .00000 OS 10 .0516 .00205 .00205 1.00000 .00000 .99795 .01651 .01651 .00000 OF 10 .0516 .00117 .001171.00000 .00000 .99883 .00509 .00509 .00000 CF 10 .0516 .00117 .001171.00000 .00000 .99883 .00509 .00509 .00000 CS 10 .0534 .00160 .00160 1.00000 .00000 .99840 .00787 .00787 .00000 NT 20 .8984 .05003 .05003 1.00000 .00000 .94997 .03274 .03274 .00000 MB 20 .0517 .00118 .00118 1.00000 .00000 .99882 .00509 .00509 .00000 RB 20 .0517 .00117 .00117 1.00000 .00000 .99883 .00506 .00506 .00000 MD 20 .0532 .00121 .00121 1.00000 .00000 .99879 .00517 .00517 .00000 RD 20 .0532 .00121 .00121 1.00000 .00000 .99879 .00516 .00516 .00000 OR 20 .3912 .05092 .05092 1.00000 .00000 .94908 .10921 .10921 .00000 OS 20 .0551 .00232 .00232 1.00000 .00000 .99768 .01824 .01824 .00000 OF 20 .0551 .00126 .00126 1.00000 .00000 .99874 .00528 .00528 .00000 CF 20 .0551 .00126 .001261.00000 .00000 .99874 .00528 .00528 .00000 CS 20 .0518 .00151 .00151 1.00000 .00000 .99849 .00740 .00740 .00000 NT 40 .9047 .04987 .04987 1.00000 .00000 .95013 .03215 .03215 .00000 MB 40 .0492 .00112 .001121.00000 .00000 .99888 .00497 .00497 .00000 RB 40 .0492 .00112 .001121.00000 .00000 .99888 .00497 .00497 .00000 MD 40 .0500 .00114 .001141.00000 .00000 .99886 .00500 .00500 .00000 RD 40 .0500 .00114 .001141.00000 .00000 .99886 .00500 .00500 .00000 OR 40 .3875 .04939 .04939 1.00000 .00000 .95061 .10702 .10702 .00000 OS 40 .0507 .00184 .00184 1.00000 .00000 .99816 .01082 .01082 .00000 OF 40 .0507 .00115 .001151.00000 .00000 .99885 .00503 .00503 .00000 CF 40 .0507 .00115 .00115 1.00000 .00000 .99885 .00503 .00503 .00000 CS 40 .0492 .00140 .001401.00000 .00000 .99860 .00696 .00696 .00000 Table 10.1.2.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P = l,p = 5 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp NT 2 .0541 .01044 .010441.00000 .00000 .98956 .04768 .04768 .00000 MB 2 .0239 .00251 .00251 1.00000 .00000 .99749 .01639 .01639 .00000 RB 2 .0239 .00248 .00248 1.00000 .00000 .99752 .01612 .01612 .00000 M D 2 .0243 .00255 .00255 1.00000 .00000 .99745 .01651 .01651 .00000 RD 2 .0243 .00254 .00254 1.00000 .00000 .99746 .01642 .01642 .00000 OR 2 .0542 .02175 .02175 1.00000 .00000 .97825 .10474 .10474 .00000 OS 2 .0295 .00670 .00670 1.00000 .00000 .99330 .05249 .05249 .00000 OF 2 .0295 .00314 .00314 1.00000 .00000 .99686 .01861 .01861 .00000 CF 2 .0295 .00314 .00314 1.00000 .00000 .99686 .01861 .01861 .00000 CS 2 .0542 .00652 .00652 1.00000 .00000 .99348 .02986 .02986 .00000 NT 4 .0530 .01021 .01021 1.00000 .00000 .98979 .04679 .04679 .00000 MB 4 .0251 .00261 .002611.00000 .00000 .99739 .01656 .01656 .00000 RB 4 .0251 .00259 .00259 1.00000 .00000 .99741 .01638 .01638 .00000 MD 4 .0255 .00266 .00266 1.00000 .00000 .99734 .01676 .01676 .00000 RD 4 .0255 .00263 .00263 1.00000 .00000 .99737 .01650 .01650 .00000 OR 4 .0532 .02020 .02020 1.00000 .00000 .97980 .09704 .09704 .00000 OS 4 .0280 .00593 .005931.00000 .00000 .99407 .04519 .04519 .00000 OF 4 .0280 .00296 .002961.00000 .00000 .99704 .01787 .01787 .00000 CF 4 .0280 .00296 .00296 1.00000 .00000 .99704 .01787 .01787 .00000 CS 4 .0532 .00603 .006031.00000 .00000 .99397 .02714 .02714 .00000 NT 10 .0488 .00976 .00976 1.00000 .00000 .99024 .04612 .04612 .00000 MB 10 .0225 .00239 .00239 1.00000 .00000 .99761 .01623 .01623 .00000 RB 10 .0225 .00236 .00236 1.00000 .00000 .99764 .01589 .01589 .00000 MD 10 .0227 .00241 .00241 1.00000 .00000 .99759 .01629 .01629 .00000 RD 10 .0227 .00238 .00238 1.00000 .00000 .99762 .01595 .01595 .00000 OR 10 .0490 .01837 .01837 1.00000 .00000 .98163 .09201 .09201 .00000 OS 10 .0233 .00542 .00542 1.00000 .00000 .99458 .04403 .04403 .00000 OF 10 .0233 .00250 .00250 1.00000 .00000 .99750 .01673 .01673 .00000 CF 10 .0233 .00250 .00250 1.00000 .00000 .99750 .01673 .01673 .00000 CS 10 .0491 .00557 .00557 1.00000 .00000 .99443 .02585 .02585 .00000 NT 20 .0503 .00989 .00989 1.00000 .00000 .99011 .04617 .04617 .00000 MB 20 .0239 .00253 .00253 1.00000 .00000 .99747 .01657 .01657 .00000 RB 20 .0239 .00250 .00250 1.00000 .00000 .99750 .01630 .01630 .00000 MD 20 .0241 .00256 .002561.00000 .00000 .99744 .01672 .01672 .00000 RD 20 .0241 .00252 .002521.00000 .00000 .99748 .01636 .01636 .00000 OR 20 .0507 .01902 .01902 1.00000 .00000 .98098 .09382 .09382 .00000 OS 20 .0247 .00570 .00570 1.00000 .00000 .99430 .04543 .04543 .00000 OF 20 .0247 .00264 .00264 1.00000 .00000 .99736 .01706 .01706 .00000 CF 20 .0247 .00264 .00264 1.00000 .00000 .99736 .01706 .01706 .00000 CS 20 .0507 .00568 .00568 1.00000 .00000 .99432 .02588 .02588 .00000 NT 40 .0483 .00933 .00933 1.00000 .00000 .99067 .04470 .04470 .00000 MB 40 .0228 .00242 .00242 1.00000 .00000 .99758 .01625 .01625 .00000 RB 40 .0228 .00239 .00239 1.00000 .00000 .99761 .01598 .01598 .00000 MD 40 .0234 .00249 .00249 1.00000 .00000 .99751 .01652 .01652 .00000 RD 40 .0234 .00245 .00245 1.00000 .00000 .99755 .01616 .01616 .00000 OR 40 .0484 .01835 .01835 1.00000 .00000 .98165 .09256 .09256 .00000 OS 40 .0237 .00525 .00525 1.00000 .00000 .99475 .04190 .04190 .00000 OF 40 .0237 .00252 .00252 1.00000 .00000 .99748 .01660 .01660 .00000 CF 40 .0237 .00252 .002521.00000 .00000 .99748 .01660 .01660 .00000 CS 40 .0486 .00537 .005371.00000 .00000 .99463 .02486 .02486 .00000 Table 10.1.2.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P = I, p = 10 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp NT 2 .0550 .00602 .00602 1.00000 .00000 .99398 .02612 .02612 .00000 MB 2 .0154 .00037 .000371.00000 .00000 .99963 .00303 .00303 .00000 RB 2 .0154 .00037 .00037 1.00000 .00000 .99963 .00303 .00303 .00000 MD 2 .0155 .00037 .00037 1.00000 .00000 .99963 .00306 .00306 .00000 RD 2 .0155 .00037 .00037 1.00000 .00000 .99963 .00304 .00304 .00000 OR 2 .0550 .01847 .018471.00000 .00000 .98153 .08915 .08915 .00000 OS 2 .0193 .00154 .00154 1.00000 .00000 .99846 .01774 .01774 .00000 OF 2 .0193 .00047 .00047 1.00000 .00000 .99953 .00353 .00353 .00000 CF 2 .0193 .00047 .00047 1.00000 .00000 .99953 .00353 .00353 .00000 CS 2 .0550 .00170 .00170 1.00000 .00000 .99830 .00819 .00819 .00000 NT 4 .0478 .00517 .00517 1.00000 .00000 .99483 .02407 .02407 .00000 MB 4 .0119 .00027 .00027 1.00000 .00000 .99973 .00253 .00253 .00000 RB 4 .0119 .00027 .00027 1.00000 .00000 .99973 .00253 .00253 .00000 MD 4 .0120 .00028 .00028 1.00000 .00000 .99972 .00254 .00254 .00000 RD 4 .0120 .00028 .00028 1.00000 .00000 .99972 .00254 .00254 .00000 OR 4 .0478 .01573 .01573 1.00000 .00000 .98427 .08192 .08192 .00000 OS 4 .0133 .00090 .00090 1.00000 .00000 .99910 .01265 .01265 .00000 OF 4 .0133 .00031 .00031 1.00000 .00000 .99969 .00271 .00271 .00000 CF 4 .0133 .00031 .000311.00000 .00000 .99969 .00271 .00271 .00000 CS 4 .0478 .00137 .00137 1.00000 .00000 .99863 .00691 .00691 .00000 NT 10 .0534 .00586 .00586 1.00000 .00000 .99414 .02567 .02567 .00000 MB 10 .0143 .00034 .00034 1.00000 .00000 .99966 .00285 .00285 .00000 RB 10 .0143 .00034 .00034 1.00000 .00000 .99966 .00285 .00285 .00000 MD 10 .0145 .00034 .00034 1.00000 .00000 .99966 .00287 .00287 .00000 RD 10 .0145 .00034 .00034 1.00000 .00000 .99966 .00287 .00287 .00000 OR 10 .0534 .01810 .01810 1.00000 .00000 .98190 .08920 .08920 .00000 OS 10 .0151 .00104 .00104 1.00000 .00000 .99896 .01553 .01553 .00000 OF 10 .0151 .00035 .00035 1.00000 .00000 .99965 .00292 .00292 .00000 CF 10 .0151 .00035 .00035 1.00000 .00000 .99965 .00292 .00292 .00000 CS 10 .0534 .00160 .001601.00000 .00000 .99840 .00787 .00787 .00000 NT 20 .0518 .00566 .00566 1.00000 .00000 .99434 .02511 .02511 .00000 MB 20 .0149 .00035 .00035 1.00000 .00000 .99965 .00295 .00295 .00000 RB 20 .0149 .00035 .00035 1.00000 .00000 .99965 .00290 .00290 .00000 MD 20 .0152 .00036 .000361.00000 .00000 .99964 .00300 .00300 .00000 RD 20 .0152 .00036 .00036 1.00000 .00000 .99964 .00298 .00298 .00000 OR 20 .0518 .01646 .016461.00000 .00000 .98354 .08282 .08282 .00000 OS 20 .0155 .00121 .00121 1.00000 .00000 .99879 .01724 .01724 .00000 OF 20 .0155 .00037 .000371.00000 .00000 .99963 .00307 .00307 .00000 CF 20 .0155 .00037 .00037 1.00000 .00000 .99963 .00307 .00307 .00000 CS 20 .0518 .00151 .00151 1.00000 .00000 .99849 .00740 .00740 .00000 NT 40 .0492 .00532 .005321.00000 .00000 .99468 .02420 .02420 .00000 MB 40 .0137 .00032 .000321.00000 .00000 .99968 .00272 .00272 .00000 RB 40 .0137 .00032 .00032 1.00000 .00000 .99968 .00272 .00272 .00000 MD 40 .0138 .00032 .00032 1.00000 .00000 .99968 .00273 .00273 .00000 RD 40 .0138 .00032 .00032 1.00000 .00000 .99968 .00273 .00273 .00000 OR 40 .0492 .01526 .015261.00000' .00000 .98474 .07925 .07925 .00000 OS 40 .0140 .00079 .00079 1.00000 .00000 .99921 .00906 .00906 .00000 OF 40 .0140 .00032 .00032 1.00000 .00000 .99968 .00275 .00275 .00000 CF 40 .0140 .00032 .000321.00000 .00000 .99968 .00275 .00275 .00000 CS 40 .0492 .00140 .001401.00000 .00000 .99860 .00696 .00696 .00000 Table 10.2.1.1.1.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P = 5, mNz = .1, pNz = .2 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .3401 .05187 .05036 .94210 .05790 .94964 .06976 .07754 .16417 .0687 1.1167 .5345 .0657 MB 2 .0416 .00535 .00529 .99440 .00560 .99471 .02303 .02559 .05309 .0200 i;0524 .5140 .0285 RB 2 .0415 .00532 .00525 .99440 .00560 .99475 .02284 .02538 .05309 .0225 1.0590 .5157 .0321 MD 2 .0432 .00555 .00550 .99425 .00575 .99450 .02346 .02612 .05378 .0156 1.0403 .5109 .0221 RD 2 .0431 .00551 .00545 .99425 .00575 .99455 .02321 .02583 .05378 .0188 1.0487 .5131 .0266 OR 2 .2097 .05208 .05200 .94760 .05240 .94800 .12875 .13179 .17750 .0037 1.0061 .5020 .0036 OS 2 .0622 .01170 .01150 .98750 .01250 .98850 .05858 .05923 .08772 .0320 1.0750 .5203 .0412 OF 2 .0595 .00762 .00759 .99225 .00775 .99241 .02739 .03047 .06217 .0077 1.0188 .5053 .0105 CF 2 .0595 .00762 .00759 .99225 .00775 .99241 .02739 .03047 .06217 .0077 1.0188 .5053 .0105 CS 2 .0481 .00700 .00690 .99260 .00740 .99310 .03113 .03283 .06241 .0252 1.0637 .5170 .0347 NT 4 .3386 .05468 .05049 .92855 .07145 .94951 .07150 .07808 .18076 .1751 1.3123 .5789 .1611 MB 4 .0399 .00578 .00508 .99140 .00860 .99492 .02397 .02511 .06539 .1883 1.5940 .6034 .2561 RB 4 .0399 .00577 .00506 .99140 .00860 .99494 .02391 .02502 .06539 .1891 1.5975 .6037 .2573 MD 4 .0406 .00588 .00516 .99125 .00875 .99484 .02420 .02531 .06595 .1887 1.5939 .6034 .2562 RD 4 .0405 .00586 .00514 .99125 .00875 .99486 .02408 .02519 .06595 .1904 1.6008 .6041 .2584 OR 4 .2226 .05694 .05583 .93860 .06140 .94418 .12936 .13267 .18744 .0477 1.0776 .5242 .0446 OS 4 .0521 .01128 .01028 .98470 .01530 .98973 .05861 .05829 .09496 .1539 1.4115 .5834 .1940 OF 4 .0478 .00698 .00609 .98945 .01055 .99391 .02629 .02742 .07255 .2008 1.6215 .6069 .2661 CF 4 .0478 .00698 .00609 .98945 .01055 .99391 .02629 .02742 .07255 .2008 1.6215 .6069 .2661 CS 4 .0466 .00705 .00661 .99120 .00880 .99339 .02969 .03165 .06688 .1037 1.2861 .5627 .1409 NT 10 .3285 .06084 .04931 .89305 .10695 .95069 .07609 .07747 .21815 .4086 1.8065 .6499 .3415 MB 10 .0374 .00713 .00478 .98345 .01655 .99523 .02717 .02454 .09139 .4608 2.9689 .6808 .5480 RB 10 .0372 .00707 .00473 .98355 .01645 .99528 .02682 .02423 .09113 .4620 2.9814 .6811 .5496 MD 10 .0378 .00727 .00483 .98295 .01705 .99518 .02746 .02466 .09266 .4692 3.0173 .6823 .5546 RD 10 .0376 .00721 .00479 .98310 .01690 .99521 .02711 .02444 .09228 .4684 3.0155 .6822 .5543 OR 10 .2475 .06652 .06370 .92220 .07780 .93630 .13938 .14108 .20965 .1044 1.1662 .5491 .0921 OS 10 .0472 .01314 .01031 .97555 .02445 .98969 .06389 .06017 .12074 .3453 2.0953 .6481 .4007 OF 10 .0400 .00774 .00513 .98180 .01820 .99488 .02836 .02547 .09550 .4748 3.0232 .6829 .5560 CF 10 .0400 .00774 .00513 .98180 .01820 .99488 .02836 .02547 .09550 .4748 3.0232 .6829 .5560 CS 10 .0495 .00895 .00683 .98255 .01745 .99318 .03303 .03123 .09445 .3568 2.2623 .6549 .4333 NT 20 .3304 .07360 .04939 .82955 .17045 .95061 .08231 .07728 .26754 .6984 2.4820 .7094 .5015 MB 20 .0381 .01079 .00486 .96550 .03450 .99514 .03281 .02468 .12889 .7670 5.4139 .7222 .7463 RB 20 .0378 .01069 .00481 .96580 .03420 .99519 .03235 .02450 .12799 .7667 5.4249 .7222 .7467 MD 20 .0391 .01096 .00499 .96515 .03485 .99501 .03305 .02497 .12947 .7628 5.3369 .7217 .7429 RD 20 .0388 .01089 .00494 .96530 .03470 .99506 .03275 .02479 .12903 .7644 5.3660 .7219 .7442 OR 20 .2970 .08846 .08150 .88370 .11630 .91850 .16041 .16197 .25205 .2014 1.2978 .5843 .1572 OS 20 .0591 .02053 .01359 .95170 .04830 .98641 .07932 .06930 .17167 .5474 2.8847 .6885 .5485 OF 20 .0406 .01135 .00518 .96395 .03605 .99483 .03359 .02540 .13163 .7654 5.3097 .7219 .7419 CF 20 .0406 .01135 .00518 .96395 .03605 .99483 .03359 .02540 .13163 .7654 5.3097 .7219 .7419 CS 20 .0636 .01426 .00883 .96400 .03600 .99118 .04148 .03540 .13400 .5738 3.3097 .6956 .5974 NT 40 .3455 .09941 .05121 .70780 .29220 .94879 .08984 .07761 .32137 1.0862 3.2677 .7697 .6195 MB 40 .0400 .02023 .00510 .91925 .08075 .99490 .04363 .02523 .19237 1.1689 10.1732 .7532 .8720 RB 40 .0391 .02005 .00495 .91955 .08045 .99505 .04310 .02470 .19159 1.1773 10.4179 .7536 .8752 MD 40 .0404 .02043 .00515 .91845 .08155 .99485 .04384 .02534 .19321 1.1709 10.1605 .7534 .8719 RD 40 .0395 .02026 .00501 .91875 .08125 .99499 .04333 .02490 .19242 1.1783 10.3794 .7537 .8747 OR 40 .3737 .12910 .11073 .79740 .20260 .88928 .19046 .19066 .31963 .3903 1.4934 .6392 .2426 OS 40 .0874 .03993 .02230 .88955 .11045 .97770 .11315 .09545 .25977 .7843 3.5523 .7221 .6368 OF 40 .0409 .02074 .00521 .91715 .08285 .99479 .04414 .02548 .19459 1.1753 10.1725 .7538 .8722 CF 40 .0409 .02074 .00521 .91715 .08285 .99479 .04414 .02548 .19459 1.1753 10.1725 .7538 .8722 CS 40 .0794 .02598 .01100 .91410 .08590 .98900 .05375 .03946 .20031 .9239 5.4157 .7369 .7566 Table 10.2.1.1.1.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p - 5, mNz - .1, pNz - .4 N:p O.EX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .2703 .05338 .05095 .94298 .05703 .94905 .07035 .08970 .11557 .0555 1.0933 .5282 .0531 MB 2 .0316 .00552 .00532 .99418 .00583 .99468 .02336 .02957 .03805 .0320 1.0845 .5219 .0454 RB 2 .0315 .00550 .00530 .99420 .00580 .99470 .02323 .02953 .03797 .0315 1.0834 .5217 .0448 MD 2 .0326 .00571 .00548 .99395 .00605 .99452 .02376 .03001 .03874 .0345 1.0912 .5236 .0488 RD 2 .0326 .00569 .00548 .99400 .00600 .99452 .02364 .03001 .03859 .0316 1.0832 .5217 .0447 OR 2 .1831 .05469 .05363 .94373 .05628 .94637 .13272 .14015 .15558 .0238 1.0387 .5124 .0226 OS 2 .0522 .01267 .01250 .98708 .01293 .98750 .06175 .06583 .07460 .0129 1.0294 .5083 .0165 OF 2 .0471 .00801 .00793 .99188 .00813 .99207 .02802 .03588 .04489 .0087 1.0212 .5059 .0118 CF 2 .0471 .00801 .00793 .99188 .00813 .99207 .02802 .03588 .04489 .0087 1.0212 .5059 .0118 CS 2 .0400 .00759 .00742 .99215 .00785 .99258 .03255 .03812 .04745 .0206 1.0513 .5139 .0282 NT 4 .2644 .05871 .05000 .92823 .07178 .95000 .07377 .08951 .12964 .1822 1.3271 .5816 .1676 MB 4 .0311 .00666 .00525 .99123 .00878 .99475 .02603 .02949 .04735 .1839 1.5742 .6013 .2497 RB 4 .0310 .00660 .00520 .99130 .00870 .99480 .02570 .02917 .04690 .1841 1.5758 .6015 .2501 MD 4 .0319 .00682 .00538 .99103 .00898 .99462 .02634 .02984 .04784 .1835 1.5702 .6009 .2484 RD 4 .0319 .00676 .00535 .99113 .00887 .99465 .02601 .02957 .04733 .1816 1.5635 .6002 .2461 OR 4 .2075 .06480 .06193 .93090 .06910 .93807 .14065 .14849 .16764 .0562 1.0886 .5278 .0509 OS 4 .0432 .01333 .01097 .98313 .01688 .98903 .06527 .06461 .08535 .1685 1.4504 .5890 .2093 OF 4 .0359 .00803 .00612 .98910 .01090 .99388 .02854 .03204 .05250 .2115 1.6612 .6109 .2789 CF 4 .0359 .00803 .00612 .98910 .01090 .99388 .02854 .03204 .05250 . .2115 1.6612 .6109 .2789 CS 4 .0400 .00880 .00740 .98910 .01090 .99260 .03380 .03809 .05574 .1434 1.4039 .5812 .1896 NT 10 .2586 .07220 .04932 .89348 .10653 .95068 .08353 .08938 .15941 .4063 1.8012 .6493 .3399 MB 10 .0282 .00959 .00473 .98313 .01688 .99527 .03145 .02789 .06584 .4717 3.0424 .6829 .5577 RB 10 .0276 .00946 .00462 .98328 .01673 .99538 .03083 .02745 .06530 .4767 3.0872 .6840 .5632 MD 10 .0286 .00977 .00480 .98278 .01723 .99520 .03174 .02807 .06650 .4751 3.0578 .6835 .5598 RD 10 .0280 .00965 .00468 .98290 .01710 .99532 .03118 .02765 .06602 .4807 3.1063 .6846 .5658 OR 10 .2549 .08852 .08185 .90148 .09853 .91815 .16537 .17240 .20044 .1027 1.1477 .5469 .0834 OS 10 .0470 .01993 .01355 .97050 .02950 .98645 .08538 .07658 .12013 .3219 1.9340 .6392 .3634 OF 10 .0299 .01028 .00503 .98185 .01815 .99497 .03250 .02881 .06798 .4800 3.0650 .6840 .5613 CF 10 .0299 .01028 .00503 .98185 .01815 .99497 .03250 .02881 .06798 .4800 3.0650 .6840 .5613 CS 10 .0468 .01412 .00852 .97748 .02253 .99148 .04302 .03996 .08031 .3818 2.3119 .6590 .4456 NT 20 .2587 .09603 .04905 .83350 .16650 .95095 .09504 .08884 .19466 .6860 2.4583 .7072 .4969 MB 20 .0293 .01667 .00498 .96580 .03420 .99502 .04117 .02897 .09236 .7546 5.2589 .7209 .7389 RB 20 .0288 .01643 .00490 .96628 .03373 .99510 .04034 .02874 .09108 .7541 5.2774 .7209 .7397 MD 20 .0296 .01695 .00503 .96518 .03483 .99497 .04150 .02910 .09318 .7594 5.2905 .7214 .7407 RD 20 .0291 .01670 .00495 .96568 .03433 .99505 .04061 .02888 .09174 .7586 5.3063 .7213 .7413 OR 20 .3525 .14112 .12350 .83245 .16755 .87650 .20793 .21256 .25763 .1938 1.2282 .5783 .1261 OS 20 .0700 .03882 .02300 .93745 .06255 .97700 .12382 .10493 .18008 .4617 2.2584 .6682 .4459 OF 20 .0312 .01755 .00532 .96410 .03590 .99468 .04223 .02995 .09454 .7541 5.1660 .7207 .7349 CF 20 .0312 .01755 .00532 .96410 .03590 .99468 .04223 .02995 .09454 .7541 5.1660 .7207 .7349 CS 20 .0657 .02716 .01200 .95010 .04990 .98800 .05845 .04727 .11816 .6113 3.2968 .6995 .5999 NT 40 .2656 .14730 .05038 .70733 .29268 .94962 .10858 .09008 .23517 1.0956 3.3130 .7707 .6245 MB 40 .0302 .03645 .00513 .91658 .08343 .99487 .06072 .02937 .14291 1.1843 10.3657 .7543 .8748 RB 40 .0289 .03579 .00488 .91785 .08215 .99512 .05915 .02850 .13997 1.1932 10.7122 .7546 .8789 MD 40 .0310 .03689 .00527 .91568 .08433 .99473 .06100 .02972 .14356 1.1813 10.2139 .7543 .8729 RD 40 .0297 .03626 .00503 .91690 .08310 .99497 .05948 .02901 .14074 1.1890 10.5180 .7545 .8767 OR 40 ' 5034 .24692 .19838 .68028 .31973 .80162 .25497 .26058 .32758 .3789 1.2832 .6327 .1553 OS 40 .1357 .09561 .05125 .83785 .16215 .94875 .19592 .16083 .29224 .6472 2.3334 .7002 .4729 OF 40 .0313 .03728 .00532 .91478 .08523 .99468 .06132 .02985 .14438 1.1838 10.2093 .7545 .8730 CF 40 .0313 .03728 .00532 .91478 .08523 .99468 .06132 .02985 .14438 1.1838 10.2093 .7545 .8730 CS 40 .0897 .06054 .01645 .87333 .12668 .98355 .08267 .05482 .17854 .9911 5.0689 .7456 .7448 123 Table 10.2.1.1.1.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I,p = 5, mNz = S,pNz = .6 N:p OEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp d' P A' B" NT 2 .1851 .05453 .05040 .94272 .05728 .94960 .07194 .11045 .09554 .0630 1.1067 .5319 .0603 MB 2 .0203 .00587 .00510 .99362 .00638 .99490 .02405 .03552 .03268 .0788 1.2205 .5506 .1111 RB 2 .0203 .00586 .00510 .99363 .00637 .99490 .02399 .03552 .03264 .0778 1.2176 .5501 .1098 MD 2 .0208 .00604 .00523 .99342 .00658 .99478 .02440 .03594 .03323 .0813 1.2275 .5519 .1144 RD 2 .0208 .00602 .00523 .99345 .00655 .99478 .02429 .03594 .03307 .0795 1.2220 .5509 .1119 OR 2 .1474 .05825 .05623 .94040 .05960 .94378 .13783 .15676 .14961 .0291 1.0469 .5151 .0273 OS 2 .0378 .01415 .01338 .98533 .01467 .98663 .06796 .07860 .07448 .0362 1.0827 .5223 .0454 OF 2 .0307 .00846 .00775 .99107 .00893 .99225 .02899 .04376 .03856 .0521 1.1329 .5334 .0703 CF 2 .0307 .00846 .00775 .99107 .00893 .99225 .02899 .04376 .03856 .0521 1.1329 .5334 .0703 CS 2 .0273 .00808 .00738 .99145 .00855 .99263 .03404 .04585 .04271 .0539 1.1388 .5347 .0732 NT 4 .1845 .06247 .04990 .92915 .07085 .95010 .07781 .10948 .10835 .1763 1.3161 .5794 .1627 MB 4 .0194 .00711 .00493 .99143 .00857 .99508 .02688 .03528 .03836 .1972 1.6316 .6072 .2682 RB 4 .0194 .00707 .00490 .99148 .00852 .99510 .02667 .03502 .03804 .1968 1.6307 .6071 .2679 MD 4 .0199 .00726 .00505 .99127 .00873 .99495 .02719 .03570 .03882 .1957 1.6228 .6064 .2655 RD 4 .0199 .00720 .00503 .99135 .00865 .99498 .02687 .03544 .03830 .1938 1.6163 .6057 .2634 OR 4 .1818 .07467 .07085 .92278 .07722 .92915 .15538 .17452 .16804 .0454 1.0680 .5223 .0396 OS 4 .0339 .01631 .01260 .98122 .01878 .98740 .07923 .07908 .09034 .1588 1.4089 .5839 .1940 OF 4 .0234 .00882 .00600 .98930 .01070 .99400 .03014 .03923 .04310 .2113 1.6628 .6110 .2793 CF 4 .0234 .00882 .00600 .98930 .01070 .99400 .03014 .03923 .04310 .2113 1.6628 .6110 .2793 CS 4 .0297 .01117 .00810 .98678 .01322 .99190 .03945 .04832 .05287 .1846 1.5323 .5981 .2376 NT 10 .1823 .08343 .04940 .89388 .10612 .95060 .09146 .10896 .13429 .4033 1.7938 .6485 .3377 MB 10 .0190 .01191 .00478 .98333 .01667 .99523 .03554 .03440 .05452 .4637 2.9868 .6814 .5504 RB 10 .0189 .01178 .00473 .98352 .01648 .99528 .03498 .03404 .05373 .4628 2.9865 .6813 .5503 MD 10 .0191 .01211 .00480 .98302 .01698 .99520 .03584 .03449 .05501 .4694 3.0211 .6824 .5550 RD 10 .0190 .01201 .00475 .98315 .01685 .99525 .03540 .03413 .05449 .4699 3.0290 .6826 .5560 OR 10 .2485 .11644 .10388 .87518 .12482 .89613 .19545 .21118 .21728 .1085 1.1398 .5478 .0798 OS 10 .0438 .02937 .01860 .96345 .03655 .98140 .11477 .10139 .13761 .2914 1.7588 .6273 .3172 OF 10 .0200 .01281 .00503 .98200 .01800 .99498 .03684 .03527 .05656 .4772 3.0479 .6835 .5590 CF 10 .0200 .01281 .00503 .98200 .01800 .99498 .03684 .03527 .05656 .4772 3.0479 .6835 .5590 CS 10 .0378 .02103 .01003 .97163 .02837 .98998 .05529 .05190 .08029 .4201 2.4317 .6663 .4705 NT 20 .1810 .11943 .04903 .83363 .16637 .95098 .11017 .10870 .16797 .6858 2.4581 .7072 .4968 MB 20 .0194 .02217 .00498 .96637 .03363 .99503 .04893 .03580 .07733 .7477 5.1949 .7202 .7357 RB 20 .0189 .02166 .00485 .96713 .03287 .99515 .04728 .03538 .07497 .7461 5.2140 .7201 .7364 MD 20 .0196 .02251 .00503 .96583 .03417 .99498 .04948 .03597 .07828 .7513 5.2158 .7206 .7368 RD 20 .0192 .02196 .00493 .96668 .03332 .99508 .04762 .03563 .07549 .7469 5.2011 .7202 .7359 OR 20 .3761 .20763 .17450 .77028 .22972 .82550 .25752 .26987 .28724 .1968 1.1793 .5768 .1025 OS 20 .0799 .06470 .03783 .91738 .08262 .96218 .17792 .14951 .21434 .3888 1.8499 .6472 .3512 OF 20 .0206 .02322 .00528 .96482 .03518 .99473 .05025 .03679 .07930 .7477 5.1170 .7200 .7322 CF 20 .0206 .02322 .00528 .96482 .03518 .99473 .05025 .03679 .07930 .7477 5.1170 .7200 .7322 CS 20 .0599 .04611 .01598 .93380 .06620 .98403 .08130 .06539 .12128 .6403 3.2172 .7024 .5945 NT 40 .1857 .19607 .05083 .70710 .29290 .94918 .12988 .11146 .20338 1.0920 3.2912 .7704 .6222 MB 40 .0204 .05268 .00523 .91568 .08432 .99478 .07623 .03663 .12387 1.1840 10.2855 .7544 .8739 RB 40 .0195 .05106 .00498 .91822 .08178 .99503 .07269 .03562 .11848 1.1844 10.5007 .7541 .8763 MD 40 .0205 .05345 .00528 .91443 .08557 .99473 .07680 .03696 .12482 1.1887 10.3119 .7548 .8743 RD 40 .0197 .05178 .00505 .91707 .08293 .99495 .07311 .03605 .11912 1.1868 10.4712 .7543 .8761 OR 40 .5847 .38982 .30690 .55490 .44510 .69310 .30592 .32861 .34361 .3666 1.1250 .6275 .0746 OS 40 .2013 .18549 .11000 .76418 .23582 .89000 .29798 .25433 .35451 .5067 1.6374 .6687 .2960 OF 40 .0208 .05400 .00535 .91357 .08643 .99465 .07711 .03720 .12533 1.1893 10.2603 .7549 .8737 CF 40 .0208 .05400 .00535 .91357 .08643 .99465 .07711 .03720 .12533 1.1893 10.2603 .7549 .8737 CS 40 .0859 .10953 .02330 .83298 .16702 .97670 .11620 .07903 .17915 1.0239 4.5416 .7519 .7188 124 Table 10.2.1.1.1.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P = 5, mNz = A,pNz = .8 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .0977 .05596 .05070 .94273 .05728 .94930 .07286 .15695 .08279 .0600 1.1014 .5304 .0574 MB 2 .0089 .00617 .00445 .99340 .00660 .99555 .02464 .04696 .02867 .1375 1.4195 .5820 .1935 RB 2 .0089 .00615 .00445 .99343 .00658 .99555 .02448 .04696 .02851 .1362 1.4148 .5813 .1917 MD 2 .0093 .00637 .00465 .99320 .00680 .99535 .02507 .04800 .02911 .1332 1.4014 .5796 .1867 RD 2 .0093 .00634 .00465 .99324 .00676 .99535 .02490 .04800 .02899 .1312 1.3946 .5786 .1841 OR 2 .0973 .06160 .05845 .93761 .06239 .94155 .14251 .18871 .14700 .0329 1.0523 .5168 .0305 OS 2 .0216 .01455 .01270 .98499 .01501 .98730 .06925 .08994 .07217 .0655 1.1552 .5391 .0823 OF 2 .0139 .00877 .00695 .99078 .00923 .99305 .02946 .05854 .03390 .1034 1.2827 .5622 .1395 CF 2 .0139 .00877 .00695 .99078 .00923 .99305 .02946 .05854 .03390 .1034 1.2827 .5622 .1395 CS 2 .0140 .00859 .00735 .99110 .00890 .99265 .03577 .06302 .03932 .0699 1.1831 .5439 .0946 NT 4 .1010 .06659 .05190 .92974 .07026 .94810 .08158 .15703 .09339 .1529 1.2674 .5702 .1407 MB 4 .0094 .00770 .00470 .99155 .00845 .99530 .02819 .04825 .03303 .2083 1.6807 .6119 .2834 RB 4 .0093 .00764 .00465 .99161 .00839 .99535 .02785 .04800 .03269 .2092 1.6858 .6123 .2849 MD 4 .0096 .00787 .00480 .99136 .00864 .99520 .02852 .04876 .03343 .2091 1.6816 .6120 .2838 RD 4 .0095 .00779 .00475 .99145 .00855 .99525 .02808 .04850 .03296 .2090 1.6822 .6121 .2840 OR 4 .1266 .08413 .07790 .91431 .08569 .92210 .16798 .21791 .17295 .0515 1.0745 .5248 .0434 OS 4 .0236 .01883 .01450 .98009 .01991 .98550 .08760 .09870 .09160 .1279 1.3115 .5693 .1546 OF 4 .0121 .00954 .00605 .98959 .01041 .99395 .03135 .05467 .03678 .1981 1.6119 .6058 .2630 CF 4 .0121 .00954 .00605 .98959 .01041 .99395 .03135 .05467 .03678 .1981 1.6119 .6058 .2630 CS 4 .0176 .01318 .00890 .98575 .01425 .99110 .04486 .06687 .05136 .1794 1.5054 .5952 .2285 NT 10 .0949 .09429 .04865 .89430 .10570 .95135 .09699 .15219 .11506 .4084 1.8107 .6499 .3426 MB 10 .0095 .01453 .00475 .98303 .01698 .99525 .03935 .04850 .04750 .4729 3.0482 .6831 .5585 RB 10 .0093 .01434 .00465 .98324 .01676 .99535 .03861 .04800 .04673 .4751 3.0733 .6837 .5615 MD 10 .0098 .01483 .00490 .98269 .01731 .99510 .03971 .04926 .04795 .4701 3.0152 .6824 .5545 RD 10 .0097 .01467 .00485 .98287 .01713 .99515 .03909 .04901 .04728 .4692 3.0147 .6823 .5543 OR 10 .2011 .14403 .12675 .85165 .14835 .87325 .21859 .27114 .22782 .0984 1.1135 .5426 .0661 OS 10 .0363 .03922 .02355 .95686 .04314 .97645 .13640 .12893 .14689 .2700 1.6481 .6185 .2844 OF 10 .0106 .01571 .00530 .98169 .01831 .99470 .04089 .05121 .04932 .4657 2.9497 .6809 .5465 CF 10 .0106 .01571 .00530 .98169 .01831 .99470 .04089 .05121 .04932 .4657 2.9497 .6809 .5465 CS 10 .0226 .02747 .01145 .96853 .03148 .98855 .06421 .07579 .07515 .4156 2.3610 .6641 .4585 NT 20 .0967 .14325 .04960 .83334 .16666 .95040 .11968 .15360 .14418 .6813 2.4381 .7064 .4932 MB 20 .0106 .02849 .00540 .96574 .03426 .99460 .05573 .05264 .06805 .7276 4.9036 .7179 .7207 RB 20 .0104 .02777 .00530 .96661 .03339 .99470 .05361 .05217 .06557 .7224 4.8808 .7174 .7192 MD 20 .0108 .02899 .00550 .96514 .03486 .99450 .05640 .05310 .06889 .7290 4.8935 .7179 .7203 RD 20 .0107 .02819 .00545 .96613 .03388 .99455 .05404 .05287 .06605 .7192 4.8183 .7169 .7158 OR 20 .3427 .27641 .22780 .71144 .28856 .77220 .29018 .34419 .30291 .1885 1.1308 .5723 .0771 OS 20 .0814 .09421 .05645 .89635 .10365 .94355 .22361 .20197 .23951 .3243 1.5864 .6264 .2712 OF 20 .0110 .02993 .00560 .96399 .03601 .99440 .05734 .05356 .07004 .7374 4.9457 .7188 .7235 CF 20 .0110 .02993 .00560 .96399 .03601 .99440 .05734 .05356 .07004 .7374 4.9457 .7188 .7235 CS 20 .0367 .06639 .01875 .92170 .07830 .98125 .09915 .09708 .11808 .6637 3.1912 .7053 .5937 NT 40 .0986 .24494 .05075 .70651 .29349 .94925 .14387 .15573 .17520 1.0944 3.2981 .7707 .6229 MB 40 .0096 .06923 .00485 .91468 .08533 .99515 .08815 .04951 .10918 1.2162 11.0893 .7560 .8835 RB 40 .0090 .06623 .00455 .91835 .08165 .99545 .08228 .04801 .10212 1.2142 11.3572 .7554 .8861 MD 40 .0101 .07022 .00510 .91350 .08650 .99490 .08883 .05074 .10996 1.2063 10.7128 .7557 .8793 RD 40 .0092 .06717 .00465 .91720 .08280 .99535 .08280 .04851 .10277 1.2143 11.2569 .7556 .8851 OR 40 .5664 .52793 .40995 .44258 .55742 .59005 .31484 .40458 .32721 .3721 1.0156 .6286 .0098 OS 40 .2370 .28114 .17815 .69311 .30689 .82185 .36687 .34205 .38986 .4177 1.3473 .6440 .1846 OF 40 .0104 .07097 .00525 .91260 .08740 .99475 .08916 .05146 .11037 1.2020 10.5210 .7556 .8771 CF 40 .0104 .07097 .00525 .91260 .08740 .99475 .08916 .05146 .11037 1.2020 10.5210 .7556 .8771 CS 40 .0587 .16678 .03025 .79909 .20091 .96975 .14275 .12293 .17253 1.0388 4.0975 .7564 .6910 125 Table 10.2.1.1.2.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P = 5, mNz = .3, pNz = .2 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' P A' B" NT 2 .3341 .06647 .05011 .86810 .13190 .94989 .07912 .07848 .23876 .5263 2.0681 .6765 .4127 MB 2 .0404 .00811 .00513 .97995 .02005 .99488 .02831 .02516 .09937 .5146 3.2826 .6898 .5879 RB 2 .0400 .00805 .00506 .98000 .02000 .99494 .02800 .02496 .09925 .5178 3.3116 .6905 .5911 MD 2 .0421 .00843 .00534 .97920 .02080 .99466 .02881 .02564 .10109 .5157 3.2662 .6897 .5865 RD 2 .0417 .00837 .00529 .97930 .02070 .99471 .02851 .02553 .10086 .5169 3.2802 .6900 .5880 OR 2 .2613 .07737 .07288 .90465 .09535 .92713 .15867 .16110 .23289 .1462 1.2238 .5650 .1215 OS 2 .0692 .02003 .01550 .96185 .03815 .98450 .08324 .07839 .15173 .3845 2.1286 .6542 .4126 OF 2 .0590 .01153 .00756 .97260 .02740 .99244 .03356 .03058 .11511 .5089 3.0248 .6860 .5605 CF 2 .0590 .01153 .00756 .97260 .02740 .99244 .03356 .03058 .11511 .5089 3.0248 .6860 .5605 CS 2 .0579 .01175 .00860 .97565 .02435 .99140 .04158 .03785 .11416 .4112 2.4476 .6657 .4718 NT 4 .3355 .09161 .05055 .74415 .25585 .94945 .08811 .07887 .30623 .9834 3.0918 .7547 .5973 MB 4 .0402 .01630 .00516 .93915 .06085 .99484 .03986 .02556 .16963 1.0171 8.0956 .7428 .8351 RB 4 .0400 .01619 .00511 .93950 .06050 .99489 .03946 .02532 .16850 1.0175 8.1293 .7428 .8357 MD 4 .0410 .01662 .00528 .93800 .06200 .99473 .04032 .02587 .17105 1.0191 8.0588 .7430 .8345 RD 4 .0406 .01645 .00519 .93850 .06150 .99481 .03973 .02549 .16977 1.0208 8.1281 .7431 .8359 OR 4 .3449 .11934 .10489 .82285 .17715 .89511 .18959 .18960 .30332 .3279 1.4297 .6222 .2165 OS 4 .0802 .03566 .02169 .90845 .09155 .97831 .11050 .09670 .23558 .6888 3.1716 .7086 .5935 OF 4 .0473 .01859 .00610 .93145 .06855 .99390 .04235 .02779 .17925 1.0196 7.6575 .7435 .8266 CF 4 .0473 .01859 .00610 .93145 .06855 .99390 .04235 .02779 .17925 1.0196 7.6575 .7435 .8266 CS 4 .0786 .02234 .01135 .93370 .06630 .98865 .05304 .04168 .18113 .7745 4.3265 .7211 .6931 NT 10 .3246 .15315 .04953 .43235 .56765 .95048 .09397 .07938 .34512 1.8199 3.8415 .8645 .6781 MB 10 .0391 .05302 .00508 .75520 .24480 .99492 .06548 .02573 .30657 1.8797 21.4449 .8051 .9468 RB 10 .0373 .05224 .00480 .75800 .24200 .99520 .06407 .02479 .30240 1.8900 22.3966 .8046 .9492 MD 10 .0398 .05347 .00516 .75330 .24670 .99484 .06574 .02592 .30765 1.8798 21.2089 .8055 .9462 RD 10 .0379 .05270 .00488 .75600 .24400 .99513 .06435 .02496 .30344 1.8911 22.1877 .8051 .9487 OR 10 .4933 .21752 .16113 .55690 .44310 .83888 .22278 .22677 .39985 .8467 1.6155 .7431 .2922 OS 10 .1815 .11247 .05609 .66200 .33800 .94391 .18009 .15600 .40764 1.1706 3.2360 .7832 .6173 OF 10 .0424 .05531 .00555 .74565 .25435 .99445 .06674 .02705 .31031 1.8787 20.2114 .8071 .9434 CF 10 .0424 .05531 .00555 .74565 .25435 .99445 .06674 .02705 .31031 1.8787 20.2114 .8071 .9434 CS 10 .0921 .06054 .01324 .75025 .24975 .98676 .07374 .04446 .30440 1.5439 9.3405 .7967 .8697 NT 20 .3261 .21336 .04990 .13280 .86720 .95010 .07934 .07968 .23784 2.7591 2.0849 .9507 .4168 MB 20 .0435 .12583 .00569 .39360 .60640 .99431 .07293 .02722 .34357 2.8009 23.7231 .8987 .9537 RB 20 .0381 .12361 .00496 .40180 .59820 .99504 .07129 .02541 .34032 2.8271 26.9297 .8970 .9597 MD 20 .0447 .12649 .00585 .39095 .60905 .99415 .07306 .02762 .34329 2.7979 23.0938 .8993 .9523 RD 20 .0385 .12415 .00501 .39930 .60070 .99499 .07126 .02552 .34010 2.8301 26.6469 .8976 .9593 OR 20 .6012 .33430 .21274 .17945 .82055 .78726 .22170 .25384 .30238 1.7144 .9019 .8782 -.0643 OS 20 .3774 .24973 .12005 .23155 .76845 .87995 .20617 .21272 .36541 1.9085 1.5232 .8952 .2549 OF 20 .0469 .12755 .00615 .38685 .61315 .99385 .07307 .02834 .34225 2.7910 22.0258 .9002 .9498 CF 20 .0469 .12755 .00615 .38685 .61315 .99385 .07307 .02834 .34225 2.7910 22.0258 .9002 .9498 CS 20 .0869 .12243 .01215 .43645 .56355 .98785 .07256 .04156 .31176 2.4123 12.4753 .8842 .9069 NT 40 .3366 .23888 .05063 .00810 .99190 .94938 .06418 .07884 .06313 4.0432 .2127 .9851 -.7136 MB 40 .0486 .19358 .00641 .05775 .94225 .99359 .04041 .02907 .16536 4.0625 6.4102 .9838 .7904 RB 40 .0391 .19171 .00505 .06165 .93835 .99495 .03940 .02543 .16979 4.1135 8.3406 .9832 .8402 MD 40 .0498 .19387 .00656 .05690 .94310 .99344 .04042 .02935 .16421 4.0617 6.2076 .9839 .7833 RD 40 .0404 .19210 .00524 .06045 .93955 .99476 .03934 .02597 .16830 4.1107 7.9512 .9834 .8319 OR 40 .6511 .38196 .22979 .00935 .99065 .77021 .20613 .25636 .07027 3.0910 .0828 .9390 -.9005 OS 40 .5084 .32576 .16021 .01205 .98795 .83979 .18736 .23125 .08649 3.2491 .1287 .9559 -.8374 OF 40 .0503 .19400 .00663 .05650 .94350 .99338 .04040 .02947 .16374 4.0618 6.1217 .9840 .7802 CF 40 .0503 .19400 .00663 .05650 .94350 .99338 .04040 .02947 .16374 4.0618 6.1217 .9840 .7802 CS 40 .0599 .18362 .00856 .11615 .88385 .99144 .05259 .03615 .21387 3.5785 8.4014 .9683 .8472 Table 10.2.1.1.2.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P *!,/> = 5, mNz = .3, pNz = A N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" N 2 .2595 .08155 .05010 .87128 .12873 .94990 .09023 .09145 .17787 .5114 2.0339 .6734 .4042 MB 2 .0334 .01112 .00567 .98070 .01930 .99433 .03395 .03075 .07082 .4638 2.9065 .6800 .5412 RB 2 .0332 .01101 .00563 .98093 .01908 .99437 .03346 .03067 .06986 .4611 2.8928 .6795 .5392 MD 2 .0349 .01145 .00593 .98028 .01973 .99407 .03444 .03151 .07163 .4566 2.8424 .6783 .5325 RD 2 .0347 .01132 .00588 .98053 .01948 .99412 .03388 .03129 .07055 .4544 2.8330 .6779 .5311 OR 2 .2870 .11327 .10112 .86850 .13150 .89888 .19815 .20122 .24060 .1559 1.2052 .5662 .1137 OS 2 .0688 .03372 .02338 .95078 .04923 .97662 .12252 .11061 .16530 .3360 1.8435 .6379 .3441 OF 2 .0458 .01534 .00788 .97348 .02653 .99212 .03973 .03654 .08241 .4798 2.8382 .6804 5350 CF 2 .0458 .01534 .00788 .97348 .02653 .99212 .03973 .03654 .08241 .4798 2.8382 .6804 .5350 CS 2 .0629 .02057 .01243 .96723 .03278 .98757 .05741 .05197 .10251 .4020 2.2728 .6603 .4416 N 4 .2614 .13266 .05095 .74478 .25523 .94905 .11105 .09311 .23724 .9776 3.0685 .7539 5944 MB 4 .0318 .02842 .00550 .93720 .06280 .99450 .05593 .03096 .13022 1.0110 7.8431 .7425 .8299 RB 4 .0310 .02768 .00528 .93873 .06128 .99472 .05374 .02986 .12571 1.0126 7.9739 .7425 .8326 MD 4 .0323 .02884 .00558 .93628 .06373 .99442 .05636 .03117 .13128 1.0132 7.8276 .7427 .8297 RD 4 .0316 .02814 .00538 .93773 .06228 .99462 .05439 .03012 .12730 1.0142 7.9418 .7427 .8320 OR 4 .4361 .21673 .17462 .72010 .27990 .82538 .25517 .25667 .32356 .3529 1.3075 .6259 .1661 OS 4 .1163 .08418 .04837 .86210 .13790 .95163 .19423 .16451 .27994 5711 2.1934 .6858 .4418 OF 4 .0377 .03250 .00658 .92863 .07137 .99342 .05960 .03405 .13821 1.0136 7.3836 .7432 .8204 CF 4 .0377 .03250 .00658 .92863 .07137 .99342 .05960 .03405 .13821 1.0136 7.3836 .7432 .8204 CS 4 .0904 .05165 .01747 .89708 .10293 .98253 .08518 .05954 .17401 .8441 4.1538 .7293 .6865 N 10 .2471 .25692 .04878 .43088 .56913 .95122 .12223 .09265 .27221 1.8309 3.8856 .8653 .6818 MB 10 .0306 .10354 .00530 .74910 .25090 .99470 .10147 .03046 .24651 1.8840 20.9057 .8064 .9454 RB 10 .0261 .09911 .00445 .75890 .24110 .99555 .09563 .02758 .23434 1.9131 23.9137 .8048 .9527 MD 10 .0307 .10450 .00532 .74673 .25328 .99468 .10190 .03050 .24762 1.8903 20.9513 .8071 .9456 RD 10 .0264 .10000 .00450 .75675 .24325 .99550 .09598 .02773 .23507 1.9162 23.7905 .8053 .9525 OR 10 .7010 .46404 .32370 .32545 .67455 .67630 .26902 .30700 .33581 .9099 1.0022 .7597 .0014 OS 10 .3699 .30613 .16872 .48775 51225 .83128 .30551 .27889 .43296 .9900 15835 .7710 .2809 OF 10 .0325 .10760 .00563 .73945 .26055 .99437 .10297 .03139 .24989 1.8927 20.1968 .8087 .9435 CF 10 .0325 .10760 .00563 .73945 .26055 .99437 .10297 .03139 .24989 1.8927 20.1968 .8087 .9435 CS 10 .1135 .15556 .02212 .64427 .35573 .97788 .11230 .06661 .25228 1.6420 7.0667 .8197 .8275 N 20 .2511 .37594 .04907 .13375 .86625 .95093 .09076 .09180 .18314 2.7628 2.1235 .9507 .4258 MB 20 .0383 .25408 .00670 .37485 .62515 .99330 .11363 .03439 .27771 2.7920 20.2240 .9030 .9448 RB 20 .0286 .24247 .00497 .40128 59873 .99503 .10947 .02949 .27056 2.8282 26.9005 .8971 .9597 MD 20 .0391 .25538 .00688 .37188 .62813 .99312 .11340 .03504 .27697 2.7902 19.6973 .9036 .9431 RD 20 .0291 .24376 .00505 .39817 .60183 .99495 .10907 .02971 .26948 2.8305 26.4508 .8979 .9589 OR 20 .8065 .62774 .41073 .04675 .95325 .58927 .20817 .31854 .13487 1.9029 .2513 .8724 -.6890 OS 20 .6920 57143 .33643 .07608 .92393 .66357 .23765 .32571 .21705 1.8542 .3921 .8803 -.5211 OF 20 .0402 .25710 .00710 .36790 .63210 .99290 .11305 .03566 .27592 2.7896 19.0988 .9046 .9412 CF 20 .0402 .25710 .00710 .36790 .63210 .99290 .11305 .03566 .27592 2.7896 19.0988 .9046 .9412 CS 20 .1029 .28203 .01968 .32445 .67555 .98032 .09502 .06155 .21558 2.5156 7.5296 .9100 .8382 N 40 .2580 .42667 .05028 .00875 .99125 .94972 .05840 .09269 .04781 4.0181 .2289 .9850 -.6926 MB 40 .0453 .38503 .00817 .04968 .95033 .99183 .05255 .03895 .11679 4.0494 4.5967 .9853 .7071 RB 40 .0295 .37830 .00522 .06207 .93793 .99478 .05388 .03070 .12735 4.0987 8.1466 .9830 .8363 MD 40 .0463 .38559 .00835 .04855 .95145 .99165 .05203 .03937 .11525 4.0523 4.4262 .9856 .6960 RD 40 .0300 .37878 .00532 .06103 .93898 .99468 .05359 .03104 .12643 4.1007 7.9041 .9832 .8310 OR 40 .8267 .65286 .42207 .00095 .99905 .57793 .18914 .31456 .01578 3.3020 .0082 .8940 -.9922 OS 40 .7590 .61963 .36688 .00125 .99875 .63312 .19262 .31995 .02058 3.3635 .0110 .9077 -.9893 OF 40 .0468 .38577 .00843 .04822 .95178 .99157 .05183 .03953 .11465 4.0519 4.3643 .9856 .6918 CF 40 .0468 .38577 .00843 .04822 .95178 .99157 .05183 .03953 .11465 4.0519 4.3643 .9856 .6918 CS 40 .0660 .37660 .01275 .07763 .92237 .98725 .05954 .05144 .12473 3.6550 4.4143 .9769 .7010 Table 10.2.1.1.2.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P*L/? = 5, mNz = .3, pNz = .6 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .1746 .09861 .04925 .86848 .13152 .95075 .10585 .11369 .16134 .5329 2.0927 .6780 .4185 MB 2 .0221 .01426 .00570 .98003 .01997 .99430 .04018 .03847 .06224 .4758 2.9760 .6822 .5508 RB 2 .0220 .01401 .00568 .98043 .01957 .99433 .03892 .03840 .06019 .4690 2.9368 .6810 5454 MD 2 .0228 .01462 .00588 .97955 .02045 .99413 .04063 .03901 .06295 .4750 2.9566 .6818 .5485 RD 2 .0227 .01434 .00585 .98000 .02000 .99415 .03927 .03893 .06069 .4673 2.9123 .6804 .5423 OR 2 .3013 .16897 .14363 .81413 .18587 .85638 .25351 .26146 .28343 .1709 1.1821 .5691 .1033 OS 2 .0697 .05581 .03665 .93142 .06858 .96335 .17615 .15687 .20788 .3045 1.6471 .6247 .2881 OF 2 .0304 .01969 .00795 .97248 .02752 .99205 .04726 .04582 .07281 .4926 2.9049 .6827 .5447 CF 2 .0304 .01969 .00795 .97248 .02752 .99205 .04726 .04582 .07281 .4926 2.9049 .6827 .5447 CS 2 .0544 .03575 .01605 .95112 .04888 .98395 .08102 .07189 .11663 .4874 2.5238 .6763 .4929 NT 4 .1772 .17217 .05033 .74660 .25340 .94968 .14321 .11543 .22706 .9779 3.0872 .7538 .5967 MB 4 .0198 .04021 .00513 .93640 .06360 .99488 .07388 .03664 .12051 1.0420 8.4341 .7445 .8423 RB 4 .0191 .03846 .00493 .93918 .06082 .99508 .06892 .03581 .11250 1.0331 8.4387 .7438 .8420 MD 4 .0202 .04088 .00523 .93535 .06465 .99478 .07480 .03697 .12205 1.0437 8.3965 .7447 .8417 RD 4 .0196 .03905 .00505 .93828 .06172 .99495 .06956 .03622 .11356 1.0319 8.3477 .7438 .8403 OR 4 .4932 .33960 .26645 .61163 .38837 .73355 .32338 .33070 .36746 .3400 1.1667 .6200 .0972 OS 4 .1643 .15993 .09678 .79797 .20203 .90322 .29532 .24854 .35451 .4658 1.6439 .6594 .2969 OF 4 .0235 .04607 .00610 .92728 .07272 .99390 .07956 .04001 .12983 1.0505 8.0127 .7458 .8350 CF 4 .0235 .04607 .00610 .92728 .07272 .99390 .07956 .04001 .12983 1.0505 8.0127 .7458 .8350 CS 4 .0823 .09617 .02440 .85598 .14402 .97560 .13017 .08842 .19737 .9079 3.9619 .7383 .6763 NT 10 .1709 .35992 .04878 .43265 .56735 .95123 .16567 .11496 .26572 1.8265 3.8891 .8648 .6821 MB 10 .0210 .15865 .00555 .73928 .26072 .99445 .14990 .03930 .24705 1.8984 20.4726 .8088 .9443 RB 10 .0169 .14641 .00435 .75888 .24112 .99565 .13466 .03382 .22319 1.9209 24.4052 .8049 .9538 MD 10 .0214 .16034 .00565 .73653 .26347 .99435 .15056 .03960 .24805 1.9006 20.2592 .8095 .9437 RD 10 .0170 .14782 .00438 .75655 .24345 .99563 .13500 .03391 .22375 1.9264 24.4076 .8055 .9538 OR 10 .7779 .66984 .47820 .20240 .79760 .52180 .26548 .35447 .28497 .8878 .7079 .7531 -.2144 OS 10 5132 .51031 .32008 .36287 .63713 .67993 .37763 .37451 .43608 .8183 1.0489 .7410 .0302 OF 10 .0231 .16486 .00615 .72933 .27067 .99385 .15191 .04168 .25022 1.8926 19.0490 .8109 .9399 CF 10 .0231 .16486 .00615 .72933 .27067 .99385 .15191 .04168 .25022 1.8926 19.0490 .8109 .9399 CS 10 .1165 .27527 .03405 56392 .43608 .96595 .16352 .10095 .25744 1.6634 5.2131 .8345 .7641 NT 20 .1719 .53840 .04925 .13550 .86450 .95075 .11486 .11549 .17437 2.7529 2.1361 .9501 .4288 MB 20 .0323 .39077 .00885 .35462 .64538 .99115 .16779 .05059 .27541 2.7447 15.5378 .9071 .9262 RB 20 .0193 .36077 .00508 .40210 59790 .99492 .15858 .03699 .26311 2.8186 26.4025 .8968 .9589 MD 20 .0328 .39258 .00898 .35168 .64832 .99103 .16746 .05088 .27485 2.7474 15.3025 .9078 .9249 RD 20 .0194 .36249 .00510 .39925 .60075 .99490 .15805 .03707 .26225 2.8243 26.2385 .8976 .9586 OR 20 .8715 .81593 56752 .01847 .98153 .43248 .15025 .33915 .07644 1.9164 .1151 .8448 -.8625 OS 20 .8101 .78564 .52093 .03788 .96212 .47908 .19690 .36136 .16212 1.7233 .2069 .8449 -.7451 OF 20 .0336 .39501 .00918 .34777 .65223 .99083 .16668 .05133 .27357 2.7498 14.9488 .9087 .9229 CF 20 .0336 .39501 .00918 .34777 .65223 .99083 .16668 .05133 .27357 2.7498 14.9488 .9087 .9229 CS 20 .0990 .46087 .02948 .25153 .74847 .97053 .12303 .09586 .19082 2.5582 4.7546 .9254 .7362 NT 40 .1760 .61530 .05060 .00823 .99177 .94940 .05299 .11754 .03992 4.0375 .2159 .9851 -.7094 MB 40 .0442 58080 .01228 .04018 .95982 .98773 .06383 .06026 .09684 3.9970 2.7154 .9866 .5217 RB 40 .0213 .56533 .00563 .06153 .93847 .99438 .07168 .03905 .11637 4.0769 7.5668 .9830 .8234 MD 40 .0448 .58120 .01245 .03963 .96037 .98755 .06336 .06069 .09593 3.9979 2.6524 .9867 5117 RD 40 .0217 56604 .00575 .06043 .93957 .99425 .07110 .03959 .11532 4.0783 7.3167 .9833 .8171 OR 40 .8846 .83130 57855 .00020 .99980 .42145 .13308 .33229 .00577 3.3419 .0019 .8552 -.9984 OS 40 .8462 .81803 .54555 .00032 .99968 .45445 .14051 .35016 .01166 3.3025 .0029 .8634 -.9974 OF 40 .0453 58145 .01258 .03930 .96070 .98743 .06322 .06092 .09557 3.9980 2.6116 .9868 .5050 CF 40 .0453 .58145 .01258 .03930 .96070 .98743 .06322 .06092 .09557 3.9980 2.6116 .9868 .5050 CS 40 .0700 .57913 .02115 .04888 .95112 .97885 .06378 .08376 .08655 3.6863 1.9953 .9820 .3838 128 Table 10.2.1.1.2.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P*I,p = 5, mNz = .3,pNz = .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .0928 .11405 .04855 .86958 .13043 .95145 .11483 .15515 .13707 .5347 2.1047 .6785 .4212 MB 2 .0118 .01748 .00600 .97965 .02035 .99400 .04471 .05536 .05393 .4656 2.8898 .6799 .5395 RB 2 .0115 .01712 .00585 .98006 .01994 .99415 .04314 .05469 .05209 .4660 2.9046 .6802 .5413 MD 2 .0121 .01793 .00625 .97915 .02085 .99375 .04538 .05733 .05460 .4612 2.8451 .6787 .5335 RD 2 .0117 .01748 .00595 .97964 .02036 .99405 .04350 .05514 .05256 .4688 2.9129 .6806 .5426 OR 2 .2678 .21484 .18130 .77678 .22323 .81870 .28345 .32433 .29426 .1491 1.1327 .5598 .0776 OS 2 .0643 .07329 .04835 .92048 .07953 .95165 .20763 .19504 .21956 .2528 1.4740 .6062 .2281 OF 2 .0151 .02379 .00785 .97223 .02778 .99215 .05295 .06453 .06355 .5013 2.9604 .6844 .5523 CF 2 .0151 .02379 .00785 .97223 .02778 .99215 .05295 .06453 .06355 .5013 2.9604 .6844 .5523 CS 2 .0357 .04917 .01940 .94339 .05661 .98060 .10119 .10428 .11700 .4824 2.4121 .6738 .4747 NT 4 .0985 .21273 .05140 .74694 .25306 .94860 .15928 .15878 .19388 .9665 3.0336 .7524 .5899 MB 4 .0096 .05180 .00480 .93645 .06355 .99520 .08530 .04876 .10521 1.0643 8.9356 .7459 .8514 RB 4 .0090 .04911 .00450 .93974 .06026 .99550 .07806 .04722 .09637 1.0595 9.0809 .7453 .8534 MD 4 .0103 .05270 .00515 .93541 .06459 .99485 .08628 .05048 .10633 1.0482 8.4989 .7450 .8437 RD 4 .0094 .04984 .00470 .93888 .06113 .99530 .07879 .04825 .09727 1.0518 8.8328 .7449 .8493 OR 4 .4944 .45181 .35815 .52478 .47523 .64185 .34340 .40221 .35953 .3013 1.0662 .6072 .0407 OS 4 .1931 .22921 .15095 .75123 .24878 .84905 .35809 .32726 .37993 .3540 1.3537 .6271 .1864 OF 4 .0118 .05928 .00600 .92740 .07260 .99400 .09219 .05536 .11316 1.0554 8.1210 .7461 .8373 CF 4 .0118 .05928 .00600 .92740 .07260 .99400 .09219 .05536 .11316 1.0554 8.1210 .7461 .8373 CS 4 .0541 .14081 .02875 .83118 .16883 .97125 .16284 .12349 .19439 .9407 3.8358 .7435 .6681 NT 10 .0905 .46394 .04750 .43195 36805 .95250 .18280 .15410 .22567 1.8410 3.9712 .8657 .6886 MB 10 .0137 .21808 .00720 .72920 .27080 .99280 .17984 .06244 .22261 1.8367 16.5755 .8097 .9301 RB 10 .0094 .19478 .00475 .75771 .24229 .99525 .15307 .04902 .19067 1.8946 22.6212 .8048 .9498 MD 10 .0139 .22072 .00730 .72592 .27408 .99270 .18085 .06283 .22385 1.8416 16.4732 .8105 .9297 RD 10 .0098 .19667 .00495 .75540 .24460 .99505 .15343 .05001 .19110 1.8877 21.9169 .8052 .9481 OR 10 .7823 .83714 .61135 .10641 .89359 .38865 .19123 .39005 .18914 .9630 .4790 .7605 -.4284 OS 10 .6129 .71032 .48660 .23375 .76625 .51340 .36218 .43208 .37858 .7601 .7685 .7274 -.1649 OF 10 .0150 .22719 .00790 .71799 .28201 .99210 .18268 .06548 .22600 1.8366 15.5819 .8121 .9255 CF 10 .0150 .22719 .00790 .71799 .28201 .99210 .18268 .06548 .22600 1.8366 15.5819 .8121 .9255 CS 10 .0782 .40898 .04150 .49915 .50085 .95850 .18615 .14639 .22730 1.7357 4.4932 .8491 .7255 NT 20 .0957 .70150 .05010 .13565 .86435 .94990 .12142 .15746 .14835 2.7440 2.1088 .9498 .4226 MB 20 .0263 .54470 .01385 .32259 .67741 .98615 .19752 .08622 .24436 2.6620 10.1483 .9131 .8823 RB 20 .0103 .47914 .00525 .40239 .59761 .99475 .17945 .05194 .22408 2.8061 25.6225 .8967 .9575 MD 20 .0268 .54719 .01410 .31954 .68046 .98590 .19680 .08690 .24346 2.6635 9.9535 .9138 .8798 RD 20 .0104 .48144 .00530 .39953 .60048 .99470 .17907 .05217 .22359 2.8102 25.3602 .8974 .9570 OR 20 .8558 .93381 .69240 .00584 .99416 .30760 .07890 .36235 .02993 2.0192 .0472 .8211 -.9469 OS 20 .8332 .92775 .67900 .01006 .98994 .32100 .10196 .37533 .07155 1.8591 .0748 .8207 -.9126 OF 20 .0272 .55010 .01435 .31596 .68404 .98565 .19569 .08786 .24206 2.6666 9.7574 .9146 .8772 CF 20 .0272 .55010 .01435 .31596 .68404 .98565 .19569 .08786 .24206 2.6666 9.7574 .9146 .8772 CS 20 .0800 .65106 .04300 .19693 .80308 .95700 .12120 .15051 .14686 2.5695 3.0354 .9352 .5870 NT 40 .0966 .80350 .05060 .00828 .99173 .94940 .04089 .15825 .03447 4.0356 .2169 .9851 -.7082 MB 40 .0429 .78283 .02295 .02720 .97280 .97705 .06111 .11158 .07039 3.9199 1.1531 .9871 .0826 RB 40 .0098 .75151 .00495 .06185 .93815 .99505 .08008 .05001 .09975 4.1187 8.5121 .9831 .8435 MD 40 .0436 .78334 .02330 .02665 .97335 .97670 .06057 .11229 .06957 3.9224 1.1192 .9872 .0654 RD 40 .0101 .75242 .00510 .06075 .93925 .99490 .07934 .05074 .09881 4.1175 8.1733 .9834 .8367 OR 40 .8656 .94006 .70055 .00006 .99994 .29945 .07143 .35675 .00279 3.3101 .0007 .8248 -.9994 OS 40 .8472 .93820 .69135 .00009 .99991 .30865 .07372 .36807 .00331 3.2529 .0010 .8271 -.9992 OF 40 .0436 .78354 .02330 .02640 .97360 .97670 .06029 .11229 .06922 3.9265 1.1105 .9873 .0608 CF 40 .0436 .78354 .02330 .02640 .97360 .97670 .06029 .11229 .06922 3.9265 1.1105 .9873 .0608 CS 40 .0562 .78479 .03050 .02664 .97336 .96950 .05140 .12931 .05586 3.8062 .8935 .9853 -.0656 Table 10.2.1.1.3.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P = 5, mNz- .5,pNz- .2 N:p CtEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' P A' B" NT 2 .3249 .10477 .04985 .67555 .32445 .95015 .09115 .08020 .32034 1.1910 3.4957 .7838 .6446 MB 2 .0412 .01981 .00531 .92220 .07780 .99469 .04380 .02601 .18855 1.1348 95377 .7511 .8628 RB 2 .0406 .01960 .00524 .92295 .07705 .99476 .04308 .02584 .18666 1.1345 9.5883 .7511 .8635 MD 2 .0425 .02026 .00550 .92070 .07930 .99450 .04429 .02654 .19043 1.1329 9.3830 .7512 .8606 RD 2 .0420 .02002 .00541 .92155 .07845 .99459 .04347 .02623 .18808 1.1327 9.4403 .7511 .8614 OR 2 .3677 .13804 .11776 .78085 .21915 .88224 .20768 .20819 .32796 .4112 1.4966 .6444 .2445 OS 2 .1065 .05218 .03158 .86540 .13460 .96843 .13905 .12356 .28052 .7532 3.0524 .7180 .5841 OF 2 .0577 .02607 .00750 .89965 .10035 .99250 .05016 .03087 .21215 1.1528 8.4960 .7547 .8477 CF 2 .0577 .02607 .00750 .89965 .10035 .99250 .05016 .03087 .21215 1.1528 8.4960 .7547 .8477 CS 2 .0869 .02822 .01313 .91140 .08860 .98687 .06197 .04687 .21143 .8731 4.7553 .7321 .7235 NT 4 .3253 .16930 .05081 .35675 .64325 .94919 .09224 .08196 .32683 2.0042 3.5699 .8863 .6527 MB 4 .0415 .06358 .00549 .70405 .29595 .99451 .06804 .02704 .31820 2.0074 21.9988 .8184 .9490 RB 4 .0384 .06254 .00501 .70735 .29265 .99499 .06625 .02559 .31407 2.0293 23.7208 .8180 .9529 MD 4 .0420 .06425 .00556 .70100 .29900 .99444 .06830 .02725 .31908 2.0115 21.8371 .8191 .9486 RD 4 .0389 .06313 .00509 .70470 .29530 .99491 .06642 .02581 .31458 2.0319 23.5069 .8186 .9525 OR 4 5198 .25273 .18345 .47015 52985 .81655 .23727 .24782 .39440 .9772 1.4982 .7695 .249C OS 4 .2271 .14898 .07841 56875 .43125 .92159 .20773 .19144 .42387 1.2426 2.6840 .8003 5448 OF 4 .0502 .06965 .00668 .67845 .32155 .99333 .07007 .02983 .32449 2.0109 19.1769 .8241 .941C CF 4 .0502 .06965 .00668 .67845 .32155 .99333 .07007 .02983 .32449 2.0109 19.1769 .8241 .9410 CS 4 .1045 .07297 .01536 .69660 .30340 .98464 .07972 .04864 .32126 1.6460 9.0404 .8105 .8664 NT 10 .3152 .23359 .05020 .03285 .96715 .94980 .06994 .08349 .12449 3.4834 .7089 .9784 -.2002 MB 10 .0444 .17323 .00601 .15790 .84210 .99399 .05601 .02921 .25382 3.5145 14.1605 .9585 .9140 RB 10 .0375 .17076 .00494 .16595 .83405 .99506 .05522 .02584 .25669 3.5505 17.4252 .9568 .9314 MD 10 .0455 .17386 .00615 .15530 .84470 .99385 .05579 .02947 .25217 3.5174 13.7287 .9591 .9110 RD 10 .0380 .17114 .00501 .16435 .83565 .99499 .05504 .02607 .25548 3.5517 17.0853 .9572 .9299 OR 10 .6144 .37227 .22483 .03795 .96205 .77517 .21364 .26277 .13977 2.5310 .2754 .9293 -.6536 OS 10 .4578 .31245 .15279 .04890 .95110 .84721 .19864 .23742 .17568 2.6802 .4293 .9454 -.4713 OF 10 .0492 .17538 .00669 .14985 .85015 .99331 .05559 .03078 .24885 3.5107 12.4491 .9603 .9009 CF 10 .0492 .17538 .00669 .14985 .85015 .99331 .05559 .03078 .24885 3.5107 12.4491 .9603 .9009 CS 10 .0833 .16212 .01205 .23760 .76240 .98795 .06487 .04303 .26154 2.9696 9.8629 .9359 .8767 NT 20 .3171 .24013 .05023 .00025 .99975 .94978 .06639 .08293 .01118 5.1234 .0090 .9874 -.9896 MB 20 .0481 .20446 .00655 .00390 .99610 .99345 .02565 .03027 .04399 5.1416 .6303 .9974 -.2523 RB 20 .0388 .20324 .00515 .00440 .99560 .99485 .02284 .02631 .04670 5.1853 .8690 .9976 -.0782 MD 20 .0492 .20464 .00675 .00380 .99620 .99325 .02609 .03090 .04343 5.1396 .5996 .9973 -.2783 RD 20 .0395 .20334 .00525 .00430 .99570 .99475 .02300 .02659 .04617 5.1865 .8369 .9976 -.0990 OR 20 .6246 .38657 .23325 .00015 .99985 .76675 .21449 .26810 .00866 4.3435 .0019 .9416 -.9983 OS 20 .4914 .33260 .16581 .00025 .99975 .83419 .19608 .24505 .01118 4.4516 .0037 .9585 -.9964 OF 20 .0513 .20489 .00705 .00375 .99625 .99295 .02659 .03158 .04314 5.1285 .5702 .9973 -.3041 CF 20 .0513 .20489 .00705 .00375 .99625 .99295 .02659 .03158 .04314 5.1285 5702 .9973 -.3041 CS 20 .0668 .20509 .00981 .01380 .98620 .99019 .03563 .03920 .08192 45 364 1.3445 .9940 .1669 NT 40 .3221 .24044 .05055 .00000 1.00000 .94945 .06587 .08234 .00000 5.9044 .0000 .9874 -1.0000 MB 40 .0483 .20516 .00645 .00000 1.00000 .99355 .02357 .02946 .00000 6.7514 .0000 .9984-1.000C RB 40 .0393 .20414 .00518 .00000 1.00000 .99483 .02095 .02619 .00000 6.8288 .0000 .9987 -1.0000 MD 40 .0495 .20529 .00661 .00000 1.00000 .99339 .02386 .02982 .00000 6.7425 .0000 .9983 -1.0000 RD 40 .0403 .20424 .00530 .00000 1.00000 .99470 .02117 .02646 .00000 6.8205 .0000 .9987 -1.0000 OR 40 .6266 .38802 .23503 .00000 1.00000 .76498 .21411 .26764 .00000 4.9873 .0000 .9412-1.0000 OS 40 .4933 .33335 .16669 .00000 1.00000 .83331 .19446 .24308 .00000 5.2322 .0000 .9583 -1.0000 OF 40 .0502 .20537 .00671 .00000 1.00000 .99329 .02405 .03006 .00000 6.7372 .0000 .9983 -1.0000 CF 40 .0502 .20537 .00671 .00000 1.00000 .99329 .02405 .03006 .00000 6.7372 .0000 .9983 -1.0000 CS 40 .0661 .20782 .00979 .00005 .99995 .99021 .03195 .03992 .00500 6.2250 .0079 .9975 -.9897 130 Table 10.2.1.1.3.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P*I,p = 5, mNz- .5,pNz = A N:p OLEX Rej Fp Fn Tp Tn s:Rej s:FpTn s:FnTp a" P A' B" NT 2 .2496 .15977 .04978 .67525 .32475 .95022 .11988 .09474 .25960 1.1925 3.5007 .7840 .6451 MB 2 .0321 .03400 .00572 .92358 .07643 .99428 .06255 .03246 .14609 1.0996 8.8159 .7491 .8509 RB 2 .0308 .03296 .00542 .92573 .07427 .99458 .05951 .03111 .14006 1.1034 9.0493 .7491 .8547 MD 2 .0328 .03467 .00583 .92208 .07792 .99417 .06307 .03274 .14726 1.1029 8.7881 .7494 .8506 RD 2 .0316 .03364 .00555 .92423 .07578 .99445 .06009 .03144 .14152 1.1055 8.9919 .7493 .8539 OR 2 .4994 .27457 .21530 .63653 .36348 .78470 .28055 .28423 .35553 .4390 1.2836 .6491 .1559 OS 2 .1618 .12597 .07605 .79915 .20085 .92395 .24248 .21250 .33793 .5936 1.9619 .6891 .3910 OF 2 .0461 .04432 .00828 .90163 .09838 .99172 .07163 .03917 .16593 1.1053 7.6728 .7517 .8305 CF 2 .0461 .04432 .00828 .90163 .09838 .99172 .07163 .03917 .16593 1.1053 7.6728 .7517 .8305 CS 2 .1032 .07101 .02110 .85413 .14588 .97890 .10210 .06892 .20998 .9773 4.5169 .7457 .7156 NT 4 .2423 .28735 .05037 .35718 .64283 .94963 .12291 .09935 .26963 2.0073 3.5965 .8864 .6552 MB 4 .0337 .12573 .00607 .69477 .30523 .99393 .11083 .03403 .26919 1.9988 20.4070 .8203 .9447 RB 4 .0293 .11958 .00507 .70865 .29135 .99493 .10356 .02966 .25450 2.0218 23.4462 .8176 .9523 MD 4 .0344 .12694 .00623 .69200 .30800 .99377 .11118 .03472 .26966 1.9971 20.0027 .8209 .9435 RD 4 .0301 .12084 .00522 .70572 .29428 .99478 .10395 .03024 .25523 2.0202 22.9514 .8182 .9512 OR 4 .7088 .51233 .34825 .24155 .75845 .65175 .26240 .32141 .30436 1.0914 .8438 .7926 -.1067 OS 4 .4369 .37738 .21455 .37838 .62163 .78545 .31401 .31158 .42306 1.1005 1.3030 .7933 .1652 OF 4 .0414 .13688 .00747 .66900 .33100 .99253 .11362 .03764 .27481 1.9968 17.5773 .8259 .9352 CF 4 .0414 .13688 .00747 .66900 .33100 .99253 .11362 .03764 .27481 1.9968 17.5773 .8259 .9352 CS 4 .1222 .18465 .02518 37615 .42385 .97482 .11925 .07470 .26279 1.7648 6.6603 .8374 .8173 NT 10 .2317 .41567 .04875 .03395 .96605 .95125 .06914 .09882 .09867 3.4828 .7456 .9785 -.1715 MB 10 .0403 .34855 .00750 .13988 .86013 .99250 .08325 .03865 .20024 3.5133 10.7411 .9626 .8835 RB 10 .0274 .33740 .00497 .16395 .83605 .99503 .08430 .03078 .20763 3.5565 17.1985 .9573 .9304 MD 10 .0413 .34936 .00768 .13813 .86187 .99232 .08284 .03908 .19886 3.5124 10.4254 .9630 .8796 RD 10 .0277 .33818 .00502 .16208 .83793 .99498 .08380 .03091 .20641 3.5606 16.9187 .9578 .9291 OR 10 .7957 .64683 .41425 .00430 .99570 .58575 .19686 .32611 .03751 2.8442 .0324 .8942 -.9653 OS 10 .7179 .61054 .35592 .00753 .99248 .64408 .20288 .33119 .06423 2.8006 .0557 .9074 -.9369 OF 10 .0433 .35138 .00808 .13368 .86633 .99192 .08182 .04012 .19568 3.5143 9.7492 .9640 .8705 CF 10 .0433 .35138 .00808 .13368 .86633 .99192 .08182 .04012 .19568 3.5143 9.7492 .9640 .8705 CS 10 .0873 .34674 .01817 .16040 .83960 .98183 .07755 .06462 .16344 3.0860 5.4622 .9537 .7661 NT 20 .2403 .42984 .04998 .00038 .99963 .95002 .05880 .09804 .00968 5.0156 .0132 .9874 -.9843 MB 20 .0432 .40362 .00813 .00315 .99685 .99187 .02644 .04035 .02899 5.1346 .4299 .9972 -.4396 RB 20 .0259 .40110 .00473 .00435 .99565 .99527 .02211 .03018 .03419 5.2183 .9274 .9977 -.0420 MD 20 .0443 .40381 .00833 .00297 .99703 .99167 .02651 .04079 .02824 5.1445 .3997 .9972 -.4717 RD 20 .0263 .40117 .00483 .00433 .99568 .99517 .02231 .03062 .03410 5.2131 .9056 .9977 -.0553 OR 20 .7959 .65439 .42398 .00000 1.00000 .57602 .19877 .33129 .00000 4.4566 .0000 .8940 • 1.0000 OS 20 .7261 .62316 .37193 .00000 1.00000 .62807 .20268 .33779 .00000 4.5916 .0000 .9070-1.0000 OF 20 .0457 .40404 .00863 .00285 .99715 .99137 .02687 .04161 .02747 5.1455 .3727 .9971 -.5015 CF 20 .0457 .40404 .00863 .00285 .99715 .99137 .02687 .04161 .02747 5.1455 .3727 .9971 -.5015 CS 20 .0728 .40573 .01463 .00762 .99238 .98537 .03821 .05659 .04328 4.6063 .5668 .9944 -.3117 NT 40 .2391 .43048 .05080 .00000 1.00000 .94920 .06076 .10126 .00000 5.9020 .0000 .9873 -1.0000 MB 40 .0449 .40514 .00857 .00000 1.00000 .99143 .02517 .04195 .00000 6.6487 .0000 .9979 -1.0000 RB 40 .0284 .40309 .00515 .00000 1.00000 .99485 .01875 .03125 .00000 6.8305 .0000 .9987 -1.0000 MD 40 .0457 .40523 .00872 .00000 1.00000 .99128 .02541 .04235 .00000 6.6423 .0000 .9978 -1.000C RD 40 .0290 .40317 .00528 .00000 1.00000 .99472 .01905 .03175 .00000 6.8216 .0000 .9987 -1.0000 OR 40 .7983 .65469 .42448 .00000 1.00000 .57552 .19784 .32974 .00000 4.4553 .0000 .8939 -1.0000 OS 40 .7317 .62250 .37083 .00000 1.00000 .62917 .20118 .33530 .00000 4.5945 .0000 .9073 -1.0000 OF 40 .0462 .40530 .00883 .00000 1.00000 .99117 .02561 .04269 .00000 6.6374 .0000 .9978 -1.0000 CF 40 .0462 .40530 .00883 .00000 1.00000 .99117 .02561 .04269 .00000 6.6374 .0000 .9978 -1.0000 CS 40 .0753 .409401 .01567 .00000 1.00000 .98433 .03644 .06073 .00000 6.4177 .0000 .9961 -1.0000 Table 10.2.1.1.3.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I, p = 5, mNz = .5, pNz = .6 N:p CLEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp d' P A' B" NT 2 .1609 .21461 .04905 .67502 .32498 .95095 .16638 .12246 .26725 1.2003 3.5435 .7848 .6493 MB 2 .0225 .05028 .00618 .92032 .07968 .99383 .08881 .04293 .14453 1.0948 8.4981 .7491 .8456 RB 2 .0214 .04713 .00573 .92527 .07473 .99428 .07991 .03983 .13072 1.0872 8.6556 .7482 .8479 MD 2 .0229 .05115 .00630 .91895 .08105 .99370 .08963 .04342 .14593 1.0968 8.4566 .7494 .8449 RD 2 .0219 .04797 .00585 .92395 .07605 .99415 .08069 .04020 .13201 1.0889 8.6051 .7484 .8471 OR 2 .5505 .43369 .32615 .49462 .50538 .67385 .34546 .36505 .39575 .4641 1.1067 .6552 .0643 OS 2 .2150 .23357 .14330 .70625 .29375 .85670 .35265 .31012 .42194 .5231 1.5229 .6719 .2565 OF 2 .0303 .06395 .00840 .89902 .10098 .99160 .09982 .05042 .16239 1.1151 7.7255 .7525 .8319 CF 2 .0303 .06395 .00840 .89902 .10098 .99160 .09982 .05042 .16239 1.1151 7.7255 .7525 .8319 CS 2 .0992 .14015 .03335 .78865 .21135 .96665 .16306 .11226 .24410 1.0319 3.8955 .7566 .6759 NT 4 .1574 .40587 .04960 .35662 .64338 .95040 .17856 .12774 .28569 2.0163 3.6388 .8869 .6591 MB 4 .0232 .19398 .00658 .68108 .31892 .99343 .17931 .04515 .29567 2.0090 19.3679 .8234 .9416 RB 4 .0175 .17534 .00470 .71090 .28910 .99530 .15844 .03627 .26333 2.0411 24.9787 .8174 .9555 MD 4 .0236 .19573 .00680 .67832 .32168 .99320 .17979 .04681 .29619 2.0047 18.8684 .8240 .9400 RD 4 .0181 .17704 .00485 .70817 .29183 .99515 .15921 .03676 .26454 2.0383 24.3959 .8179 .9544 OR 4 .7684 .70457 .49203 .15373 .84627 .50798 .25876 .37033 .27152 1.0405 .5942 .7790 -.3153 OS 4 .5520 57298 .36315 .28713 .71287 .63685 .37152 .39631 .42461 .9118 .9080 .7599 -.061C OF 4 .0284 .20951 .00818 .65627 .34373 .99183 .18249 .05126 .30008 1.9987 16.4693 .8286 .9306 CF 4 .0284 .20951 .00818 .65627 .34373 .99183 .18249 .05126 .30008 1.9987 16.4693 .8286 .9306 CS 4 .1206 .32448 .04085 .48643 .51357 .95915 .18276 .12388 .28176 1.7749 4.5485 .8533 .7288 NT 10 .1506 .59886 .04818 .03402 .96598 .95183 .07586 .12762 .09385 3.4876 .7539 .9786 -.1651 MB 10 .0371 .52855 .01148 .12673 .87327 .98853 .12477 .06490 .20172 3.4162 6.9178 .9647 .8141 RB 10 .0172 .50225 .00473 .16607 .83393 .99528 .12881 .03770 .21366 3.5652 18.1304 .9569 .9343 MD 10 .0377 .52972 .01170 .12493 .87507 .98830 .12382 .06558 .19995 3.4175 6.7346 .9651 .8087 RD 10 .0174 .50338 .00480 .16423 .83577 .99520 .12798 .03827 .21223 3.5671 17.7495 .9573 .9327 OR 10 .8400 .82267 .55998 .00220 .99780 .44003 .14481 .35791 .02540 2.6971 .0175 .8584 -.9823 OS 10 .7936 .80702 .52530 .00517 .99483 .47470 .15843 .37533 .06215 2.5010 .0374 .8653 -.9596 OF 10 .0400 .53235 .01245 .12105 .87895 .98755 .12187 .06770 .19631 3.4127 6.2417 .9658 .7928 CF 10 .0400 .53235 .01245 .12105 .87895 .98755 .12187 .06770 .19631 3.4127 6.2417 .9658 .7928 CS 10 .0895 .54754 .03090 .10803 .89197 .96910 .09641 .11106 .13625 3.1048 2.6619 .9635 .5258 NT 20 .1520 .61940 .04898 .00032 .99968 .95103 .05181 .12902 .00726 5.0718 .0115 .9877 -.9865 MB 20 .0437 .60409 .01380 .00238 .99762 .98620 .03144 .07166 .02088 5.0253 .2109 .9959 -.7026 RB 20 .0180 .59937 .00508 .00443 .99557 .99492 .02338 .03944 .02862 5.1878 .8864 .9976 -.0672 MD 20 .0444 .60424 .01410 .00233 .99767 .98590 .03185 .07298 .02055 5.0237 .2031 .9959 -.7131 RD 20 .0183 .59942 .00518 .00442 .99558 .99483 .02349 .03990 .02858 5.1823 .8682 .9976 -.0787 OR 20 .8457 .82655 .56638 .00000 1.00000 .43363 .14270 .35674 .00000 4.0977 .0000 .8584 -1.0000 OS 20 .8079 .81426 .53565 .00000 1.00000 .46435 .14894 .37235 .00000 4.1754 .0000 .8661 • 1.0000 OF 20 .0448 .60431 .01420 .00228 .99772 .98580 .03185 .07314 .02035 5.0278 .1979 .9959 -.7201 CF 20 .0448 .60431 .01420 .00228 .99772 .98580 .03185 .07314 .02035 5.0278 .1979 .9959 -.7201 CS 20 .0803 .60809 .02833 .00540 .99460 .97168 .04731 .10784 .02970 4.4551 .2387 .9915 -.6734 NT 40 .1597 .62071 .05178 .00000 1.00000 .94823 .05346 .13366 .00000 5.8928 .0000 .9871 -1.0000 MB 40 .0444 .60562 .01405 .00000 1.00000 .98595 .02974 .07435 .00000 6.4608 .0000 .9965 -1.0000 RB 40 .0186 .60213 .00533 .00000 1.00000 .99468 .01639 .04096 .00000 6.8189 .0000 .9987 -1.0000 MD 40 .0453 .60573 .01433 .00000 1.00000 .98568 .03000 .07501 .00000 6.4532 .0000 .9964-1.000C RD 40 .0191 .60218 .00545 .00000 1.00000 .99455 .01653 .04133 .00000 6.8108 .0000 .9986-1.0000 OR 40 .8535 .82771 .56928 .00000 1.00000 .43073 .14101 .35254 .00000 4.0904 .0000 .8577 -1.0000 OS 40 .8111 .81453 .53633 .00000 1.00000 .46367 .14809 .37022 .00000 4.1737 .0000 .8659 -1.0000 OF 40 .0460 .60581 .01453 .00000 1.00000 .98548 .03016 .07539 .00000 6.4477 .0000 .9964-1.0000 CF 40 .0460 .60581 .01453 .00000 1.00000 .98548 .03016 .07539 .00000 6.4477 .0000 .9964-1.0000 CS 40 .0805 .61165] .02913 .00000 1.00000 .97088 .04474 .11184 .00000 6.1587 .0000 .9927 -1.0000 132 Table 10.2.1.1.3.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P * 1,^  = 5, mNz = .5,pNz = .8 N:p CtEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' A' B" NT 2 .0874 .26936 .04730 .67513 .32488 .95270 .18638 .15816 .22721 1.2175 3.6475 .7864 .6591 MB 2 .0107 .06562 .00575 .91941 .08059 .99425 .10481 .05694 .12805 1.1260 9.1303 .7510 .8567 RB 2 .0089 .06058 .00475 .92546 .07454 .99525 .09122 .05150 .11240 1.1507 10.1993 .7516 .8717 MD 2 .0108 .06683 .00580 .91791 .08209 .99420 .10565 .05715 .12912 1.1329 9.1874 .7515 .8578 RD 2 .0093 .06175 .00495 .92405 .07595 .99505 .09209 .05245 .11342 1.1465 9.9729 .7515 .8688 OR 2 .5781 .57126 .43315 .39421 .60579 .56685 .33796 .41602 .35491 .4367 .9784 .6474 -.0139 OS 2 .2765 .32957 .22480 .64424 .35576 .77520 .41157 .38527 .43561 .3863 1.2429 .6343 .1361 OF 2 .0153 .08405 .00825 .89700 .10300 .99175 .11967 .06825 .14577 1.1330 7.9625 .7539 .8373 CF 2 .0153 .08405 .00825 .89700 .10300 .99175 .11967 .06825 .14577 1.1330 7.9625 .7539 .8373 CS 2 .0578 .20596 .03165 .75046 .24954 .96835 .20239 .13257 .24217 1.1811 4.4634 .7745 .7187 NT 4 .0896 .52463 .04880 .35641 .64359 .95120 .19439 .16131 .24154 2.0247 3.6856 .8874 .6634 MB 4 .0193 .26816 .01095 .66754 .33246 .98905 .21840 .08158 .26876 1.8590 12.5920 .8230 .9069 RB 4 .0097 .23247 .00500 .71066 .28934 .99500 .17999 .05124 .22410 2.0205 23.6475 .8171 .9528 MD 4 .0197 .27067 .01115 .66445 .33555 .98885 .21885 .08217 .26932 1.8606 12.4405 .8237 .9058 RD 4 .0098 .23450 .00505 .70814 .29186 .99495 .18080 .05148 .22510 2.0244 23.5344 .8177 .9525 OR 4 .8021 .87012 .64045 .07246 .92754 .35955 .16266 .38661 .15896 1.0980 .3687 .7770 -.5481 OS 4 .6593 .76468 33440 .17775 .82225 .46560 .33640 .43172 .35098 .8376 .6550 .7421 -.2599 OF 4 .0219 .28877 .01235 .64213 .35788 .98765 .22082 .08616 .27157 1.8819 11.6592 .8288 .8992 CF 4 .0219 .28877 .01235 .64213 .35788 .98765 .22082 .08616 .27157 1.8819 11.6592 .8288 .8992 CS 4 .0751 .47140 .04115 .42104 .57896 .95885 .19536 .14995 .23946 1.9367 4.4353 .8725 .7214 NT 10 .0884 .78272 .04795 .03359 .96641 .95205 .06541 .15946 .07945 3.4956 .7489 .9788 -.1689 MB 10 .0323 .72334 .01795 .10031 .89969 .98205 .12997 .10224 .16083 3.3778 3.9829 .9695 .6732 RB 10 .0103 .66915 .00530 .16489 .83511 .99470 .14362 .05265 .17991 3.5302 16.2924 .9570 .9263 MD 10 .0331 .72463 .01835 .09880 .90120 .98165 .12893 .10315 .15953 3.3775 3.8656 .9697 .6635 RD 10 .0106 .67073 .00550 .16296 .83704 .99450 .14275 .05404 .17885 3.5251 15.6449 .9574 .9229 OR 10 .8421 .93750 .68930 .00045 .99955 .31070 .07453 .37119 .00847 2.8262 .0046 .8272 -.9958 OS 10 .8196 .93515 .67800 .00056 .99944 .32200 .07771 .38410 .01316 2.7951 .0055 .8300 -.9949 OF 10 .0340 .72673 .01890 .09631 .90369 .98110 .12709 .10485 .15718 3.3799 3.6998 .9702 .6487 CF 10 .0340 .72673 .01890 .09631 .90369 .98110 .12709 .10485 .15718 3.3799 3.6998 .9702 .6487 CS 10 .0702 .75177 .03970 .07021 .92979 .96030 .07664 .15125 .09249 3.2284 1.5713 .9710 .2626 NT 20 .0898 .80969 .04965 .00030 .99970 .95035 .03300 .16466 .00612 5.0799 .0108 .9875 -.9874 MB 20 .0458 .80436 .02675 .00124 .99876 .97325 .02770 .12850 .01323 4.9572 .0662 .9930 -.9094 RB 20 .0102 .79757 .00530 .00436 .99564 .99470 .02171 .05312 .02509 5.1783 .8407 .9976 -.0966 MD 20 .0466 .80447 .02720 .00121 .99879 .97280 .02780 .12947 .01311 4.9562 .0641 .9929 -.9125 RD 20 .0103 .79759 .00535 .00435 .99565 .99465 .02162 .05335 .02506 5.1760 .8316 .9976 -.1026 OR 20 .8450 .93793 .68965 .00000 1.00000 .31035 .07386 .36929 .00000 3.7700 .0000 .8276-1.0000 OS 20 .8237 .93580 .67900 .00000 1.00000 .32100 .07632 .38161 .00000 3.8000 .0000 .8302 -1.OOO0 OF 20 .0468 .80452 .02730 .00118 .99883 .97270 .02774 .12964 .01282 4.9641 .0621 .9929 -.9153 CF 20 .0468 .80452 .02730 .00118 .99883 .97270 .02774 .12964 .01282 4.9641 .0621 .9929 -.9153 CS 20 .0612 .80623 .03560 .00111 .99889 .96440 .03027 .14675 .01174 4.8626 .0474 .9908 -.9373 NT 40 .0896 .80985 .04925 .00000 1.00000 .95075 .03265 .16325 .00000 5.9171 .0000 .9877 -1.0000 MB 40 .0459 .80536 .02680 .00000 1.00000 .97320 .02572 .12858 .00000 6.1949 .0000 .9933 -1.0000 RB 40 .0097 .80101 .00505 .00000 1.00000 .99495 .01039 .05196 .00000 6.8373 .0000 .9987 -1.0000 MD 40 .0466 .80543 .02715 .00000 1.00000 .97285 .02584 .12919 .00000 6.1893 .0000 .9932 -1.0000 RD 40 .0100 .80104 .00520 .00000 1.00000 .99480 .01053 .05266 .00000 6.8271 .0000 .9987 -1.0OO0 OR 40 .8434 .93768 .68840 .00000 1.00000 .31160 .07403 .37016 .00000 3.7736 .0000 .8279 -l.OOOO OS 40 .8239 .93573 .67865 .00000 1.00000 .32135 .07628 .38141 .00000 3.8010 .0000 .8303 -1.0000 OF 40 .0468 .80545 .02725 .00000 1.00000 .97275 .02587 .12936 .00000 6.1877 .0000 .9932 -1.0000 CF 40 .0468 .80545 .02725 .00000 1.00000 .97275 .02587 .12936 .00000 6.1877 .0000 .9932-1.000C CS 40 .0611 .80700 .03500 .00000 1.00000 .96500 .02879 .14397 .00000 6.0768 .0000 .9913-1.000C 133 Table 10.2.1.2.1.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P*\,p = 10, mNz = .l,pNz = .2 N:p OEX Rej Fp Fn Tp Tn s.Rej s:FpTn s.FnTp d' P A' B" NT 2 .8449 .05427 .05022 .92956 .07044 .94978 .03427 .03650 .08902 .1702 1.3036 .5771 .1571 MB 2 .0378 .00132 .00107 .99768 .00232 .99893 .00538 .00544 .01635 .2395 2.0273 .6352 .3688 RB 2 .0378 .00132 .00107 .99769 .00231 .99893 .00537 .00544 .01632 .2380 2.0185 .6346 .3668 MD 2 .0384 .00135 .00109 .99759 .00241 .99891 .00546 .00550 .01664 .2462 2.0631 .6374 .3772 RD 2 .0383 .00135 .00108 .99759 .00241 .99892 .00544 .00548 .01664 .2477 2.0728 .6380 .3794 OR 2 .3951 .06235 .06110 .93264 .06736 .93890 .13031 .12969 .15125 .0498 1.0787 .5249 .0454 OS 2 .0629 .00444 .00388 .99334 .00666 .99612 .02891 .02777 .04371 .1867 1.6154 .6048 .2617 OF 2 .0552 .00191 .00159 .99679 .00321 .99841 .00652 .00669 .01920 .2246 1.8914 .6267 .3372 CF 2 .0552 .00191 .00159 .99679 .00321 .99841 .00652 .00669 .01920 .2246 1.8914 .6267 .3372 CS 2 .0607 .00264 .00231 .99607 .00393 .99769 .01069 .01045 .02392 .1741 1.6127 .6033 .2585 NT 4 .8398 .05857 .04974 .90610 .09390 .95026 .03561 .03632 .10217 .3303 1.6316 .6292 .2857 MB 4 .0386 .00168 .00109 .99599 .00401 .99891 .00607 .00552 .02102 .4122 3.2470 .6825 .5703 RB 4 .0385 .00168 .00109 .99599 .00401 .99891 .00606 .00551 .02102 .4130 3.2546 .6827 .5711 MD 4 .0393 .00171 .00111 .99591 .00409 .99889 .00613 .00556 .02121 .4134 3.2504 .6826 .5708 RD 4 .0392 .00171 .00111 .99591 .00409 .99889 .00611 .00556 .02121 .4142 3.2579 .6828 .5716 OR 4 .4548 .07980 .07770 .91180 .08820 .92230 .14467 .14492 .16695 .0688 1.1000 .5326 .0576 OS 4 .0581 .00451 .00354 .99161 .00839 .99646 .02956 .02709 .04882 .3019 2.1544 .6458 .4049 OF 4 .0480 .00203 .00136 .99531 .00469 .99864 .00663 .00612 .02261 .3995 3.0579 .6783 .5489 CF 4 .0480 .00203 .00136 .99531 .00469 .99864 .00663 .00612 .02261 .3995 3.0579 .6783 .5489 CS 4 .0724 .00346 .00258 .99302 .00698 .99742 .01173 .01032 .03171 .3384 2.4331 .6586 .4583 NT 10 .8412 .07352 .05024 .83339 .16661 .94976 .04042 .03697 .13579 .6748 2.4126 .7052 .4885 MB 10 .0385 .00307 .00109 .98900 .01100 .99891 .00841 .00549 .03545 .7745 7.9547 .7277 .8182 RB 10 .0382 .00306 .00108 .98902 .01098 .99892 .00837 .00547 .03539 .7760 7.9969 .7279 .8191 MD 10 .0394 .00316 .00112 .98867 .01133 .99888 .00853 .00557 .03590 .7783 7.9776 .7279 .8189 RD 10 .0393 .00315 .00111 .98871 .01129 .99889 .00848 .00554 .03581 .7783 7.9868 .7279 .8191 OR 10 .5951 .13628 .12920 .83539 .16461 .87080 .19232 .19142 .23096 .1545 1.1767 .5640 .1000 OS 10 .0730 .01231 .00841 .97209 .02791 .99159 .06306 .05536 .10941 .4781 2.7975 .6796 .5298 OF 10 .0411 .00333 .00117 .98802 .01198 .99883 .00876 .00570 .03698 .7863 8.0407 .7284 .8207 CF 10 .0411 .00333 .00117 .98802 .01198 .99883 .00876 .00570 .03698 .7863 8.0407 .7284 .8207 CS 10 .1242 .00887 .00469 .97440 .02560 .99531 .02013 .01431 .06492 .6484 4.3683 .7095 .6849 NT 20 .8370 .09820 .04990 .70858 .29142 .95010 .04527 .03665 .17102 1.0966 3.3319 .7707 .6266 MB 20 .0426 .00733 .00121 .96816 .03184 .99879 .01309 .00577 .06075 1.1799 17.8877 .7482 .9248 RB 20 .0423 .00730 .00119 .96829 .03171 .99881 .01298 .00573 .06028 1.1809 17.9776 .7482 .9252 MD 20 .0436 .00747 .00123 .96760 .03240 .99877 .01319 .00583 .06126 1.1808 17.7706 .7483 .9244 RD 20 .0435 .00743 .00123 .96779 .03221 .99877 .01310 .00582 .06081 1.1788 17.7216 .7482 .9241 OR 20 .7674 .23810 .21436 .66694 .33306 .78564 .23857 .23709 .30427 .3599 1.2461 .6269 .1376 OS 20 .1645 .04708 .03229 .89377 .10623 .96771 .13328 .11592 .23434 .6013 2.5358 .6931 .5048 OF 20 .0450 .00766 .00127 .96679 .03321 .99873 .01338 .00591 .06214 1.1824 17.6287 .7484 .9239 CF 20 .0450 .00766 .00127 .96679 .03321 .99873 .01338 .00591 .06214 1.1824 17.6287 .7484 .9239 CS 20 .2055 .02257 .00776 .91822 .08178 .99224 .03042 .01748 .11618 1.0266 7.0800 .7449 .8139 NT 40 .8415 .14361 .04983 .48126 .51874 .95018 .04791 .03641 .19073 1.6936 3.8747 .8494 .6812 MB 40 .0407 .02174 .00115 .89588 .10412 .99885 .02279 .00563 .11145 1.7901 47.2206 .7730 .9757 RB 40 .0400 .02151 .00113 .89697 .10303 .99887 .02241 .00557 .10965 1.7899 47.7069 .7728 .9759 MD 40 .0414 .02202 .00117 .89456 .10544 .99883 .02292 .00567 .11201 1.7923 46.9278 .7733 .9755 RD 40 .0406 .02177 .00114 .89574 .10426 .99886 .02251 .00560 .11014 1.7923 47.4745 .7731 .9758 OR 40 .9354 .40941 .34450 .33096 .66904 .65550 .24508 .25886 .28908 .8375 .9846 .7451 -.0098 OS 40 .4740 .18579 .13030 .59226 .40774 .86970 .23824 .21475 .40430 .8916 1.8323 .7499 .3612 OF 40 .0421 .02222 .00119 .89364 .10636 .99881 .02298 .00572 .11229 1.7923 46.5129 .7735 .9753 CF 40 .0421 .02222 .00119 .89364 .10636 .99881 .02298 .00572 .11229 1.7923 46.5129 .7735 .9753 CS 40 .2871 .05757 .01081 .75538 .24462 .98919 .04055 .01973 .17165 1.6056 11.0157 .7980 .8906 Table 10.2.1.2.1.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I,p = 10, mNz = .l,pNz = .4 N:p OLEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp d' P A' B" NT 2 .7512 .05828 .04996 .92923 .07077 .95004 .03615 .04194 .06452 .1752 1.3137 .5790 .1616 MB 2 .0285 .00156 .00107 .99770 .00230 .99893 .00587 .00626 .01142 .2372 2.0145 .6344 .3658 RB 2 .0285 .00156 .00107 .99770 .00230 .99893 .00587 .00626 .01142 .2372 2.0145 .6344 .3658 MD 2 .0296 .00161 .00111 .99764 .00236 .99889 .00598 .00637 .01156 .2344 1.9933 .6331 .3609 RD 2 .0294 .00160 .00110 .99764 .00236 .99890 .00594 .00635 .01155 .2357 2.0013 .6336 .3628 OR 2 .4038 .07881 .07627 .91739 .08261 .92373 .15040 .15082 .15983 .0429 1.0623 5209 .0365 OS 2 .0545 .00592 .00481 .99243 .00757 .99519 .03875 .03602 .04650 .1597 1.4928 .5916 .2209 OF 2 .0405 .00217 .00153 .99686 .00314 .99847 .00698 .00749 .01337 .2296 1.9227 .6289 .3451 CF 2 .0405 .00217 .00153 .99686 .00314 .99847 .00698 .00749 .01337 .2296 1.9227 .6289 .3451 CS 2 .0586 .00385 .00278 .99454 .00546 .99722 .01330 .01247 .02197 .2277 1.8323 .6235 .3245 NT 4 .7520 .06766 .05017 .90609 .09391 .94983 .03952 .04204 .07586 .3262 1.6206 .6280 .2821 MB 4 .0292 .00223 .00109 .99607 .00393 .99891 .00709 .00633 .01511 .4061 3.1955 .6813 5642 RB 4 .0292 .00223 .00109 .99607 .00393 .99891 .00709 .00633 .01511 .4061 3.1955 .6813 .5642 MD 4 .0297 .00228 .00111 .99596 .00404 .99889 .00717 .00638 .01530 .4100 3.2222 .6820 .5675 RD 4 .0296 .00228 .00111 .99597 .00403 .99889 .00715 .00637 .01527 .4105 3.2281 .6821 .5682 OR 4 5192 .12228 .11694 .86973 .13027 .88306 .18774 .18752 .20089 .0653 1.0785 .5293 .0463 OS 4 .0600 .00991 .00721 .98604 .01396 .99279 .05828 .05160 .07304 .2480 1.7791 .6225 .3156 OF 4 .0355 .00270 .00133 .99523 .00477 .99867 .00779 .00697 .01662 .4123 3.1702 .6811 .5626 CF 4 .0355 .00270 .00133 .99523 .00477 .99867 .00779 .00697 .01662 .4123 3.1702 .6811 .5626 CS 4 .0903 .00724 .00420 .98820 .01180 .99580 .01839 .01466 .03361 .3720 2.4872 .6629 .4720 NT 10 .7534 .09725 .05078 .83305 .16695 .94922 .04863 .04270 .10217 .6711 2.3956 .7046 .4853 MB 10 .0286 .00507 .00108 .98893 .01107 .99892 .01094 .00633 .02546 .7798 8.0722 .7282 .8209 RB 10 .0285 .00505 .00107 .98898 .01102 .99893 .01087 .00632 .02530 .7793 8.0694 .7281 .8208 MD 10 .0291 .00520 .00110 .98864 .01136 .99890 .01106 .00639 .02573 .7848 8.1306 .7284 .8223 RD 10 .0290 .00517 .00109 .98871 .01129 .99891 .01096 .00638 .02552 .7833 8.1108 .7284 .8219 OR 10 .7464 .26960 .24715 .69672 .30328 .75285 .26537 .26391 .28912 .1685 1.1063 .5649 .0635 OS 10 .1152 .04202 .03051 .94071 .05929 .96949 .14363 .12572 .17915 .3126 1.7105 .6288 .3069 OF 10 .0308 .00552 .00116 .98794 .01206 .99884 .01142 .00655 .02658 .7909 8.1366 .7287 .8229 CF 10 .0308 .00552 .00116 .98794 .01206 .99884 .01142 .00655 .02658 .7909 8.1366 .7287 .8229 CS 10 .1924 .02492 .00945 .95188 .04812 .99055 .03627 .02207 .07285 .6840 3.9423 .7106 .6606 NT 20 .7431 .14718 .04995 .70697 .29303 .95005 .05819 .04263 .13022 1.1008 3.3377 .7713 .6272 MB 20 .0324 .01366 .00122 .96767 .03233 .99878 .01868 .00674 .04531 1.1825 17.8854 .7483 .9249 RB 20 .0316 .01352 .00119 .96799 .03201 .99881 .01839 .00663 .04469 1.1865 18.1954 .7484 .9262 MD 20 .0330 .01388 .00124 .96716 .03284 .99876 .01880 .00680 .04560 1.1841 17.8221 .7484 .9247 RD 20 .0325 .01376 .00122 .96744 .03256 .99878 .01852 .00672 .04500 1.1856 17.9893 .7485 .9254 OR 20 .9353 51333 .45039 .39227 .60773 .54961 .27930 .29066 .29711 .3981 .9708 .6363 -.0188 OS 20 .3318 .18756 .14383 .74684 .25316 .85617 .29823 .26460 .36738 .3987 1.4112 .6399 .2111 OF 20 .0337 .01419 .00127 .96644 .03356 .99873 .01899 .00686 .04610 1.1876 17.8053 .7486 .9247 CF 20 .0337 .01419 .00127 .96644 .03356 .99873 .01899 .00686 .04610 1.1876 17.8053 .7486 .9247 CS 20 .3339 .07031 .01730 .85018 .14982 .98270 .05610 .02876 .12163 1.0758 5.4440 .7548 .7645 NT 40 .7439 .23760 .05011 .48116 51884 .94989 .06395 .04271 .14626 1.6911 3.8572 .8492 .6797 MB 40 .0320 .04286 .00120 .89465 .10535 .99880 .03408 .00664 .08461 1.7840 45.8029 .7732 .9749 RB 40 .0304 .04186 .00114 .89707 .10293 .99886 .03285 .00645 .08163 1.7869 47.3175 .7727 .9757 MD 40 .0328 .04343 .00123 .89327 .10673 .99877 .03430 .00672 .08513 1.7842 45.2143 .7735 .9746 RD 40 .0309 .04241 .00116 .89571 .10429 .99884 .03304 .00650 .08209 1.7895 47.0671 .7730 .9756 OR 40 .9975 .74774 .64184 .09339 .90661 .35816 .17897 .23884 .12901 .9568 .4469 .7578 -.4616 OS 40 .8033 57515 .46509 .25976 .74024 .53491 .32810 .32658 .37238 .7317 .8158 .7215 -.1281 OF 40 .0331 .04381 .00125 .89236 .10764 .99875 .03448 .00681 .08554 1.7846 44.8760 .7737 .9744 CF 40 .0331 .04381 .00125 .89236 .10764 .99875 .03448 .00681 .08554 1.7846 44.8760 .7737 .9744 CS 40 .4464 .16366 .02393 .62673 .37327 .97607 .06409 .03254 .14558 1.6554 6.7209 .8234 .8184 Table 10.2.1.2.1.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P*I,p = 10, mNz = ,l,pNz = .6 N:p OEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp d' P A' B" NT 2 .5971 .06201 .04956 .92969 .07031 .95044 .03837 .05137 .05383 .1757 1.3156 .5792 .1624 MB 2 .0187 .00176 .00105 .99777 .00223 .99895 .00628 .00765 .00919 .2320 1.9871 .6326 .3592 RB 2 .0187 .00176 .00105 .99777 .00223 .99895 .00628 .00765 .00919 .2320 1.9871 .6326 .3592 MD 2 .0192 .00181 .00108 .99770 .00230 .99892 .00640 .00774 .00931 .2341 1.9955 .6332 .3613 RD 2 .0191 .00180 .00107 .99771 .00229 .99893 .00636 .00772 .00930 .2346 1.9991 .6334 .3622 OR 2 .4034 .09925 .09469 .89771 .10229 .90531 .17445 .17551 .18064 .0438 1.0581 .5207 .0344 OS 2 .0459 .00777 .00611 .99112 .00888 .99389 .04926 .04622 .05346 .1355 1.3914 .5788 .1839 OF 2 .0264 .00246 .00149 .99689 .00311 .99851 .00752 .00916 .01087 .2327 1.9419 .6302 .3498 CF 2 .0264 .00246 .00149 .99689 .00311 .99851 .00752 .00916 .01087 .2327 1.9419 .6302 .3498 CS 2 .0535 .00567 .00357 .99293 .00707 .99643 .01723 .01639 .02291 .2369 1.8391 .6248 .3278 NT 4 .6040 .07674 .05031 .90563 .09437 .94969 .04423 .05168 .06521 .3275 1.6227 .6283 .2828 MB 4 .0192 .00278 .00108 .99608 .00392 .99892 .00804 .00774 .01244 .4089 3.2249 .6819 .5676 RB 4 .0192 .00277 .00108 .99610 .00390 .99892 .00799 .00774 .01235 .4073 3.2112 .6816 .5660 MD 4 .0193 .00284 .00108 .99599 .00401 .99892 .00813 .00776 .01262 .4156 3.2803 .6833 .5740 RD 4 .0193 .00283 .00108 .99601 .00399 .99892 .00807 .00776 .01250 .4134 3.2613 .6828 .5719 OR 4 .5449 .17081 .16024 .82214 .17786 .83976 .22936 .22940 .23789 .0699 1.0693 .5300 .0415 OS 4 .0585 .01727 .01240 .97948 .02052 .98760 .08839 .07710 .09864 .2013 1.5398 .6010 .2427 OF 4 .0231 .00335 .00129 .99529 .00471 .99871 .00881 .00845 .01365 .4167 3.2173 .6822 .5680 CF 4 .0231 .00335 .00129 .99529 .00471 .99871 .00881 .00845 .01365 .4167 3.2173 .6822 .5680 CS 4 .0896 .01276 .00598 .98273 .01727 .99402 .02723 .02066 .03892 .3995 2.5199 .6662 .4811 NT 10 3989 .12044 .05041 .83287 .16713 .94959 .05749 .05251 .08845 .6753 2.4113 .7053 .4882 MB 10 .0187 .00713 .00106 .98883 .01117 .99894 .01317 .00777 .02129 .7880 8.2551 .7288 .8249 RB 10 .0187 .00708 .00106 .98890 .01110 .99894 .01303 .00771 .02109 .7873 8.2518 .7287 .8248 MD 10 .0190 .00731 .00108 .98853 .01147 .99892 .01337 .00782 .02163 .7934 8.3252 .7291 .8265 RD 10 .0189 .00724 .00107 .98866 .01134 .99893 .01317 .00780 .02129 .7908 8.2872 .7289 .8257 OR 10 .8334 .42006 .37919 .55269 .44731 .62081 .30457 .30740 .31601 .1752 1.0393 .5655 .0245 OS 10 .1693 .09562 .07404 .89000 .11000 .92596 .23582 .20844 .25903 .2198 1.3415 .5914 .1763 OF 10 .0200 .00777 .00113 .98780 .01220 .99887 .01380 .00801 .02234 .8020 8.3875 .7295 .8282 CF 10 .0200 .00777 .00113 .98780 .01220 .99887 .01380 .00801 .02234 .8020 8.3875 .7295 .8282 CS 10 .2187 .04904 .01542 .92855 .07145 .98458 .05491 .03292 .08164 .6940 3.5170 .7103 .6275 NT 20 .5958 .19574 .05028 .70729 .29271 .94972 .07273 .05256 .11587 1.0966 3.3184 .7709 .6251 MB 20 .0223 .01980 .00126 .96784 .03216 .99874 .02337 .00837 .03837 1.1720 17.3754 .7480 .9225 RB 20 .0219 .01951 .00123 .96830 .03170 .99877 .02290 .00830 .03762 1.1710 17.4530 .7479 .9228 MD 20 .0228 .02013 .00128 .96730 .03270 .99872 .02355 .00846 .03865 1.1728 17.2654 .7481 .9221 RD 20 .0223 .01984 .00126 .96776 .03224 .99874 .02305 .00837 .03787 1.1731 17.4100 .7480 .9227 OR 20 .9814 .72023 .63628 .22381 .77619 .36372 .23392 .27173 .22902 .4109 .7964 .6412 -.1424 OS 20 .4848 .36833 .30357 .58850 .41150 .69643 .40176 .36752 .43442 .2905 1.1131 .6043 .0678 OF 20 .0234 .02057 .00132 .96659 .03341 .99868 .02384 .00856 .03914 1.1747 17.1670 .7482 .9217 CF 20 .0234 .02057 .00132 .96659 .03341 .99868 .02384 .00856 .03914 1.1747 17.1670 .7482 .9217 CS 20 .3713 .13439 .02821 .79483 .20517 .97179 .08129 .04310 .12533 1.0846 4.3975 .7612 .7122 NT 40 .5908 .33160 .04991 .48061 .51939 .95009 .08056 .05262 .12952 1.6943 3.8690 .8495 .6807 MB 40 .0217 .06484 .00123 .89275 .10725 .99877 .04529 .00837 .07521 1.7861 45.2485 .7737 .9746 RB 40 .0202 .06252 .00113 .89656 .10344 .99887 .04277 .00793 .07111 1.7907 47.6301 .7729 .9759 MD 40 .0221 .06570 .00126 .89133 .10867 .99874 .04560 .00844 .07572 1.7883 44.9384 .7740 .9744 RD 40 .0208 .06332 .00117 .89525 .10475 .99883 .04300 .00804 .07148 1.7892 46.8052 .7731 .9755 OR 40 .9999 .89478 .79484 .03860 .96140 .20516 .09835 .18220 .06107 .9438 .2945 .7463 -.6292 OS 40 .9145 .80569 .69573 .12101 .87899 .30427 .26688 .28958 .27386 .6578 .5751 .7027 -.3312 OF 40 .0223 .06624 .00127 .89044 .10956 .99873 .04589 .00848 .07619 1.7905 44.8417 .7742 .9744 CF 40 .0223 .06625 .00127 .89043 .10957 .99873 .04589 .00848 .07619 1.7905 44.8427 .7742 .9744 CS 40 .4713 .28821 .03801 .54499 .45501 .96199 .08454 .04883 .13329 1.6612 4.7951 .8375 .7430 Table 10.2.1.2.1.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P * \,p = 10, mNz = ,\>pNz - .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .3528 .06615 .04873 .92949 .07051 .95127 .04115 .07389 .04807 .1852 1.3362 5829 .1714 MB 2 .0107 .00202 .00120 .99777 .00223 .99880 .00682 .01159 .00804 .1917 1.7569 .6156 .2994 RB 2 .0107 .00202 .00120 .99777 .00223 .99880 .00682 .01159 .00804 .1917 1.7569 .6156 .2994 MD 2 .0110 .00208 .00123 .99771 .00229 .99877 .00694 .01175 .00815 .1928 1.7598 .6159 .3003 RD 2 .0110 .00207 .00123 .99772 .00228 .99877 .00689 .01175 .00812 .1909 1.7502 .6151 .2975 OR 2 .3567 .12203 .11598 .87646 .12354 .88402 .20221 .21244 .20447 .0379 1.0456 .5174 .0273 OS 2 .0341 .01122 .00887 .98819 .01181 .99113 .06803 .06525 .07024 .1078 1.2839 .5630 .1408 OF 2 .0142 .00277 .00159 .99694 .00306 .99841 .00798 .01329 .00940 .2091 1.8132 .6207 .3163 CF 2 .0142 .00277 .00159 .99694 .00306 .99841 .00798 .01329 .00940 .2091 1.8132 .6207 .3163 CS 2 .0396 .00824 .00504 .99096 .00904 .99496 .02255 .02679 .02550 .2087 1.6741 .6115 .2818 NT 4 .3637 .08541 .05008 .90576 .09424 .94992 .04936 .07427 .05884 .3290 1.6272 .6288 .2843 MB 4 .0108 .00329 .00120 .99619 .00381 .99880 .00880 .01149 .01061 .3673 2.8507 .6719 5201 RB 4 .0107 .00328 .00119 .99620 .00380 .99881 .00876 .01143 .01057 .3691 2.8676 .6724 .5224 MD 4 .0110 .00337 .00122 .99610 .00390 .99878 .00889 .01159 .01072 .3698 2.8636 .6724 .5221 RD 4 .0110 .00336 .00122 .99611 .00389 .99878 .00886 .01159 .01068 .3688 2.8563 .6722 .5210 OR 4 .5353 .22676 .21091 .76927 .23073 .78909 .26666 .27608 .27064 .0668 1.0528 .5278 .0322 OS 4 .0569 .02844 .02111 .96972 .03028 .97889 .12549 .11237 .13059 .1546 1.3526 5780 .1738 OF 4 .0131 .00394 .00146 .99543 .00457 .99854 .00957 .01263 .01155 .3699 2.8092 .6711 .5155 CF 4 .0131 .00394 .00146 .99543 .00457 .99854 .00957 .01263 .01155 .3699 2.8092 .6711 .5155 CS 4 .0651 .01998 .00821 .97708 .02292 .99179 .03728 .03308 .04348 .4026 2.4227 .6642 .4667 NT 10 .3655 .14397 .05014 .83257 .16743 .94986 .06686 .07406 .08121 .6791 2.4241 .7060 .4907 MB 10 .0105 .00926 .00120 .98873 .01128 .99880 .01556 .01180 .01917 .7547 7.4353 .7259 .8058 RB 10 .0104 .00917 .00119 .98883 .01117 .99881 .01532 .01175 .01889 .7539 7.4378 .7259 .8058 MD 10 .0108 .00946 .00123 .98848 .01152 .99877 .01573 .01196 .01938 .7546 7.3875 .7258 .8048 RD 10 .0107 .00936 .00122 .98860 .01140 .99878 .01547 .01191 .01907 .7533 7.3803 .7257 .8045 OR 10 .8617 .55677 50034 .42912 57088 .49966 .30762 .32991 .31085 .1778 .9842 5662 -.0101 OS 10 .2203 .16527 .13283 .82662 .17338 .86717 .31699 .28574 .32779 .1722 1.1935 .5702 .1088 OF 10 .0111 .01000 .00127 .98782 .01218 .99873 .01620 .01211 .01997 .7679 7.5656 .7267 .8097 CF 10 .0111 .01000 .00127 .98782 .01218 .99873 .01620 .01211 .01997 .7679 7.5656 .7267 .8097 CS 10 .1706 .07954 .02212 .90610 .09390 .97788 .07444 .05271 .08873 .6947 3.1779 .7095 .5946 NT 20 .3687 .24415 .05064 .70748 .29253 .94936 .08706 .07438 .10703 1.0926 3.2986 .7704 .623C MB 20 .0110 .02597 .00126 .96785 .03215 .99874 .02779 .01206 .03458 1.1719 17.3712 .7480 .9225 RB 20 .0107 .02543 .00122 .96852 .03148 .99878 .02698 .01191 .03358 1.1707 17.4987 .7479 .9230 MD 20 .0111 .02640 .00127 .96732 .03268 .99873 .02803 .01211 .03487 1.1765 17.4649 .7482 .9230 RD 20 .0109 .02588 .00124 .96797 .03203 .99876 .02721 .01201 .03386 1.1730 17.4606 .7480 .9229 OR 20 .9892 .84567 .75982 .13286 .86714 .24018 .16826 .23811 .16253 .4072 .6905 .6426 -.2260 OS 20 5978 .52712 .45566 .45501 .54499 .54434 .43812 .41427 .44883 .2244 .9998 .5820 -.0001 OF 20 .0112 .02695 .00128 .96663 .03337 .99872 .02837 .01216 .03530 1.1833 17.6288 .7485 .9239 CF 20 .0112 .02695 .00128 .96663 .03337 .99872 .02837 .01216 .03530 1.1833 17.6288 .7485 .9239 CS 20 .2900 .20879 .03960 .74891 .25109 .96040 .10618 .06878 .12825 1.0843 3.7264 .7656 .6635 NT 40 .3666 .42540 .05079 .48094 .51906 .94921 .09725 .07493 .11997 1.6850 3.8158 .8489 .6763 MB 40 .0107 .08718 .00121 .89133 .10868 .99879 .05611 .01175 .07008 1.7993 46.4477 .7741 .9753 RB 40 .0100 .08280 .00112 .89678 .10322 .99888 .05161 .01122 .06447 1.7924 47.9861 .7728 .9761 MD 40 .0110 .08831 .00124 .88993 .11008 .99876 .05653 .01190 .07059 1.7986 45.7264 .7744 .9749 RD 40 .0103 .08389 .00116 .89543 .10457 .99884 .05191 .01138 .06485 1.7911 47.1597 .7731 .9756 OR 40 1.0000 .95792 .87333 .02094 .97906 .12667 .05082 .15316 .03595 .8925 .2423 .7357 -.6873 OS 40 .9574 .91370 .82189 .06334 .93666 .17811 .20017 .23885 .20088 .6047 .4768 .6917 -.4232 OF 40 .0110 .08904 .00124 .88901 .11099 .99876 .05675 .01190 .07086 1.8034 45.9990 .7747 .9751 CF 40 .0110 .08904 .00124 .88901 .11099 .99876 .05675 .01190 .07086 1.8034 45.9990 .7747 .9751 CS 40 .3792 .42553 .05492 .48182 .51818 .94508 .10397 .08040 .12637 1.6445 35865 .8460 .6558 Table 10.2.1.2.2.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P * l,p = 10, mNz ~ 3,pNz = .2 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' A' B" N 2 .8329 .09138 .05022 .74399 .25601 .94978 .04956 .03802 .19376 .9870 3.1090 .7551 .5995 MB 2 .0381 .00484 .00108 .98013 .01987 .99892 .01120 .00549 .05121 1.0106 13.3176 .7411 .8950 RB 2 .0381 .00480 .00108 .98030 .01970 .99892 .01107 .00549 .05054 1.0072 13.2227 .7409 .8941 MD 2 .0392 .00494 .00111 .97976 .02024 .99889 .01135 .00556 .05188 1.0101 13.1906 .7411 .8940 RD 2 .0389 .00490 .00110 .97990 .02010 .99890 .01122 .00554 .05128 1.0094 13.2015 .7410 .8941 OR 2 .6936 .21114 .19063 .70682 .29318 .80937 .24574 .24156 .31913 .3315 1.2653 .6191 .1464 OS 2 .1487 .04270 .03052 .90857 .09143 .96948 .13637 .11997 .23484 .5413 2.3808 .6823 .4748 OF 2 .0554 .00646 .00159 .97409 .02591 .99841 .01302 .00671 .05916 1.0043 11.6733 .7407 .8813 CF 2 .0554 .00646 .00159 .97409 .02591 .99841 .01302 .00671 .05916 1.0043 11.6733 .7407 .8813 CS 2 .1941 .02037 .00818 .93089 .06911 .99182 .03429 .02005 .12370 .9183 5.9477 .7358 .7760 N 4 .8246 .13496 .04990 .52478 .47522 .95010 .05555 .03833 .23018 1.5837 3.8668 .8357 .6805 MB 4 .0399 .01700 .00114 .91957 .08043 .99886 .02257 .00566 .11038 1.6492 39.3497 .7663 .9697 RB 4 .0394 .01678 .00113 .92058 .07942 .99888 .02215 .00563 .10842 1.6461 39.4156 .7661 .9697 MD 4 .0408 .01726 .00117 .91834 .08166 .99883 .02278 .00574 .11140 1.6501 38.9313 .7666 .9694 RD 4 .0401 .01703 .00114 .91942 .08058 .99886 .02230 .00567 .10916 1.6487 39.2278 .7663 .9696 OR 4 .8894 .37573 .31955 .39952 .60048 .68045 .26335 .26869 .33896 .7235 1.0806 .7202 .0491 OS 4 .3941 .16285 .11691 .65338 .34662 .88309 .24301 .21835 .41253 .7961 1.8794 .7307 .3738 OF 4 .0479 .01913 .00138 .90986 .09014 .99863 .02408 .00623 .11763 1.6545 36.0730 .7684 .9671 CF 4 .0479 .01913 .00138 .90986 .09014 .99863 .02408 .00623 .11763 1.6545 36.0730 .7684 .9671 CS 4 .2771 .05218 .01118 .78383 .21617 .98882 .04679 .02172 .19663 1.4990 9.9788 .7889 .8775 N 10 .8283 .21323 .05026 .13488 .86512 .94974 .04242 .03860 .14457 2.7460 2.0952 .9500 .4194 MB 10 .0425 .08549 .00122 .57743 .42257 .99878 .04654 .00587 .23123 2.8362 97.1204 .8547 .9901 RB 10 .0380 .08341 .00108 .58727 .41273 .99892 .04532 .00550 .22558 2.8466107.7040 .8524 .9911 MD 10 .0439 .08602 .00126 .57496 .42504 .99874 .04659 .00597 .23139 2.8323 94.2883 .8553 .9898 RD 10 .0395 .08406 .00112 .58420 .41580 .99888 .04536 .00560 .22580 2.8432 104.2106 .8531 .9908 OR 10 .9905 34538 .44036 .03453 .96547 .55964 .21439 .26078 .09400 1.9680 .1937 .8705 -.7617 OS 10 .9342 .45374 .33521 .07212 .92788 .66479 .22607 .25872 .20773 1.8857 .3770 .8826 -.5381 OF 10 .0465 .08764 .00134 .56716 .43284 .99866 .04678 .00616 .23215 2.8340 89.5751 .8572 .9892 CF 10 .0465 .08764 .00134 .56714 .43286 .99866 .04678 .00616 .23215 2.8340 89.5756 .8573 .9892 CS 10 .2497 .12817 .00960 .39757 .60243 .99040 .04256 .01944 .18975 2.6012 14.9939 .8957 .9236 N 20 .8221 .23796 .04960 .00862 .99138 .95040 .03147 .03861 .03340 4.0302 .2284 .9852 -.6930 MB 20 .0486 .17508 .00139 .13018 .86982 .99861 .02975 .00626 .14686 4.1163 46.4664 .9670 .9758 RB 20 .0402 .17295 .00114 .13981 .86019 .99886 .03019 .00562 .14953 4.1326 58.6188 .9647 .9813 MD 20 .0502 .17539 .00144 .12882 .87118 .99856 .02964 .00637 .14617 4.1125 44.7462 .9673 .9747 RD 20 .0414 .17332 .00118 .13810 .86190 .99882 .03005 .00573 .14865 4.1302 56.3690 .9651 .9804 OR 20 .9948 .56643 .45819 .00059 .99941 .54181 .20682 .25838 .00880 3.3492 .0052 .8851 -.9953 OS 20 .9894 .49616 .37036 .00068 .99932 .62964 .20040 .25032 .00960 3.5348 .0062 .9071 -.9942 OF 20 .0517 .17580 .00149 .12696 .87304 .99851 .02950 .00648 .14532 4.1115 43.0083 .9678 .9736 CF 20 .0517 .17580 .00149 .12696 .87304 .99851 .02950 .00648 .14532 4.1115 43.0083 .9678 .9736 CS 20 .1168 .17393 .00429 .14753 .85247 .99571 .02546 .01343 .10743 3.6753 18.2760 .9617 .9343 N 40 .8254 .23983 .04979 .00000 1.00000 .95021 .03064 .03829 .00000 5.9118 .0000 .9876-1.000C MB 40 .0490 .20089 .00141 .00118 .99882 .99859 .00560 .00631 .01222 6.0284 .8492 .9994 -.0890 RB 40 .0389 .20061 .00112 .00143 .99857 .99888 .00521 .00564 .01340 6.0390 1.2565 .9994 .1240 MD 40 .0502 .20093 .00144 .00112 .99888 .99856 .00562 .00637 .01197 6.0357 .7953 .9994 -.1244 RD 40 .0400 .20064 .00115 .00140 .99860 .99885 .00526 .00573 .01326 6.0374 1.1971 .9994 .0979 OR 40 .9946 .56441 .45552 .00000 1.00000 .54448 .20371 .25464 .00000 4.3766 .0000 .8861 -1.0000 OS 40 .9892 .49444 .36805 .00000 1.00000 .63195 .19783 .24729 .00000 4.6019 .0000 .9080-l.oood OF 40 .0508 .20095 .00146 .00110 .99890 .99854 .00564 .00640 .01187 6.0382 .7727 .9994 -.1399 CF 40 .0508 .20095 .00146 .00110 .99890 .99854 .00564 .00640 .01187 6.0382 .7727 .9994 -.1399 CS 40 .0663 .19613 .00257 .02964 .97036 .99743 .01429 .01117 .05036 4.6842 8.4686 .9919 .8364| 138 Table 10.2.1.2.2.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P * \,p = 10, mNz - .3,pNz - .4 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .7234 .13163 .04934 .74495 .25505 .95066 .06875 .04471 .15730 .9926 3.1468 .7557 .6040 MB 2 .0270 .00874 .00100 .97967 .02033 .99900 .01601 .00604 .03890 1.0422 14.5334 .7425 .9042 RB 2 .0266 .00866 .00099 .97984 .02016 .99901 .01576 .00599 .03832 1.0431 14.6272 .7425 .9047 MD 2 .0283 .00891 .00105 .97930 .02070 .99895 .01619 .00617 .03935 1.0357 14.1343 .7422 .9014 RD 2 .0279 .00882 .00104 .97951 .02049 .99896 .01591 .00613 .03867 1.0358 14.1989 .7422 .9019 OR 2 .8525 .42885 .37566 .49137 .50863 .62434 .31131 .30850 .34833 .3385 1.0512 .6186 .0318 OS 2 .2597 .14823 .11430 .80087 .19913 .88570 .28418 .25158 .35158 .3592 1.4448 .6304 .2234 OF 2 .0396 .01165 .00149 .97310 .02690 .99851 .01880 .00739 .04559 1.0416 12.8208 .7425 .8925 CF 2 .0396 .01165 .00149 .97310 .02690 .99851 .01880 .00739 .04559 1.0416 12.8208 .7425 .8925 CS 2 .2949 .05953 .01677 .87634 .12366 .98323 .06664 .03184 .14219 .9687 4.9028 .7433 .7359 NT 4 .7212 .22075 .04991 .52298 .47702 .95009 .08175 .04569 .19227 15881 3.8674 .8362 .6806 MB 4 .0292 .03310 .00109 .91888 .08112 .99891 .03614 .00633 .08974 1.6662 41.1368 .7667 .9711 RB 4 .0284 .03222 .00106 .92105 .07895 .99894 .03452 .00625 .08577 1.6599 41.3321 .7661 .9712 MD 4 .0298 .03357 .00112 .91775 .08225 .99888 .03650 .00642 .09059 1.6667 40.6855 .7669 .9708 RD 4 .0288 .03265 .00108 .91999 .08001 .99892 .03479 .00629 .08644 1.6629 41.2253 .7664 .9712 OR 4 .9839 .69702 .60040 .15806 .84194 .39960 .23088 .26980 .22179 .7481 .6249 .7228 -.2865 OS 4 .6551 .46728 .37696 .39724 .60276 .62304 .37417 .35225 .44277 .5740 1.0153 .6843 .0097 OF 4 .0357 .03720 .00135 .90902 .09098 .99865 .03873 .00710 .09612 1.6648 36.8898 .7687 .9679 CF 4 .0357 .03720 .00135 .90902 .09098 .99865 .03873 .00710 .09612 1.6648 36.8898 .7687 .9679 CS 4 .4185 .14803 .02459 .66681 .33319 .97541 .08397 .03695 .19120 1.5359 6.3073 .8106 .8051 NT 10 .7263 .37663 .05073 .13452 .86548 .94927 .05492 .04629 .11874 2.7431 2.0758 .9499 .4148 MB 10 .0340 .17483 .00130 .56488 .43512 .99870 .07978 .00706 .19889 2.8472 91.6965 .8578 .9895 RB 10 .0285 .16601 .00109 58661 .41339 .99891 .07499 .00642 .18720 2.8470107.3227 .8525 .9911 MD 10 .0352 .17611 .00136 .56177 .43823 .99864 .07987 .00723 .19907 2.8433 88.5968 .8586 .9891 RD 10 .0294 .16720 .00112 .58368 .41632 .99888 .07520 .00651 .18769 2.8455 104.5564 .8532 .9908 OR 10 1.0000 .82275 .70791 .00500 .99500 .29209 .13052 .21393 .02033 2.0285 .0421 .8179 -.9530 OS 10 .9954 .78891 .65490 .01008 .98992 .34510 .15123 .23644 .06843 1.9249 .0728 .8273 -.9154 OF 10 .0376 .17931 .00144 .55390 .44610 .99856 .07989 .00743 .19916 2.8438 83.8468 .8605 .9884 CF 10 .0376 .17931 .00144 55390 .44610 .99856 .07989 .00743 .19916 2.8438 83.8468 .8605 .9884 CS 10 .3459 .30074 .01879 .27632 .72368 .98121 .05633 .03164 .13067 2.6732 7.2843 .9231 .8312 NT 20 .7170 .42640 .04971 .00856 .99144 .95029 .02896 .04592 .02486 4.0320 .2265 .9852 -.6955 MB 20 .0455 .35455 .00176 .11627 .88373 .99824 .04625 .00826 .11504 4.1116 34.6034 .9704 .9663 RB 20 .0299 .34486 .00113 .13954 .86046 .99887 .04899 .00647 .12219 4.1372 59.1599 .9647 .9814 MD 20 .0464 .35512 .00180 .11491 .88509 .99820 .04592 .00833 .11421 4.1127 33.7342 .9707 .9653 RD 20 .0308 .34554 .00116 .13791 .86209 .99884 .04871 .00659 .12144 4.1349 56.9714 .9651 .9806 OR 20 1.0000 .82876 .71464 .00006 .99994 .28536 .12641 .21064 .00184 3.2746 .0007 .8213 -.9994 OS 20 1.0000 .79945 .66580 .00007 .99993 .33420 .13770 .22946 .00200 3.3721 .0008 .8335 -.9994 OF 20 .0478 .35592 .00185 .11298 .88702 .99815 .04540 .00845 .11294 4.1132 32.4194 .9712 .9638 CF 20 .0478 .35592 .00185 .11298 .88702 .99815 .04540 .00845 .11294 4.1132 32.4194 .9712 .9638 CS 20 .1448 .36907 .00734 .08834 .91166 .99266 .02876 .02073 .06098 3.7910 7.8776 .9757 .8340 NT 40 .7208 .43009 .05016 .00001 .99999 .94984 .02781 .04635 .00056 6.0377 .0002 .9875 -.9998 MB 40 .0497 .40079 .00196 .00096 .99904 .99804 .00610 .00884 .00774 5.9860 .5208 .9993 -.3422 RB 40 .0297 .40007 .00115 .00154 .99846 .99885 .00555 .00669 .00975 6.0077 1.3113 .9993 .1470 MD 40 .0508 .40083 .00201 .00096 .99904 .99799 .00615 .00898 .00772 5.9795 .5060 .9993 -.3561 RD 40 .0305 .40011 .00118 .00150 .99850 .99882 .00556 .00680 .00963 6.0081 1.2438 .9993 .1186 OR 40 1.0000 .82734 .71223 .00000 1.00000 .28777 .12593 .20988 .00000 3.7050 .0000 .8219-1.0000 OS 40 .9999 .79831 .66384 .00000 1.00000 .33616 .13662 .22770 .00000 3.8419 .0000 .8340-1.0000 OF 40 .0514 .40084 .00204 .00094 .99906 .99796 .00616 .00903 .00768 5.9795 .4956 .9993 -.3660 CF 40 .0514 .40084 .00204 .00094 .99906 .99796 .00616 .00903 .00768 5.9795 .4956 .9993 -.3660 CS 40 .0808 .39647 .00430 .01528 .98472 .99570 .01532 .01683 .02539 4.7899 3.0425 .9951 .5567 Table 10.2.1.2.2.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P*I,p = 10, mNz = ,3,pNz = .6 N:p a£X Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .5605 .17218 .04930 .74590 .25410 .95070 .09261 .05697 .14932 .9900 3.1428 .7553 .6035 MB 2 .0176 .01248 .00101 .97987 .02013 .99899 .02033 .00765 .03354 1.0374 14.3833 .7423 .9031 RB 2 .0174 .01229 .00099 .98018 .01982 .99901 .01981 .00761 .03266 1.0345 14.3444 .7422 .9027 MD 2 .0183 .01274 .00104 .97946 .02054 .99896 .02058 .00779 .03393 1.0347 14.1356 .7422 .9014 RD 2 .0180 .01252 .00103 .97981 .02019 .99897 .02003 .00773 .03302 1.0322 14.1350 .7421 .9013 OR 2 .9052 .60987 33948 .34320 .65680 .46052 .32068 .32745 .33363 .3046 .9263 .6083 -.0486 OS 2 .3659 .28227 .23223 .68438 .31562 .76777 .39223 .35457 .42631 .2515 1.1646 .5932 .0956 OF 2 .0277 .01665 .00159 .97331 .02669 .99841 .02430 .00964 .03998 1.0171 11.9669 .7414 .8845 CF 2 .0277 .01665 .00159 .97331 .02669 .99841 .02430 .00964 .03998 1.0171 11.9669 .7414 .8845 CS 2 .3129 .11520 .02731 .82620 .17380 .97269 .10715 .05058 .16364 .9826 4.0783 .7484 .6878 NT 4 3593 .30555 .04952 .52376 .47624 .95048 .11391 .05754 .18577 1.5899 3.8910 .8362 .6825 MB 4 .0202 .04998 .00113 .91745 .08255 .99887 .05204 .00787 .08647 1.6662 40.4908 .7670 .9707 RB 4 .0188 .04779 .00105 .92104 .07896 .99895 .04821 .00761 .08020 1.6636 41.8021 .7662 .9716 MD 4 .0209 .05068 .00117 .91631 .08369 .99883 .05252 .00806 .08727 1.6621 39.4878 .7672 .9699 RD 4 .0193 .04847 .00108 .91994 .08006 .99892 .04860 .00770 .08085 1.6633 41.2455 .7664 .9712 OR 4 .9941 .85773 .76151 .07813 .92187 .23849 .16119 .22145 .14663 .7066 .4713 .7116 -.4321 OS 4 .7747 .67654 38265 .26086 .73914 .41735 .38177 .37194 .40421 .4320 .8324 .6467 -.1155 OF 4 .0244 .05589 .00137 .90776 .09224 .99863 .05577 .00868 .09269 1.6692 36.8987 .7690 .9679 CF 4 .0244 .05589 .00137 .90776 .09224 .99863 .05577 .00868 .09269 1.6692 36.8987 .7690 .9679 CS 4 .4425 .26318 .03915 .58747 .41253 .96085 .12400 .05687 .19644 1.5396 43974 .8234 .7313 NT 10 3551 33911 .04938 .13440 .86560 .95062 .07130 .05777 .11220 2.7567 2.1198 .9504 .4250 MB 10 .0269 .27060 .00159 35005 .44995 .99841 .12047 .00994 .20031 2.8242 76.9632 .8614 .9873 RB 10 .0191 .24827 .00110 38695 .41305 .99890 .10880 .00801 .18117 2.8421 105.9766 .8524 .9910 MD 10 .0276 .27259 .00163 34676 .45324 .99837 .12058 .01004 .20049 2.8250 75.3619 .8622 .9870 RD 10 .0196 .25005 .00113 .58400 .41600 .99887 .10897 .00811 .18146 2.8422103.7517 .8532 .9908 OR 10 .9999 .93360 .83692 .00195 .99805 .16308 .06438 .15764 .00990 1.9046 .0251 .7874 -.9719 OS 10 .9981 .92248 .81212 .00394 .99606 .18788 .08171 .17881 .04352 1.7714 .0434 .7909 -.9498 OF 10 .0299 .27746 .00176 33874 .46126 .99824 .12075 .01041 .20075 2.8208 70.3014 .8641 .9860 CF 10 .0299 .27746 .00176 .53874 .46126 .99824 .12075 .01041 .20075 2.8208 70.3014 .8641 .986C CS 10 .3516 .48554 .02953 .21045 .78955 .97047 .06875 .04959 .10895 2.6926 4.2965 .9364 .7058 NT 20 .5564 .61505 .05007 .00829 .99171 .94993 .02652 .05889 .02129 4.0400 .2191 .9852 -.7052 MB 20 .0438 34126 .00263 .09966 .90034 .99737 .06224 .01275 .10323 4.0744 21.5632 .9743 .9432 RB 20 .0193 .51688 .00111 .13928 .86072 .99889 .06987 .00803 .11632 4.1439 60.0798 .9648 .9817 MD 20 .0451 .54213 .00271 .09825 .90175 .99729 .06173 .01293 .10237 4.0731 20.7846 .9746 .9409 RD 20 .0196 .51782 .00113 .13771 .86229 .99887 .06944 .00814 .11559 4.1450 583422 .9652 .9812 OR 20 1.0000 .93586 .83967 .00002 .99998 .16033 .06227 .15565 .00091 3.0900 .0004 .7900 -.9997 OS 20 1.0000 .92701 .81757 .00003 .99997 .18243 .06942 .17351 .00098 3.1410 .0004 .7956 -.9997 OF 20 .0462 .54307 .00277 .09673 .90327 .99723 .06108 .01308 .10126 4.0740 20.1019 .9750 .9387 CF 20 .0462 .54307 .00277 .09673 .90327 .99723 .06108 .01308 .10126 4.0740 20.1019 .9750 .9387 CS 20 .1505 .56958 .01196 .05868 .94132 .98804 .03002 .03362 .04190 3.8245 3.7599 .9820 .6476 NT 40 3580 .61998 .04995 .00001 .99999 .95005 .02340 .05849 .00052 5.9768 .0003 .9875 -.9997 MB 40 .0461 .60072 .00283 .00068 .99932 .99717 .00623 .01348 .00529 5.9711 .2714 .9991 -.6126 RB 40 .0201 39953 .00117 .00156 .99844 .99883 .00594 .00834 .00822 5.9992 1.3063 .9993 .1450 MD 40 .0475 .60077 .00291 .00066 .99934 .99709 .00628 .01366 .00522 5.9695 .2577 .9991 -.6300 RD 40 .0204 .59957 .00119 .00151 .99849 .99881 .00592 .00845 .00810 6.0032 1.2478 .9993 .1204 OR 40 1.0000 .93533 .83833 .00000 1.00000 .16167 .06275 .15687 .00000 3.2773 .0000 .7904-1.000C OS 40 1.0000 .92679 .81698 .00000 1.00000 .18302 .06942 .17356 .00000 3.3610 .0000 .7958 -1.0000 OF 40 .0484 .60080 .00297 .00065 .99935 .99703 .00632 .01382 .00518 5.9676 .2490 .9991 -.6413 CF 40 .0484 .60080 .00297 .00065 .99935 .99703 .00632 .01382 .00518 5.9676 .2490 .9991 -.6413 CS 40 .0867 .59830 .00736 .00774 .99226 .99264 .01540 .02826 .01524 4.8602 1.0464 .9962 .0256 Table 10.2.1.2.2.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I,p = 10, mNz = .3,pNz = .8 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' P A' B" NT 2 .3173 .21289 .04826 .74595 .25405 .95174 .11745 .08467 .14482 1.0002 3.1968 .7566 .6099 MB 2 .0100 .01634 .00113 .97986 .02014 .99887 .02522 .01149 .03142 1.0019 12.8946 .7407 .8915 RB 2 .0100 .01599 .00113 .98030 .01970 .99887 .02423 .01149 .03016 .9929 12.6572 .7403 .8893 MD 2 .0103 .01669 .00117 .97943 .02058 .99883 .02553 .01165 .03180 1.0021 12.7883 .7407 .8907 RD 2 .0102 .01631 .00116 .97990 .02010 .99884 .02452 .01160 .03053 .9953 12.6465 .7404 .8893 OR 2 .9177 .73039 .65617 .25106 .74894 .34383 .29976 .32549 .30272 .2691 .8655 .5984 -.0909 OS 2 .4393 .39096 .33701 59555 .40445 .66299 .44701 .41597 .45871 .1788 1.0610 .5671 .0376 OF 2 .0146 .02182 .00166 .97313 .02687 .99834 .03046 .01382 .03791 1.0083 11.6267 .7409 .8811 CF 2 .0146 .02182 .00166 .97313 .02687 .99834 .03046 .01382 .03791 1.0083 11.6267 .7409 .8811 CS 2 .2332 .18078 .03830 .78360 .21640 .96170 .15081 .08536 .18123 .9864 3.5260 .7521 .6431 NT 4 .3256 .39096 .04954 .52368 .47632 .95046 .14604 .08505 .18121 1.5899 3.8896 .8363 .6824 MB 4 .0103 .06729 .00114 .91617 .08383 .99886 .06829 .01122 .08528 1.6702 40.4137 .7673 .9707 RB 4 .0098 .06329 .00109 .92116 .07884 .99891 .06135 .01095 .07662 1.6519 40.3859 .7660 .9705 MD 4 .0108 .06827 .00120 .91497 .08503 .99880 .06888 .01149 .08602 1.6637 39.1138 .7675 .9697 RD 4 .0101 .06417 .00112 .92007 .07993 .99888 .06185 .01111 .07724 1.6503 39.6962 .7662 .9700 OR 4 .9966 .93420 .84846 .04437 .95563 .15154 .10641 .18813 .09906 .6723 .3992 .7048 -.5040 OS 4 .8373 .79475 .71102 .18431 .81569 .28898 .35480 .35673 .36094 .3427 .7793 .6226 -.1549 OF 4 .0123 .07532 .00137 .90619 .09381 .99863 .07296 .01225 .09113 1.6786 37.3601 .7695 .9684 CF 4 .0123 .07532 .00137 .90619 .09381 .99863 .07296 .01225 .09113 1.6786 37.3601 .7695 .9684 CS 4 .3353 .39246 .05571 .52336 .47664 .94429 .16413 .09780 .19986 1.5333 3.5440 .8322 .6517 NT 10 .3247 .70271 .04946 .13398 .86602 .95054 .08822 .08484 .10820 2.7579 2.1126 .9505 .4233 MB 10 .0171 .37743 .00202 52872 .47128 .99798 .16570 .01605 .20690 2.8026 62.1332 .8665 .9839 RB 10 .0105 .33109 .00119 .58643 .41357 .99881 .14048 .01165 .17556 2.8201 98.7238 .8525 .9903 MD 10 .0176 .38014 .00209 52534 .47466 .99791 .16576 .01635 .20696 2.8009 60.3657 .8673 .9834 RD 10 .0106 .33349 .00120 .58343 .41657 .99880 .14075 .01170 .17588 2.8250 98.0482 .8532 .9902 OR 10 .9999 .97904 .89944 .00106 .99894 .10056 .02814 .13570 .00620 1.7950 .0201 .7723 -.9769 OS 10 .9993 .97686 .89132 .00175 .99825 .10868 .03868 .14778 .02531 1.6859 .0302 .7727 -.9645 OF 10 .0187 .38649 .00222 .51745 .48255 .99778 .16559 .01685 .20673 2.8010 57.1330 .8692 .9824 CF 10 .0187 .38649 .00222 .51745 .48255 .99778 .16559 .01685 .20673 2.8010 57.1330 .8692 .9824 CS 10 .2803 .68180 .04576 .15919 .84081 .95424 .07675 .08917 .09261 2.6853 2.5243 .9447 5081 NT 20 .3249 .80313 .04946 .00845 .99155 .95054 .02322 .08477 .02000 4.0389 .2250 .9853 -.6974 MB 20 .0391 .74077 .00481 .07524 .92476 .99519 .07274 .02520 .09048 4.0269 10.1566 .9798 .8712 RB 20 .0094 .68907 .00109 .13893 .86107 .99891 .08958 .01139 .11197 4.1500 60.8196 .9649 .9820 MD 20 .0398 .74174 .00492 .07406 .92594 .99508 .07204 .02566 .08958 4.0275 9.8320 .9801 .8667 RD 20 .0094 .69039 .00110 .13729 .86271 .99890 .08899 .01155 .11122 4.1544 59.7698 .9653 .9816 OR 20 1.0000 .98045 .90230 .00002 .99998 .09770 .02628 .13132 .00068 2.8546 .0004 .7744 -.9996 OS 20 1.0000 .97898 .89500 .00002 .99998 .10500 .02841 .14196 .00073 2.8604 .0005 .7762 -.9996 OF 20 .0408 .74264 .00503 .07296 .92704 .99497 .07123 .02588 .08858 4.0277 95285 .9803 .8621 CF 20 .0408 .74264 .00503 .07296 .92704 .99497 .07123 .02588 .08858 4.0277 9.5285 .9803 .8621 CS 20 .1287 .77469 .02087 .03686 .96314 .97913 .02813 .06435 .02931 3.8246 1.6061 .9852 .2694 NT 40 .3271 .81015 .05078 .00001 .99999 .94922 .01748 .08739 .00039 6.0317 .0002 .9873 -.9998 MB 40 .0462 .80094 .00588 .00030 .99970 .99412 .00615 .02857 .00295 5.9510 .0663 .9985 -.9024 RB 40 .0093 .79886 .00109 .00170 .99830 .99891 .00644 .01150 .00760 5.9944 1.5001 .9993 .2181 MD 40 .0473 .80098 .00600 .00028 .99972 .99400 .00614 .02878 .00283 5.9619 .0611 .9984 -.9102 RD 40 .0095 .79890 .00112 .00165 .99835 .99888 .00638 .01176 .00748 5.9941 1.4222 .9993 .1901 OR 40 .9999 .98017 .90083 .00000 1.00000 .09917 .02681 .13405 .00000 2.9786 .0000 .7748 -1.0000 OS 40 .9999 .97869 .89346 .00000 1.00000 .10654 .02878 .14389 .00000 3.0198 .0000 .7766-1.0000 OF 40 .0475 .80098 .00602 .00028 .99972 .99398 .00615 .02882 .00283 5.9606 .0609 .9984 -.9105 CF 40 .0475 .80098 .00602 .00028 .99972 .99398 .00615 .02882 .00283 5.9606 .0609 .9984 -.9105 CS 40 .0846 .80128 .01537 .00224 .99776 .98463 .01391 .06047 .00759 5.0021 .1821 .9956 -.7422 141 Table 10.2.1.2.3.1 Table of empirical results for tests of correlations with no preliminary omnibus test when P * L p = 10, mNz = .S,pNz - .2 N:p CtEX Rej Fp Fn Tp Tn s:Rej s:FpTn S.FnTp d' P A' B" NT 2 .8044 .16903 .05024 .35579 .64421 .94976 .06001 .04196 .24812 2.0123 3.5990 .8869 .6554 MB 2 .0402 .3050 .00118 .85221 .14779 .99882 .03508 .00593 .17298 1.9953 59.0123 .7847 .9815 RB 2 .0391 .02983 .00114 .85541 .14459 .99886 .03398 .00581 .16779 1.9915 59.9670 .7839 .9818 MD 2 .0411 .03091 .00121 .85027 .14973 .99879 .03533 .00600 .17417 1.9967 58.2732 .7852 .9813 RD 2 .0399 .03021 .00117 .85361 .14639 .99883 .03424 .00590 .16901 1.9921 59.1481 .7844 .9815 OR 2 .9403 .45475 .37358 .22056 .77944 .62643 .25977 .28300 .29250 1.0927 .7829 .7922 -.1530 OS 2 .6060 .27964 .20415 .41842 .58158 .79585 .28184 .26863 .44557 1.0328 1.3780 .7808 .1993 OF 2 .0568 .03713 .00168 .82107 .17893 .99832 .03853 .00708 .18958 2.0132 48.3013 .7920 .9774 CF 2 .0568 .03713 .00168 .82107 .17893 .99832 .03853 .00708 .18958 2.0132 48.3013 .7920 .9774 CS 2 .3100 .08226 .01393 .64442 .35558 .98607 .05746 .02625 .24371 1.8289 10.4812 .8268 .8869 NT 4 .7957 .22404 .04956 .07800 .92200 .95044 .04124 .04150 .12530 3.0678 1.4242 .9660 .2085 MB 4 .0424 .10830 .00126 .46354 .53646 .99874 .05408 .00620 .26896 3.1122 95.3939 .8834 .9899 RB 4 .0383 .10583 .00113 .47537 .52463 .99887 .05297 .00583 .26393 3.1154 105.6717 .8805 .9910 MD 4 .0426 .10888 .00127 .46068 33932 .99873 .05404 .00624 .26878 3.1167 943666 .8841 .9898 RD 4 .0390 .10645 .00116 .47238 .52762 .99884 .05301 .00591 .26408 3.1163103.5246 .8812 .9908 OR 4 .9888 .55337 .44576 .01620 .98380 .55424 .21905 .27080 .06408 2.2758 .1024 .8794 -.8788 OS 4 .9518 .47350 .35156 .03876 .96124 .64844 .22535 .26781 .16201 2.1464 .2264 .8936 -.7191 OF 4 .0501 .11347 .00151 .43868 36132 .99849 .05380 .00681 .26731 3.1204 80.3806 .8895 .9878 CF 4 .0501 .11347 .00151 .43868 36132 .99849 .05380 .00681 .26731 3.1204 80.3806 .8895 .9878 CS 4 .2213 .14463 .00927 .31391 .68609 .99073 .04335 .02130 .18895 2.8395 14.2212 .9174 .9182 NT 10 .7934 .23964 .04962 .00028 .99972 .95038 .03385 .04229 .00577 5.1010 .0100 .9875 -.9883 MB 10 .0467 .19847 .00140 .01326 .98674 .99860 .01055 .00658 .04631 5.2075 7.4300 .9963 .8069 RB 10 .0378 .19787 .00112 .01514 .98486 .99888 .01084 .00583 .04953 5.2229 10.2255 .9959 .8605 MD 10 .0482 .19856 .00144 .01300 .98700 .99856 .01049 .00667 .04578 5.2055 7.1005 .9964 .7979 RD 10 .0390 .19794 .00116 .01493 .98507 .99884 .01080 .00592 .04914 5.2189 9.8133 .9960 .8545 OR 10 .9896 35815 .44769 .00002 .99998 35231 .21705 .27130 .00157 4.2146 .0002 .8881 -.9998 OS 10 .9818 .49504 .36881 .00002 .99998 .63119 .21251 .26563 .00157 4.4181 .0003 .9078 -.9998 OF 10 .0513 .19875 .00154 .01240 .98760 .99846 .01036 .00686 .04447 5.2049 6.4439 .9965 .7774 CF 10 .0513 .19875 .00154 .01240 .98760 .99846 .01036 .00686 .04447 5.2049 6.4439 .9965 .7774 CS 10 .0992 .19124 .00455 .06201 .93799 .99545 .02133 .01687 .06991 4.1464 9.1950 .9832 .8555 NT 20 .7906 .23966 .04958 .00000 1.00000 .95042 .03388 .04234 .00000 5.9139 .0000 .9876-1.0000 MB 20 .0464 .20112 .00139 .00000 1.00000 .99861 .00527 .00659 .00000 7.2550 .0000 .9997 -1.0000 RB 20 .0383 .20091 .00114 .00000 1.00000 .99886 .00474 .00592 .00000 7.3156 .0000 .9997 1.000C MD 20 .0475 .20114 .00143 .00000 1.00000 .99857 .00533 .00666 .00000 7.2478 .0000 .9996-1.0000 RD 20 .0395 .20094 .00118 .00000 1.00000 .99882 .00481 .00601 .00000 7.3062 .0000 .9997 • 1.0000 OR 20 .9912 .56394 .45493 .00000 1.00000 .54507 .21695 .27119 .00000 4.3781 .0000 .8863 -1.0000 OS 20 .9835 .49747 .37184 .00000 1.00000 .62816 .21223 .26529 .00000 4.5919 .0000 .9070-1.0000 OF 20 .0492 .20119 .00148 .00000 1.00000 .99852 .00544 .00680 .00000 7.2361 .0000 .9996-1.0000 CF 20 .0492 .20119 .00148 .00000 1.00000 .99852 .00544 .00680 .00000 7.2361 .0000 .9996-1.0000 CS 20 .0910 .20300 .00422 .00187 .99813 .99578 .01318 .01596 .01428 5.5341 .4795 .9985 -.3853 NT 40 .7916 .23982 .04977 .00000 1.00000 .95023 .03360 .04200 .00000 5.9120 .0000 .9876-1.0000 MB 40 .0473 .20114 .00142 .00000 1.00000 .99858 .00529 .00661 .00000 7.2490 .0000 .9996-1.0000 RB 40 .0389 .20093 .00116 .00000 1.00000 .99884 .00474 .00593 .00000 7.3112 .0000 .9997-1.0000 MD 40 .0483 .20116 .00145 .00000 1.00000 .99855 .00534 .00668 .00000 7.2424 .0000 .9996-1.0000 RD 40 .0395 .20094 .00118 .00000 1.00000 .99883 .00477 .00597 .00000 7.3069 .0000 .9997 -1.0000 OR 40 .9908 .56369 .45461 .00000 1.00000 34539 .21646 .27057 .00000 4.3789 .0000 .8863 -1.0000 OS 40 .9840 .49789 .37236 .00000 1.00000 .62764 .21093 .26366 .00000 4.5905 .0000 .9069 -1.0000 OF 40 .0491 .20118 .00148 .00000 1.00000 .99852 .00540 .00675 .00000 7.2366 .0000 .9996 -1.0000 CF 40 .0491 .20118 .00148 .00000 1.00000 .99852 .00540 .00675 .00000 7.2366 .0000 .9996-1.0000 CS 40 .0906 .20324 .00405 .00000 1.00000 .99595 .01242 .01553 .00000 6.9125 .0000 .9990-1.0000 Table 10.2.1.2.3.2 Table of empirical results for tests of correlations with no preliminary omnibus test when P * !,/> = 10, mNz - .5,pNz = .4 N:p CtEX Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .6747 .28707 .04951 .35658 .64342 .95049 .09198 .05143 .21752 2.0172 3.6439 .8870 .6596 MB 2 .0277 .06116 .00106 .84869 .15131 .99894 .06058 .00639 .15091 2.0423 66.0658 .7859 .9837 RB 2 .0262 .05855 .00100 .85512 .14488 .99900 .05678 .00624 .14154 2.0305 67.4237 .7843 .9839 MD 2 .0284 .06198 .00109 .84669 .15331 .99891 .06101 .00649 .15196 2.0425 64.9796 .7863 .9834 RD 2 .0266 .05927 .00102 .85336 .14664 .99898 .05714 .00628 .14244 2.0338 67.0657 .7847 .9839 OR 2 .9951 .76198 .64538 .06313 .93687 .35462 .18600 .25630 .14108 1.1562 .3331 .7833 -5893 OS 2 .8353 .62608 50441 .19143 .80857 .49559 .32036 .33305 .36096 .8616 .6834 .7475 -.2352 OF 2 .0406 .07377 .00161 .81800 .18200 .99839 .06659 .00808 .16580 2.0379 50.7321 .7930 .9786 CF 2 .0406 .07377 .00161 .81800 .18200 .99839 .06659 .00808 .16580 2.0379 50.7321 .7930 .9786 CS 2 .4098 .21427 .02722 .50516 .49484 .97278 .09403 .04335 .21612 1.9104 6.3569 .8564 .8084 NT 4 .6688 .39860 .04969 .07802 .92198 .95031 .05173 .05222 .10642 3.0664 1.4215 .9660 .2075 MB 4 .0354 .22258 .00142 .44569 .55431 .99858 .09609 .00773 .23962 3.1206 85.0299 .8878 .9886 RB 4 .0274 .21088 .00107 .47439 52561 .99893 .09183 .00655 .22932 3.1342 111.0879 .8808 .9915 MD 4 .0361 .22375 .00145 .44281 55719 .99855 .09596 .00783 .23929 3.1216 83.3590 .8885 .9883 RD 4 .0281 .21216 .00110 .47124 .52876 .99890 .09189 .00662 .22946 3.1350 108.6185 .8815 .9912 OR 4 .9994 .81964 .70069 .00193 .99807 .29931 .13677 .22671 .01371 2.3634 .0177 .8229 -.9818 OS 4 .9972 .78867 .65038 .00390 .99610 .34962 .15120 .24602 .04297 2.2743 .0313 .8340 -.9664 OF 4 .0421 .23224 .00172 .42197 57803 .99828 .09497 .00858 .23670 3.1225 70.8403 .8936 .9860 CF 4 .0421 .23224 .00172 .42197 57803 .99828 .09497 .00858 .23670 3.1225 70.8403 .8936 .9860 CS 4 .2809 .32740 .01773 .20811 .79189 .98227 .05727 .03644 .12917 2.9161 6.5598 .9414 .8088 NT 10 .6713 .43009 .05035 .00029 .99971 .94965 .03169 .05284 .00433 5.0781 .0105 .9873 -.9878 MB 10 .0439 .39683 .00184 .01068 .98932 .99816 .01409 .00923 .03296 5.2051 4.7930 .9969 .7033 RB 10 .0280 .39462 .00111 .01512 .98488 .99889 .01633 .00676 .03999 5.2257 10.2828 .9959 .8613 MD 10 .0450 .39692 .00189 .01053 .98947 .99811 .01401 .00933 .03266 5.2031 4.6308 .9969 .6935 RD 10 .0285 .39472 .00113 .01489 .98511 .99887 .01618 .00681 .03958 5.2269 9.9937 .9960 .8571 OR 10 .9996 .82315 .70525 .00000 1.00000 .29475 .13684 .22807 .00000 3.7253 .0000 .8237 -1.000C OS 10 .9993 .79451 .65752 .00000 1.00000 .34248 .14812 .24687 .00000 3.8592 .0000 .8356 -1.000C OF 10 .0475 .39717 .00201 .01008 .98992 .99799 .01385 .00970 .03188 5.1996 4.2130 .9970 .6652 CF 10 .0475 .39717 .00201 .01008 .98992 .99799 .01385 .00970 .03188 5.1996 4.2130 .9970 .6652 CS 10 .1164 .39138 .00796 .03350 .96650 .99204 .02428 .02756 .03620 4.2425 3.4158 .9895 .6079 NT 20 .6633 .42981 .04969 .00000 1.00000 .95031 .03161 .05268 .00000 5.9128 .0000 .9876 -1.0000 MB 20 .0436 .40108 .00181 .00000 1.00000 .99819 .00543 .00904 .00000 7.1748 .0000 .9995 -1.0000 RB 20 .0274 .40067 .00112 .00000 1.00000 .99888 .00425 .00708 .00000 7.3217 .0000 .9997 1.0000 MD 20 .0448 .40112 .00187 .00000 1.00000 .99813 .00554 .00923 .00000 7.1647 .0000 .9995 -1.0000 RD 20 .0286 .40070 .00116 .00000 1.00000 .99884 .00431 .00718 .00000 7.3100 .0000 .9997 1.000C OR 20 .9996 .82164 .70274 .00000 1.00000 .29726 .13753 .22922 .00000 3.7326 .0000 .8243 1.0000 OS 20 .9996 .79354 .65590 .00000 1.00000 .34410 .14811 .24685 .00000 3.8636 .0000 .8360 1.0000 OF 20 .0469 .40117 .00195 .00000 1.00000 .99805 .00563 .00939 .00000 7.1513 .0000 .9995 1.0000 CF 20 .0469 .40117 .00195 .00000 1.00000 .99805 .00563 .00939 .00000 7.1513 .0000 .9995 1.0000 CS 20 .1082 .40416 .00743 .00075 .99925 .99257 .01637 .02681 .00641 5.6103 .1258 .9980 -.8156 NT 40 .6607 .43015 .05026 .00000 1.00000 .94974 .03226 .05377 .00000 5.9073 .0000 .9874-1.0000 MB 40 .0461 .40120 .00199 .00000 1.00000 .99801 .00588 .00981 .00000 7.1442 .0000 .9995 • 1.0000 RB 40 .0287 .40072 .00121 .00000 1.00000 .99879 .00449 .00748 .00000 7.2987 .0000 .9997 • 1.0000 MD 40 .0475 .40123 .00204 .00000 1.00000 .99796 .00594 .00989 .00000 7.1361 .0000 .9995 • 1.0000 RD 40 .0288 .40073 .00121 .00000 1.00000 .99879 .00451 .00751 .00000 7.2969 .0000 .9997 1.000C OR 40 .9996 .82304 .70507 .00000 1.00000 .29493 .13702 .22837 .00000 3.7259 .0000 .8237 -1.0000 OS 40 .9994 .79476 .65794 .00000 1.00000 .34206 .14659 .24431 .00000 3.8580 .0000 .8355 -1.0000 OF 40 .0479 .40124 .00206 .00000 1.00000 .99794 .00595 .00992 .00000 7.1338 .0000 .9995-1.0000 CF 40 .0479 .40124 .00206 .00000 1.00000 .99794 .00595 .00992 .00000 7.1338 .0000 .9995 -1.0000 CS 40 .1137 .40462 .00769 .00000 1.00000 .99231 .01574 .02623 .00000 6.6881 .0000 .9981 -1.0000 143 Table 10.2.1.2.3.3 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I,p = 10, mNz = £,pNz = .6 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' P A' B" NT 2 .4983 .40612 .04918 .35592 .64408 .95082 .13450 .06783 .21954 2.0223 3.6612 .8873 .6612 MB 2 .0187 .09331 .00116 .84525 .15475 .99884 .09244 .00885 .15381 2.0308 61.9172 .7866 .9825 RB 2 .0173 .08650 .00107 .85654 .14346 .99893 .08198 .00847 .13647 2.0061 63.3432 .7838 .9828 MD 2 .0195 .09457 .00121 .84319 .15681 .99879 .09323 .00903 .15510 2.0266 60.0841 .7870 .9820 RD 2 .0174 .08758 .00107 .85474 .14526 .99893 .08256 .00849 .13743 2.0125 63.5731 .7842 .9829 OR 2 .9983 .89964 .79392 .02989 .97011 .20608 .11568 .20284 .09170 1.0624 .2380 .7592 -.6989 OS 2 .8902 .80221 .68963 .12274 .87726 .31037 .29629 .31637 .30953 .6666 .5758 .7046 -.3306 OF 2 .0289 .11236 .00185 .81397 .18603 .99815 .10174 .01147 .16910 2.0101 45.3478 .7936 .9759 CF 2 .0289 .11236 .00185 .81397 .18603 .99815 .10174 .01147 .16910 2.0101 45.3478 .7936 .9759 CS 2 .4009 .36774 .04262 .41551 .58449 .95738 .13607 .07088 .21554 1.9345 4.2987 .8733 .7123 NT 4 .5007 .57281 .04978 .07850 .92150 .95022 .06792 .06834 .10510 3.0622 1.4259 .9658 .2093 MB 4 .0276 .34483 .00179 .42649 37351 .99821 .14988 .01171 .24935 3.0975 68.2577 .8924 .9855 RB 4 .0178 .31500 .00109 .47574 32426 .99891 .13894 .00856 .23153 3.1242 108.8686 .8804 .9913 MD 4 .0280 .34683 .00182 .42316 .57684 .99818 .14968 .01176 .24903 3.1022 67.3893 .8932 .9853 RD 4 .0181 .31685 .00111 .47266 .52734 .99889 .13902 .00861 .23166 3.1274 107.3172 .8812 .9911 OR 4 1.0000 .93214 .83162 .00084 .99916 .16838 .06922 .17156 .00778 2.1795 .0115 .7907 -.9880 OS 4 .9984 .92113 .80653 .00247 .99753 .19347 .08506 .19269 .04070 1.9452 .0280 .7947 -.9689 OF 4 .0327 .35880 .00212 .40341 39659 .99788 .14786 .01273 .24593 3.1039 57.8690 .8980 .9826 CF 4 .0327 .35880 .00212 .40341 .59659 .99788 .14786 .01273 .24593 3.1039 57.8690 .8980 .9826 CS 4 .2807 .52080 .02858 .15106 .84894 .97142 .07000 .05965 .10827 2.9339 3.5839 .9527 .6440 NT 10 .4901 .61957 .04932 .00026 .99974 .95068 .02759 .06892 .00326 5.1225 .0095 .9876 -.9890 MB 10 .0412 .59635 .00276 .00791 .99209 .99724 .01596 .01480 .02475 5.1884 2.5624 .9973 .4815 RB 10 .0182 39138 .00112 .01511 .98489 .99888 .02220 .00866 .03664 5.2245 10.2294 .9959 .8606 MD 10 .0419 .59646 .00282 .00777 .99223 .99718 .01588 .01502 .02454 5.1879 2.4718 .9973 .4660 RD 10 .0185 .59155 .00113 .01484 .98516 .99887 .02185 .00871 .03605 5.2273 9.9340 .9960 .8562 OR 10 1.0000 .93187 .82967 .00000 1.00000 .17033 .06848 .17120 .00000 3.3120 .0000 .7926 -1.0000 OS 10 .9999 .92260 .80651 .00000 1.00000 .19349 .07583 .18958 .00000 3.3998 .0000 .7984 •1.0000 OF 10 .0433 .59671 .00289 .00742 .99258 .99711 .01552 .01515 .02383 5.1958 2.3154 .9974 .4368 CF 10 .0433 .59671 .00289 .00742 .99258 .99711 .01552 .01515 .02383 5.1958 2.3154 .9974 .4368 CS 10 .1200 .59355 .01348 .01974 .98026 .98652 .02557 .04630 .02338 4.2711 1.3860 .9916 .1853 NT 20 .4859 .61979 .04947 .00000 1.00000 .95053 .02794 .06985 .00000 5.9149 .0000 .9876 -1.0000 MB 20 .0432 .60115 .00287 .00000 1.00000 .99713 .00594 .01485 .00000 7.0269 .0000 .9993 -1.0000 RB 20 .0192 .60049 .00122 .00000 1.00000 .99878 .00376 .00940 .00000 7.2964 .0000 .9997 1.0000 MD 20 .0440 .60118 .00294 .00000 1.00000 .99706 .00603 .01508 .00000 7.0194 .0000 .9993 -1.0000 RD 20 .0199 .60050 .00126 .00000 1.00000 .99874 .00380 .00951 .00000 7.2869 .0000 .9997 • 1.OOO0 OR 20 .9999 .93262 .83156 .00000 1.00000 .16844 .06822 .17056 .00000 3.3046 .0000 .7921 -1.0000 OS 20 .9999 .92331 .80827 .00000 1.00000 .19173 .07563 .18908 .00000 3.3934 .0000 .7979-1.0000 OF 20 .0448 .60121 .00302 .00000 1.00000 .99698 .00617 .01542 .00000 7.0103 .0000 .9992 -1.0000 CF 20 .0448 .60121 .00302 .00000 1.00000 .99698 .00617 .01542 .00000 7.0103 .0000 .9992-1.0000 CS 20 .1198 .60537 .01369 .00017 .99983 .98631 .01874 .04662 .00253 5.7826 .0190 .9965 -.9745 NT 40 .4915 .61992 .04980 .00000 1.00000 .95020 .02816 .07039 .00000 5.9117 .0000 .9875 -1.0000 MB 40 .0415 .60115 .00288 .00000 1.00000 .99712 .00629 .01573 .00000 7.0263 .0000 .9993 -1.0000 RB 40 .0178 .60047 .00118 .00000 1.00000 .99882 .00381 .00952 .00000 7.3062 .0000 .9997 -1.0000 MD 40 .0424 .60118 .00294 .00000 1.00000 .99706 .00635 .01588 .00000 7.0194 .0000 .9993 -1.0000 RD 40 .0178 .60047 .00118 .00000 1.00000 .99882 .00383 .00957 .00000 7.3048 .0000 .9997 -1.000C OR 40 1.0000 .93226 .83066 .00000 1.00000 .16934 .06893 .17234 .00000 3.3081 .0000 .7923 -1.0000 OS 40 .9999 .92330 .80825 .00000 1.00000 .19175 .07629 .19073 .00000 3.3934 .0000 .7979 -1.0000 OF 40 .0426 .60118 .00296 .00000 1.00000 .99704 .00637 .01593 .00000 7.0176 .0000 .9993 -1.0000 CF 40 .0426 .60118 .00296 .00000 1.00000 .99704 .00637 .01593 .00000 7.0176 .0000 .9993-1.0000 CS 40 .1181 .60544 .01359 .00000 1.00000 .98641 .01867 .04667 .00000 6.4738 .0000 .9966 -1.0000 Table 10.2.1.2.3.4 Table of empirical results for tests of correlations with no preliminary omnibus test when P * I,/? = 10, mNz = J5,pNz = .8 N:p OLEX Rej Fp Fn Tp Tn s.Rej s:FpTn s:FnTp d' P A' B" NT 2 .2657 .52462 .04840 .35632 .64368 .95160 .17536 .10299 .21709 2.0289 3.7096 .8876 .6655 MB 2 .0118 .12842 .00150 .83985 .16015 .99850 .12800 .01552 .15984 1.9739 49.8932 .7874 .9780 RB 2 .0103 .11470 .00127 .85694 .14306 .99873 .10647 .01364 .13302 1.9526 54.0152 .7833 .9796 MD 2 .0122 .13016 .00156 .83769 .16231 .99844 .12905 .01579 .16115 1.9715 48.6889 .7879 .9774 RD 2 .0104 .11621 .00128 .85506 .14494 .99872 .10732 .01368 .13409 1.9583 54.0602 .7838 .9796 OR 2 .9986 .95948 .87027 .01822 .98178 .12973 .07655 .17356 .06862 .9643 .2117 .7433 -.7265 OS 2 .9212 .89043 .79829 .08654 .91346 .20171 .26353 .28906 .26725 .5269 .5605 .6743 -.3415 OF 2 .0154 .15398 .00209 .80804 .19196 .99791 .14077 .01900 .17573 1.9937 41.4041 .7948 .9735 CF 2 .0154 .15399 .00209 .80804 .19196 .99791 .14077 .01900 .17573 1.9937 41.4045 .7948 .9735 CS 2 .2992 53556 .06430 .34662 .65338 .93570 .17675 .13206 .21350 1.9141 2.9355 .8828 .5802 NT 4 .2727 .74755 .04953 .07795 .92205 .95047 .08416 .10397 .10182 3.0684 1.4240 .9661 .2084 MB 4 .0184 .48328 .00258 .39654 .60346 .99742 .20737 .02174 .25880 3.0595 48.3091 .8995 .9787 RB 4 .0081 .42021 .00099 .47498 52502 .99901 .18332 .01134 .22915 3.1563119.4687 .8807 .9921 MD 4 .0194 .48606 .00270 .39310 .60690 .99730 .20695 .02209 .25826 3.0534 46.2190 .9003 .9777 RD 4 .0082 .42271 .00100 .47186 52814 .99900 .18344 .01140 .22930 3.1608118.1880 .8814 .9920 OR 4 .9999 .97913 .89732 .00042 .99958 .10268 .02953 .14484 .00442 2.0714 .0085 .7745 -.9909 OS 4 .9992 .97680 .88843 .00111 .99889 .11157 .04096 .15823 .02665 1.8398 .0196 .7751 -.9778 OF 4 .0229 .50118 .00312 .37431 .62569 .99688 .20340 .02323 .25382 3.0551 39.9585 .9049 .9738 CF 4 .0229 .50118 .00312 .37431 .62569 .99688 .20340 .02323 .25382 3.0551 39.9585 .9049 .9738 CS 4 .2186 .72375 .04752 .10719 .89281 .95248 .07808 .11767 .09003 2.9110 1.8638 .9586 .3578 NT 10 .2710 .80968 .04949 .00028 .99972 .95051 .02088 .10368 .00323 5.1023 .0101 .9876 -.9883 MB 10 .0416 .79748 .00594 .00463 .99537 .99406 .01561 .03312 .01754 5.1175 .8012 .9973 -.1233 RB 10 .0086 .78804 .00108 .01521 .98479 .99892 .02820 .01218 .03512 5.2324 10.6289 .9959 .8659 MD 10 .0423 .79762 .00607 .00450 .99550 .99393 .01538 .03349 .01718 5.1205 .7662 .9973 -.1478 RD 10 .0088 .78827 .00111 .01494 .98506 .99889 .02781 .01242 .03462 5.2306 10.1739 .9960 .8597 OR 10 .9997 .97932 .89659 .00000 1.00000 .10341 .02898 .14488 .00000 3.0025 .0000 .7759 -1.0000 OS 10 .9997 .97766 .88828 .00000 1.00000 .11172 .03129 .15644 .00000 3.0475 .0000 .7779 -1.0000 OF 10 .0437 .79778 .00622 .00433 .99567 .99378 .01518 .03372 .01688 5.1242 .7248 .9973 -.1780 CF 10 .0437 .79778 .00622 .00433 .99567 .99378 .01518 .03372 .01688 5.1242 .7248 .9973 -.1780 CS 10 .1208 .79828 .02869 .00932 .99068 .97131 .02443 .09690 .01499 4.2532 .3821 .9904 -.5024 NT 20 .2647 .80981 .04904 .00000 1.00000 .95096 .02110 .10549 .00000 5.9191 .0000 .9877 -1.0000 MB 20 .0402 .80119 .00596 .00000 1.00000 .99404 .00698 .03488 .00000 6.7797 .0000 .9985 1.0000 RB 20 .0076 .80021 .00104 .00000 1.00000 .99896 .00270 .01348 .00000 7.3422 .0000 .9997 -1.0000 MD 20 .0409 .80122 .00610 .00000 1.00000 .99390 .00710 .03550 .00000 6.7712 .0000 .9985 -1.000C RD 20 .0079 .80022 .00108 .00000 1.00000 .99892 .00272 .01361 .00000 7.3328 .0000 .9997 1.0000 OR 20 1.0000 .97932 .89662 .00000 1.00000 .10338 .02869 .14343 .00000 3.0024 .0000 .7758 1.000C OS 20 .9998 .97765 .88823 .00000 1.00000 .11177 .03119 .15595 .00000 3.0477 .0000 .7779 -1.0000 OF 20 .0415 .80124 .00619 .00000 1.00000 .99381 .00715 .03573 .00000 6.7661 .0000 .9985 1.0000 CF 20 .0415 .80124 .00619 .00000 1.00000 .99381 .00715 .03573 .00000 6.7661 .0000 .9985 1.0000 CS 20 .1110 .80559 .02808 .00003 .99997 .97192 .01990 .09940 .00088 5.9408 .0018 .9930 -.9980 NT 40 .7916 .23982 .04977 .00000 1.00000 .95023 .03360 .04200 .00000 5.9120 .0000 .9876-1.0000 MB 40 .0399 .80120 .00601 .00000 1.00000 .99399 .00709 .03545 .00000 6.7764 .0000 .9985 -1.000C RB 40 .0080 .80023 .00113 .00000 1.00000 .99887 .00278 .01392 .00000 7.3178 .0000 .9997 -1.0000 MD 40 .0404 .80122 .00609 .00000 1.00000 .99391 .00714 .03570 .00000 6.7718 .0000 .9985 -1.000C RD 40 .0081 .80023 .00114 .00000 1.00000 .99886 .00279 .01396 .00000 7.3148 .0000 .9997-1.0000 OR 40 .9999 .97984 .89922 .00000 1.00000 .10078 .02864 .14320 .00000 2.9878 .0000 .7752 -1.0000 OS 40 .9999 .97812 .89059 .00000 1.00000 .10941 .03115 .15577 .00000 3.0352 .0000 .7774-1.000C OF 40 .0408 .80123 .00613 .00000 1.00000 .99387 .00715 .03576 .00000 6.7693 .0000 .9985 -1.0000 CF 40 .0408 .80123 .00613 .00000 1.00000 .99387 .00715 .03576 .00000 6.7693 .0000 .9985 -1.0000 CS 40 .1151 .80591 .02956 .00000 1.00000 .97044 .02060 .10298 .00000 6.1523 .0000 .9926-1.0000 145 Table 10.2.2.1.1.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz - .2 N:p Ct£X Rej Fp Fn Tp Tn s.Rej s:FpTn S.FnTp d' P A' B" NT 2 .0526 .01127 .01114 .98820 .01180 .98886 .04944 .05178 .08100 .0221 1.0515 .5142 .0285 MB 2 .0203 .00273 .00263 .99685 .00315 .99738 .01702 .01852 .04019 .0595 1.1787 .5418 .0906 RB 2 .0202 .00270 .00259 .99685 .00315 .99741 .01676 .01823 .04019 .0642 1.1941 3448 .0978 MD 2 .0210 .00281 .00273 .99685 .00315 .99728 .01730 .01893 .04019 .0474 1.1396 .5338 .0721 RD 2 .0209 .00277 .00268 .99685 .00315 .99733 .01695 .01852 .04019 .0534 1.1588 .5378 .0813 OR 2 .0560 .02353 .02335 .97575 .02425 .97665 .11098 .11121 .13356 .0160 1.0323 .5095 .0184 OS 2 .0276 .00728 .00706 .99185 .00815 .99294 .05506 .05485 .07489 .0519 1.1344 .5336 .0709 OF 2 .0253 .00341 .00331 .99620 .00380 .99669 .01938 .02099 .04400 .0458 1.1312 .5322 .0683 CF 2 .0253 .00341 .00331 .99620 .00380 .99669 .01938 .02099 .04400 .0458 1.1312 .5322 .0683 CS 2 .0481 .00700 .00690 .99260 .00740 .99310 .03113 .03283 .06241 .0252 1.0637 3170 .0347 NT 4 .0544 .01189 .01131 .98580 .01420 .98869 .05079 .05186 .08860 .0880 1.2174 .5516 .1117 MB 4 .0213 .00298 .00275 .99610 .00390 .99725 .01786 .01892 .04455 .1156 1.3692 .5740 .1724 RB 4 .0213 .00297 .00274 .99610 .00390 .99726 .01778 .01880 .04455 .1171 1.3748 .5748 .1746 MD 4 .0216 .00301 .00279 .99610 .00390 .99721 .01800 .01904 .04455 .1112 1.3525 .5716 .1658 RD 4 .0215 .00299 .00276 .99610 .00390 .99724 .01784 .01888 .04455 .1141 1.3636 .5732 .1702 OR 4 .0585 .02341 .02300 .97495 .02505 .97700 .10611 .10632 .13285 .0363 1.0744 .5210 .0416 OS 4 .0268 .00742 .00704 .99105 .00895 .99296 .05553 .05505 .07743 .0877 1.2354 .5539 .1187 OF 4 .0232 .00331 .00301 .99550 .00450 .99699 .01903 .01989 .04827 .1344 1.4333 .5830 .1973 CF 4 .0232 .00331 .00301 .99550 .00450 .99699 .01903 .01989 .04827 .1344 1.4333 .5830 .1973 CS 4 .0466 .00705 .00661 .99120 .00880 .99339 .02969 .03165 .06688 .1037 1.2861 .5627 .1409 NT 10 .0637 .01548 .01263 .97310 .02690 .98738 .05776 .05259 .12561 .3091 1.9039 .6363 .3548 MB 10 .0212 .00406 .00275 .99070 .00930 .99725 .02153 .01909 .07010 .4227 2.9572 .6777 .5412 RB 10 .0211 .00401 .00271 .99080 .00920 .99729 .02114 .01872 .06976 .4232 2.9659 .6779 .5423 MD 10 .0213 .00412 .00276 .99045 .00955 .99724 .02175 .01913 .07095 .4311 3.0143 .6794 .5489 RD 10 .0212 .00407 .00274 .99060 .00940 .99726 .02137 .01888 .07044 .4282 2.9973 .6789 .5466 OR 10 .0719 .02995 .02799 .96220 .03780 .97201 .11809 .11557 .16209 .1344 1.2813 .5674 .1442 OS 10 .0280 .00943 .00779 .98400 .01600 .99221 .06113 .05756 .10293 .2743 1.8699 .6304 .3416 OF 10 .0219 .00429 .00286 .99000 .01000 .99714 .02233 .01960 .07246 .4368 3.0389 .6802 .5524 CF 10 .0219 .00429 .00286 .99000 .01000 .99714 .02233 .01960 .07246 .4368 3.0389 .6802 .5524 CS 10 .0495 .00895 .00683 .98255 .01745 .99318 .03303 .03123 .09445 .3568 2.2623 .6549 .4333 NT 20 .0919 .02427 .01673 .94555 .05445 .98328 .07126 .05768 .18443 .5235 2.6545 .6828 .5158 MB 20 .0255 .00673 .00329 .97950 .02050 .99671 .02724 .02062 .10189 .6741 4.9767 .7142 .7194 RB 20 .0252 .00663 .00324 .97980 .02020 .99676 .02667 .02040 .10071 .6731 4.9831 .7142 .7196 MD 20 .0258 .00678 .00333 .97940 .02060 .99668 .02735 .02073 .10211 .6724 4.9466 .7140 .7178 RD 20 .0255 .00671 .00328 .97955 .02045 .99673 .02698 .02051 .10153 .6744 4.9835 .7143 .7198 OR 20 .1094 .04699 .04283 .93635 .06365 .95718 .14517 .14174 .20863 .1940 1.3697 .5872 .1850 OS 20 .0423 .01565 .01141 .96740 .03260 .98859 .07669 .06757 .14980 .4325 2.4374 .6678 .4730 OF 20 .0264 .00696 .00340 .97880 .02120 .99660 .02774 .02094 .10369 .6769 4.9676 .7144 .7193 CF 20 .0264 .00696 .00340 .97880 .02120 .99660 .02774 .02094 .10369 .6769 4.9676 .7144 .7193 CS 20 .0636 .01426 .00883 .96400 .03600 .99118 .04148 .03540 .13400 .5738 3.3097 .6956 3974 NT 40 .1440 .04427 .02413 .87515 .12485 .97588 .09176 .06476 .27748 .8241 3.6260 .7275 .6455 MB 40 .0313 .01451 .00401 .94350 .05650 .99599 .03912 .02259 .16796 1.0662 9.5646 .7454 .8605 RB 40 .0304 .01433 .00386 .94380 .05620 .99614 .03849 .02199 .16702 1.0764 9.8552 .7460 .8647 MD 40 .0314 .01460 .00403 .94310 .05690 .99598 .03928 .02263 .16857 1.0686 9.5911 .7456 .8610 RD 40 .0305 .01443 .00389 .94340 .05660 .99611 .03869 .02213 .16763 1.0777 9.8533 .7461 .8648 OR 40 .1857 .08294 .07062 .86780 .13220 .92938 .18607 .17839 .29348 .3551 1.5831 .6330 .2722 OS 40 .0757 .03343 .02079 .91600 .08400 .97921 .11189 .09473 .24176 .6591 3.0829 .7043 .5816 OF 40 .0317 .01477 .00406 .94240 .05760 .99594 .03953 .02272 .16966 1.0716 9.6038 .7458 .8613 CF 40 .0317 .01477 .00406 .94240 .05760 .99594 .03953 .02272 .16966 1.0716 9.6038 .7458 .8613 CS 40 .0794 .02598 .01100 .91410 .08590 .98900 .05375 .03946 .20031 .9239 5.4157 .7369 .7566 146 Table 10.2.2.1.1.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz - .4 N.p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp cT P A' B" NT 2 .0484 .01193 .01153 .98748 .01253 .98847 .05043 .05583 .06671 .0317 1.0741 .5200 .0407 MB 2 .0166 .00308 .00282 .99653 .00348 .99718 .01796 .02187 .02969 .0692 1.2081 .5475 .1043 RB 2 .0165 .00306 .00280 .99655 .00345 .99720 .01780 .02181 .02959 .0687 1.2068 .5473 .1037 MD 2 .0172 .00315 .00292 .99650 .00350 .99708 .01820 .02223 .02980 .0602 1.1783 .5418 .0906 RD 2 .0172 .00313 .00292 .99655 .00345 .99708 .01803 .02223 .02959 .0554 1.1631 .5388 .0835 OR 2 .0567 .02558 .02507 .97365 .02635 .97493 .11517 .11731 .12642 .0215 1.0427 .5125 .0243 OS 2 .0263 .00829 .00805 .99135 .00865 .99195 .05850 .06027 .06755 .0264 1.0652 .5175 .0356 OF 2 .0217 .00383 .00370 .99598 .00403 .99630 .02041 .02512 .03225 .0283 1.0784 .5203 .0419 CF 2 .0217 .00383 .00370 .99598 .00403 .99630 .02041 .02512 .03225 .0283 1.0784 .5203 .0419 CS 2 .0400 .00759 .00742 .99215 .00785 .99258 .03255 .03812 .04745 .0206 1.0513 .5139 .0282 NT 4 .0530 .01459 .01253 .98233 .01768 .98747 .05616 .05796 .08105 .1360 1.3439 .5740 .1677 MB 4 .0177 .00364 .00302 .99543 .00458 .99698 .02017 .02271 .03533 .1396 1.4528 .5855 .2045 RB 4 .0176 .00358 .00297 .99550 .00450 .99703 .01973 .02229 .03471 .1394 1.4533 .5856 .2046 MD 4 .0179 .00367 .00305 .99540 .00460 .99695 .02029 .02283 .03541 .1378 1.4455 .5846 .2019 RD 4 .0179 .00361 .00302 .99550 .00450 .99698 .01985 .02247 .03471 .1339 1.4315 .5828 .1966 OR 4 .0659 .02932 .02798 .96868 .03133 .97202 .11992 .12087 .13487 .0496 1.0981 .5275 .0546 OS 4 .0261 .00927 .00805 .98890 .01110 .99195 .06249 .06101 .07707 .1197 1.3244 .5695 .1578 OF 4 .0194 .00416 .00337 .99465 .00535 .99663 .02179 .02438 .03820 .1574 1.5131 .5932 .2266 CF 4 .0194 .00416 .00337 .99465 .00535 .99663 .02179 .02438 .03820 .1574 1.5131 .5932 .2266 CS 4 .0400 .00880 .00740 .98910 .01090 .99260 .03380 .03809 .05574 .1434 1.4039 .5812 .1896 NT 10 .0713 .02405 .01582 .96360 .03640 .98418 .07237 .06180 .12202 .3549 2.0133 .6466 .3852 MB 10 .0167 .00611 .00282 .98895 .01105 .99718 .02634 .02174 .05514 .4797 3.3637 .6883 .5911 RB 10 .0162 .00599 .00272 .98910 .01090 .99728 .02564 .02124 .05449 .4863 3.4342 .6897 .5983 MD 10 .0171 .00622 .00288 .98878 .01123 .99712 .02660 .02199 .05562 .4781 3.3388 .6879 .5885 RD 10 .0166 .00611 .00278 .98890 .01110 .99722 .02596 .02149 .05502 .4853 3.4134 .6894 .5963 OR 10 .0984 .04778 .04280 .94475 .05525 .95720 .15136 .14862 .17784 .1231 1.2264 .5596 .1205 OS 10 .0336 .01579 .01122 .97735 .02265 .98878 .08345 .07416 .11369 .2811 1.8262 .6291 .3324 OF 10 .0175 .00643 .00297 .98838 .01163 .99703 .02709 .02241 .05643 .4821 3.3547 .6884 .5905 CF 10 .0175 .00643 .00297 .98838 .01163 .99703 .02709 .02241 .05643 .4821 3.3547 .6884 .5905 CS 10 .0468 .01412 .00852 .97748 .02253 .99148 .04302 .03996 .08031 .3818 2.3119 .6590 .4456 NT 20 .1107 .04568 .02302 .92033 .07968 .97698 .09650 .07052 .18079 .5878 2.7183 .6923 .5306 MB 20 .0226 .01257 .00387 .97438 .02563 .99613 .03749 .02575 .08307 .7141 5.1917 .7177 .7327 RB 20 .0221 .01233 .00378 .97485 .02515 .99622 .03654 .02549 .08158 .7134 5.2118 .7178 .7335 MD 20 .0226 .01273 .00387 .97398 .02603 .99613 .03775 .02575 .08377 .7208 5.2594 .7184 .7362 RD 20 .0221 .01248 .00378 .97448 .02553 .99622 .03675 .02549 .08212 .7198 5.2768 .7184 .7368 OR 20 .1761 .09211 .07800 .88673 .11328 .92200 .20506 .19735 .24991 .2094 1.3167 .5874 .1655 OS 20 .0607 .03397 .02143 .94723 .05278 .97857 .12296 .10399 .17567 .4065 2.0970 .6565 .4089 OF 20 .0235 .01308 .00403 .97335 .02665 .99597 .03838 .02636 .08487 .7168 5.1658 .7178 .7318 CF 20 .0235 .01308 .00403 .97335 .02665 .99597 .03838 .02636 .08487 .7168 5.1658 .7178 .7318 CS 20 .0657 .02716 .01200 .95010 .04990 .98800 .05845 .04727 .11816 .6113 3.2968 .6995 .5999 NT 40 .1736 .09958 .03448 .80278 .19723 .96552 .12928 .08140 .26592 .9671 3.6369 .7484 .6525 MB 40 .0274 .03214 .00467 .92665 .07335 .99533 .05959 .02810 .13959 1.1483 10.2352 .7513 .8721 RB 40 .0261 .03148 .00442 .92793 .07208 .99558 .05794 .02718 .13648 1.1579 10.6075 .7517 .8766 MD 40 .0282 .03248 .00480 .92600 .07400 .99520 .05988 .02847 .14023 1.1433 10.0488 .7512 .8697 RD 40 .0269 .03185 .00457 .92723 .07278 .99543 .05828 .02771 .13725 1.1516 10.3724 .7514 .8738 OR 40 .3439 .19798 .15523 .73790 .26210 .84477 .27173 .26031 .34647 .3774 1.3655 .6336 .1919 OS 40 .1321 .09065 .05065 .84935 .15065 .94935 .19679 .16071 .29279 .6049 2.2440 .6923 .4537 OF 40 .0285 .03275 .00485 .92540 .07460 .99515 .06021 .02860 .14102 1.1440 10.0180 .7513 .8693 CF 40 .0285 .03275 .00485 .92540 .07460 .99515 .06021 .02860 .14102 1.1440 10.0180 .7513 .8693 CS 40 .0897 .06054 .01645 .87333 .12668 .98355 .08267 .05482 .17854 .9911 5.0689 .7456 .7448 147 Table 10.2.2.1.1.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .6 N:p OLEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' P A' B" NT 2 .0354 .01284 .01155 .98630 .01370 .98845 .05293 .06465 .06326 .0660 1.1592 .5398 .0841 MB 2 .0103 .00337 .00260 .99612 .00388 .99740 .01875 .02561 .02601 .1323 1.4348 .5829 .1973 RB 2 .0103 .00336 .00260 .99613 .00387 .99740 .01867 .02561 .02596 .1309 1.4293 .5822 .1953 MD 2 .0105 .00343 .00265 .99605 .00395 .99735 .01895 .02585 .02632 .1319 1.4320 .5826 .1963 RD 2 .0105 .00341 .00265 .99608 .00392 .99735 .01880 .02585 .02611 .1290 1.4212 .5812 .1923 OR 2 .0515 .02777 .02680 .97158 .02842 .97320 .12090 .12819 .12637 .0255 1.0500 .5146 .0284 OS 2 .0206 .00970 .00905 .98987 .01013 .99095 .06510 .07198 .06963 .0422 1.1039 .5270 .0559 OF 2 .0140 .00422 .00358 .99535 .00465 .99643 .02168 .03031 .02883 .0890 1.2653 .5581 .1302 CF 2 .0140 .00422 .00358 .99535 .00465 .99643 .02168 .03031 .02883 .0890 1.2653 .5581 .1302 CS 2 .0273 .00808 .00738 .99145 .00855 .99263 .03404 .04585 .04271 .0539 1.1388 .5347 .0732 NT 4 .0438 .01843 .01365 .97838 .02162 .98635 .06389 .06848 .08180 .1858 1.4810 .5942 .2220 MB 4 .0112 .00409 .00288 .99510 .00490 .99713 .02131 .02735 .03016 .1789 1.6130 .6038 .2595 RB 4 .0112 .00405 .00285 .99515 .00485 .99715 .02104 .02701 .02975 .1782 1.6109 .6036 .2588 MD 4 .0113 .00413 .00290 .99505 .00495 .99710 .02149 .02746 .03047 .1796 1.6150 .6040 .2602 RD 4 .0113 .00407 .00288 .99513 .00487 .99713 .02108 .02712 .02979 .1765 1.6032 .6028 .2563 OR 4 .0717 .03813 .03568 .96023 .03977 .96433 .13928 .14452 .14747 .0498 1.0927 .5268 .0521 OS 4 .0226 .01204 .00972 .98642 .01358 .99028 .07690 .07466 .08604 .1277 1.3367 .5720 .1636 OF 4 .0127 .00482 .00333 .99418 .00582 .99668 .02372 .02992 .03354 .1908 1.6481 .6077 .2714 CF 4 .0127 .00482 .00333 .99418 .00582 .99668 .02372 .02992 .03354 .1908 1.6481 .6077 .2714 CS 4 .0297 .01117 .00810 .98678 .01322 .99190 .03945 .04832 .05287 .1846 1.5323 .5981 .2376 NT 10 .0640 .03390 .01845 .95580 .04420 .98155 .08663 .07448 .12008 .3830 2.0665 .6522 .3999 MB 10 .0132 .00860 .00333 .98788 .01212 .99668 .03162 .02886 .04843 .4605 3.1382 .6836 .5663 RB 10 .0131 .00847 .00328 .98807 .01193 .99673 .03097 .02843 .04752 .4596 3.1395 .6836 .5664 MD 10 .0132 .00871 .00333 .98770 .01230 .99668 .03186 .02886 .04881 .4663 3.1793 .6847 .5714 RD 10 .0131 .00861 .00328 .98783 .01217 .99673 .03135 .02843 .04821 .4671 3.1926 .6849 .5728 OR 10 .1176 .07013 .05960 .92285 .07715 .94040 .18676 .18341 .20609 .1336 1.2205 .5615 .1191 OS 10 .0366 .02539 .01675 .96885 .03115 .98325 .11374 .09929 .13532 .2619 1.6862 .6192 .2939 OF 10 .0133 .00909 .00335 .98708 .01292 .99665 .03266 .02896 .05008 .4827 3.2946 .6876 .5850 CF 10 .0133 .00909 .00335 .98708 .01292 .99665 .03266 .02896 .05008 .4827 3.2946 .6876 .585C CS 10 .0378 .02103 .01003 .97163 .02837 .98998 .05529 .05190 .08029 .4201 2.4317 .6663 .4705 NT 20 .1007 .07303 .02820 .89708 .10292 .97180 .12119 .08856 .17763 .6428 2.7728 .7007 .5422 MB 20 .0159 .01866 .00410 .97163 .02837 .99590 .04675 .03272 .07368 .7384 5.3625 .7200 .7419 RB 20 .0154 .01815 .00398 .97240 .02760 .99603 .04499 .03226 .07114 .7369 5.3889 .7199 .7429 MD 20 .0160 .01891 .00413 .97123 .02877 .99588 .04730 .03282 .07462 .7424 5.3959 .7203 .7436 RD 20 .0156 .01836 .00403 .97208 .02792 .99598 .04531 .03244 .07162 .7376 5.3798 .7200 .7426 OR 20 .2410 .15602 .12680 .82450 .17550 .87320 .26584 .25827 .29554 .2090 1.2420 .5833 .1330 OS 20 .0755 .06062 .03665 .92340 .07660 .96335 .17804 .14869 .21399 .3626 1.7927 .6408 .3341 OF 20 .0168 .01944 .00433 .97048 .02952 .99568 .04804 .03354 .07556 .7376 5.2840 .7197 .7386 CF 20 .0168 .01944 .00433 .97048 .02952 .99568 .04804 .03354 .07556 .7376 5.2840 .7197 .7386 CS 20 .0599 .04611 .01598 .93380 .06620 .98403 .08130 .06539 .12128 .6403 3.2172 .7024 .5945 NT 40 .1467 .16190 .04083 .75738 .24262 .95918 .15535 .10352 .23820 1.0433 3.5692 .7605 .6487 MB 40 .0195 .04997 .00500 .92005 .07995 .99500 .07628 .03588 .12383 1.1704 10.2765 .7532 .8733 RB 40 .0186 .04835 .00475 .92258 .07742 .99525 .07268 .03486 .11834 1.1709 10.4979 .7529 .8758 MD 40 .0195 .05066 .00503 .91892 .08108 .99498 .07688 .03614 .12482 1.1763 10.3403 .7536 .8742 RD 40 .0187 .04899 .00480 .92155 .07845 .99520 .07313 .03521 .11902 1.1743 10.5055 .7532 .8760 OR 40 .4804 .34850 .26988 .59908 .40092 .73013 .33516 .33639 .37596 .3622 1.1694 .6266 .0987 OS 40 .2000 .18237 .10968 .76917 .23083 .89033 .29929 .25431 .35644 .4922 1.6216 .6652 .2903 OF 40 .0198 .05113 .00510 .91818 .08182 .99490 .07721 .03639 .12536 1.1760 10.2744 .7537 .8735 CF 40 .0198 .05113 .00510 .91818 .08182 .99490 .07721 .03639 .12536 1.1760 10.2744 .7537 .8735 CS 40 .0859 .10953 .02330 .83298 .16702 .97670 .11620 .07903 .17915 1.0239 4.5416 .7519 .7188 148 Table 10.2.2.1.1.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .1, pNz = .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .0212 .01349 .01175 .98608 .01393 .98825 .05460 .08299 .05863 .0658 1.1583 .5396 .0836 MB 2 .0050 .00338 .00250 .99640 .00360 .99750 .01883 .03527 .02186 .1196 1.3889 .5767 .1798 RB 2 .0050 .00336 .00250 .99643 .00358 .99750 .01862 .03527 .02165 .1173 1.3803 5754 .1764 MD 2 .0053 .00347 .00265 .99633 .00368 .99735 .01916 .03631 .02213 .1077 1.3423 .5700 .1616 RD 2 .0053 .00344 .00265 .99636 .00364 .99735 .01893 .03631 .02196 .1042 1.3300 .5681 .1566 OR 2 .0411 .02899 .02750 .97064 .02936 .97250 .12470 .14123 .12743 .0286 1.0560 .5163 .0318 OS 2 .0137 .00968 .00865 .99006 .00994 .99135 .06610 .07779 .06815 .0516 1.1291 .5327 .0686 OF 2 .0064 .00417 .00320 .99559 .00441 .99680 .02153 .03987 .02470 .1078 1.3339 .5690 .1587 CF 2 .0064 .00417 .00320 .99559 .00441 .99680 .02153 .03987 .02470 .1078 1.3339 .5690 .1587 CS 2 .0140 .00859 .00735 .99110 .00890 .99265 .03577 .06302 .03932 .0699 1.1831 .5439 .0946 NT 4 .0309 .02131 .01640 .97746 .02254 .98360 .06959 .09424 .07618 .1306 1.3102 .5696 .1546 MB 4 .0067 .00474 .00335 .99491 .00509 .99665 .02314 .04079 .02677 .1416 1.4533 .5858 .2051 RB 4 .0066 .00468 .00330 .99498 .00503 .99670 .02272 .04049 .02634 .1423 1.4570 .5863 .2064 MD 4 .0069 .00482 .00345 .99484 .00516 .99655 .02338 .04139 .02704 .1369 1.4340 .5834 .1980 RD 4 .0068 .00474 .00340 .99492 .00508 .99660 .02284 .04109 .02644 .1358 1.4309 .5829 .1968 OR 4 .0610 .04460 .04135 .95459 .04541 .95865 .15261 .17268 .15597 .0442 1.0786 .5234 .0447 OS 4 .0190 .01458 .01220 .98483 .01518 .98780 .08562 .09302 .08882 .0853 1.2072 .5498 .1072 OF 4 .0080 .00558 .00400 .99403 .00598 .99600 .02543 .04454 .02951 .1385 1.4299 .5831 .1970 CF 4 .0080 .00558 .00400 .99403 .00598 .99600 .02543 .04454 .02951 .1385 1.4299 .5831 .1970 CS 4 .0176 .01318 .00890 .98575 .01425 .99110 .04486 .06687 .05136 .1794 1.5054 .5952 .2285 NT 10 .0410 .04418 .02130 .95010 .04990 .97870 .09775 .10487 .11276 .3818 2.0162 .6506 .3892 MB 10 .0063 .01082 .00315 .98726 .01274 .99685 .03565 .03956 .04303 .4976 3.4403 .6906 .6004 RB 10 .0061 .01063 .00305 .98748 .01253 .99695 .03482 .03893 .04216 .5017 3.4905 .6915 .6053 MD 10 .0063 .01100 .00315 .98704 .01296 .99685 .03596 .03956 .04344 .5044 3.4928 .6917 .6059 RD 10 .0062 .01084 .00310 .98723 .01278 .99690 .03525 .03925 .04268 .5040 3.4991 .6918 .6064 OR 10 .1161 .09438 .07895 .90176 .09824 .92105 .21612 .23270 .22454 .1205 1.1769 .5543 .0984 OS 10 .0325 .03485 .02165 .96185 .03815 .97835 .13577 .12553 .14587 .2482 1.6013 .6123 .2680 OF 10 .0069 .01162 .00345 .98634 .01366 .99655 .03708 .04139 .04472 .4948 3.3680 .6894 .5935 CF 10 .0069 .01162 .00345 .98634 .01366 .99655 .03708 .04139 .04472 .4948 3.3680 .6894 .5935 CS 10 .0226 .02747 .01145 .96853 .03148 .98855 .06421 .07579 .07515 .4156 2.3610 .6641 .4585 NT 20 .0630 .09935 .03265 .88398 .11603 .96735 .13719 .12810 .16264 .6481 2.6766 .7012 .5291 MB 20 .0095 .02510 .00485 .96984 .03016 .99515 .05430 .05002 .06620 .7079 4.8568 .7162 .7167 RB 20 .0093 .02438 .00475 .97071 .02929 .99525 .05208 .04952 .06359 .7021 4.8284 .7156 .7148 MD 20 .0096 .02555 .00490 .96929 .03071 .99510 .05500 .05026 .06708 .7124 4.8852 .7166 .7185 RD 20 .0095 .02475 .00485 .97028 .02973 .99515 .05252 .05002 .06409 .7015 4.7983 .7155 .7133 OR 20 .2589 .22289 .18050 .76651 .23349 .81950 .30914 .32974 .32206 .1861 1.1649 .5729 .095C OS 20 .0796 .09019 .05550 .90114 .09886 .94450 .22418 .20093 .24006 .3057 1.5533 .6211 .2591 OF 20 .0097 .02630 .00495 .96836 .03164 .99505 .05593 .05050 .06822 .7220 4.9615 .7176 .7230 CF 20 .0097 .02630 .00495 .96836 .03164 .99505 .05593 .05050 .06822 .7220 4.9615 .7176 .7230 CS 20 .0367 .06639 .01875 .92170 .07830 .98125 .09915 .09708 .11808 .6637 3.1912 .7053 .5937 NT 40 .0888 .22274 .04580 .73303 .26698 .95420 .16677 .14901 .20189 1.0650 3.4198 .7651 .6349 MB 40 .0095 .06775 .00480 .91651 .08349 .99520 .08846 .04927 .10955 1.2079 11.0108 .7554 .8825 RB 40 .0089 .06475 .00450 .92019 .07981 .99550 .08255 .04775 .10245 1.2057 11.2743 .7548 .8850 MD 40 .0100 .06867 .00505 .91543 .08458 .99495 .08916 .05050 .11036 1.1974 10.6266 .7551 .8781 RD 40 .0091 .06562 .00460 .91913 .08088 .99540 .08311 .04826 .10313 1.2053 11.1663 .7549 .8840 OR 40 .5170 .49661 .38100 .47449 .52551 .61900 .34845 .40970 .36249 .3668 1.0448 .6271 .0278 OS 40 .2369 .27941 .17810 .69526 .30474 .82190 .36792 .34204 .39115 .4118 1.3433 .6424 .1828 OF 40 .0103 .06936 .00520 .91460 .08540 .99480 .08952 .05122 .11080 1.1926 10.4289 .7549 .8758 CF 40 .0103 .06936 .00520 .91460 .08540 .99480 .08952 .05122 .11080 1.1926 10.4289 .7549 .8758 CS 40 .0587 .16678 .03025 .79909 .20091 .96975 .14275 .12293 .17253 1.0388 4.0975 .7564 .6910 149 Table 10.2.2.1.2.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .2 N:p OLEX Rej Fp Fn Tp Tn s:Rej s.FpTn s:FnTp d' P A' B" NT 2 .0741 .01872 .01454 .96455 .03545 .98546 .06467 .05682 .14856 .3764 2.1182 .6528 .4095 MB 2 . .0240 .00472 .00308 .98870 .01130 .99693 .02249 .01984 .07598 .4595 3.1690 .6840 .5694 RB 2 .0236 .00466 .00301 .98875 .01125 .99699 .02210 .01957 .07582 .4646 3.2157 .6851 .5748 MD 2 .0246 .00488 .00315 .98820 .01180 .99685 .02285 .02007 .07753 .4682 3.2198 .6854 .5757 RD 2 .0242 .00482 .00310 .98830 .01170 .99690 .02247 .01992 .07723 .4702 3.2425 .6859 .5782 OR 2 .0868 .03977 .03754 .95130 .04870 .96246 .14362 .14214 .18610 .1224 1.2342 .5602 .1237 OS 2 .0398 .01412 .01169 .97615 .02385 .98831 .08044 .07575 .12887 .2872 1.8403 .6306 .3368 OF 2 .0308 .00594 .00403 .98640 .01360 .99598 .02574 .02304 .08316 .4413 2.9216 .6784 .5398 CF 2 .0308 .00594 .00403 .98640 .01360 .99598 .02574 .02304 .08316 .4413 2.9216 .6784 .5398 CS 2 .0579 .01175 .00860 .97565 .02435 .99140 .04158 .03785 .11416 .4112 2.4476 .6657 .4718 NT 4 .1250 .03686 .02218 .90440 .09560 .97782 .08645 .06492 .24580 .7037 3.2137 .7108 .5990 MB 4 .0298 .01116 .00386 .95965 .04035 .99614 .03487 .02241 .14352 .9172 7.5587 .7352 .8192 RB 4 .0296 .01105 .00381 .96000 .04000 .99619 .03439 .02214 .14213 .9176 7.5935 .7353 .8200 MD 4 .0302 .01132 .00393 .95910 .04090 .99608 .03527 .02264 .14450 .9181 7.5331 .7353 .8187 RD 4 .0298 .01115 .00384 .95960 .04040 .99616 .03457 .02221 .14290 .9200 7.6105 .7354 .8205 OR 4 .1572 .07302 .06414 .89145 .10855 .93586 .18195 .17515 .27009 .2867 1.4843 .6141 .2343 OS 4 .0650 .02882 .01973 .93480 .06520 .98028 .10896 .09577 .21413 .5469 2.6560 .6860 .5183 OF 4 .0335 .01219 .00438 .95655 .04345 .99563 .03675 .02397 .14963 .9097 7.1788 .7346 .8103 CF 4 .0335 .01219 .00438 .95655 .04345 .99563 .03675 .02397 .14963 .9097 7.1788 .7346 .8103 CS 4 .0786 .02234 .01135 .93370 .06630 .98865 .05304 .04168 .18113 .7745 4.3265 .7211 .6931 NT 10 .2304 .10159 .03718 .64075 .35925 .96283 .12038 .07537 .42146 1.4240 4.6051 .8078 .7309 MB 10 .0366 .04500 .00476 .79405 .20595 .99524 .06534 .02502 .30335 1.7721 20.5768 .7948 .9437 RB 10 .0348 .04423 .00449 .79680 .20320 .99551 .06385 .02405 .29886 1.7828 21.5256 .7944 .9463 MD 10 .0373 .04533 .00485 .79275 .20725 .99515 .06566 .02522 .30460 1.7703 20.3211' .7950 .9429 RD 10 .0354 .04456 .00456 .79545 .20455 .99544 .06416 .02423 .29999 1.7819 21.2933 .7946 .9457 OR 10 .3525 .17673 .13179 .64350 .35650 .86821 .23848 .22720 .42418 .7502 1.7459 .7223 .3344 OS 10 .1765 .10264 .05546 .70865 .29135 .94454 .18259 .15597 .40995 1.0446 3.0635 .7648 .5952 OF 10 .0397 .04657 .00521 .78800 .21200 .99479 .06685 .02633 .30792 1.7619 19.3133 .7958 .9398 CF 10 .0397 .04657 .00521 .78800 .21200 .99479 .06685 .02633 .30792 1.7619 19.3133 .7958 .9398 CS 10 .0921 .06054 .01324 .75025 .24975 .98676 .07374 .04446 .30440 1.5439 9.3405 .7967 .8697 NT 20 .3111 .19640 .04800 .21000 .79000 .95200 .10254 .07931 .35540 2.4710 2.8870 .9297 .5681 MB 20 .0432 .12188 .00565 .41320 .58680 .99435 .07682 .02715 .36281 2.7526 24.1602 .8937 .9547 RB 20 .0378 .11966 .00493 .42140 37860 .99508 .07515 .02533 .35928 2.7794 27.4193 .8920 .9606 MD 20 .0444 .12249 .00581 .41080 .58920 .99419 .07703 .02754 .36291 2.7488 23.5275 .8942 .9534 RD 20 .0382 .12015 .00498 .41915 .58085 .99503 .07520 .02544 .35945 2.7816 27.1422 .8925 .9601 OR 20 .5675 .32127 .20634 .21900 .78100 .79366 .23504 .25583 .36035 1.5948 1.0354 .8650 .0217 OS 20 .3761 .24458 .11989 .25665 .74335 .88011 .21053 .21277 .39271 1.8293 1.6117 .8868 .2878 OF 20 .0466 .12344 .00611 .40725 .59275 .99389 .07720 .02826 .36268 2.7402 22.4535 .8950 .9509 CF 20 .0466 .12344 .00611 .40725 .59275 .99389 .07720 .02826 .36268 2.7402 22.4535 .8950 .9509 CS 20 .0869 .12243 .01215 .43645 .56355 .98785 .07256 .04156 .31176 2.4123 12.4753 .8842 .9069 NT 40 .3364 .23851 .05060 .00985 .99015 .94940 .06501 .07884 .07667 3.9711 .2526 .9846 -.6625 MB 40 .0486 .19348 .00641 .05825 .94175 .99359 .04076 .02907 .16744 4.0582 6.4538 .9836 .7919 RB 40 .0391 .19161 .00505 .06215 .93785 .99495 .03976 .02543 .17180 4.1094 8.3934 .9830 .8413 MD 40 .0498 .19377 .00656 .05740 .94260 .99344 .04077 .02935 .16631 4.0573 6.2505 .9838 .7849 RD 40 .0404 .19200 .00524 .06095 .93905 .99476 .03970 .02597 .17033 4.1066 8.0026 .9833 .8331 OR 40 .6508 .38166 .22970 .01050 .98950 .77030 .20653 .25638 .07931 3.0478 .0917 .9386 -.8891 OS 40 .5084 .32560 .16021 .01285 .98715 .83979 .18756 .23125 .09144 3.2243 .1361 .9556 -.8277 OF 40 .0503 .19390 .00663 .05700 .94300 .99338 .04075 .02947 .16584 4.0574 6.1643 .9839 .7818 CF 40 .0503 .19390 .00663 .05700 .94300 .99338 .04075 .02947 .16584 4.0574 6.1643 .9839 .7818 CS 40 .0599 .18362 .00856 .11615 .88385 .99144 .05259 .03615 .21387 3.5785 8.4014 .9683 .8472 150 Table 10.2.2.1.2.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .4 N:p CLEX Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .0865 .03231 .01980 .94893 .05108 .98020 .08554 .07030 .15008 .4234 2.1851 .6611 .4281 MB 2 .0246 .00796 .00420 .98640 .01360 .99580 .02995 .02675 .06146 .4269 2.8124 .6752 .5247 RB 2 .0244 .00785 .00417 .98663 .01338 .99583 .02938 .02665 .06033 .4231 2.7920 .6744 .5216 MD 2 .0253 .00816 .00433 .98610 .01390 .99567 .03036 .02725 .06221 .4248 2.7869 .6745 5212 RD 2 .0251 .00803 .00428 .98635 .01365 .99572 .02971 .02700 .06094 .4217 2.7722 .6739 5189 OR 2 .1276 .06922 .06050 .91770 .08230 .93950 .18985 .18310 .22515 .1608 1.2667 .5720 .1412 OS 2 .0530 .02814 .02070 .96070 .03930 .97930 .12127 .10904 .15952 .2806 1.7040 .6231 .3013 OF 2 .0310 .01020 .00542 .98263 .01738 .99458 .03458 .03093 .07003 .4368 2.7663 .6751 5203 CF 2 .0310 .01020 .00542 .98263 .01738 .99458 .03458 .03093 .07003 .4368 2.7663 .6751 .5203 CS 2 .0629 .02057 .01243 .96723 .03278 .98757 .05741 .05197 .10251 .4020 2.2728 .6603 .4416 NT 4 .1508 .08265 .03162 .84080 .15920 .96838 .12684 .08211 .25478 .8598 3.4126 .7333 .6277 MB 4 .0270 .02431 .00470 .94628 .05373 .99530 .05417 .02887 .12548 .9874 7.9800 .7404 .8315 RB 4 .0262 .02357 .00448 .94780 .05220 .99552 .05184 .02768 .12068 .9894 8.1354 .7405 .8345 MD 4 .0274 .02463 .00477 .94558 .05443 .99523 .05460 .02905 .12652 .9889 7.9615 .7406 .8312 RD 4 .0267 .02393 .00457 .94703 .05298 .99543 .05250 .02791 .12228 .9904 8.0969 .7406 .8338 OR 4 .2781 .16646 .13213 .78205 .21795 .86787 .26634 .25268 .33591 .3372 1.3766 .6232 .1956 OS 4 .1090 .07839 .04712 .87470 .12530 .95288 .19486 .16420 .27941 .5246 2.0965 .6765 .4188 OF 4 .0315 .02726 .00555 .94018 .05983 .99445 .05780 .03162 .13315 .9833 7.4908 .7405 .8213 CF 4 .0315 .02726 .00555 .94018 .05983 .99445 .05780 .03162 .13315 .9833 7.4908 .7405 .8213 CS 4 .0904 .05165 .01747 .89708 .10293 .98253 .08518 .05954 .17401 .8441 4.1538 .7293 .6865 NT 10 .2281 .23777 .04545 .47375 52625 .95455 .14658 .09104 .32484 1.7565 4.1662 .8543 .7036 MB 10 .0302 .10178 .00523 .75340 .24660 .99477 .10238 .03028 .24866 1.8748 20.9487 .8054 .9455 RB 10 .0257 .09735 .00438 .76320 .23680 .99562 .09651 .02739 .23642 1.9044 24.0010 .8037 .9528 MD 10 .0303 .10270 .00525 .75113 .24888 .99475 .10284 .03033 .24985 1.8809 20.9922 .8060 .9456 RD 10 .0260 .09820 .00443 .76115 .23885 .99557 .09690 .02754 .23724 1.9071 23.8716 .8042 .9526 OR 10 .6432 .44338 .30738 .35263 .64738 .69262 .29259 .31346 .37206 .8815 1.0567 .7540 .0349 OS 10 .3695 .30403 .16865 .49290 .50710 .83135 .30720 .27891 .43723 .9773 1.5844 .7686 .2813 OF 10 .0321 .10569 .00557 .74412 .25588 .99443 .10402 .03122 .25237 1.8824 20.2208 .8075 .9435 CF 10 .0321 .10569 .00557 .74412 .25588 .99443 .10402 .03122 .25237 1.8824 20.2208 .8075 .9435 CS 10 .1135 .15556 .02212 .64427 .35573 .97788 .11230 .06661 .25228 1.6420 7.0667 .8197 .8275 NT 20 .2508 .37505 .04902 .13590 .86410 .95098 .09358 .09178 .19078 2.7534 2.1486 .9501 .4317 MB 20 .0383 .25398 .00670 .37510 .62490 .99330 .11380 .03439 .27816 2.7913 20.2282 .9029 .9448 RB 20 .0286 .24237 .00497 .40153 59848 .99503 .10965 .02949 .27100 2.8275 26.9048 .8970 .9597 MD 20 .0391 .25528 .00688 .37213 .62788 .99312 .11358 .03504 .27742 2.7895 19.7016 .9036 .9431 RD 20 .0291 .24366 .00505 .39843 .60158 .99495 .10925 .02971 .26992 2.8298 26.4552 .8978 .9589 OR 20 .8039 .62678 .40995 .04797 .95203 .59005 .21046 .31906 .14153 1.8925 .2567 .8720 -.6823 OS 20 .6920 .57131 .33643 .07637 .92363 .66357 .23790 .32571 .21809 1.8521 .3933 .8802 -5198 OF 20 .0402 .25700 .00710 .36815 .63185 .99290 .11324 .03566 .27638 2.7889 19.1031 .9045 .9412 CF 20 .0402 .25700 .00710 .36815 .63185 .99290 .11324 .03566 .27638 2.7889 19.1031 .9045 .9412 CS 20 .1029 .28203 .01968 .32445 .67555 .98032 .09502 .06155 .21558 2.5156 7.5296 .9100 .8382 NT 40 .2580 .42667 .05028 .00875 .99125 .94972 .05840 .09269 .04781 4.0181 .2289 .9850 -.6926 MB 40 .0453 .38503 .00817 .04968 .95033 .99183 .05255 .03895 .11679 4.0494 4.5967 .9853 .7071 RB 40 .0295 .37830 .00522 .06207 .93793 .99478 .05388 .03070 .12735 4.0987 8.1466 .9830 .8363 MD 40 .0463 .38559 .00835 .04855 .95145 .99165 .05203 .03937 .11525 4.0523 4.4262 .9856 .696C RD 40 .0300 .37878 .00532 .06103 .93898 .99468 .05359 .03104 .12643 4.1007 7.9041 .9832 .8310 OR 40 .8267 .65286 .42207 .00095 .99905 57793 .18914 .31456 .01578 3.3020 .0082 .8940 -.9922 OS 40 .7590 .61963 .36688 .00125 .99875 .63312 .19262 .31995 .02058 3.3635 .0110 .9077 -.9893 OF 40 .0468 .38577 .00843 .04822 .95178 .99157 .05183 .03953 .11465 4.0519 4.3643 .9856 .6918 CF 40 .0468 .38577 .00843 .04822 .95178 .99157 .05183 .03953 .11465 4.0519 4.3643 .9856 .6918 CS 40 .0660 .37660 .01275 .07763 .92237 .98725 .05954 .05144 .12473 3.6550 4.4143 .9769 .7010 151 Table 10.2.2.1.2.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p - 5, mNz = .3, pNz = .6 N:p ct£X Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .0735 .05250 .02308 .92788 .07212 .97693 .10986 .08846 .16034 .5338 2.5142 .6826 .4960 MB 2 .0167 .01159 .00435 .98358 .01642 .99565 .03764 .03400 .05841 .4895 3.2042 .6868 .5770 RB 2 .0166 .01134 .00433 .98398 .01602 .99568 .03627 .03391 .05619 .4816 3.1534 .6854 3708 MD 2 .0172 .01189 .00448 .98317 .01683 .99553 .03808 .03444 .05912 .4899 3.1919 .6866 .5758 RD 2 .0171 .01161 .00445 .98362 .01638 .99555 .03661 .03436 .05668 .4809 3.1344 .6851 .5687 OR 2 .1721 .12091 .09872 .86430 .13570 .90128 .25412 .24518 .28311 .1890 1.2532 .5784 .1372 OS 2 .0603 .05114 .03430 .93763 .06237 .96570 .17606 .15553 .20712 .2858 1.6155 .6198 .2768 OF 2 .0218 .01532 .00580 .97833 .02167 .99420 .04415 .03989 .06793 3036 3.1403 .6871 .5723 CF 2 .0218 .01532 .00580 .97833 .02167 .99420 .04415 .03989 .06793 .5036 3.1403 .6871 .5723 CS 2 .0544 .03575 .01605 .95112 .04888 .98395 .08102 .07189 .11663 .4874 23238 .6763 .4929 NT 4 .1196 .13427 .03548 .79987 .20013 .96453 .16389 .10325 .25275 .9647 3.5848 .7484 .6478 MB 4 .0181 .03798 .00470 .93983 .06017 .99530 .07355 .03522 .11990 1.0438 8.7243 .7444 .8472 RB 4 .0174 .03623 .00450 .94262 .05738 .99550 .06850 .03435 .11175 1.0349 8.7386 .7437 .8470 MD 4 .0183 .03855 .00475 .93892 .06108 .99525 .07448 .03539 .12145 1.0478 8.7452 .7447 .8477 RD 4 .0177 .03672 .00458 .94185 .05815 .99543 .06915 .03461 .11282 1.0359 8.7009 .7438 .8465 OR 4 .3818 .29427 .22680 .66075 .33925 .77320 .34663 .33380 .39302 .3349 1.2152 .6192 .1221 OS 4 .1616 .15660 .09610 .80307 .19693 .90390 .29643 .24846 .35596 .4515 1.6272 .6559 .2909 OF 4 .0210 .04306 .00548 .93188 .06812 .99453 .07935 .03810 .12937 1.0543 8.3872 .7457 .842C CF 4 .0210 .04306 .00548 .93188 .06812 .99453 .07935 .03810 .12937 1.0543 8.3872 .7457 .8420 CS 4 .0823 .09617 .02440 .85598 .14402 .97560 .13017 .08842 .19737 .9079 3.9619 .7383 .6763 NT 10 .1632 .35092 .04683 .44635 .55365 .95318 .18028 .11359 .28750 1.8113 4.0396 .8618 .6940 MB 10 .0210 .15812 .00555 .74017 .25983 .99445 .15029 .03930 .24769 1.8957 20.4369 .8086 .9442 RB 10 .0169 .14588 .00435 .75977 .24023 .99565 .13504 .03382 .22381 1.9181 24.3565 .8047 .9536 MD 10 .0214 .15978 .00565 .73747 .26253 .99435 .15097 .03960 .24873 1.8977 20.2225 .8092 .9436 RD 10 .0170 .14726 .00438 .75748 .24252 .99563 .13540 .03391 .22441 1.9234 24.3569 .8053 .9537 OR 10 .7497 .65688 .46693 .21648 .78352 .53308 .28913 .36142 .31398 .8671 .7379 .7495 -.1894 OS 10 .5132 30965 .32008 .36397 .63603 .67993 .37843 .37451 .43745 .8154 1.0500 .7404 .0309 OF 10 .0231 .16423 .00615 .73038 .26962 .99385 .15238 .04168 .25101 1.8894 19.0120 .8106 .9398 CF 10 .0231 .16423 .00615 .73038 .26962 .99385 .15238 .04168 .25101 1.8894 19.0120 .8106 .9398 CS 10 .1165 .27527 .03405 .56392 .43608 .96595 .16352 .10095 .25744 1.6634 5.2131 .8345 .7641 NT 20 .1719 .53822 .04925 .13580 .86420 .95075 .11557 .11549 .17561 2.7516 2.1394 .9500 .4296 MB 20 .0323 .39075 .00885 .35465 .64535 .99115 .16783 .05059 .27548 2.7446 15.5384 .9071 .9262 RB 20 .0193 .36075 .00508 .40213 .59787 .99492 .15862 .03699 .26318 2.8185 26.4031 .8968 .9589 MD 20 .0328 .39256 .00898 .35172 .64828 .99103 .16750 .05088 .27491 2.7473 15.3030 .9078 .9249 RD 20 .0194 .36247 .00510 .39928 .60072 .99490 .15809 .03707 .26232 2.8242 26.2391 .8975 .9586 OR 20 .8705 .81556 .56713 .01882 .98118 .43288 .15182 .33954 .08007 1.9098 .1169 .8446 -.8601 OS 20 .8101 .78562 .52093 .03792 .96208 .47908 .19697 .36136 .16230 1.7229 .2071 .8448 -.7449 OF 20 .0336 .39499 .00918 .34780 .65220 .99083 .16672 .05133 .27363 2.7497 14.9493 .9087 .9229 CF 20 .0336 .39499 .00918 .34780 .65220 .99083 .16672 .05133 .27363 2.7497 14.9493 .9087 .9229 CS 20 .0990 .46087 .02948 .25153 .74847 .97053 .12303 .09586 .19082 2.5582 4.7546 .9254 .7362 NT 40 .1760 .61530 .05060 .00823 .99177 .94940 .05299 .11754 .03992 4.0375 .2159 .9851 -.7094 MB 40 .0442 .58080 .01228 .04018 .95982 .98773 .06383 .06026 .09684 3.9970 2.7154 .9866 .5217 RB 40 .0213 .56533 .00563 .06153 .93847 .99438 .07168 .03905 .11637 4.0769 7.5668 .9830 .8234 MD 40 .0448 .58120 .01245 .03963 .96037 .98755 .06336 .06069 .09593 3.9979 2.6524 .9867 .5117 RD 40 .0217 .56604 .00575 .06043 .93957 .99425 .07110 .03959 .11532 4.0783 7.3167 .9833 .8171 OR 40 .8846 .83130 .57855 .00020 .99980 .42145 .13308 .33229 .00577 3.3419 .0019 .8552 -.9984 OS 40 .8462 .81803 .54555 .00032 .99968 .45445 .14051 .35016 .01166 3.3025 .0029 .8634 -.9974 OF 40 .0453 .58145 .01258 .03930 .96070 .98743 .06322 .06092 .09557 3.9980 2.6116 .9868 3050 CF 40 .0453 .58145 .01258 .03930 .96070 .98743 .06322 .06092 .09557 3.9980 2.6116 .9868 .5050 CS 40 .0700 .57913 .02115 .04888 .95112 .97885 .06378 .08376 .08655 3.6863 1.9953 .9820 .3838 152 Table 10.2.2.1.2.4 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .3, pNz = .8 N:p OEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp d' P A' B" NT 2 .0480 .06789 .02595 .92163 .07838 .97405 .12395 .11939 .14509 .5279 2.4275 .6807 .4816 MB 2 .0097 .01497 .00495 .98253 .01748 .99505 .04277 .05050 .05155 .4704 3.0120 .6823 .5542 RB 2 .0094 .01461 .00480 .98294 .01706 .99520 .04111 .04977 .04961 .4713 3.0332 .6828 .5566 MD 2 .0099 .01533 .00515 .98213 .01788 .99485 .04343 .05243 .05220 .4658 2.9643 .6812 .5482 RD 2 .0095 .01488 .00485 .98261 .01739 .99515 .04143 .05002 .05003 .4754 3.0541 .6834 .5595 OR 2 .1845 .16190 .13440 .83123 .16878 .86560 .29142 .30215 .30199 .1468 1.1637 .5608 .0933 OS 2 .0607 .06880 .04655 .92564 .07436 .95345 .20793 .19316 .21968 .2352 1.4439 .6008 .2160 OF 2 .0116 .01961 .00610 .97701 .02299 .99390 .05066 .05756 .06069 .5107 3.1567 .6879 .5749 CF 2 .0116 .01961 .00610 .97701 .02299 .99390 .05066 .05756 .06069 .5107 3.1567 .6879 .5749 CS 2 .0357 .04917 .01940 .94339 .05661 .98060 .10119 .10428 .11700 .4824 2.4121 .6738 .4747 NT 4 .0749 .18098 .03950 .78365 .21635 .96050 .18275 .14227 .22018 .9719 3.4380 .7504 .6343 MB 4 .0090 .04997 .00450 .93866 .06134 .99550 .08532 .04722 .10521 1.0684 9.2073 .7459 .8556 RB 4 .0084 .04728 .00420 .94195 .05805 .99580 .07802 .04564 .09629 1.0642 9.3792 .7454 .8579 MD 4 .0097 .05081 .00485 .93770 .06230 .99515 .08631 .04901 .10635 1.0506 8.7174 .7450 .8474 RD 4 .0088 .04795 .00440 .94116 .05884 .99560 .07877 .04670 .09721 1.0551 9.0929 .7450 .8534 OR 4 .4212 .40619 .31580 .57121 .42879 .68420 .37783 .40421 .39514 .3000 1.1039 .6072 .0626 OS 4 .1924 .22666 .15060 .75433 .24568 .84940 .35930 .32715 .38135 .3457 1.3467 .6247 .1832 OF 4 .0112 .05693 .00570 .93026 .06974 .99430 .09239 .05402 .11338 1.0524 8.2405 .7457 .8393 CF 4 .0112 .05693 .00570 .93026 .06974 .99430 .09239 .05402 .11338 1.0524 8.2405 .7457 .8393 CS 4 .0541 .14081 .02875 .83118 .16883 .97125 .16284 .12349 .19439 .9407 3.8358 .7435 .6681 NT 10 .0891 .46146 .04680 .43488 .56513 .95320 .18799 .15317 .23174 1.8407 4.0238 .8652 .6927 MB 10 .0136 .21798 .00715 .72931 .27069 .99285 .17993 .06224 .22272 1.8389 16.6742 .8098 .9306 RB 10 .0093 .19468 .00470 .75783 .24218 .99530 .15317 .04877 .19078 1.8978 22.8300 .8048 .9503 MD 10 .0138 .22061 .00725 .72605 .27395 .99275 .18096 .06263 .22397 1.8437 16.5695 .8105 .9302 RD 10 .0097 .19656 .00490 .75553 .24448 .99510 .15354 .04976 .19122 1.8908 22.1100 .8052 .9486 OR 10 .7762 .83253 .60745 .11120 .88880 .39255 .20650 .39255 .20620 .9475 .4930 .7583 -.4139 OS 10 .6128 .71018 .48655 .23391 .76609 .51345 .36243 .43210 .37888 .7597 .7688 .7273 -.1646 OF 10 .0149 .22706 .00785 .71814 .28186 .99215 .18281 .06530 .22614 1.8385 15.6651 .8121 .9259 CF 10 .0149 .22706 .00785 .71814 .28186 .99215 .18281 .06530 .22614 1.8385 15.6651 .8121 .9259 CS 10 .0782 .40898 .04150 .49915 .50085 .95850 .18615 .14639 .22730 1.7357 4.4932 .8491 .7255 NT 20 .0957 .70150 .05010 .13565 .86435 .94990 .12142 .15746 .14835 2.7440 2.1088 .9498 .4226 MB 20 .0263 .54470 .01385 .32259 .67741 .98615 .19752 .08622 .24436 2.6620 10.1483 .9131 .8823 RB 20 .0103 .47914 .00525 .40239 .59761 .99475 .17945 .05194 .22408 2.8061 25.6225 .8967 .9575 MD 20 .0268 .54719 .01410 .31954 .68046 .98590 .19680 .08690 .24346 2.6635 9.9535 .9138 .8798 RD 20 .0104 .48144 .00530 .39953 .60048 .99470 .17907 .05217 .22359 2.8102 25.3602 .8974 .9570 OR 20 .8558 .93381 .69240 .00584 .99416 .30760 .07890 .36235 .02993 2.0192 .0472 .8211 -.9469 OS 20 .8332 .92775 .67900 .01006 .98994 .32100 .10196 .37533 .07155 1.8591 .0748 .8207 -.9126 OF 20 .0272 .55010 .01435 .31596 .68404 .98565 .19569 .08786 .24206 2.6666 9.7574 .9146 .8772 CF 20 .0272 .55010 .01435 .31596 .68404 .98565 .19569 .08786 .24206 2.6666 9.7574 .9146 .8772 CS 20 .0800 .65106 .04300 .19693 .80308 .95700 .12120 .15051 .14686 2.5695 3.0354 .9352 .5870 NT 40 .0966 .80350 .05060 .00828 .99173 .94940 .04089 .15825 .03447 4.0356 .2169 .9851 -.7082 MB 40 .0429 .78283 .02295 .02720 .97280 .97705 .06111 .11158 .07039 3.9199 1.1531 .9871 .0826 RB 40 .0098 .75151 .00495 .06185 .93815 .99505 .08008 .05001 .09975 4.1187 8.5121 .9831 .8435 MD 40 .0436 .78334 .02330 .02665 .97335 .97670 .06057 .11229 .06957 3.9224 1.1192 .9872 .0654 RD 40 .0101 .75242 .00510 .06075 .93925 .99490 .07934 .05074 .09881 4.1175 8.1733 .9834 .8367 OR 40 .8656 .94006 .70055 .00006 .99994 .29945 .07143 .35675 .00279 3.3101 .0007 .8248 -.9994 OS 40 .8472 .93820 .69135 .00009 .99991 .30865 .07372 .36807 .00331 3.2529 .0010 .8271 -.9992 OF 40 .0436 .78354 .02330 .02640 .97360 .97670 .06029 .11229 .06922 3.9265 1.1105 .9873 .0608 CF 40 .0436 .78354 .02330 .02640 .97360 .97670 .06029 .11229 .06922 3.9265 1.1105 .9873 .0608 CS 40 .0562 .78479 .03050 .02664 .97336 .96950 .05140 .12931 .05586 3.8062 .8935 .9853 -.0656 153 Table 10.2.2.1.3.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .2 N:p aEX Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .1438 .04528 .02546 .87545 .12455 .97454 .09562 .06911 .27896 .7996 3.4598 .7243 .6292 MB 2 .0337 .01406 .00438 .94720 .05280 .99563 .03922 .02384 .16222 1.0034 8.3909 .7414 .8398 RB 2 .0331 .01385 .00430 .94795 .05205 .99570 .03838 .02366 .15990 1.0023 8.4253 .7413 .8403 MD 2 .0343 .01429 .00448 .94645 .05355 .99553 .03964 .02421 .16374 1.0026 8.3156 .7414 .8384 RD 2 .0338 .01405 .00439 .94730 .05270 .99561 .03867 .02387 .16086 1.0015 8.3569 .7413 .8391 OR 2 .1896 .09236 .08085 .86160 .13840 .91915 .20791 .20083 .30357 .3118 1.4737 .6196 .2321 OS 2 .0910 .04269 .02960 .90495 .09505 .97040 .13832 .12301 .25835 .5764 2.5128 .6890 .4993 OF 2 .0452 .01733 .00594 .93710 .06290 .99406 .04495 .02791 .17999 .9850 7.3370 .7407 .8180 CF 2 .0452 .01733 .00594 .93710 .06290 .99406 .04495 .02791 .17999 .9850 7.3370 .7407 .8180 CS 2 .0869 .02822 .01313 .91140 .08860 .98687 .06197 .04687 .21143 .8731 4.7553 .7321 .7235 NT 4 .2554 .12005 .04176 .56680 .43320 .95824 .12420 .07966 .43578 1.5624 4.4075 .8280 .7197 MB 4 .0392 .05441 .00520 .74875 .25125 .99480 .06923 .02642 .32142 1.8917 21.2787 .8067 .9465 RB 4 .0361 .05337 .00473 .75205 .24795 .99528 .06733 .02493 .31687 1.9144 23.0121 .8063 .9508 MD 4 .0397 .05487 .00528 .74675 .25325 .99473 .06959 .02664 .32272 1.8930 21.0973 .8071 .9460 RD 4 .0366 .05375 .00480 .75045 .24955 .99520 .06759 .02516 .31774 1.9140 22.7690 .8067 .9503 OR 4 .4059 .21314 .15860 .56870 .43130 .84140 .25732 .24969 .43909 .8272 1.6246 .7391 .2953 OS 4 .2217 .13646 .07771 .62855 .37145 .92229 .21249 .19148 .43740 1.0926 2.5994 .7773 .5302 OF 4 .0473 .05869 .00631 .73180 .26820 .99369 .07223 .02914 .33163 1.8759 18.5289 .8100 .9381 CF 4 .0473 .05869 .00631 .73180 .26820 .99369 .07223 .02914 .33163 1.8759 18.5289 .8100 .9381 CS 4 .1045 .07297 .01536 .69660 .30340 .98464 .07972 .04864 .32126 1.6460 9.0404 .8105 .8664 NT 10 .3146 .23184 .05013 .04130 .95870 .94988 .07342 .08348 .15603 3.3794 .8558 .9761 -.0919 MB 10 .0444 .17283 .00601 .15990 .84010 .99399 .05686 .02921 .25834 3.5063 14.2778 .9580 .9148 RB 10 .0375 .17037 .00494 .16790 .83210 .99506 .05607 .02584 .26109 3.5427 17.5570 .9563 .9321 MD 10 .0455 .17345 .00615 .15735 .84265 .99385 .05668 .02947 .25685 3.5088 13.8478 .9586 .9119 RD 10 .0380 .17074 .00501 .16635 .83365 .99499 .05591 .02607 .26002 3.5437 17.2195 .9567 .9306 OR 10 .6121 .37097 .22440 .04275 .95725 .77560 .21536 .26294 .15922 2.4770 .3037 .9276 -.6193 OS 10 .4578 .31183 .15279 .05200 .94800 .84721 .19935 .23742 .18493 2.6503 .4508 .9444 -.4484 OF 10 .0492 .17495 .00669 .15200 .84800 .99331 .05653 .03078 .25387 3.5015 12.5677 .9598 .9020 CF 10 .0492 .17495 .00669 .15200 .84800 .99331 .05653 .03078 .25387 3.5015 12.5677 .9598 .902C CS 10 .0833 .16212 .01205 .23760 .76240 .98795 .06487 .04303 .26154 2.9696 9.8629 .9359 .8767 NT 20 .3171 .24013 .05023 .00025 .99975 .94978 .06639 .08293 .01118 5.1234 .0090 .9874 -.9896 MB 20 .0481 .20446 .00655 .00390 .99610 .99345 .02565 .03027 .04399 5.1416 .6303 .9974 -.2523 RB 20 .0388 .20324 .00515 .00440 .99560 .99485 .02284 .02631 .04670 5.1853 .8690 .9976 -.0782 MD 20 .0492 .20464 .00675 .00380 .99620 .99325 .02609 .03090 .04343 5.1396 .5996 .9973 -.2783 RD 20 .0395 .20334 .00525 .00430 .99570 .99475 .02300 .02659 .04617 5.1865 .8369 .9976 -.099C OR 20 .6246 .38657 .23325 .00015 .99985 .76675 .21449 .26810 .00866 4.3435 .0019 .9416 -.9983 OS 20 .4914 .33260 .16581 .00025 .99975 .83419 .19608 .24505 .01118 4.4516 .0037 .9585 -.9964 OF 20 .0513 .20489 .00705 .00375 .99625 .99295 .02659 .03158 .04314 5.1285 .5702 .9973 -.3041 CF 20 .0513 .20489 .00705 .00375 .99625 .99295 .02659 .03158 .04314 5.1285 .5702 .9973 -.3041 CS 20 .0668 .20509 .00981 .01380 .98620 .99019 .03563 .03920 .08192 4.5364 1.3445 .9940 .1669 NT 40 .3221 .24044 .05055 .00000 1.00000 .94945 .06587 .08234 .00000 5.9044 .0000 .9874-1.000C MB 40 .0483 .20516 .00645 .00000 1.00000 .99355 .02357 .02946 .00000 6.7514 .0000 .9984-1.0000 RB 40 .0393 .20414 .00518 .00000 1.00000 .99483 .02095 .02619 .00000 6.8288 .0000 .9987 -1.0000 MD 40 .0495 .20529 .00661 .00000 1.00000 .99339 .02386 .02982 .00000 6.7425 .0000 .9983 -1.0000 RD 40 .0403 .20424 .00530 .00000 1.00000 .99470 .02117 .02646 .00000 6.8205 .0000 .9987 -1.0000 OR 40 .6266 .38802 .23503 .00000 1.00000 .76498 .21411 .26764 .00000 4.9873 .0000 .9412-1.0000 OS 40 .4933 .33335 .16669 .00000 1.00000 .83331 .19446 .24308 .00000 5.2322 .0000 .9583 -1.0000 OF 40 .0502 .20537 .00671 .00000 1.00000 .99329 .02405 .03006 .00000 6.7372 .0000 .9983 -1.0000 CF 40 .0502 .20537 .00671 .00000 1.00000 .99329 .02405 .03006 .00000 6.7372 .0000 .9983 -1.0000 CS 40 .0661 .20782 .00979 .00005 .99995 .99021 .03195 .03992 .00500 6.2250 .0079 .9975 -.9897 154 Table 10.2.2.1.3.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .4 N:p OEX Rej Fp Fn Tp Tn s.Rej s:FpTn s:FnTp d' P A' B" NT 2 .1713 .11088 .03623 .77715 .22285 .96377 .14303 .08784 .29690 1.0336 3.7522 .7578 .6644 MB 2 .0291 .03069 .00522 .93110 .06890 .99478 .06161 .03124 .14337 1.0771 8.8331 .7471 .8503 RB 2 .0278 .02965 .00492 .93325 .06675 .99508 .05847 .02983 .13710 1.0812 9.0862 .7471 .8544 MD 2 .0296 .03124 .00530 .92985 .07015 .99470 .06213 .03144 .14455 1.0809 8.8309 .7474 .8504 RD 2 .0284 .03021 .00502 .93200 .06800 .99498 .05905 .03009 .13857 1.0838 9.0536 .7474 .8540 OR 2 .3514 .22556 .17585 .69988 .30013 .82415 .30112 .28704 .38026 .4073 1.3449 .6412 .1835 OS 2 .1556 .12015 .07502 .81215 .18785 .92498 .24400 .21246 .33983 .5536 1.9033 .6807 .3747 OF 2 .0405 .03902 .00735 .91348 .08653 .99265 .07101 .03733 .16358 1.0772 7.7514 .7487 .8310 CF 2 .0405 .03902 .00735 .91348 .08653 .99265 .07101 .03733 .16358 1.0772 7.7514 .7487 .8310 CS 2 .1032 .07101 .02110 .85413 .14588 .97890 .10210 .06892 .20998 .9773 4.5169 .7457 .7156 NT 4 .2309 .27388 .04838 .38788 .61213 .95162 .14333 .09853 .31555 1.9456 3.8131 .8783 .6752 MB 4 .0335 .12434 .00603 .69820 .30180 .99397 .11177 .03395 .27145 1.9910 20.4038 .8194 .9447 RB 4 .0291 .11819 .00503 .71208 .28793 .99497 .10448 .02958 .25671 2.0141 23.4538 .8167 .9523 MD 4 .0342 .12552 .00620 .69550 .30450 .99380 .11215 .03465 .27201 1.9891 19.9966 .8199 .9435 RD 4 .0299 .11942 .00518 .70923 .29078 .99482 .10490 .03016 .25751 2.0122 22.9547 .8173 .9512 OR 4 .6686 .49698 .33690 .26290 .73710 .66310 .28313 .32681 .34115 1.0554 .8935 .7866 -.0710 OS 4 .4364 .37537 .21447 .38328 .61673 .78553 .31599 .31161 .42834 1.0879 1.3084 .7911 .1677 OF 4 .0411 .13514 .00742 .67328 .32673 .99258 .11493 .03754 .27797 1.9874 17.5893 .8247 .9352 CF 4 .0411 .13514 .00742 .67328 .32673 .99258 .11493 .03754 .27797 1.9874 17.5893 .8247 .9352 CS 4 .1222 .18465 .02518 .57615 .42385 .97482 .11925 .07470 .26279 1.7648 6.6603 .8374 .8173 NT 10 .2317 .41567 .04875 .03395 .96605 .95125 .06914 .09882 .09867 3.4828 .7456 .9785 -.1715 MB 10 .0403 .34855 .00750 .13988 .86013 .99250 .08325 .03865 .20024 3.5133 10.7411 .9626 .8835 RB 10 .0274 .33740 .00497 .16395 .83605 .99503 .08430 .03078 .20763 3.5565 17.1985 .9573 .9304 MD 10 .0413 .34936 .00768 .13813 .86187 .99232 .08284 .03908 .19886 3.5124 10.4254 .9630 .8796 RD 10 .0277 .33818 .00502 .16208 .83793 .99498 .08380 .03091 .20641 3.5606 16.9187 .9578 .9291 OR 10 .7957 .64683 .41425 .00430 .99570 .58575 .19686 .32611 .03751 2.8442 .0324 .8942 -.9653 OS 10 .7179 .61054 .35592 .00753 .99248 .64408 .20288 .33119 .06423 2.8006 .0557 .9074 -.9369 OF 10 .0433 .35138 .00808 .13368 .86633 .99192 .08182 .04012 .19568 3.5143 9.7492 .9640 .8705 CF 10 .0433 .35138 .00808 .13368 .86633 .99192 .08182 .04012 .19568 3.5143 9.7492 .9640 .8705 CS 10 .0873 .34674 .01817 .16040 .83960 .98183 .07755 .06462 .16344 3.0860 5.4622 .9537 .7661 NT 20 .2403 .42984 .04998 .00038 .99963 .95002 .05880 .09804 .00968 5.0156 .0132 .9874 -.9843 MB 20 .0432 .40362 .00813 .00315 .99685 .99187 .02644 .04035 .02899 5.1346 .4299 .9972 -.4396 RB 20 .0259 .40110 .00473 .00435 .99565 .99527 .02211 .03018 .03419 5.2183 .9274 .9977 -.0420 MD 20 .0443 .40381 .00833 .00297 .99703 .99167 .02651 .04079 .02824 5.1445 .3997 .9972 -.4717 RD 20 .0263 .40117 .00483 .00433 .99568 .99517 .02231 .03062 .03410 5.2131 .9056 .9977 -.0553 OR 20 .7959 .65439 .42398 .00000 1.00000 .57602 .19877 .33129 .00000 4.4566 .0000 .8940-1.0000 OS 20 .7261 .62316 .37193 .00000 1.00000 .62807 .20268 .33779 .00000 4.5916 .0000 .9070-1.000C OF 20 .0457 .40404 .00863 .00285 .99715 .99137 .02687 .04161 .02747 5.1455 .3727 .9971 -.5015 CF 20 .0457 .40404 .00863 .00285 .99715 .99137 .02687 .04161 .02747 5.1455 .3727 .9971 -.5015 CS 20 .0728 .40573 .01463 .00762 .99238 .98537 .03821 .05659 .04328 4.6063 .5668 .9944 -.3117 NT 40 .2391 .43048 .05080 .00000 1.00000 .94920 .06076 .10126 .00000 5.9020 .0000 .9873 -1.0000 MB 40 .0449 .40514 .00857 .00000 1.00000 .99143 .02517 .04195 .00000 6.6487 .0000 .9979 -1.0000 RB 40 .0284 .40309 .00515 .00000 1.00000 .99485 .01875 .03125 .00000 6.8305 .0000 .9987 -1.000C MD 40 .0457 .40523 .00872 .00000 1.00000 .99128 .02541 .04235 .00000 6.6423 .0000 .9978 -1.0000 RD 40 .0290 .40317 .00528 .00000 1.00000 .99472 .01905 .03175 .00000 6.8216 .0000 .9987 -1.0000 OR 40 .7983 .65469 .42448 .00000 1.00000 .57552 .19784 .32974 .00000 4.4553 .0000 .8939-1.0000 OS 40 .7317 .62250 .37083 .00000 1.00000 .62917 .20118 .33530 .00000 4.5945 .0000 .9073 -l.oood OF 40 .0462 .40530 .00883 .00000 1.00000 .99117 .02561 .04269 .00000 6.6374 .0000 .9978 -l.oood CF 40 .0462 .40530 .00883 .00000 1.00000 .99117 .02561 .04269 .00000 6.6374 .0000 .9978 -l.oood CS 40 .0753 .40940 .01567 .00000 1.00000 .98433 .03644 .06073 .00000 6.4177 .0000 .9961 -l.ooool 155 Table 10.2.2.1.3.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 5, mNz = .5, pNz = .6 N:p aEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .1196 .18302 .03840 .72057 .27943 .96160 .18906 .11446 29141 1.1850 4.0343 .7783 .6901 MB 2 .0208 .04879 .00575 .92252 .07748 .99425 .08880 .04174 .14446 1.1049 8.8627 .7495 .8519 RB 2 .0197 .04564 .00530 .92747 .07253 .99470 .07985 .03853 .13056 1.0984 9.0603 .7486 .8547 MD 2 .0211 .04957 .00585 .92128 .07872 .99415 .08964 .04217 .14588 1.1073 8.8333 .7497 .8515 RD 2 .0201 .04639 .00540 .92628 .07372 .99460 .08063 .03884 .13186 1.1004 9.0220 .7489 .8542 OR 2 .4512 .39263 .28990 .53888 .46112 .71010 .37484 .37323 .42850 .4561 1.1601 .6531 .0938 OS 2 .2121 .23080 .14258 .71038 .28962 .85743 .35401 .31016 .42385 .5143 1.5181 .6698 .2546 OF 2 .0275 .06140 .00770 .90280 .09720 .99230 .10015 .04877 .16275 1.1252 8.1099 .7527 .8398 CF 2 .0275 .06140 .00770 .90280 .09720 .99230 .10015 .04877 .16275 1.1252 8.1099 .7527 .8398 CS 2 .0992 .14015 .03335 .78865 .21135 .96665 .16306 .11226 .24410 1.0319 3.8955 .7566 .6759 NT 4 .1522 .39823 .04830 .36848 .63152 .95170 .19208 .12696 .30639 1.9974 3.7584 .8841 .6701 MB 4 .0231 .19363 .00655 .68165 .31835 .99345 .17959 .04508 .29612 2.0087 19.4187 .8233 .9418 RB 4 .0174 .17499 .00468 .71147 .28853 .99533 .15871 .03619 .26378 2.0413 25.0747 .8172 .9557 MD 4 .0235 .19537 .00678 .67890 .32110 .99323 .18009 .04675 .29665 2.0044 18.9156 .8238 .9401 RD 4 .0180 .17668 .00483 .70875 .29125 .99518 .15950 .03668 .26499 2.0384 24.4857 .8178 .9545 OR 4 .7428 .69292 .48193 .16642 .83358 .51808 .28197 .37677 .30070 1.0137 .6263 .7752 -.2857 OS 4 .5518 .57242 .36310 .28803 .71197 .63690 .37229 .39634 .42590 .9093 .9094 .7594 -.0600 OF 4 .0283 .20901 .00815 .65708 .34292 .99185 .18292 .05120 .30079 1.9976 16.4989 .8284 .9307 CF 4 .0283 .20901 .00815 .65708 .34292 .99185 .18292 .05120 .30079 1.9976 16.4989 .8284 .9307 CS 4 .1206 .32448 .04085 .48643 .51357 .95915 .18276 .12388 .28176 1.7749 4.5485 .8533 .7288 NT 10 .1506 .59884 .04818 .03405 .96595 .95183 .07601 .12762 .09416 3.4872 .7545 .9786 -.1646 MB 10 .0371 .52855 .01148 .12673 .87327 .98853 .12477 .06490 .20172 3.4162 6.9178 .9647 .8141 RB 10 .0172 .50225 .00473 .16607 .83393 .99528 .12881 .03770 .21366 3.5652 18.1304 .9569 .9343 MD 10 .0377 .52972 .01170 . .12493 .87507 .98830 .12382 .06558 .19995 3.4175 6.7346 .9651 .8087 RD 10 .0174 .50338 .00480 .16423 .83577 .99520 .12798 .03827 .21223 3.5671 17.7495 .9573 .9327 OR 10 .8400 .82267 .55998 .00220 .99780 .44003 .14481 .35791 .02540 2.6971 .0175 .8584 -.9823 OS 10 .7936 .80702 .52530 .00517 .99483 .47470 .15843 .37533 .06215 2.5010 .0374 .8653 -.9596 OF 10 .0400 .53235 .01245 .12105 .87895 .98755 .12187 .06770 .19631 3.4127 6.2417 .9658 .7928 CF 10 .0400 .53235 .01245 .12105 .87895 .98755 .12187 .06770 .19631 3.4127 6.2417 .9658 .7928 CS 10 .0895 .54754 .03090 .10803 .89197 .96910 .09641 .11106 .13625 3.1048 2.6619 .9635 .5258 NT 20 .1520 .61940 .04898 .00032 .99968 .95103 .05181 .12902 .00726 5.0718 .0115 .9877 -.9865 MB 20 .0437 .60409 .01380 .00238 .99762 .98620 .03144 .07166 .02088 5.0253 .2109 .9959 -.7026 RB 20 .0180 .59937 .00508 .00443 .99557 .99492 .02338 .03944 .02862 5.1878 .8864 .9976 -.0672 MD 20 .0444 .60424 .01410 .00233 .99767 .98590 .03185 .07298 .02055 5.0237 .2031 .9959 -.7131 RD 20 .0183 .59942 .00518 .00442 .99558 .99483 .02349 .03990 .02858 5.1823 .8682 .9976 -.0787 OR 20 .8457 .82655 .56638 .00000 1.00000 .43363 .14270 .35674 .00000 4.0977 .0000 .8584-1.0000 OS 20 .8079 .81426 .53565 .00000 1.00000 .46435 .14894 .37235 .00000 4.1754 .0000 .8661 1.0000 OF 20 .0448 .60431 .01420 .00228 .99772 .98580 .03185 .07314 .02035 5.0278 .1979 .9959 -.7201 CF 20 .0448 .60431 .01420 .00228 .99772 .98580 .03185 .07314 .02035 5.0278 .1979 .9959 -.7201 CS 20 .0803 .60809 .02833 .00540 .99460 .97168 .04731 .10784 .02970 4.4551 .2387 .9915 -.6734 NT 40 .1597 .62071 .05178 .00000 1.00000 .94823 .05346 .13366 .00000 5.8928 .0000 .9871 -1.0000 MB 40 .0444 .60562 .01405 .00000 1.00000 .98595 .02974 .07435 .00000 6.4608 .0000 .9965 -1.0000 RB 40 .0186 .60213 .00533 .00000 1.00000 .99468 .01639 .04096 .00000 6.8189 .0000 .9987 -1.000C MD 40 .0453 .60573 .01433 .00000 1.00000 .98568 .03000 .07501 .00000 6.4532 .0000 .9964-1.0000 RD 40 .0191 .60218 .00545 .00000 1.00000 .99455 .01653 .04133 .00000 6.8108 .0000 .9986-1.0000 OR 40 .8535 .82771 .56928 .00000 1.00000 .43073 .14101 .35254 .00000 4.0904 .0000 .8577 -1.0000 OS 40 .8111 .81453 .53633 .00000 1.00000 .46367 .14809 .37022 .00000 4.1737 .0000 .8659 -1.0000 OF 40 .0460 .60581 .01453 .00000 1.00000 .98548 .03016 .07539 .00000 6.4477 .0000 .9964-1.0000 CF 40 .0460 .60581 .01453 .00000 1.00000 .98548 .03016 .07539 .00000 6.4477 .0000 .9964-1.000C CS 40 .0805 .61165 .02913 .00000 1.00000 .97088 .04474 .11184 .00000 6.1587 .0000 .9927 -1.0000 156 Table 10.2.2.1.3.4 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p ~ 5, mNz = .5, pNz = .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s:FnTp d' A' B" NT 2 .0688 .24623 .03790 .70169 .29831 .96210 .20827 .14497 .25213 1.2463 4.2051 .7859 .7033 MB 2 .0106 .06463 .00570 .92064 .07936 .99430 .10495 .05673 .12822 1.1208 9.0954 .7506 .8560 RB 2 .0088 .05959 .00470 .92669 .07331 .99530 .09133 .05127 .11253 1.1456 10.1665 .7512 .8712 MD 2 .0107 .06579 .00575 .91920 .08080 .99425 .10581 .05694 .12931 1.1274 9.1485 .7511 .8571 RD 2 .0092 .06071 .00490 .92534 .07466 .99510 .09222 .05221 .11357 1.1409 9.9332 .7511 .8682 OR 2 .5174 .53126 .39705 .43519 .56481 .60295 .38050 .42337 .39935 .4242 1.0210 .6438 .0132 OS 2 .2758 .32777 .22445 .64640 .35360 .77555 .41274 .38524 .43701 .3816 1.2413 .6329 .1353 OF 2 .0149 .08244 .00805 .89896 .10104 .99195 .12011 .06753 .14630 1.1310 8.0229 .7535 .8384 CF 2 .0149 .08244 .00805 .89896 .10104 .99195 .12011 .06753 .14630 1.1310 8.0229 .7535 .8384 CS 2 .0578 .20596 .03165 .75046 .24954 .96835 .20239 .13257 .24217 1.1811 4.4634 .7745 .7187 NT 4 .0882 .52303 .04810 .35824 .64176 .95190 .19802 ,16043 .24565 2.0267 3.7351 .8872 .6678 MB 4 .0193 .26812 .01095 .66759 .33241 .98905 .21844 .08158 .26881 1.8588 12.5912 .8230 .9069 RB 4 .0097 .23243 .00500 .71071 .28929 .99500 .18003 .05124 .22415 2.0204 23.6456 .8171 .9527 MD 4 .0197 .27062 .01115 .66451 .33549 .98885 .21890 .08217 .26938 1.8604 12.4395 .8237 .9057 RD 4 .0098 .23445 .00505 .70820 .29180 .99495 .18085 .05148 .22516 2.0243 23.5320 .8177 .9525 OR 4 .7967 .86660 .63680 .07595 .92405 .36320 .17652 .38904 .17419 1.0829 .3809 .7754 -.5344 OS 4 .6593 .76461 .53440 .17784 .82216 .46560 .33654 .43172 .35117 .8373 .6552 .7420 -.2597 OF 4 .0219 .28871 .01235 .64220 .35780 .98765 .22088 .08616 .27165 1.8817 11.6584 .8288 .8992 CF 4 .0219 .28871 .01235 .64220 .35780 .98765 .22088 .08616 .27165 1.8817 11.6584 .8288 .8992 CS 4 .0751 .47140 .04115 .42104 .57896 .95885 .19536 .14995 .23946 1.9367 4.4353 .8725 .7214 NT 10 .0884 .78272 .04795 .03359 .96641 .95205 .06541 .15946 .07945 3.4956 .7489 .9788 -.1689 MB 10 .0323 .72334 .01795 .10031 .89969 .98205 .12997 .10224 .16083 3.3778 3.9829 .9695 .6732 RB 10 .0103 .66915 .00530 .16489 .83511 .99470 .14362 .05265 .17991 3.5302 16.2924 .9570 .9263 MD 10 .0331 .72463 .01835 .09880 .90120 .98165 .12893 .10315 .15953 3.3775 3.8656 .9697 .6635 RD 10 .0106 .67073 .00550 .16296 .83704 .99450 .14275 .05404 .17885 3.5251 15.6449 .9574 .9229 OR 10 .8421 .93750 .68930 .00045 .99955 .31070 .07453 .37119 .00847 2.8262 .0046 .8272 -.9958 OS 10 .8196 .93515 .67800 .00056 .99944 .32200 .07771 .38410 .01316 2.7951 .0055 .8300 -.9949 OF 10 .0340 .72673 .01890 .09631 .90369 .98110 .12709 .10485 .15718 3.3799 3.6998 .9702 .6487 CF 10 .0340 .72673 .01890 .09631 .90369 .98110 .12709 .10485 .15718 3.3799 3.6998 .9702 .6487 CS 10 .0702 .75177 .03970 .07021 .92979 .96030 .07664 .15125 .09249 3.2284 1.5713 .9710 .2626 NT 20 .0898 .80969 .04965 .00030 .99970 .95035 .03300 .16466 .00612 5.0799 .0108 .9875 -.9874 MB 20 .0458 .80436 .02675 .00124 .99876 .97325 .02770 .12850 .01323 4.9572 .0662 .9930 -.9094 RB 20 .0102 .79757 .00530 .00436 .99564 .99470 .02171 .05312 .02509 5.1783 .8407 .9976 -.0966 MD 20 .0466 .80447 .02720 .00121 .99879 .97280 .02780 .12947 .01311 4.9562 .0641 .9929 -.9125 RD 20 .0103 .79759 .00535 .00435 .99565 .99465 .02162 .05335 .02506 5.1760 .8316 .9976 -.1026 OR 20 .8450 .93793 .68965 .00000 1.00000 .31035 .07386 .36929 .00000 3.7700 .0000 .8276 1.0000 OS 20 .8237 .93580 .67900 .00000 1.00000 .32100 .07632 .38161 .00000 3.8000 .0000 .8302 1.0000 OF 20 .0468 .80452 .02730 .00118 .99883 .97270 .02774 .12964 .01282 4.9641 .0621 .9929 -.9153 CF 20 .0468 .80452 .02730 .00118 .99883 .97270 .02774 .12964 .01282 4.9641 .0621 .9929 -.9153 CS 20 .0612 .80623 .03560 .00111 .99889 .96440 .03027 .14675 .01174 4.8626 .0474 .9908 -.9373 NT 40 .0896 .80985 .04925 .00000 1.00000 .95075 .03265 .16325 .00000 5.9171 .0000 .9877 -1.0000 MB 40 .0459 .80536 .02680 .00000 1.00000 .97320 .02572 .12858 .00000 6.1949 .0000 .9933 -1.0000 RB 40 .0097 .80101 .00505 .00000 1.00000 .99495 .01039 .05196 .00000 6.8373 .0000 .9987 • 1.0000 MD 40 .0466 .80543 .02715 .00000 1.00000 .97285 .02584 .12919 .00000 6.1893 .0000 .9932-1.0000 RD 40 .0100 .80104 .00520 .00000 1.00000 .99480 .01053 .05266 .00000 6.8271 .0000 .9987 -1.0000 OR 40 .8434 .93768 .68840 .00000 1.00000 .31160 .07403 .37016 .00000 3.7736 .0000 .8279 -1.0000 OS 40 .8239 .93573 .67865 .00000 1.00000 .32135 .07628 .38141 .00000 3.8010 .0000 .8303-1.0000 OF 40 .0468 .80545 .02725 .00000 i.ooooo .97275 .02587 .12936 .00000 6.1877 .0000 .9932 -1.0000 CF 40 .0468 .80545 .02725 .00000 1.00000 .97275 .02587 .12936 .00000 6.1877 .0000 .9932 -1.0000 CS 40 .0611 .80700 .03500 .00000 1.00000 .96500 .02879 .14397 .00000 6.0768 .0000 .9913-1.0000 Table 10.2.2.2.1.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz - .2 N:p CLEX Rej Fp Fn Tp Tn s.Rej s.FpTn S.FnTp d' P A' B" NT 2 .0787 .00887 .00799 .98763 .01237 .99201 .03159 .02954 .05530 .1638 1.4639 .5895 .2128 MB 2 .0142 .00053 .00041 .99902 .00098 .99959 .00357 .00352 .01096 .2464 2.2112 .6443 .4050 RB 2 .0142 .00052 .00041 .99903 .00097 .99959 .00354 .00352 .01090 .2430 2.1882 .6431 .4002 MD 2 .0143 .00054 .00042 .99899 .00101 .99958 .00363 .00357 .01112 .2527 2.2523 .6464 .4133 RD 2 .0142 .00053 .00041 .99899 .00101 .99959 .00359 .00352 .01112 .2564 2.2803 .6478 .4189 OR 2 .0787 .02796 .02720 .96899 .03101 .97280 .11245 .11077 .12745 .0575 1.1151 .5317 .0635 OS 2 .0231 .00284 .00251 .99583 .00417 .99749 .02806 .02685 .04005 .1670 1.5754 .5996 .2466 OF 2 .0178 .00069 .00055 .99876 .00124 .99945 .00429 .00425 .01251 .2389 2.1196 .6397 .3867 CF 2 .0178 .00069 .00055 .99876 .00124 .99945 .00429 .00425 .01251 .2389 2.1196 .6397 .3867 CS 2 .0607 .00264 .00231 .99607 .00393 .99769 .01069 .01045 .02392 .1741 1.6127 .6033 .2585 NT 4 .1051 .01191 .00975 .97946 .02054 .99025 .03616 .03106 .07262 .2932 1.9001 .6341 .3515 MB 4 .0145 .00065 .00041 .99838 .00162 .99959 .00400 .00342 .01378 .4016 3.5356 .6869 .5952 RB 4 .0144 .00065 .00041 .99838 .00162 .99959 .00398 .00341 .01378 .4035 3.5579 .6874 .5974 MD 4 .0148 .00066 .00042 .99836 .00164 .99958 .00404 .00346 .01387 .4003 3.5136 .6865 .5931 RD 4 .0147 .00066 .00042 .99836 .00164 .99958 .00402 .00344 .01387 .4021 3.5354 .6870 .5953 OR 4 .1061 .03803 .03691 .95752 .04248 .96309 .12821 .12673 .14483 .0650 1.1209 .5342 .0672 OS 4 .0245 .00298 .00247 .99498 .00502 .99753 .02888 .02649 .04463 .2363 1.8895 .6276 .3391 OF 4 .0179 .00078 .00051 .99814 .00186 .99949 .00436 .00381 .01467 .3841 3.2821 .6818 .5695 CF 4 .0179 .00078 .00051 .99814 .00186 .99949 .00436 .00381 .01467 .3841 3.2821 .6818 .5695 CS 4 .0724 .00346 .00258 .99302 .00698 .99742 .01173 .01032 .03171 .3384 2.4331 .6586 .4583 NT 10 .2246 .02758 .01816 .93473 .06527 .98184 .05292 .03825 .13723 .5814 2.8523 .6925 .5478 MB 10 .0231 .00193 .00066 .99298 .00702 .99934 .00712 .00436 .02961 .7550 8.4939 .7281 .8269 RB 10 .0228 .00192 .00065 .99299 .00701 .99935 .00708 .00433 .02959 .7581 8.5819 .7283 .8287 MD 10 .0237 .00198 .00068 .99280 .00720 .99932 .00723 .00444 .02994 .7556 8.4542 .7280 .8262 RD 10 .0236 .00197 .00067 .99284 .00716 .99933 .00717 .00440 .02983 .7558 8.4720 .7280 .8266 OR 10 .2295 .08820 .08276 .89003 .10997 .91724 .19169 .18707 .23116 .1600 1.2326 .5693 .1264 OS 10 .0522 .01070 .00776 .97753 .02247 .99224 .06289 .05524 .10696 .4149 2.5047 .6674 .4810 OF 10 .0245 .00206 .00071 .99252 .00748 .99929 .00740 .00453 .03071 .7589 8.4550 .7281 .8265 CF 10 .0245 .00206 .00071 .99252 .00748 .99929 .00740 .00453 .03071 .7589 8.4550 .7281 .8265 CS 10 .1242 .00887 .00469 .97440 .02560 .99531 .02013 .01431 .06492 .6484 4.3683 .7095 .6849 NT 20 .4568 .06358 .03165 .80872 .19128 .96835 .06927 .04174 .22297 .9838 3.8308 .7498 .6692 MB 20 .0336 .00621 .00096 .97276 .02724 .99904 .01269 .00518 .05868 1.1808 19.4467 .7478 .9305 RB 20 .0333 .00618 .00094 .97289 .02711 .99906 .01257 .00514 .05819 1.1821 19.5764 .7478 .9309 MD 20 .0344 .00632 .00098 .97233 .02767 .99902 .01280 .00524 .05919 1.1807 19.2862 .7478 .9299 RD 20 .0343 .00628 .00098 .97252 .02748 .99903 .01269 .00523 .05871 1.1785 19.2265 .7478 .9297 OR 20 .4863 .19898 .17827 .71819 .28181 .82173 .25560 .24784 .33194 .3445 1.2947 .6234 .1602 OS 20 .1503 .04544 .03184 .90018 .09982 .96816 .13360 .11598 .23481 .5718 2.4520 .6878 .4891 OF 20 .0357 .00647 .00101 .97171 .02829 .99899 .01300 .00533 .06008 1.1796 19.0036 .7479 .9289 CF 20 .0357 .00647 .00101 .97171 .02829 .99899 .01300 .00533 .06008 1.1796 19.0036 .7479 .9289 CS 20 .2055 .02257 .00776 .91822 .08178 .99224 .03042 .01748 .11618 1.0266 7.0800 .7449 .8139 NT 40 .7598 .13377 .04655 .51737 .48263 .95345 .06435 .03849 .24475 1.6357 4.0918 .8402 .6981 MB 40 .0399 .02124 .00113 .89832 .10168 .99887 .02302 .00558 .11246 1.7823 47.2496 .7724 .9756 RB 40 .0392 .02100 .00111 .89941 .10059 .99889 .02263 .00552 .11066 1.7821 47.7431 .7722 .9759 MD 40 .0406 .02150 .00115 .89707 .10293 .99885 .02316 .00562 .11308 1.7842 46.9325 .7727 .9755 RD 40 .0398 .02125 .00112 .89824 .10176 .99888 .02274 .00555 .11119 1.7842 47.4903 .7724 .9758 OR 40 .8595 .39784 .33483 .35014 .64986 .66517 .25870 .26660 .32131 .8115 1.0171 .7396 .0107 OS 40 .4705 .18492 .13018 .59609 .40391 .86982 .23882 .21481 .40713 .8823 1.8291 .7481 .3603 OF 40 .0413 .02170 .00117 .89617 .10383 .99883 .02322 .00567 .11337 1.7841 46.5086 .7729 .9753 CF 40 .0413 .02170 .00117 .89617 .10383 .99883 .02322 .00567 .11337 1.7841 46.5086 .7729 .9753 CS 40 .2871 .05757 .01081 .75538 .24462 .98919 .04055 .01973 .17165 1.6056 11.0157 .7980 .8906 158 Table 10.2.2.2.1.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz - A N:p ctEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp a" P A' B" NT 2 .1036 .01251 .00990 .98358 .01642 .99010 .03743 .03273 .05372 .1961 1.5493 .6009 .2447 MB 2 .0117 .00073 .00044 .99884 .00116 .99956 .00419 .00413 .00831 .2765 2.4126 .6540 .4442 RB 2 .0117 .00073 .00044 .99884 .00116 .99956 .00419 .00413 .00831 .2765 2.4126 .6540 .4442 MD 2 .0121 .00075 .00046 .99881 .00119 .99954 .00429 .00420 .00842 .2759 2.4021 .6536 .4424 RD 2 .0119 .00074 .00045 .99882 .00118 .99955 .00424 .00417 .00840 .2790 2.4281 .6547 .4470 OR 2 .1079 .04099 .03937 .95658 .04342 .96063 .13739 .13565 .14500 .0458 1.0826 .5244 .0468 OS 2 .0255 .00428 .00352 .99458 .00542 .99648 .03815 .03522 .04506 .1471 1.4704 .5881 .2115 OF 2 .0145 .00093 .00056 .99852 .00148 .99944 .00493 .00474 .00961 .2847 2.4271 .6550 .4479 CF 2 .0145 .00093 .00056 .99852 .00148 .99944 .00493 .00474 .00961 .2847 2.4271 .6550 .4479 CS 2 .0586 .00385 .00278 .99454 .00546 .99722 .01330 .01247 .02197 .2277 1.8323 .6235 .3245 NT 4 .1726 .02233 .01508 .96679 .03321 .98492 .04855 .03755 .07706 .3324 1.9452 .6411 .3674 MB 4 .0133 .00124 .00050 .99765 .00235 .99950 .00556 .00429 .01216 .4657 4.1577 .6977 .6507 RB 4 .0133 .00124 .00050 .99765 .00235 .99950 .00556 .00429 .01216 .4657 4.1577 .6977 .6507 MD 4 .0134 .00127 .00050 .99758 .00242 .99950 .00562 .00431 .01234 .4733 4.2439 .6989 .6572 RD 4 .0134 .00127 .00050 .99758 .00242 .99950 .00561 .00431 .01230 .4726 4.2351 .6988 .6566 OR 4 .1862 .07606 .07168 .91737 .08263 .92832 .18359 .17983 .19654 .0758 1.1142 .5361 .0651 OS 4 .0364 .00829 .00623 .98862 .01138 .99377 .05798 .05128 .07199 .2215 1.6973 .6145 .2902 OF 4 .0156 .00148 .00058 .99718 .00282 .99942 .00612 .00463 .01338 .4801 4.2373 .6991 .6577 CF 4 .0156 .00148 .00058 .99718 .00282 .99942 .00612 .00463 .01338 .4801 4.2373 .6991 .6577 CS 4 .0903 .00724 .00420 .98820 .01180 .99580 .01839 .01466 .03361 .3720 2.4872 .6629 .4720 NT 10 .4095 .06297 .03114 .88928 .11072 .96886 .07151 .04533 .13259 .6416 2.6923 .7002 .5309 MB. 10 .0238 .00428 .00090 .99064 .00936 .99910 .01045 .00579 .02422 .7714 8.2579 .7282 .8238 RB 10 .0237 .00426 .00089 .99069 .00931 .99911 .01037 .00578 .02406 .7708 8.2549 .7281 .8237 MD 10 .0240 .00437 .00090 .99043 .00957 .99910 .01055 .00581 .02447 .7775 8.3614 .7286 .8261 RD 10 .0239 .00434 .00090 .99049 .00951 .99910 .01045 .00580 .02424 .7761 8.3419 .7285 .8256 OR 10 .4736 .22480 .20397 .74394 .25606 .79603 .28526 .27712 .31324 .1720 1.1360 .5672 .0797 OS 10 .1063 .04079 .03014 .94324 .05676 .96986 .14381 .12574 .17932 .2961 1.6693 .6241 .2936 OF 10 .0252 .00462 .00095 .98988 .01012 .99905 .01091 .00594 .02530 .7842 8.4006 .7289 .8273 CF 10 .0252 .00462 .00095 .98988 .01012 .99905 .01091 .00594 .02530 .7842 8.4006 .7289 .8273 CS 10 .1924 .02492 .00945 .95188 .04812 .99055 .03627 .02207 .07285 .6840 3.9423 .7106 .6606 NT 20 .6611 .13604 .04575 .72853 .27147 .95425 .07472 .04431 .15914 1.0791 3.4514 .7670 .6383 MB 20 .0313 .01338 .00118 .96831 .03169 .99882 .01871 .00663 .04536 1.1838 18.1476 .7483 .9259 RB 20 .0305 .01324 .00115 .96863 .03137 .99885 .01842 .00653 .04473 1.1880 18.4755 .7484 .9273 MD 20 .0319 .01360 .00120 .96781 .03219 .99880 .01883 .00669 .04566 1.1852 18.0728 .7484 .9257 RD 20 .0314 .01347 .00118 .96809 .03191 .99882 .01855 .00661 .04505 1.1869 18.2500 .7484 .9264 OR 20 .8418 .49581 .43411 .41165 .58835 .56589 .30152 .30614 .32584 .3892 .9889 .6337 -.0071 OS 20 .3297 .18716 .14375 .74771 .25229 .85625 .29845 .26464 .36787 .3963 1.4092 .6392 .2103 OF 20 .0326 .01390 .00123 .96711 .03289 .99877 .01903 .00676 .04617 1.1885 18.0436 .7486 .9257 CF 20 .0326 .01390 .00123 .96711 .03289 .99877 .01903 .00676 .04617 1.1885 18.0436 .7486 .9257 CS 20 .3339 .07031 .01730 .85018 .14982 .98270 .05610 .02876 .12163 1.0758 5.4440 .7548 .7645 NT 40 .7427 .23737 .05006 .48166 .51834 .94994 .06463 .04274 .14767 1.6902 3.8602 .8491 .6800 MB 40 .0320 .04285 .00120 .89467 .10533 .99880 .03409 .00664 .08463 1.7839 45.7977 .7732 .9749 RB 40 .0304 .04185 .00114 .89708 .10292 .99886 .03285 .00645 .08165 1.7868 47.3119 .7727 .9757 MD 40 .0328 .04342 .00123 .89329 .10671 .99877 .03431 .00672 .08515 1.7841 45.2092 .7735 .9746 RD 40 .0309 .04240 .00116 .89573 .10427 .99884 .03305 .00650 .08211 1.7895 47.0617 .7730 .9756 OR 40 .9956 .74722 .64133 .09394 .90606 .35867 .18058 .23968 .13217 .9548 .4486 .7576 -.4598 OS 40 .8033 .57514 .46509 .25979 .74021 .53491 .32811 .32658 .37243 .7316 .8158 .7215 -.1281 OF 40 .0331 .04380 .00125 .89237 .10763 .99875 .03449 .00681 .08556 1.7845 44.8710 .7737 .9744 CF 40 .0331 .04380 .00125 .89237 .10763 .99875 .03449 .00681 .08556 1.7845 44.8710 .7737 .9744 CS 40 .4464 .16366 .02393 .62673 .37327 .97607 .06409 .03254 .14558 1.6554 6.7209 .8234 .8184 159 Table 10.2.2.2.1.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .1, pNz = .6 N:p aEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .1176 .01707 .01219 .97968 .02032 .98781 .04340 .03785 .05408 .2040 1.5502 .6021 .2463 MB 2 .0082 .00094 .00047 .99874 .00126 .99953 .00480 .00519 .00714 .2879 2.4879 .6573 .4578 RB 2 .0082 .00094 .00047 .99874 .00126 .99953 .00480 .00519 .00714 .2879 2.4879 .6573 .4578 MD 2 .0084 .00096 .00048 .99872 .00128 .99952 .00488 .00525 .00719 .2866 2.4736 .6567 .4554 RD 2 .0083 .00095 .00047 .99873 .00127 .99953 .00485 .00522 .00718 .2890 2.4939 .6575 .4589 OR 2 .1419 .05932 .05566 .93825 .06175 .94434 .16631 .16300 .17235 .0520 1.0849 .5263 .0486 OS 2 .0263 .00612 .00489 .99307 .00693 .99511 .04877 .04545 .05268 .1223 1.3613 .5739 .1711 OF 2 .0110 .00126 .00064 .99833 .00167 .99936 .00578 .00618 .00841 .2857 2.4096 .6544 .4454 CF 2 .0110 .00126 .00064 .99833 .00167 .99936 .00578 .00618 .00841 .2857 2.4096 .6544 .4454 CS 2 .0535 .00567 .00357 .99293 .00707 .99643 .01723 .01639 .02291 .2369 1.8391 .6248 .3278 NT 4 .2055 .03438 .01984 .95592 .04408 .98016 .05923 .04484 .07879 .3519 1.9385 .6437 .3685 MB 4 .0103 .00192 .00057 .99717 .00283 .99943 .00699 .00561 .01097 .4851 4.3057 .6999 .6626 RB 4 .0103 .00191 .00057 .99719 .00281 .99943 .00693 .00561 .01087 .4829 4.2802 .6996 .6607 MD 4 .0104 .00197 .00058 .99711 .00289 .99942 .00707 .00564 .01111 .4899 4.3581 .7006 .6664 RD 4 .0104 .00196 .00058 .99713 .00287 .99942 .00702 .00564 .01101 .4878 4.3329 .7003 .6646 OR 4 .2681 .12412 .11489 .86972 .13028 .88511 .23484 .22904 .24412 .0759 1.0922 .5339 .0540 OS 4 .0448 .01587 .01160 .98129 .01871 .98840 .08835 .07690 .09847 .1891 1.5089 .5968 .2313 OF 4 .0125 .00228 .00069 .99667 .00333 .99931 .00767 .00617 .01200 .4839 4.1784 .6986 .6544 CF 4 .0125 .00228 .00069 .99667 .00333 .99931 .00767 .00617 .01200 .4839 4.1784 .6986 .6544 CS 4 .0896 .01276 .00598 .98273 .01727 .99402 .02723 .02066 .03892 .3995 2.5199 .6662 .4811 NT 10 .4476 .09836 .03929 .86227 .13773 .96071 .07961 .05277 .11568 .6684 2.5916 .7043 .5176 MB 10 .0169 .00665 .00096 .98956 .01044 .99904 .01301 .00741 .02102 .7920 8.5264 .7294 .8300 RB 10 .0169 .00661 .00096 .98962 .01038 .99904 .01287 .00735 .02082 .7913 8.5242 .7293 .8299 MD 10 .0170 .00680 .00097 .98931 .01069 .99903 .01321 .00743 .02135 .7992 8.6566 .7298 .8327 RD 10 .0169 .00673 .00096 .98943 .01057 .99904 .01300 .00741 .02101 .7967 8.6185 .7297 .8319 OR 10 .6635 .38544 .34591 .58821 .41179 .65409 .33341 .32840 .34742 .1734 1.0552 .5652 .0341 OS 10 .1657 .09487 .07381 .89109 .10891 .92619 .23606 .20848 .25937 .2157 1.3351 .5901 .1734 OF 10 .0177 .00722 .00101 .98864 .01136 .99899 .01364 .00757 .02207 .8103 8.7973 .7305 .8357 CF 10 .0177 .00722 .00101 .98864 .01136 .99899 .01364 .00757 .02207 .8103 8.7973 .7305 .8357 CS 10 .2187 .04904 .01542 .92855 .07145 .98458 .05491 .03292 :08164 .6940 3.5170 .7103 .6275 NT 20 .5811 .19273 .04931 .71165 .28835 .95069 .07873 .05280 .12409 1.0934 3.3472 .7701 .6281 MB 20 .0222 .01973 .00125 .96795 .03205 .99875 .02339 .00835 .03841 1.1718 17.3962 .7480 .9226 RB 20 .0218 .01944 .00123 .96841 .03159 .99877 .02293 .00828 .03766 1.1708 17.4745 .7479 .9229 MD 20 .0227 .02006 .00128 .96742 .03258 .99872 .02358 .00844 .03870 1.1725 17.2838 .7480 .9222 RD 20 .0222 .01977 .00125 .96788 .03212 .99875 .02308 .00835 .03791 1.1729 17.4294 .7480 .9228 OR 20 .9537 .71423 .63048 .22994 .77006 .36952 .24821 .28135 .24538 .4059 .8045 .6397 -.1363 OS 20 .4846 .36822 .30356 .58867 .41133 .69644 .40185 .36753 .43456 .2901 1.1130 .6042 .0677 OF 20 .0233 .02049 .00131 .96672 .03328 .99869 .02387 .00854 .03918 1.1743 17.1799 .7482 .9218 CF 20 .0233 .02049 .00131 .96672 .03328 .99869 .02387 .00854 .03918 1.1743 17.1799 .7482 .9218 CS 20 .3713 .13439 .02821 .79483 .20517 .97179 .08129 .04310 .12533 1.0846 4.3975 .7612 .7122 NT 40 .5908 .33159 .04991 .48062 .51938 .95009 .08058 .05262 .12956 1.6943 3.8691 .8495 .6807 MB 40 .0217 .06484 .00123 .89275 .10725 .99877 .04529 .00837 .07521 1.7861 45.2485 .7737 .9746 RB 40 .0202 .06252 .00113 .89656 .10344 .99887 .04277 .00793 .07111 1.7907 47.6301 .7729 .9759 MD 40 .0221 .06570 .00126 .89133 .10867 .99874 .04560 .00844 .07572 1.7883 44.9384 .7740 .9744 RD 40 .0208 .06332 .00117 .89525 .10475 .99883 .04300 .00804 .07148 1.7892 46.8052 .7731 .9755 OR 40 .9998 .89477 .79483 .03860 .96140 .20517 .09841 .18224 .06113 .9438 .2945 .7463 -.6292 OS 40 .9145 .80569 .69573 .12101 .87899 .30427 .26688 .28958 .27386 .6578 .5751 .7027 -.3312 OF 40 .0223 .06624 .00127 .89044 .10956 .99873 .04589 .00848 .07619 1.7905 44.8417 .7742 .9744 CF 40 .0223 .06625 .00127 .89043 .10957 .99873 .04589 .00848 .07619 1.7905 44.8427 .7742 .9744 CS 40 .4713 .28821 .03801 .54499 .45501 .96199 .08454 .04883 .13329 1.6612 4.7951 .8375 .7430 160 Table 10.2 2.2.1.4 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz - .1, pNz = .8 N:p OLEX Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .0927 .02247 .01474 .97559 .02441 .98526 .04980 .05129 .05525 .2067 1.5350 .6014 .2421 MB 2 .0054 .00124 .00061 .99861 .00139 .99939 .00557 .00837 .00662 .2429 2.1299 .6404 .3894 RB 2 .0054 .00124 .00061 .99861 .00139 .99939 .00557 .00837 .00662 .2429 2.1299 .6404 .3894 MD 2 .0055 .00127 .00062 .99857 .00143 .99938 .00566 .00844 .00671 .2456 2.1443 .6413 .3926 RD 2 .0055 .00126 .00062 .99858 .00142 .99938 .00563 .00844 .00667 .2438 2.1329 .6406 .3901 OR 2 .1693 .08169 .07692 .91712 .08288 .92308 .19945 .20151 .20168 .0401 1.0580 .5196 .0341 OS 2 .0240 .00962 .00768 .98989 .01011 .99232 .06776 .06425 .06991 .1016 1.2726 .5607 .1355 OF 2 .0067 .00161 .00076 .99818 .00182 .99924 .00649 .00927 .00769 .2651 2.2390 .6466 .4134 CF 2 .0067 .00161 .00076 .99818 .00182 .99924 .00649 .00927 .00769 .2651 2.2390 .6466 .4134 CS 2 .0396 .00824 .00504 .99096 .00904 .99496 .02255 .02679 .02550 .2087 1.6741 .6115 .2818 NT 4 .1650 .04742 .02418 .94678 .05322 .97582 .06801 .06048 .07760 .3599 1.9074 .6439 .3622 MB 4 .0063 .00254 .00070 .99699 .00301 .99930 .00804 .00879 .00974 .4475 3.7788 .6924 .6215 RB 4 .0062 .00253 .00069 .99701 .00299 .99931 .00799 .00872 .00969 .4509 3.8222 .6931 .6252 MD 4 .0065 .00260 .00072 .99693 .00307 .99928 .00811 .00893 .00983 .4454 3.7417 .6918 .6183 RD 4 .0065 .00259 .00072 .99694 .00306 .99928 .00809 .00893 .00980 .4445 3.7326 .6916 .6175 OR 4 .3348 .18012 .16489 .81608 .18392 .83511 .28014 .27972 .28452 .0740 1.0719 .5316 .0431 OS 4 .0500 .02722 .02034 .97107 .02893 .97966 .12558 .11213 .13067 .1500 1.3441 .5764 .1700 OF 4 .0077 .00298 .00086 .99649 .00351 .99914 .00871 .00971 .01055 .4405 3.6127 .6897 .6073 CF 4 .0077 .00298 .00086 .99649 .00351 .99914 .00871 .00971 .01055 .4405 3.6127 .6897 .6073 CS 4 .0651 .01998 .00821 .97708 .02292 .99179 .03728 .03308 .04348 .4026 2.4227 .6642 .4667 NT 10 .3165 .13056 .04406 .84782 .15218 .95594 .08403 .07233 .10009 .6783 2.5264 .7059 .5078 MB 10 .0101 .00902 .00116 .98902 .01098 .99884 .01553 .01160 .01913 .7560 7.5216 .7261 .8079 RB 10 .0100 .00893 .00114 .98912 .01088 .99886 .01528 .01154 .01884 .7553 7.5266 .7261 .8079 MD 10 .0104 .00921 .00119 .98878 .01122 .99881 .01569 .01175 .01933 .7555 7.4651 .7260 .8066 RD 10 .0103 .00911 .00118 .98890 .01110 .99882 .01544 .01170 .01902 .7543 7.4598 .7259 .8064 OR 10 .7718 .53267 .47704 .45342 .54658 .52296 .33741 .35011 .34169 .1746 .9948 .5650 -.0033 OS 10 .2198 .16493 .13278 .82703 .17297 .86722 .31715 .28576 .32798 .1709 1.1920 .5697 .1081 OF 10 .0107 .00973 .00122 .98814 .01186 .99878 .01617 .01191 .01994 .7684 7.6388 .7269 .8113 CF 10 .0107 .00973 .00122 .98814 .01186 .99878 .01617 .01191 .01994 .7684 7.6388 .7269 .8113 CS 10 .1706 .07954 .02212 .90610 .09390 .97788 .07444 .05271 .08873 .6947 3.1779 .7095 .5946 NT 20 .3666 .24332 .05041 .70846 .29154 .94959 .08894 .07436 .10920 1.0920 3.3056 .7703 .6237 MB 20 .0110 .02596 .00126 .96786 .03214 .99874 .02780 .01206 .03459 1.1717 17.3650 .7480 .9225 RB 20 .0107 .02542 .00122 .96853 .03147 .99878 .02699 .01191 .03359 1.1705 17.4923 .7479 .9230 MD 20 .0111 .02638 .00127 .96734 .03266 .99873 .02803 .01211 .03488 1.1763 17.4587 .7482 .9230 RD 20 .0109 .02586 .00124 .96798 .03202 .99876 .02722 .01201 .03387 1.1728 17.4543 .7480 .9229 OR 20 .9824 .84348 .75776 .13509 .86491 .24224 .17681 .24279 .17178 .4036 .6952 .6416 -.2221 OS 20 .5978 .52711 .45566 .45502 .54498 .54434 .43814 .41427 .44884 .2244 .9998 .5820 -.0001 OF 20 .0112 .02694 .00128 .96664 .03336 .99872 .02838 .01216 .03531 1.1831 17.6227 .7485 .9239 CF 20 .0112 .02694 .00128 .96664 .03336 .99872 .02838 .01216 .03531 1.1831 17.6227 .7485 .9239 CS 20 .2900 .20879 .03960 .74891 .25109 .96040 .10618 .06878 .12825 1.0843 3.7264 .7656 .6635 NT 40 .3666 .42540 .05079 .48094 .51906 .94921 .09725 .07493 .11997 1.6850 3.8158 .8489 .6763 MB 40 .0107 .08718 .00121 .89133 .10868 .99879 .05611 .01175 .07008 1.7993 46.4477 .7741 .9753 RB 40 .0100 .08280 .00112 .89678 .10322 .99888 .05161 .01122 .06447 1.7924 47.9861 .7728 .9761 MD 40 .0110 .08831 .00124 .88993 .11008 .99876 .05653 .01190 .07059 1.7986 45.7264 .7744 .9749 RD 40 .0103 .08389 .00116 .89543 .10457 .99884 .05191 .01138 .06485 1.7911 47.1597 .7731 .9756 OR 40 1.0000 .95792 .87333 .02094 .97906 .12667 .05082 .15316 .03595 .8925 .2423 .7357 -.6873 OS 40 .9574 .91370 .82189 .06334 .93666 .17811 .20017 .23885 .20088 .6047 .4768 .6917 -.4232 OF 40 .0110 .08904 .00124 .88901 .11099 .99876 .05675 .01190 .07086 1.8034 45.9990 .7747 .9751 CF 40 .0110 .08904 .00124 .88901 .11099 .99876 .05675 .01190 .07086 1.8034 45.9990 .7747 .9751 CS 40 .3792 .42553 .05492 .48182 .51818 .94508 .10397 .08040 .12637 1.6445 3.5865 .8460 .6558 161 Table 10.2.2.2.2.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz - .3, pNz - .2 N:p aEX Rej Fp Fn Tp Tn s.Rej s:FpTn s.FnTp d' B A' B" NT 2 .3695 .05327 .02715 .84227 .15773 .97285 .07052 .04234 .22860 .9206 3.8490 .7405 .6683 MB 2 .0294 .00399 .00084 .98339 .01661 .99916 .01066 .00488 .04873 1.0126 14.4262 .7413 .9024 RB 2 .0294 .00396 .00084 .98354 .01646 .99916 .01053 .00488 .04802 1.0089 14.3105 .7412 .9015 MD 2 .0299 .00406 .00085 .98310 .01690 .99915 .01080 .00492 .04939 1.0148 14.4211 .7414 .9024 RD 2 .0296 .00403 .00084 .98324 .01676 .99916 .01066 .00490 .04875 1.0142 14.4455 .7414 .9026 OR 2 .3937 .17133 .15353 .75746 .24254 .84647 .25820 .24893 .33857 .3233 1.3204 .6180 .1714 OS 2 .1285 .04095 .02986 .91469 .08531 .97014 .13664 .12003 .23483 .5127 2.3024 .6768 .4586 OF 2 .0400 .00519 .00117 .97872 .02128 .99883 .01245 .00586 .05649 1.0161 13.1571 .7413 .8940 CF 2 .0400 .00519 .00117 .97872 .02128 .99883 .01245 .00586 .05649 1.0161 13.1571 .7413 .8940 CS 2 .1941 .02037 .00818 .93089 .06911 .99182 .03429 .02005 .12370 .9183 5.9477 .7358 .7760 NT 4 .6585 .11759 .04236 .58149 .41851 .95764 .07734 .04171 .29270 1.5183 4.3271 .8229 .7143 MB 4 .0372 .01637 .00106 .92240 .07760 .99894 .02270 .00549 .11093 1.6504 40.7625 .7657 .9707 RB 4 .0367 .01616 .00105 .92340 .07660 .99895 .02229 .00546 .10897 1.6474 40.8520 .7655 .9708 MD 4 .0380 .01662 .00109 .92123 .07877 .99891 .02293 .00556 .11198 1.6514 40.3578 .7660 .9705 RD 4 .0373 .01639 .00107 .92231 .07769 .99893 .02244 .00549 .10973 1.6502 40.7005 .7657 .9707 OR 4 .7514 .35514 .30172 .43116 .56884 .69828 .28248 .28074 .37712 .6929 1.1274 .7130 .0758 OS 4 .3885 .16177 .11674 .65809 .34191 .88326 .24363 .21843 .41529 .7842 1.8717 .7284 .3715 OF 4 .0444 .01839 .00128 .91314 .08686 .99872 .02430 .00603 .11850 1.6563 37.5203 .7677 .9683 CF 4 .0444 .01839 .00128 .91314 .08686 .99872 .02430 .00603 .11850 1.6563 37.5203 .7677 .9683 CS 4 .2771 .05218 .01118 .78383 .21617 .98882 .04679 .02172 .19663 1.4990 9.9788 .7889 .8775 NT 10 .8270 .21301 .05021 .13578 .86422 .94979 .04326 .03864 .14862 2.7424 2.1066 .9497 .4221 MB 10 .0425 .08548 .00122 .57747 .42253 .99878 .04655 .00587 .23129 2.8361 97.1188 .8547 .9901 RB 10 .0380 .08340 .00108 .58730 .41270 .99892 .04533 .00550 .22563 2.8465 107.7020 .8524 .9911 MD 10 .0439 .08601 .00126 .57500 .42500 .99874 .04660 .00597 .23146 2.8322 94.2863 .8553 .9898 RD 10 .0395 .08405 .00112 .58424 .41576 .99888 .04538 .00560 .22587 2.8431 104.2081 .8531 .9908 OR 10 .9890 .54518 .44024 .03509 .96491 .55976 .21486 .26095 .09855 1.9611 .1963 .8703 -.7584 OS 10 .9342 .45374 .33521 .07217 .92783 .66479 .22609 .25872 .20792 1.8854 .3772 .8825 -.5379 OF 10 .0465 .08763 .00134 .56720 .43280 .99866 .04679 .00616 .23223 2.8339 89.5734 .8572 .9892 CF 10 .0465 .08763 .00134 .56719 .43281 .99866 .04679 .00616 .23222 2.8339 89.5738 .8572 .9892 CS 10 .2497 .12817 .00960 .39757 .60243 .99040 .04256 .01944 .18975 2.6012 14.9939 .8957 .9236 NT 20 .8221 .23796 .04960 .00862 .99138 .95040 .03147 .03861 .03340 4.0302 .2284 .9852 -.6930 MB 20 .0486 .17508 .00139 .13018 .86982 .99861 .02975 .00626 .14686 4.1163 46.4664 .9670 .9758 RB 20 .0402 .17295 .00114 .13981 .86019 .99886 .03019 .00562 .14953 4.1326 58.6188 .9647 .9813 MD 20 .0502 .17539 .00144 .12882 .87118 .99856 .02964 .00637 .14617 4.1125 44.7462 .9673 .9747 RD 20 .0414 .17332 .00118 .13810 .86190 .99882 .03005 .00573 .14865 4.1302 56.3690 .9651 .9804 OR 20 .9948 .56643 .45819 .00059 .99941 .54181 .20682 .25838 .00880 3.3492 .0052 .8851 -.9953 OS 20 .9894 .49616 .37036 .00068 .99932 .62964 .20040 .25032 .00960 3.5348 .0062 .9071 -.9942 OF 20 .0517 .17580 .00149 .12696 .87304 .99851 .02950 .00648 .14532 4.1115 43.0083 .9678 .9736 CF 20 .0517 .17580 .00149 .12696 .87304 .99851 .02950 .00648 .14532 4.1115 43.0083 .9678 .9736 CS 20 .1168 .17393 .00429 .14753 .85247 .99571 .02546 .01343 .10743 3.6753 18.2760 .9617 .9343 NT 40 .8254 .23983 .04979 .00000 1.00000 .95021 .03064 .03829 .00000 5.9118 .0000 .9876 • 1.0000 MB 40 .0490 .20089 .00141 .00118 .99882 .99859 .00560 .00631 .01222 6.0284 .8492 .9994 -.0890 RB 40 .0389 .20061 .00112 .00143 .99857 .99888 .00521 .00564 .01340 6.0390 1.2565 .9994 .1240 MD 40 .0502 .20093 .00144 .00112 .99888 .99856 .00562 .00637 .01197 6.0357 .7953 .9994 -.1244 RD 40 .0400 .20064 .00115 .00140 .99860 .99885 .00526 .00573 .01326 6.0374 1.1971 .9994 .0979 OR 40 .9946 .56441 .45552 .00000 1.00000 .54448 .20371 .25464 .00000 4.3766 .0000 .8861 -1.0000 OS 40 .9892 .49444 .36805 .00000 1.00000 .63195 .19783 .24729 .00000 4.6019 .0000 .9080-1.0000 OF 40 .0508 .20095 .00146 .00110 .99890 .99854 .00564 .00640 .01187 6.0382 .7727 .9994 -.1399 CF 40 .0508 .20095 .00146 .00110 .99890 .99854 .00564 .00640 .01187 6.0382 .7727 .9994 -.1399 CS 40 .0663 .19613 .00257 .02964 .97036 .99743 .01429 .01117 .05036 4.6842 8.4686 .9919 .8364 162 Table 10.2.2.2.2.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .3, pNz = .4 N:p <XEX Rej Fp Fn Tp Tn s:Rej s.FpTn s.FnTp d' P A' B" NT 2 .5371 .11108 .03912 .78099 .21901 .96088 .08969 .04709 .18988 .9855 3.4898 .7522 .6397 MB 2 .0247 .00833 .00092 .98054 .01946 .99908 .01594 .00578 .03871 1.0503 15.1871 .7428 .9082 RB 2 .0243 .00826 .00090 .98072 .01928 .99910 .01569 .00574 .03813 1.0514 15.2997 .7429 .9089 MD 2 .0259 .00850 .00096 .98019 .01981 .99904 .01613 .00592 .03917 1.0438 14.7674 .7426 .9056 RD 2 .0255 .00841 .00095 .98039 .01961 .99905 .01584 .00587 .03848 1.0440 14.8471 .7426 .9061 OR 2 .6824 .40063 .34970 .52298 .47702 .65030 .33682 .32690 .37989 .3285 1.0756 .6157 .0463 OS 2 .2543 .14741 .11409 .80261 .19739 .88591 .28455 .25166 .35233 .3541 1.4390 .6290 .2210 OF 2 .0363 .01105 .00137 .97443 .02557 .99863 .01880 .00710 .04553 1.0460 13.2892 .7427 .8961 CF 2 .0363 .01105 .00137 .97443 .02557 .99863 .01880 .00710 .04553 1.0460 13.2892 .7427 .8961 CS 2 .2949 .05953 .01677 .87634 .12366 .98323 .06664 .03184 .14219 .9687 4.9028 .7433 .7359 NT 4 .7018 .21811 .04893 .52812 .47188 .95107 .08722 .04612 .20221 1.5848 3.9260 .8353 .6853 MB 4 .0291 .03306 .00109 .91899 .08101 .99891 .03617 .00632 .08980 1.6665 41.2245 .7666 .9712 RB 4 .0283 .03217 .00106 .92116 .07884 .99894 .03455 .00624 .08583 1.6602 41.4226 .7661 .9713 MD 4 .0297 .03353 .00111 .91786 .08214 .99889 .03652 .00641 .09065 1.6670 40.7699 .7669 .9709 RD 4 .0287 .03261 .00107 .92009 .07991 .99893 .03482 .00628 .08650 1.6632 41.3144 .7664 .9712 OR 4 .9614 .69290 .59667 .16277 .83723 .40333 .24066 .27588 .23621 .7384 .6355 .7209 -.2769 OS 4 .6548 .46720 .37695 .39743 .60257 .62305 .37427 .35226 .44300 .5735 1.0155 .6841 .0097 OF 4 .0355 .03714 .00134 .90916 .09084 .99866 .03877 .00708 .09621 1.6657 37.0335 .7687 .9680 CF 4 .0355 .03714 .00134 .90916 .09084 .99866 .03877 .00708 .09621 1.6657 37.0335 .7687 .9680 CS 4 .4185 .14803 .02459 .66681 .33319 .97541 .08397 .03695 .19120 1.5359 6.3073 .8106 .8051 NT 10 .7263 .37663 .05073 .13452 .86548 .94927 .05492 .04629 .11874 2.7431 2.0758 .9499 .4148 MB 10 .0340 .17483 .00130 .56488 .43512 .99870 .07978 .00706 .19889 2.8472 91.6965 .8578 .9895 RB 10 .0285 .16601 .00109 .58661 .41339 .99891 .07499 .00642 .18720 2.8470 107.3227 .8525 .9911 MD 10 .0352 .17611 .00136 .56177 .43823 .99864 .07987 .00723 .19907 2.8433 88.5968 .8586 .9891 RD 10 .0294 .16720 .00112 .58368 .41632 .99888 .07520 .00651 .18769 2.8455 104.5564 .8532 .9908 OR 10 1.0000 .82275 .70791 .00500 .99500 .29209 .13052 .21393 .02033 2.0285 .0421 .8179 -.9530 OS 10 .9954 .78891 .65490 .01008 .98992 .34510 .15123 .23644 .06843 1.9249 .0728 .8273 -.9154 OF 10 .0376 .17931 .00144 .55390 .44610 .99856 .07989 .00743 .19916 2.8438 83.8468 .8605 .9884 CF 10 .0376 .17931 .00144 .55390 .44610 .99856 .07989 .00743 .19916 2.8438 83.8468 .8605 .9884 CS 10 .3459 .30074 .01879 .27632 .72368 .98121 .05633 .03164 .13067 2.6732 7.2843 .9231 .8312 NT 20 .7170 .42640 .04971 .00856 .99144 .95029 .02896 .04592 .02486 4.0320 .2265 .9852 -.6955 MB 20 .0455 .35455 .00176 .11627 .88373 .99824 .04625 .00826 .11504 4.1116 34.6034 .9704 .9663 RB 20 .0299 .34486 .00113 .13954 .86046 .99887 .04899 .00647 .12219 4.1372 59.1599 .9647 .9814 MD 20 .0464 .35512 .00180 .11491 .88509 .99820 .04592 .00833 .11421 4.1127 33.7342 .9707 .9653 RD 20 .0308 .34554 .00116 .13791 .86209 .99884 .04871 .00659 .12144 4.1349 56.9714 .9651 .9806 OR 20 1.0000 .82876 .71464 .00006 .99994 .28536 .12641 .21064 .00184 3.2746 .0007 .8213 -.9994 OS 20 1.0000 .79945 .66580 .00007 .99993 .33420 .13770 .22946 .00200 3.3721 .0008 .8335 -.9994 OF 20 .0478 .35592 .00185 .11298 .88702 .99815 .04540 .00845 .11294 4.1132 32.4194 .9712 .9638 CF 20 .0478 .35592 .00185 .11298 .88702 .99815 .04540 .00845 .11294 4.1132 32.4194 .9712 .9638 CS 20 .1448 .36907 .00734 .08834 .91166 .99266 .02876 .02073 .06098 3.7910 7.8776 .9757 .8340 NT 40 .7208 .43009 .05016 .00001 .99999 .94984 .02781 .04635 .00056 6.0377 .0002 .9875 -.9998 MB 40 .0497 .40079 .00196 .00096 .99904 .99804 .00610 .00884 .00774 5.9860 .5208 .9993 -.3422 RB 40 .0297 .40007 .00115 .00154 .99846 .99885 .00555 .00669 .00975 6.0077 1.3113 .9993 .1470 MD 40 .0508 .40083 .00201 .00096 .99904 .99799 .00615 .00898 .00772 5.9795 .5060 .9993 -.3561 RD 40 .0305 .40011 .00118 .00150 .99850 .99882 .00556 .00680 .00963 6.0081 1.2438 .9993 .1186 OR 40 1.0000 .82734 .71223 .00000 1.00000 .28777 .12593 .20988 .00000 3.7050 .0000 .8219-1.0000 OS 40 .9999 .79831 .66384 .00000 1.00000 .33616 .13662 .22770 .00000 3.8419 .0000 .8340-1.0000 OF 40 .0514 .40084 .00204 .00094 .99906 .99796 .00616 .00903 .00768 5.9795 .4956 .9993 -.3660 CF 40 .0514 .40084 .00204 .00094 .99906 .99796 .00616 .00903 .00768 5.9795 .4956 .9993 -.3660 CS 40 .0808 .39647 .00430 .01528 .98472 .99570 .01532 .01683 .02539 4.7899 3.0425 .9951 .5567 163 Table 10.2.2.2.2.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .3, pNz = .6 N:p aEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' A' B" NT 2 .4800 .16043 .04353 .76164 .23836 .95647 .10746 .05739 .16806 .9995 3.3559 .7553 .6269 MB 2 .0165 .01227 .00094 .98018 .01982 .99906 .02035 .00744 .03356 1.0497 15.0402 .7428 .9074 RB 2 .0163 .01208 .00093 .98048 .01952 .99907 .01982 .00740 .03268 1.0469 15.0066 .7427 .9071 MD 2 .0172 .01253 .00098 .97977 .02023 .99902 .02060 .00757 .03395 1.0461 14.7432 .7427 .9055 RD 2 .0169 .01231 .00097 .98013 .01987 .99903 .02004 .00752 .03304 1.0439 14.7528 .7426 .9055 OR 2 .8108 .59082 .52158 .36302 .63698 .47842 .34715 .34683 .36276 .2963 .9418 .6056 -.0381 OS 2 .3638 .28188 .23211 .68494 .31506 .76789 .39249 .35464 .42669 .2504 1.1640 .5928 .0953 OF 2 .0260 .01635 .00150 .97375 .02625 .99850 .02437 .00937 .04007 1.0287 12.4758 .7419 .8893 CF 2 .0260 .01635 .00150 .97375 .02625 .99850 .02437 .00937 .04007 1.0287 12.4758 .7419 .8893 CS 2 .3129 .11520 .02731 .82620 .17380 .97269 .10715 .05058 .16364 .9826 4.0783 .7484 .6878 NT 4 .5555 .30489 .04925 .52468 .47532 .95075 .11543 .05757 .18780 1.5903 3.9076 .8361 .6838 MB 4 .0202 .04997 .00113 .91746 .08254 .99887 .05204 .00787 .08648 1.6661 40.4854 .7670 .9707 RB 4 .0188 .04778 .00105 .92106 .07894 .99895 .04822 .00761 .08021 1.6635 41.7961 .7662 .9716 MD 4 .0209 .05068 .00117 .91632 .08368 .99883 .05252 .00806 .08728 1.6620 39.4826 .7671 .9699 RD 4 .0193 .04846 .00108 .91995 .08005 .99892 .04860 .00770 .08086 1.6632 41.2398 .7664 .9712 OR 4 .9889 .85654 .76044 .07939 .92061 .23956 .16631 .22425 .15312 .7015 .4759 .7106 -.4274 OS 4 .7747 .67653 .58265 .26089 .73911 .41735 .38180 .37194 .40426 .4319 .8324 .6466 -.1155 OF 4 .0244 .05588 .00137 .90777 .09223 .99863 .05578 .00868 .09271 1.6691 36.8943 .7690 .9679 CF 4 .0244 .05588 .00137 .90777 .09223 .99863 .05578 .00868 .09271 1.6691 36.8943 .7690 .9679 CS 4 .4425 .26318 .03915 .58747 .41253 .96085 .12400 .05687 .19644 1.5396 4.5974 .8234 .7313 NT 10 .5551 .53911 .04938 .13440 .86560 .95062 .07130 .05777 .11220 2.7567 2.1198 .9504 .4250 MB 10 .0269 .27060 .00159 .55005 .44995 .99841 .12047 .00994 .20031 2.8242 76.9632 .8614 .9873 RB 10 .0191 .24827 .00110 .58695 .41305 .99890 .10880 .00801 .18117 2.8421 105.9766 .8524 .9910 MD 10 .0276 .27259 .00163 .54676 .45324 .99837 .12058 .01004 .20049 2.8250 75.3619 .8622 .9870 RD 10 .0196 .25005 .00113 .58400 .41600 .99887 .10897 .00811 .18146 2.8422 103.7517 .8532 .9908 OR 10 .9999 .93360 .83692 .00195 .99805 .16308 .06438 .15764 .00990 1.9046 .0251 .7874 -.9719 OS 10 .9981 .92248 .81212 .00394 .99606 .18788 .08171 .17881 .04352 1.7714 .0434 .7909 -.9498 OF 10 .0299 .27746 .00176 .53874 .46126 .99824 .12075 .01041 .20075 2.8208 70.3014 .8641 .9860 CF 10 .0299 .27746 .00176 .53874 .46126 .99824 .12075 .01041 .20075 2.8208 70.3014 .8641 .9860 CS 10 .3516 .48554 .02953 .21045 .78955 .97047 .06875 .04959 .10895 2.6926 4.2965 .9364 .7058 NT 20 .5564 .61505 .05007 .00829 .99171 .94993 .02652 .05889 .02129 4.0400 .2191 .9852 -.7052 MB 20 .0438 .54126 .00263 .09966 .90034 .99737 .06224 .01275 .10323 4.0744 21.5632 .9743 .9432 RB 20 .0193 .51688 .00111 .13928 .86072 .99889 .06987 .00803 .11632 4.1439 60.0798 .9648 .9817 MD 20 .0451 .54213 .00271 .09825 .90175 .99729 .06173 .01293 .10237 4.0731 20.7846 .9746 .9409 RD 20 .0196 .51782 .00113 .13771 .86229 .99887 .06944 .00814 .11559 4.1450 58.5422 .9652 .9812 OR 20 1.0000 .93586 .83967 .00002 .99998 .16033 .06227 .15565 .00091 3.0900 .0004 .7900 -.9997 OS 20 1.0000 .92701 .81757 .00003 .99997 .18243 .06942 .17351 .00098 3.1410 .0004 .7956 -.9997 OF 20 .0462 .54307 .00277 .09673 .90327 .99723 .06108 .01308 .10126 4.0740 20.1019 .9750 .9387 CF 20 .0462 .54307 .00277 .09673 .90327 .99723 .06108 .01308 .10126 4.0740 20.1019 .9750 .9387 CS 20 .1505 .56958 .01196 .05868 .94132 .98804 .03002 .03362 .04190 3.8245 3.7599 .9820 .6476 NT 40 .5580 .61998 .04995 .00001 .99999 .95005 .02340 .05849 .00052 5.9768 .0003 .9875 -.9997 MB 40 .0461 .60072 .00283 .00068 .99932 .99717 .00623 .01348 .00529 5.9711 .2714 .9991 -.6126 RB 40 .0201 .59953 .00117 .00156 .99844 .99883 .00594 .00834 .00822 5.9992 1.3063 .9993 .1450 MD 40 .0475 .60077 .00291 .00066 .99934 .99709 .00628 .01366 .00522 5.9695 .2577 .9991 -.6300 RD 40 .0204 .59957 .00119 .00151 .99849 .99881 .00592 .00845 .00810 6.0032 1.2478 .9993 .1204 OR 40 1.0000 .93533 .83833 .00000 1.00000 .16167 .06275 .15687 .00000 3.2773 .0000 .7904-1.0000 OS 40 1.0000 .92679 .81698 .00000 1.00000 .18302 .06942 .17356 .00000 3.3610 .0000 .7958 -1.0000 OF 40 .0484 .60080 .00297 .00065 .99935 .99703 .00632 .01382 .00518 5.9676 .2490 .9991 -.6413 CF 40 .0484 .60080 .00297 .00065 .99935 .99703 .00632 .01382 .00518 5.9676 .2490 .9991 -.6413 CS 40 .0867 .59830 .00736 .00774 .99226 .99264 .01540 .02826 .01524 4.8602 1.0464 .9962 .0256 164 Table 10.2.2.2.2.4 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p - 10, mNz = .3, pNz = .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .2886 .20510 .04464 .75479 .24521 .95536 .12816 .08370 .15673 1.0095 3.3393 .7570 .6254 MB 2 .0097 .01622 .00110 .97999 .02001 .99890 .02525 .01133 .03144 1.0082 13.1793 .7410 .8939 RB 2 .0097 .01588 .00110 .98043 .01957 .99890 .02425 .01133 .03019 .9991 12.9350 .7406 .8917 MD 2 .0100 .01657 .00113 .97957 .02043 .99887 .02556 .01149 .03183 1.0079 13.0543 .7410 .8929 RD 2 .0099 .01619 .00112 .98005 .01995 .99888 .02454 .01144 .03056 1.0011 12.9110 .7407 .8916 OR 2 .8676 .71627 .64291 .26539 .73461 .35709 .32581 .34358 .32972 .2606 .8786 .5954 -.0815 OS 2 .4387 .39073 .33694 .59583 .40417 .66306 .44721 .41601 .45894 .1783 1.0609 .5669 .0375 OF 2 .0143 .02164 .00162 .97336 .02664 .99838 .03052 .01369 .03798 1.0110 11.7623 J410 .8824 CF 2 .0143 .02164 .00162 .97336 .02664 .99838 .03052 .01369 .03798 1.0110 11.7623 .7410 .8824 CS 2 .2332 .18078 .03830 .78360 .21640 .96170 .15081 .08536 .18123 .9864 3.5260 .7521 .6431 NT 4 .3245 .39067 .04942 .52402 .47598 .95058 .14674 .08504 .18200 1.5902 3.8971 .8362 .6830 MB 4 .0103 .06729 .00114 .91618 .08383 .99886 .06829 .01122 .08529 1.6701 40.4127 .7673 .9707 RB 4 .0098 .06329 .00109 .92116 .07884 .99891 .06135 .01095 .07663 1.6519 40.3848 .7660 .9705 MD 4 .0108 .06826 .00120 .91497 .08503 .99880 .06888 .01149 .08603 1.6637 39.1129 .7675 .9697 RD 4 .0101 .06417 .00112 .92007 .07993 .99888 .06185 .01111 .07724 1.6503 39.6951 .7662 .9700 OR 4 .9944 .93354 .84792 .04506 .95494 .15208 .11101 .19008 .10426 .6672 .4032 .7040 -.4996 OS 4 .8372 .79474 .71101 .18432 .81568 .28899 .35482 .35675 .36096 .3427 .7793 .6226 -.1549 OF 4 .0123 .07532 .00137 .90620 .09380 .99863 .07296 .01225 .09114 1.6785 37.3584 .7695 .9684 CF 4 .0123 .07532 .00137 .90620 .09380 .99863 .07296 .01225 .09114 1.6785 37.3584 .7695 .9684 CS 4 .3353 .39246 .05571 .52336 .47664 .94429 .16413 .09780 .19986 1.5333 3.5440 .8322 .6517 NT 10 .3247 .70271 .04946 .13398 .86602 .95054 .08822 .08484 .10820 2.7579 2.1126 .9505 .4233 MB 10 .0171 .37743 .00202 .52872 .47128 .99798 .16570 .01605 .20690 2.8026 62.1332 .8665 .9839 RB 10 .0105 .33109 .00119 .58643 .41357 .99881 .14048 .01165 .17556 2.8201 98.7238 .8525 .9903 MD 10 .0176 .38014 .00209 .52534 .47466 .99791 .16576 .01635 .20696 2.8009 60.3657 .8673 .9834 RD 10 .0106 .33349 .00120 .58343 .41657 .99880 .14075 .01170 .17588 2.8250 98.0482 .8532 .9902 OR 10 .9999 .97904 .89944 .00106 .99894 .10056 .02814 .13570 .00620 1.7950 .0201 .7723 -.9769 OS 10 .9993 .97686 .89132 .00175 .99825 .10868 .03868 .14778 .02531 1.6859 .0302 .7727 -.9645 OF 10 .0187 .38649 .00222 .51745 .48255 .99778 .16559 .01685 .20673 2.8010 57.1330 .8692 .9824 CF 10 .0187 .38649 .00222 .51745 .48255 .99778 .16559 .01685 .20673 2.8010 57.1330 .8692 .9824 CS 10 .2803 .68180 .04576 .15919 .84081 .95424 .07675 .08917 .09261 2.6853 2.5243 .9447 .5081 NT 20 .3249 .80313 .04946 .00845 .99155 .95054 .02322 .08477 .02000 4.0389 .2250 .9853 -.6974 MB 20 .0391 .74077 .00481 .07524 .92476 .99519 .07274 .02520 .09048 4.0269 10.1566 .9798 .8712 RB 20 .0094 .68907 .00109 .13893 .86107 .99891 .08958 .01139 .11197 4.1500 60.8196 .9649 .9820 MD 20 .0398 .74174 .00492 .07406 .92594 .99508 .07204 .02566 .08958 4.0275 9.8320 .9801 .8667 RD 20 .0094 .69039 .00110 .13729 .86271 .99890 .08899 .01155 .11122 4.1544 59.7698 .9653 .9816 OR 20 1.0000 .98045 .90230 .00002 .99998 .09770 .02628 .13132 .00068 2.8546 .0004 .7744 -.9996 OS 20 1.0000 .97898 .89500 .00002 .99998 .10500 .02841 .14196 .00073 2.8604 .0005 .7762 -.9996 OF 20 .0408 .74264 .00503 .07296 .92704 .99497 .07123 .02588 .08858 4.0277 9.5285 .9803 .8621 CF 20 .0408 .74264 .00503 .07296 .92704 .99497 .07123 .02588 .08858 4.0277 9.5285 .9803 .8621 CS 20 .1287 .77469 .02087 .03686 .96314 .97913 .02813 .06435 .02931 3.8246 1.6061 .9852 .2694 NT 40 .3271 .81015 .05078 .00001 .99999 .94922 .01748 .08739 .00039 6.0317 .0002 .9873 -.9998 MB 40 .0462 .80094 .00588 .00030 .99970 .99412 .00615 .02857 .00295 5.9510 .0663 .9985 -.9024 RB 40 .0093 .79886 .00109 .00170 .99830 .99891 .00644 .01150 .00760 5.9944 1.5001 .9993 .2181 MD 40 .0473 .80098 .00600 .00028 .99972 .99400 .00614 .02878 .00283 5.9619 .0611 .9984 -.9102 RD 40 .0095 .79890 .00112 .00165 .99835 .99888 .00638 .01176 .00748 5.9941 1.4222 .9993 .1901 OR 40 .9999 .98017 .90083 .00000 1.00000 .09917 .02681 .13405 .00000 2.9786 .0000 .7748 -1.0000 OS 40 .9999 .97869 .89346 .00000 1.00000 .10654 .02878 .14389 .00000 3.0198 .0000 .7766-1.0000 OF 40 .0475 .80098 .00602 .00028 .99972 .99398 .00615 .02882 .00283 5.9606 .0609 .9984 -.9105 CF 40 .0475 .80098 .00602 .00028 .99972 .99398 .00615 .02882 .00283 5.9606 .0609 .9984 -.9105 CS 40 .0846 .80128 .01537 .00224 .99776 .98463 .01391 .06047 .00759 5.0021 .1821 .9956 -.7422 1 6 5 Table 10.2.2.2.3.1 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .2 N:p aEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .7364 .16087 .04726 .38467 .61533 .95274 .07449 .04346 .29593 1.9653 3.8762 .8799 .6804 MB 2 .0389 .03029 .00114 .85312 .14688 .99886 .03519 .00585 .17346 2.0007 60.4684 .7845 .9820 RB 2 .0378 .02962 .00110 .85632 .14368 .99890 .03410 .00573 .16827 1.9971 61.5012 .7838 .9823 MD 2 .0398 .03069 .00117 .85121 .14879 .99883 .03546 .00593 .17467 2.0018 59.6658 .7850 .9817 RD 2 .0386 .02999 .00113 .85456 .14544 .99887 .03436 .00582 .16951 1.9974 60.6121 .7842 .9820 OR 2 .8776 .44542 .36581 .23612 .76388 .63419 .27177 .28961 .32341 1.0618 .8191 .7872 -.1252 OS 2 .6030 .27916 .20406 .42043 .57957 .79594 .28227 .26870 .44767 1.0280 1.3799 .7799 .2001 OF 2 .0549 .03683 .00163 .82236 .17764 .99837 .03873 .00699 .19040 2.0181 49.4997 .7918 .978C CF 2 .0549 .03683 .00163 .82236 .17764 .99837 .03873 .00699 .19040 2.0181 49.4997 .7918 .9780 CS 2 .3100 .08226 .01393 .64442 .35558 .98607 .05746 .02625 .24371 1.8289 10.4812 .8268 .8869 NT 4 .7952 .22398 .04954 .07827 .92173 .95046 .04151 .04151 .12683 3.0662 1.4283 .9660 .2102 MB 4 .0424 .10830 .00126 .46354 .53646 .99874 .05408 .00620 .26896 3.1122 95.3939 .8834 .9899 RB 4 .0383 .10583 .00113 .47537 .52463 .99887 .05297 .00583 .26393 3.1154105.6717 .8805 .9910 MD 4 .0426 .10888 .00127 .46068 .53932 .99873 .05404 .00624 .26878 3.1167 94.5666 .8841 .9898 RD 4 .0390 .10645 .00116 .47238 .52762 .99884 .05301 .00591 .26408 3.1163 103.5246 .8812 .9908 OR 4 .9885 .55332 .44574 .01633 .98367 .55426 .21916 .27083 .06583 2.2726 .1031 .8793 -.8779 OS 4 .9518 .47349 .35156 .03877 .96123 .64844 .22535 .26781 .16208 2.1463 .2264 .8936 -.7190 OF 4 .0501 .11347 .00151 .43869 .56131 .99849 .05381 .00681 .26733 3.1203 80.3809 .8895 .9878 CF 4 .0501 .11347 .00151 .43869 .56131 .99849 .05381 .00681 .26733 3.1203 80.3809 .8895 .9878 CS 4 .2213 .14463 .00927 .31391 .68609 .99073 .04335 .02130 .18895 2.8395 14.2212 .9174 .9182 NT 10 .7934 .23964 .04962 .00028 .99972 .95038 .03385 .04229 .00577 5.1010 .0100 .9875 -.9883 MB 10 .0467 .19847 .00140 .01326 .98674 .99860 .01055 .00658 .04631 5.2075 7.4300 .9963 .8069 RB 10 .0378 .19787 .00112 .01514 .98486 .99888 .01084 .00583 .04953 5.2229 10.2255 .9959 .8605 MD 10 .0482 .19856 .00144 .01300 .98700 .99856 .01049 .00667 .04578 5.2055 7.1005 .9964 .7979 RD 10 .0390 .19794 .00116 .01493 .98507 .99884 .01080 .00592 .04914 5.2189 9.8133 .9960 .8545 OR 10 .9896 .55815 .44769 .00002 .99998 55231 .21705 .27130 .00157 4.2146 .0002 .8881 -.9998 OS 10 .9818 .49504 .36881 .00002 .99998 .63119 .21251 .26563 .00157 4.4181 .0003 .9078 -.9998 OF 10 .0513 .19875 .00154 .01240 .98760 .99846 .01036 .00686 .04447 5.2049 6.4439 .9965 .7774 CF 10 .0513 .19875 .00154 .01240 .98760 .99846 .01036 .00686 .04447 5.2049 6.4439 .9965 .7774 CS 10 .0992 .19124 .00455 .06201 .93799 .99545 .02133 .01687 .06991 4.1464 9.1950 .9832 .8555 NT 20 .7906 .23966 .04958 .00000 1.00000 .95042 .03388 .04234 .00000 5.9139 .0000 .9876 -1.0000 MB 20 .0464 .20112 .00139 .00000 1.00000 .99861 .00527 .00659 .00000 7.2550 .0000 .9997 -1.0000 RB 20 .0383 .20091 .00114 .00000 1.00000 .99886 .00474 .00592 .00000 7.3156 .0000 .9997 -1.0000 MD 20 .0475 .20114 .00143 .00000 1.00000 .99857 .00533 .00666 .00000 7.2478 .0000 .9996 1.0000 RD 20 .0395 .20094 .00118 .00000 1.00000 .99882 .00481 .00601 .00000 7.3062 .0000 .9997 1.0000 OR 20 .9912 .56394 .45493 .00000 1.00000 .54507 .21695 .27119 .00000 4.3781 .0000 .8863 1.000C OS 20 .9835 .49747 .37184 .00000 1.00000 .62816 .21223 .26529 .00000 4.5919 .0000 .9070 1.0000 OF 20 .0492 .20119 .00148 .00000 1.00000 .99852 .00544 .00680 .00000 7.2361 .0000 .9996 1.0000 CF 20 .0492 .20119 .00148 .00000 1.00000 .99852 .00544 .00680 .00000 7.2361 .0000 .9996 1.0000 CS 20 .0910 .20300 .00422 .00187 .99813 .99578 .01318 .01596 .01428 5.5341 .4795 .9985 -.3853 NT 40 .7916 .23982 .04977 .00000 1.00000 .95023 .03360 .04200 .00000 5.9120 .0000 .9876- 1.0000 MB 40 .0473 .20114 .00142 .00000 1,00000 .99858 .00529 .00661 .00000 7.2490 .0000 .9996- 1.0000 RB 40 .0389 .20093 .00116 .00000 1.00000 .99884 .00474 .00593 .00000 7.3112 .0000 .9997 -1.0000 MD 40 .0483 .20116 .00145 .00000 1.00000 .99855 .00534 .00668 .00000 7.2424 .0000 .9996- 1.0000 RD 40 .0395 .20094 .00118 .00000 1.00000 .99883 .00477 .00597 .00000 7.3069 .0000 .9997 -1.0000 OR 40 .9908 .56369 .45461 .00000 1.00000 .54539 .21646 .27057 .00000 4.3789 .0000 .8863 -1.0000 OS 40 .9840 .49789 .37236 .00000 1.00000 .62764 .21093 .26366 .00000 4.5905 .0000 .9069 -1.0000 OF 40 .0491 .20118 .00148 .00000 1.00000 .99852 .00540 .00675 .00000 7.2366 .0000 .9996- 1.0000 CF 40 .0491 .20118 .00148 .00000 1.00000 .99852 .00540 .00675 .00000 7.2366 .0000 .9996- 1.0000 CS 40 .0906 .20324 .00405 .00000 1.00000 .99595 .01242 .01553 .00000 6.9125 .0000 .9990 -1.0000 166 Table 10.2.2.2.3.2 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * l,p = 10, mNz = .5,pNz = A OEX Rej Fp Fn Tp Tn s:Rej s:FpTn s.FnTp a" A' B" NT 2 .6698 .28626 .04924 .35822 .64178 .95076 .09411 .05151 .22158 2.0154 3.6655 .8866 .6616 MB 2 .0277 .06114 .00106 .84873 .15127 .99894 .06060 .00639 .15095 2.0421 66.0529 .7858 .9837 RB 2 .0262 .05854 .00100 .85517 .14483 .99900 .05679 .00624 .14157 2.0303 67.4098 .7843 .9839 MD 2 .0284 .06196 .00109 .84674 .15326 .99891 .06102 .00649 .15200 2.0423 64.9640 .7863 .9834 RD 2 .0266 .05924 .00102 .85342 .14658 .99898 .05716 .00628 .14248 2.0336 67.0487 .7847 .9839 OR 2 .9877 .76021 .64380 .06517 .93483 .35620 .19164 .25911 .15195 1.1442 .3408 .7821 -.5802 OS 2 .8352 .62604 .50441 .19152 .80848 .49559 .32043 .33305 .36113 .8613 .6836 .7474 -.2350 OF 2 .0405 .07374 .00161 .81807 .18193 .99839 .06662 .00807 .16586 2.0384 50.8270 .7929 .9787 CF 2 .0405 .07374 .00161 .81807 .18193 .99839 .06662 .00807 .16586 2.0384 50.8270 .7929 .9787 CS 2 .4098 .21427 .02722 .50516 .49484 .97278 .09403 .04335 .21612 1.9104 6.3569 .8564 .8084 NT .4 .6688 .39860 .04969 .07802 .92198 .95031 .05173 .05222 .10642 3.0664 1.4215 .9660 .2075 MB 4 .0354 .22258 .00142 .44569 .55431 .99858 .09609 .00773 .23962 3.1206 85.0299 .8878 .9886 RB 4 .0274 .21088 .00107 .47439 32561 .99893 .09183 .00655 .22932 3.1342111.0879 .8808 .9915 MD 4 .0361 .22375 .00145 .44281 .55719 .99855 .09596 .00783 .23929 3.1216 83.3590 .8885 .9883 RD 4 .0281 .21216 .00110 .47124 .52876 .99890 .09189 .00662 .22946 3.1350108.6185 .8815 .9912 OR 4 .9994 .81964 .70069 .00193 .99807 .29931 .13677 .22671 .01371 2.3634 .0177 .8229 -.9818 OS 4 .9972 .78867 .65038 .00390 .99610 .34962 .15120 .24602 .04297 2.2743 .0313 .8340 -.9664 OF 4 .0421 .23224 .00172 .42197 .57803 .99828 .09497 .00858 .23670 3.1225 70.8403 .8936 .9860 CF 4 .0421 .23224 .00172 .42197 .57803 .99828 .09497 .00858 .23670 3.1225 70.8403 .8936 .9860 CS 4 .2809 .32740 .01773 .20811 .79189 .98227 .05727 .03644 .12917 2.9161 6.5598 .9414 .8088 NT 10 .6713 .43009 .05035 .00029 .99971 .94965 .03169 .05284 .00433 5.0781 .0105 .9873 -.9878 MB 10 .0439 .39683 .00184 .01068 .98932 .99816 .01409 .00923 .03296 5.2051 4.7930 .9969 .7033 RB 10 .0280 .39462 .00111 .01512 .98488 .99889 .01633 .00676 .03999 5.2257 10.2828 .9959 .8613 MD 10 .0450 .39692 .00189 .01053 .98947 .99811 .01401 .00933 .03266 5.2031 4.6308 .9969 .6935 RD 10 .0285 .39472 .00113 .01489 .98511 .99887 .01618 .00681 .03958 5.2269 9.9937 .9960 .8571 OR 10 .9996 .82315 .70525 .00000 1.00000 .29475 .13684 .22807 .00000 3.7253 .0000 .8237 -1.0000 OS 10 .9993 .79451 .65752 .00000 1.00000 .34248 .14812 .24687 .00000 3.8592 .0000 .8356 -1.0000 OF 10 .0475 .39717 .00201 .01008 .98992 .99799 .01385 .00970 .03188 5.1996 4.2130 .9970 .6652 CF 10 .0475 .39717 .00201 .01008 .98992 .99799 .01385 .00970 .03188 5.1996 4.2130 .9970 .6652 CS 10 .1164 .39138 .00796 .03350 .96650 .99204 .02428 .02756 .03620 4.2425 3.4158 .9895 .6079 NT 20 .6633 .42981 .04969 .00000 1.00000 .95031 .03161 .05268 .00000 5.9128 .0000 .9876 -1.0000 MB 20 .0436 .40108 .00181 .00000 1.00000 .99819 .00543 .00904 .00000 7.1748 .0000 .9995 -1.0000 RB 20 .0274 .40067 .00112 .00000 1.00000 .99888 .00425 .00708 .00000 7.3217 .0000 .9997 -l.OOOOj MD 20 .0448 .40112 .00187 .00000 1.00000 .99813 .00554 .00923 .00000 7.1647 .0000 .9995 -l.ooooj RD 20 .0286 .40070 .00116 .00000 1.00000 .99884 .00431 .00718 .00000 7.3100 .0000 .9997 -i.oooo| OR 20 .9996 .82164 .70274 .00000 1.00000 .29726 .13753 .22922 .00000 3.7326 .0000 .8243 -l.OOOOj OS 20 .9996 .79354 .65590 .00000 1.00000 .34410 .14811 .24685 .00000 3.8636 .0000 .8360 -1.0000 OF 20 .0469 .40117 .00195 .00000 1.00000 .99805 .00563 .00939 .00000 7.1513 .0000 .9995 -1.0000 CF 20 .0469 .40117 .00195 .00000 1.00000 .99805 .00563 .00939 .00000 7.1513 .0000 .9995 -1.0OO0 CS 20 .1082 .40416 .00743 .00075 .99925 .99257 .01637 .02681 .00641 5.6103 .1258 .9980 -.8156 NT 40 .6607 .43015 .05026 .00000 1.00000 .94974 .03226 .05377 .00000 5.9073 .0000 .9874 -1.0000 MB 40 .0461 .40120 .00199 .00000 1.00000 .99801 .00588 .00981 .00000 7.1442 .0000 .9995 -1.0000 RB 40 .0287 .40072 .00121 .00000 1.00000 .99879 .00449 .00748 .00000 7.2987 .0000 .9997-1.0000 MD 40 .0475 .40123 .00204 .00000 1.00000 .99796 .00594 .00989 .00000 7.1361 .0000 .9995 -1.0000 RD 40 .0288 .40073 .00121 .00000 1.00000 .99879 .00451 .00751 .00000 7.2969 .0000 .9997 -1.0000 OR 40 .9996 .82304 .70507 .00000 1.00000 .29493 .13702 .22837 .00000 3.7259 .0000 .8237 -1.0000 OS 40 .9994 .79476 .65794 .00000 1.00000 .34206 .14659 .24431 .00000 3.8580 .0000 .8355 -1.0000 OF 40 .0479 .40124 .00206 .00000 1.00000 .99794 .00595 .00992 .00000 7.1338 .0000 .9995 -1.0000 CF 40 .0479 .40124 .00206 .00000 1.00000 .99794 .00595 .00992 .00000 7.1338 .0000 .9995 -1.0000 CS 40 .1137 .40462 .00769 .00000 1.00000 .99231 .01574 .02623 .00000 6.6881 .0000 .9981 -1.0000 167 Table 10.2 2.23.3 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10, mNz = .5, pNz = .6 N:p OEX Rej Fp Fn Tp Tn s.Rej s:FpTn s.FnTp a" P A' B" NT 2 .4967 .40592 .04906 .35616 .64384 .95094 .13502 .06783 .22019 2.0228 3.6693 .8873 .6619 MB 2 .0187 .09331 .00116 .84526 .15474 .99884 .09244 .00885 .15382 2.0307 61.9162 .7866 .9825 RB 2 .0173 .08650 .00107 .85654 .14346 .99893 .08198 .00847 .13648 2.0061 63.3421 .7838 .9828 MD 2 .0195 .09457 .00121 .84319 .15681 .99879 .09323 .00903 .15511 2.0266 60.0832 .7870 .9820 RD 2 .0174 .08758 .00107 .85474 .14526 .99893 .08256 .00849 .13744 2.0125 63.5720 .7842 .9829 OR 2 .9966 .89927 .79353 .03023 .96977 .20647 .11806 .20407 .09481 1.0587 .2400 .7588 -.6965 OS 2 .8902 .80221 .68963 .12274 .87726 .31037 .29630 .31637 .30954 .6666 .5758 .7046 -.3306 OF 2 .0289 .11236 .00185 .81397 .18603 .99815 .10174 .01147 .16910 2.0100 45.3473 .7936 .9759 CF 2 .0289 .11236 .00185 .81397 .18603 .99815 .10174 .01147 .16910 2.0100 45.3473 .7936 .9759 CS 2 .4009 .36774 .04262 .41551 .58449 .95738 .13607 .07088 .21554 1.9345 4.2987 .8733 .7123 NT 4 .5007 .57281 .04978 .07850 .92150 .95022 .06792 .06834 .10510 3.0622 1.4259 .9658 .2093 MB 4 .0276 .34483 .00179 .42649 .57351 .99821 .14988 .01171 .24935 3.0975 68.2577 .8924 .9855 RB 4 .0178 .31500 .00109 .47574 .52426 .99891 .13894 .00856 .23153 3.1242 108.8686 .8804 .9913 MD 4 .0280 .34683 .00182 .42316 .57684 .99818 .14968 .01176 .24903 3.1022 67.3893 .8932 .9853 RD 4 .0181 .31685 .00111 .47266 .52734 .99889 .13902 .00861 .23166 3.1274 107.3172 .8812 .9911 OR 4 1.0000 .93214 .83162 .00084 .99916 .16838 .06922 .17156 .00778 2.1795 .0115 .7907 -.9880 OS 4 .9984 .92113 .80653 .00247 .99753 .19347 .08506 .19269 .04070 1.9452 .0280 .7947 -.9689 OF 4 .0327 .35880 .00212 .40341 .59659 .99788 .14786 .01273 .24593 3.1039 57.8690 .8980 .9826 CF 4 .0327 .35880 .00212 .40341 .59659 .99788 .14786 .01273 .24593 3.1039 57.8690 .8980 .9826 CS 4 .2807 .52080 .02858 .15106 .84894 .97142 .07000 .05965 .10827 2.9339 3.5839 .9527 .6440 NT 10 .4901 .61957 .04932 .00026 .99974 .95068 .02759 .06892 .00326 5.1225 .0095 .9876 -.9890 MB 10 .0412 .59635 .00276 .00791 .99209 .99724 .01596 .01480 .02475 5.1884 2.5624 .9973 .4815 RB 10 .0182 .59138 .00112 .01511 .98489 .99888 .02220 .00866 .03664 5.2245 10.2294 .9959 .8606 MD 10 .0419 .59646 .00282 .00777 .99223 .99718 .01588 .01502 .02454 5.1879 2.4718 .9973 .4660 RD 10 .0185 .59155 .00113 .01484 .98516 .99887 .02185 .00871 .03605 5.2273 9.9340 .9960 .8562 OR 10 1.0000 .93187 .82967 .00000 1.00000 .17033 .06848 .17120 .00000 3.3120 .0000 .7926 1.0000 OS 10 .9999 .92260 .80651 .00000 1.00000 .19349 .07583 .18958 .00000 3.3998 .0000 .7984 1.0000 OF 10 .0433 .59671 .00289 .00742 .99258 .99711 .01552 .01515 .02383 5.1958 2.3154 .9974 .4368 CF 10 .0433 .59671 .00289 .00742 .99258 .99711 .01552 .01515 .02383 5.1958 2.3154 .9974 .4368 CS 10 .1200 .59355 .01348 .01974 .98026 .98652 .02557 .04630 .02338 4.2711 1.3860 .9916 .1853 NT 20 .4859 .61979 .04947 .00000 1.00000 .95053 .02794 .06985 .00000 5.9149 .0000 .9876 1.0000 MB 20 .0432 .60115 .00287 .00000 1.00000 .99713 .00594 .01485 .00000 7.0269 .0000 .9993 1.0000 RB 20 .0192 .60049 .00122 .00000 1.00000 .99878 .00376 .00940 .00000 7.2964 .0000 .9997 1.0000 MD 20 .0440 .60118 .00294 .00000 1.00000 .99706 .00603 .01508 .00000 7.0194 .0000 .9993-1.0000 RD 20 .0199 .60050 .00126 .00000 1.00000 .99874 .00380 .00951 .00000 7.2869 .0000 .9997 1.0000 OR 20 .9999 .93262 .83156 .00000 1.00000 .16844 .06822 .17056 .00000 3.3046 .0000 .7921 -1.0000 OS 20 .9999 .92331 .80827 .00000 1.00000 .19173 .07563 .18908 .00000 3.3934 .0000 .7979 -1.0000 OF 20 .0448 .60121 .00302 .00000 1.00000 .99698 .00617 .01542 .00000 7.0103 .0000 .9992 1.0000 CF 20 .0448 .60121 .00302 .00000 1.00000 .99698 .00617 .01542 .00000 7.0103 .0000 .9992 -1.0000 CS 20 .1198 .60537 .01369 .00017 .99983 .98631 .01874 .04662 .00253 5.7826 .0190 .9965 -.9745 NT 40 .4915 .61992 .04980 .00000 1.00000 .95020 .02816 .07039 .00000 5.9117 .0000 .9875 -1.0000 MB 40 .0415 .60115 .00288 .00000 1.00000 .99712 .00629 .01573 .00000 7.0263 .0000 .9993 -1.0000 RB 40 .0178 .60047 .00118 .00000 1.00000 .99882 .00381 .00952 .00000 7.3062 .0000 .9997 -1.0000 MD 40 .0424 .60118 .00294 .00000 1.00000 .99706 .00635 .01588 .00000 7.0194 .0000 .9993 -1.0000 RD 40 .0178 .60047 .00118 .00000 1.00000 .99882 .00383 .00957 .00000 7.3048 .0000 .9997 -1.0000 OR 40 1.0000 .93226 .83066 .00000 1.00000 .16934 .06893 .17234 .00000 3.3081 .0000 .7923-1.0000 OS 40 .9999 .92330 .80825 .00000 1.00000 .19175 .07629 .19073 .00000 3.3934 .0000 .7979 -1.0000 OF 40 .0426 .60118 .00296 .00000 1.00000 .99704 .00637 .01593 .00000 7.0176 .0000 .9993 -1.000C CF 40 .0426 .60118 .00296 .00000 1.00000 .99704 .00637 .01593 .00000 7.0176 .0000 .9993 -l.OOOC CS 40 .1181 .60544 .01359 .00000 1.00000 .98641 .01867 .04667 .00000 6.4738 .0000 .9966-1.0000 168 Table 10.2.2.2.3.4 Table of empirical results for a preliminary omnibus test and follow-up tests of correlations when P * I, p = 10; mNz = .5, pNz = .8 N:p OEX Rej Fp Fn Tp Tn s.Rej s.FpTn s.FnTp d' P A' B" NT 2 .2654 .52452 .04837 .35645 .64355 .95163 .17566 .10299 .21744 2.0289 3.7121 .8876 .6658 MB 2 .0118 .12842 .00150 .83985 .16015 .99850 .12800 .01552 .15985 1.9739 49.8926 .7874 .9780 RB 2 .0103 .11470 .00127 .85695 .14305 .99873 .10647 .01364 .13303 1.9526 54.0145 .7833 .9796 MD 2 .0122 .13016 .00156 .83769 .16231 .99844 .12906 .01579 .16115 1.9715 48.6883 .7879 .9774 RD 2 .0104 .11620 .00128 .85506 .14494 .99872 .10732 .01368 .13409 1.9583 54.0595 .7838 .9796 OR 2 .9977 .95927 .87011 .01844 .98156 .12989 .07887 .17424 .07140 .9601 .2138 .7429 -.7239 OS 2 .9212 .89043 .79829 .08654 .91346 .20171 .26353 .28906 .26726 .5269 .5605 .6743 -.3415 OF 2 .0154 .15398 .00209 .80804 .19196 .99791 .14077 .01900 .17574 1.9937 41.4038 .7948 .9735 CF 2 .0154 .15398 .00209 .80804 .19196 .99791 .14077 .01900 .17573 1.9937 41.4041 .7948 .9735 CS 2 .2992 .53556 .06430 .34662 .65338 .93570 .17675 .13206 .21350 1.9141 2.9355 .8828 5802 NT 4 .2727 .74755 .04953 .07795 .92205 .95047 .08416 .10397 .10182 3.0684 1.4240 .9661 .2084 MB 4 .0184 .48328 .00258 .39654 .60346 .99742 .20737 .02174 .25880 3.0595 48.3091 .8995 .9787 RB 4 .0081 .42021 .00099 .47498 .52502 .99901 .18332 .01134 .22915 3.1563119.4687 .8807 .9921 MD 4 .0194 .48606 .00270 .39310 .60690 .99730 .20695 .02209 .25826 3.0534 46.2190 :9003 .9777 RD 4 .0082 .42271 .00100 .47186 .52814 .99900 .18344 .01140 .22930 3.1608118.1880 .8814 .9920 OR 4 .9999 .97913 .89732 .00042 .99958 .10268 .02953 .14484 .00442 2.0714 .0085 .7745 -.9909 OS 4 .9992 .97680 .88843 .00111 .99889 .11157 .04096 .15823 .02665 1.8398 .0196 .7751 -.9778 OF 4 .0229 .50118 .00312 .37431 .62569 .99688 .20340 .02323 .25382 3.0551 39.9585 .9049 .9738 CF 4 .0229 .50118 .00312 .37431 .62569 .99688 .20340 .02323 .25382 3.0551 39.9585 .9049 .9738 CS 4 .2186 .72375 .04752 .10719 .89281 .95248 .07808 .11767 .09003 2.9110 1.8638 .9586 .3578 NT 10 .2710 .80968 .04949 .00028 .99972 .95051 .02088 .10368 .00323 5.1023 .0101 .9876 -.9883 MB 10 .0416 .79748 .00594 .00463 .99537 .99406 .01561 .03312 .01754 5.1175 .8012 .9973 -.1233 RB 10 .0086 .78804 .00108 .01521 .98479 .99892 .02820 .01218 .03512 5.2324 10.6289 .9959 .8659 MD 10 .0423 .79762 .00607 .00450 .99550 .99393 .01538 .03349 .01718 5.1205 .7662 .9973 -.1478 RD 10 .0088 .78827 .00111 .01494 .98506 .99889 .02781 .01242 .03462 5.2306 10.1739 .9960 .8597 OR 10 .9997 .97932 .89659 .00000 1.00000 .10341 .02898 .14488 .00000 3.0025 .0000 .7759 -1.000C OS 10 .9997 .97766 .88828 .00000 1.00000 .11172 .03129 .15644 .00000 3.0475 .0000 .7779 -1.0000 OF 10 .0437 .79778 .00622 .00433 .99567 .99378 .01518 .03372 .01688 5.1242 .7248 .9973 -.1780 CF 10 .0437 .79778 .00622 .00433 .99567 .99378 .01518 .03372 .01688 5.1242 .7248 .9973 -.1780 CS 10 .1208 .79828 .02869 .00932 .99068 .97131 .02443 .09690 .01499 4.2532 .3821 .9904 -.5024 NT 20 .2647 .80981 .04904 .00000 1.00000 .95096 .02110 .10549 .00000 5.9191 .0000 .9877 -1.0000 MB 20 .0402 .80119 .00596 .00000 1.00000 .99404 .00698 .03488 .00000 6.7797 .0000 .9985 1.0000 RB 20 .0076 .80021 .00104 .00000 1.00000 .99896 .00270 .01348 .00000 7.3422 .0000 .9997-1.0000 MD 20 .0409 .80122 .00610 .00000 1.00000 .99390 .00710 .03550 .00000 6.7712 .0000 .9985 -1.0000 RD 20 .0079 .80022 .00108 .00000 1.00000 .99892 .00272 .01361 .00000 7.3328 .0000 .9997-1.0000 OR 20 1.0000 .97932 .89662 .00000 1.00000 .10338 .02869 .14343 .00000 3.0024 .0000 .7758 -1.0000 OS 20 .9998 .97765 .88823 .00000 1.00000 .11177 .03119 .15595 .00000 3.0477 .0000 .7779 -1.0000 OF 20 .0415 .80124 .00619 .00000 1.00000 .99381 .00715 .03573 .00000 6.7661 .0000 .9985 -1.0000 CF 20 .0415 .80124 .00619 .00000 1.00000 .99381 .00715 .03573 .00000 6.7661 .0000 .9985 -1.000C CS 20 .1110 .80559 .02808 .00003 .99997 .97192 .01990 .09940 .00088 5.9408 .0018 .9930 -.9980 NT 40 .2683 .81014 .05070 .00000 1.00000 .94930 .02168 .10840 .00000 5.9030 .0000 .9873 -1.0000 MB 40 .0399 .80120 .00601 .00000 1.00000 .99399 .00709 .03545 .00000 6.7764 .0000 .9985 -1.0000 RB 40 .0080 .80023 .00113 .00000 1.00000 .99887 .00278 .01392 .00000 7.3178 .0000 .9997 -1.0000 MD 40 .0404 .80122 .00609 .00000 1.00000 .99391 .00714 .03570 .00000 6.7718 .0000 .9985 -1.0000 RD 40 .0081 .80023 .00114 .00000 1.00000 .99886 .00279 .01396 .00000 7.3148 .0000 .9997 -1.000C OR 40 .9999 .97984 .89922 .00000 1.00000 .10078 .02864 .14320 .00000 2.9878 .0000 .7752 -1.0000 OS 40 .9999 .97812 .89059 .00000 1.00000 .10941 .03115 .15577 .00000 3.0352 .0000 .7774 -1.0000 OF 40 .0408 .80123 .00613 .00000 1.00000 .99387 .00715 .03576 .00000 6.7693 .0000 .9985 -1.0000 CF 40 .0408 .80123 .00613 .00000 1.00000 .99387 .00715 .03576 .00000 6.7693 .0000 .9985 -1.0000 CS 40 .1151 .80591 .02956 .00000 1.00000 .97044 .02060 .10298 .00000 6.1523 .0000 .9926-1.0000 Table 11.1 S E X f ° r tests on correlations when P = I,across N:pxOxp (5 c r£t 05 = .00427, Scrit .01 = -00562, S C R I T .001 = 00717) N:p n-5 n-10 y-5 V-10 NT 2 .3612 .8544 .0041 .005 MB 2 .0007 -.0004 -.0261 -.0346 RB 2 .0007 -.0004 -.0261 -.0346 MD 2 .0025 .0007 -.0257 -.0345 RD 2 .0025 .0007 -.0257 -.0345 OR 2 .179 .3341 .0042 .005 OS 2 .0237 .0211 -.0205 -.0307 OF 2 .0237 .0211 -.0205 -.0307 CF 2 .0237 .0211 -.0205 -.0307 CS 2 .0042 .005 .0042 .005 NT 4 .3578 .8542 .003 -.0022 MB 4 -.002 -.0015 -.0249 -.0381 RB 4 -.002 -.0015 -.0249 -.0381 MD 4 -.0008 -.0002 -.0245 -.038 RD 4 -.0008 -.0002 -.0245 -.038 OR 4 .1829 .3354 .0032 -.0022 OS 4 .0097 .0091 -.022 -.0367 OF 4 .0097 .0091 -.022 -.0367 CF 4 .0097 .0091 -.022 -.0367 CS 4 .0032 -.0022 .0032 -.0022 NT 10 .3493 .8535 -.0012 .0034 MB 10 -.004 -.0026 -.0275 -.0357 RB 10 -.004 -.0026 -.0275 -.0357 MD 10 -.0031 -.0013 -.0273 -.0355 RD 10 -.0031 -.0013 -.0273 -.0355 OR 10 .1818 .3384 -.001 .0034 OS 10 -.0004 .0016 -.0267 -.0349 OF 10 -.0004 .0016 -.0267 -.0349 CF 10 -.0004 .0016 -.0267 -.0349 CS 10 -.0009 .0034 -.0009 .0034 NT 20 .3449 .8484 .0003 .0018 MB 20 -.0025 .0017 -.0261 -.0351 RB 20 -.0025 .0017 -.0261 -.0351 MD 20 -.0017 .0032 -.0259 -.0348 RD 20 -.0017 .0032 -.0259 -.0348 OR 20 .1837 .3412 .0007 .0018 OS 20 .0002 .0051 -.0253 -.0345 OF 20 .0002 .0051 -.0253 -.0345 CF 20 .0002 .0051 -.0253 -.0345 CS 20 .0007 .0018 .0007 .0018 NT 40 .3577 .8547 -.0017 -.0008 MB 40 -.0012 -.0008 -.0272 -.0363 RB 40 -.0012 -.0008 -.0272 -.0363 MD 40 1E-04 0 -.0266 -.0362 RD 40 1E-04 0 -.0266 -.0362 OR 40 .1855 .3375 -.0016 -.0008 OS 40 .0009 .0007 -.0263 -.036 OF 40 .0009 .0007 -.0263 -.036 CF 40 .0009 .0007 -.0263 -.036 CS 40 -.0014 -.0008 -.0014 -.0008 170 Table 11.2 SEX f o r t e s t s o n correlations with no preliminary omnibus test when P * I, p = 5 across N:p x mNz x pNz (8crit . 0 5 = -00427, «5 c r i t .01 = .00562, <5crit .001 = - 0 ° 7 1 7 ) N.p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT 2 .2901 .2203 .1351 .0477 .2841 .2095 .1246 .0428 .2749 .1996 .1109 .0374 MB 2 -.0084 -.0184 -.0297 -.0411 -.0096 -.0166 -.0279 -.0382 -.0088 -.0179 -.0275 -.0393 RB 2 -.0085 -.0185 -.0297 -.0411 -.01 -.0168 -.028 -.0385 -.0094 -.0192 -.0286 -.0411 MD 2 -.0068 -.0174 -.0292 -.0407 -.0079 -.0151 -.0272 -.0379 -.0075 -.0172 -.0271 -.0392 RD 2 -.0069 -.0174 -.0292 -.0407 -.0083 -.0153 -.0273 -.0383 -.008 -.0184 -.0281 -.0407 OR 2 .1597 .1331 .0974 .0473 .2113 .237 .2513 .2178 .3177 .4494 .5005 .5281 OS 2 .0122 .0022 -.0122 -.0284 .0192 .0188 .0197 .0143 .0565 .1118 .165 .2265 OF 2 .0095 -.0029 -.0193 -.0361 .009 -.0042 -.0196 -.0349 .0077 -.0039 -.0197 -.0347 CF 2 .0095 -.0029 -.0193 -.0361 .009 -.0042 -.0196 -.0349 .0077 -.0039 -.0197 -.0347 CS 2 -.0019 -.01 -.0227 -.036 .0079 .0129 .0044 -.0143 .0369 .0532 .0492 .0078 NT 4 .2886 .2144 .1345 .051 .2855 .2114 .1272 .0485 .2753 .1923 .1074 .0396 MB 4 -.0101 -.0189 -.0306 -.0406 -.0098 -.0182 -.0302 -.0404 -.0085 -.0163 -.0268 -.0307 RB 4 -.0101 -.019 -.0306 -.0407 -.01 -.019 -.0309 -.041 -.0116 -.0207 -.0325 -.0403 MD 4 -.0094 -.0181 -.0301 -.0404 -.009 -.0177 -.0298 -.0397 -.008 -.0156 -.0264 -.0303 RD 4 -.0095 -.0181 -.0301 -.0405 -.0094 -.0184 -.0304 -.0406 -.0111 -.0199 -.0319 -.0402 OR 4 .1726 .1575 .1318 .0766 .2949 .3861 .4432 /^]/)/) .4698 .6588 .7184 .7521 OS 4 .0021 -.0068 -.0161 -.0264 .0302 .0663 .1143 .1431 .1771 .3869 .502 .6093 OF 4 -.0022 -.0141 -.0266 -.0379 -.0027 -.0123 -.0265 -.0382 .0002 -.0086 -.0216 -.0281 CF 4 -.0022 -.0141 -.0266 -.0379 -.0027 -.0123 -.0265 -.0382 .0002 -.0086 -.0216 -.0281 CS 4 -.0034 -.01 -.0203 -.0324 .0286 .0404 .0323 .0041 .0545 .0722 .0706 .0251 NT 10 .2785 .2086 .1323 .0449 .2746 .1971 .1209 .0405 .2652 .1817 .1006 .0384 MB 10 -.0126 -.0218 -.031 -.0405 -.0109 -.0194 -.029 -.0363 -.0056 -.0097 -.0129 -.0177 RB 10 -.0128 -.0224 -.0311 -.0407 -.0127 -.0239 -.0331 -.0406 -.0125 -.0226 -.0328 -.0397 MD 10 -.0122 -.0214 -.0309 -.0402 -.0102 -.0193 -.0286 -.0361 -.0045 -.0087 -.0123 -.0169 RD 10 -.0124 -.022 -.031 -.0403 -.0121 -.0236 -.033 -.0402 -.012 -.0223 -.0326 -.0394 OR 10 .1975 .2049 .1985 .1511 .4433 .651 .7279 .7323 .5644 .7457 .79 .7921 OS 10 -.0028 -.003 -.0062 -.0137 .1315 .3199 .4632 .5629 .4078 .6679 .7436 .7696 OF 10 -.01 -.0201 -.03 -.0394 -.0076 -.0175 -.0269 -.035 -.0008 -.0067 -.01 -.016 CF 10 -.01 -.0201 -.03 -.0394 -.0076 -.0175 -.0269 -.035 -.0008 -.0067 -.01 -.016 CS 10 -.0005 -.0032 -.0122 -.0274 .0421 .0635 .0665 .0282 .0333 .0373 .0395 .0202 NT 20 .2804 .2087 .131 .0467 .2761 .2011 .1219 .0457 .2671 .1903 .102 .0398 MB 20 -.0119 -.0207 -.0306 -.0394 -.0065 -.0117 -.0177 -.0237 -.0019 -.0068 -.0063 -.0042 RB 20 -.0122 -.0212 -.0311 -.0396 -.0119 -.0214 -.0307 -.0397 -.0112 -.0241 -.032 -.0398 MD 20 -.0109 -.0204 -.0304 -.0392 -.0053 -.0109 -.0172 -.0232 -.0008 -.0057 -.0056 -.0034 RD 20 -.0112 -.0209 -.0308 -.0393 -.0115 -.0209 -.0306 -.0396 -.0105 -.0237 -.0317 -.0397 OR 20 .247 .3025 .3261 .2927 .5512 .7565 .8215 .8058 .5746 .7459 .7957 .795 OS 20 .0091 .02 .0299 .0314 .3274 .642 .7601 .7832 .4414 .6761 .7579 .7737 OF 20 -.0094 -.0188 -.0294 -.039 -.0031 -.0098 -.0164 -.0228 .0013 -.0043 -.0052 -.0032 CF 20 -.0094 -.0188 -.0294 -.039 -.0031 -.0098 -.0164 -.0228 .0013 -.0043 -.0052 -.0032 CS 20 .0136 .0157 .0099 -.0133 .0369 .0529 .049 .03 .0168 .0228 .0303 .0112 NT 40 .2955 .2156 .1357 .0486 .2866 .208 .126 .0466 .2721 .1891 .1097 .0396 MB 40 -.01 -.0198 -.0296 -.0404 -.0014 -.0047 -.0058 -.0071 -.0017 -.0051 -.0056 -.0041 RB 40 -.0109 -.0211 -.0305 -.041 -.0109 -.0205 -.0287 -.0402 -.0107 -.0216 -.0314 -.0403 MD 40 -.0096 -.019 -.0295 -.0399 -.0002 -.0037 -.0052 -.0064 -.0005 -.0043 -.0047 -.0034 RD 40 -.0105 -.0203 -.0303 -.0408 -.0096 -.02 -.0283 -.0399 -.0097 -.021 -.0309 -.04 OR 40 .3237 .4534 .5347 .5164 .6011 .7767 .8346 .8156 .5766 .7483 .8035 .7934 OS 40 .0374 .0857 .1513 .187 .4584 .709 .7962 .7972 .4433 .6817 .7611 .7739 OF 40 -.0091 -.0187 -.0292 -.0396 .0003 -.0032 -.0047 -.0064 .0002 -.0038 -.004 -.0032 CF 40 -.0091 -.0187 -.0292 -.0396 .0003 -.0032 -.0047 -.0064 .0002 -.0038 -.004 -.0032 CS 40 .0294 .0397 .0359 .0087 .0099 .016 .02 .0062 .0161 .0253 .0305 .0111 171 Table 11.3 SEX f ° r t e s t s o n correlations with a preliminary omnibus test when P * I, p = 5 across N:p x mNz x pNz (8crit ,05 = -00427, SCRII M = .00562, SCRIT M L = .00717) N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT 2 .005 -.0016 -.0146 -.0288 .0241 .0365 .0235 -.002 .0938 .1213 .0696 .0188 MB 2 -.0346 -.0334 -.0397 -.045 -.026 -.0254 -.0333 -.0403 -.0163 -.0209 -.0292 -.0394 RB 2 -.0346 -.0335 -.0397 -.045 -.0264 -.0256 -.0334 -.0406 -.0169 -.0222 -.0303 -.0412 MD 2 -.0345 -.0328 -.0395 -.0447 -.0254 -.0247 -.0328 -.0401 -.0157 -.0204 -.0289 -.0393 RD 2 -.0345 -.0328 -.0395 -.0447 -.0258 -.0249 -.0329 -.0405 -.0162 -.0216 -.0299 -.0408 OR 2 .005 .0067 .0015 -.0089 .0368 .0776 .1221 .1345 .1396 .3014 .4012 .4674 OS 2 -.0307 -.0237 -.0294 -.0363 -.0102 .003 .0103 .0107 .041 .1056 .1621 .2258 OF 2 -.0307 -.0283 -.036 -.0436 -.0192 -.019 -.0282 -.0384 -.0048 -.0095 -.0225 -.0351 CF 2 -.0307 -.0283 -.036 -.0436 -.0192 -.019 -.0282 -.0384 -.0048 -.0095 -.0225 -.0351 CS 2 .005 -.01 -.0227 -.036 .0079 .0129 .0044 -.0143 .0369 .0532 .0492 .0078 NT 4 -.0022 .003 -.0062 -.0191 .075 .1008 .0696 .0249 .2054 .1809 .1022 .0382 MB 4 -.0381 -.0323 -.0388 -.0433 -.0202 -.023 -.0319 -.041 -.0108 -.0165 -.0269 -.0307 RB 4 -.0381 -.0324 -.0388 -.0434 -.0204 -.0238 -.0326 -.0416 -.0139 -.0209 -.0326 -.0403 MD 4 -.038 -.0321 -.0387 -.0431 -.0198 -.0226 -.0317 -.0403 -.0103 -.0158 -.0265 -.0303 RD 4 -.038 -.0321 -.0387 -.0432 -.0202 -.0233 -.0323 -.0412 -.0134 -.0201 -.032 -.0402 OR 4 -.0022 .0159 .0217 .011 .1072 .2281 .3318 .3712 .3559 .6186 .6928 .7467 OS 4 -.0367 -.0239 -.0274 -.031 .015 .059 .1116 .1424 .1717 .3864 .5018 .6093 OF 4 -.0367 -.0306 -.0373 -.042 -.0165 -.0185 -.029 -.0388 -.0027 -.0089 -.0217 -.0281 CF 4 -.0367 -.0306 -.0373 -.042 -.0165 -.0185 -.029 -.0388 -.0027 -.0089 -.0217 -.0281 CS 4 -.0022 -.01 -.0203 -.0324 .0286 .0404 .0323 .0041 .0545 .0722 .0706 .0251 NT 10 .0034 .0213 .014 -.009 .1804 .1781 .1132 .0391 .2646 .1817 .1006 .0384 MB 10 -.0357 -.0333 -.0368 -.0437 -.0134 -.0198 -.029 -.0364 -.0056 -.0097 -.0129 -.0177 RB 10 -.0357 -.0338 -.0369 -.0439 -.0152 -.0243 -.0331 -.0407 -.0125 -.0226 -.0328 -.0397 MD 10 -.0355 -.0329 -.0368 -.0437 -.0127 -.0197 -.0286 -.0362 -.0045 -.0087 -.0123 -.0169 RD 10 -.0355 -.0334 -.0369 -.0438 -.0146 -.024 -.033 -.0403 -.012 -.0223 -.0326 -.0394 OR 10 .0034 .0484 .0676 .0661 .3025 .5932 .6997 .7262 .5621 .7457 .79 .7921 OS 10 -.0349 -.0164 -.0134 -.0175 .1265 .3195 .4632 .5628 .4078 .6679 .7436 .7696 OF 10 -.0349 -.0325 -.0367 -.0431 -.0103 -.0179 -.0269 -.0351 -.0008 -.0067 -.01 -.016 CF 10 -.0349 -.0325 -.0367 -.0431 -.0103 -.0179 -.0269 -.0351 -.0008 -.0067 -.01 -.016 CS 10 .0034 -.0032 -.0122 -.0274 .0421 .0635 .0665 .0282 .0333 .0373 .0395 .0202 NT 20 .0018 .0607 .0507 .013 .2611 .2008 .1219 .0457 .2671 .1903 .102 .0398 MB 20 -.0351 -.0274 -.0341 -.0405 -.0068 -.0117 -.0177 -.0237 -.0019 -.0068 -.0063 -.0042 RB 20 -.0351 -.0279 -.0346 -.0407 -.0122 -.0214 -.0307 -.0397 -.0112 -.0241 -.032 -.0398 MD 20 -.0348 -.0274 -.034 -.0404 -.0056 -.0109 -.0172 -.0232 -.0008 -.0057 -.0056 -.0034 RD 20 -.0348 -.0279 -.0344 -.0405 -.0118 -.0209 -.0306 -.0396 -.0105 -.0237 -.0317 -.0397 OR 20 .0018 .1261 .191 .2089 .5175 .7539 .8205 .8058 .5746 .7459 .7957 .795 OS 20 -.0345 .0107 .0255 .0296 .3261 .642 .7601 .7832 .4414 .6761 .7579 .7737 OF 20 -.0345 -.0265 -.0332 -.0403 -.0034 -.0098 -.0164 -.0228 .0013 -.0043 -.0052 -.0032 CF 20 -.0345 -.0265 -.0332 -.0403 -.0034 -.0098 -.0164 -.0228 .0013 -.0043 -.0052 -.0032 CS 20 .0018 .0157 .0099 -.0133 .0369 .0529 .049 .03 .0168 .0228 .0303 .0112 NT 40 -.0008 .1236 .0967 .0388 .2864 .208 .126 .0466 .2721 .1891 .1097 .0396 MB 40 -.0363 -.0226 -.0305 -.0405 -.0014 -.0047 -.0058 -.0071 -.0017 -.0051 -.0056 -.0041 RB 40 -.0363 -.0239 -.0314 -.0411 -.0109 -.0205 -.0287 -.0402 -.0107 -.0216 -.0314 -.0403 MD 40 -.0362 -.0218 -.0305 -.04 -.0002 -.0037 -.0052 -.0064 -.0005 -.0043 -.0047 -.0034 RD 40 -.0362 -.0231 -.0313 -.0409 -.0096 -.02 -.0283 -.0399 -.0097 -.021 -.0309 -.04 OR 40 -.0008 .2939 .4304 .467 .6008 .7767 .8346 .8156 .5766 .7483 .8035 .7934 OS 40 -.036 .0821 .15 .1869 .4584 .709 .7962 .7972 .4433 .6817 .7611 .7739 OF 40 -.036 -.0215 -.0302 -.0397 .0003 -.0032 -.0047 -.0064 .0002 -.0038 -.004 -.0032 CF 40 -.036 -.0215 -.0302 -.0397 .0003 -.0032 -.0047 -.0064 .0002 -.0038 -.004 -.0032 CS 40 -.0008 .0397 .0359 .0087 .0099 .016 .02 .0062 .0161 .0253 .0305 .0111 172 Table 11.4 SEX f ° r t e s t s o n correlations with no preliminary omnibus test when P * I, p = 10 across N:p x mNz x pNz(8cr[t . 0 5 = .00427, t 5 c r j t .o i = .00562, t 5 c r j t .001 = -00717) N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT 2 .7949 .7012 .5471 .3028 .7829 .6734 .5105 .2673 .7544 .6247 .4483 .2157 MB 2 -.0122 -.0215 -.0313 -.0393 -.0119 -.023 -.0324 -.04 -.0098 -.0223 -.0313 -.0382 RB 2 -.0122 -.0215 -.0313 -.0393 -.0119 -.0234 -.0326 -.04 -.0109, -.0238 -.0327 -.0397 MD 2 -.0116 -.0204 -.0308 -.039 -.0108 -.0217 -.0317 -.0397 -.0089 -.0216 -.0305 -.0378 RD 2 -.0117 -.0206 -.0309 -.039 -.0111 -.0221 -.032 -.0398 -.0101 -.0234 -.0326 -.0396 OR 2 .3451 .3538 .3534 .3067 .6436 .8025 .8552 .8677 .8903 .9451 .9483 .9486 OS 2 .0129 .0045 -.0041 -.0159 .0987 .2097 .3159 .3893 .556 .7853 .8402 .8712 OF 2 .0052 -.0095 -.0236 -.0358 .0054 -.0104 -.0223 -.0354 .0068 -.0094 -.0211 -.0346 CF 2 .0052 -.0095 -.0236 -.0358 .0054 -.0104 -.0223 -.0354 .0068 -.0094 -.0211 -.0346 CS 2 .0107 .0086 .0035 -.0104 .1441 .2449 .2629 .1832 .26 .3598 .3509 .2492 NT 4 .7898 .702 .554 .3137 .7746 .6712 .5093 .2756 .7457 .6188 .4507 .2227 MB 4 -.0114 -.0208 -.0308 -.0392 -.0101 -.0208 -.0298 -.0397 -.0076 -.0146 -.0224 -.0316 RB 4 -.0115 -.0208 -.0308 -.0393 -.0106 -.0216 -.0312 -.0402 -.0117 -.0226 -.0322 -.0419 MD 4 -.0107 -.0203 -.0307 -.039 -.0092 -.0202 -.0291 -.0392 -.0074 -.0139 -.022 -.0306 RD 4 -.0108 -.0204 -.0307 -.039 -.0099 -.0212 -.0307 -.0399 -.011 -.0219 -.0319 -.0418 OR 4 .4048 .4692 .4949 .4853 .8394 .9339 .9441 .9466 .9388 .9494 .95 .9499 OS 4 .0081 .01 .0085 .0069 .3441 .6051 .7247 .7873 .9018 .9472 .9484 .9492 OF 4 -.002 -.0145 -.0269 -.0369 -.0021 -.0143 -.0256 -.0377 1E-04 -.0079 -.0173 -.0271 CF 4 -.002 -.0145 -.0269 -.0369 -.0021 -.0143 -.0256 -.0377 1E-04 -.0079 -.0173 -.0271 CS 4 .0224 .0403 .0396 .0151 .2271 .3685 .3925 .2853 .1713 .2309 .2307 .1686 NT 10 .7912 .7034 5489 .3155 .7783 .6763 .5051 .2747 .7434 .6213 .4401 .221 MB 10 -.0115 -.0214 -.0313 -.0395 -.0075 -.016 -.0231 -.0329 -.0033 -.0061 -.0088 -.0084 RB 10 -.0118 -.0215 -.0313 -.0396 -.012 -.0215 -.0309 -.0395 -.0122 -.022 -.0318 -.0414 MD 10 -.0106 -.0209 -.031 -.0392 -.0061 -.0148 -.0224 -.0324 -.0018 -.005 -.0081 -.0077 RD 10 -.0107 -.021 -.0311 -.0393 -.0105 -.0206 -.0304 -.0394 -.011 -.0215 -.0315 -.0412 OR 10 .5451 .6964 .7834 .8117 .9405 .95 .9499 .9499 .9396 .9496 .95 .9497 OS 10 .023 .0652 .1193 .1703 .8842 .9454 .9481 .9493 .9318 .9493 .9499 .9497 OF 10 -.0089 -.0192 -.03 -.0389 -.0035 -.0124 -.0201 -.0313 .0013 -.0025 -.0067 -.0063 CF 10 -.0089 -.0192 -.03 -.0389 -.0035 -.0124 -.0201 -.0313 .0013 -.0025 -.0067 -.0063 CS 10 .0742 .1424 .1687 .1206 .1997 .2959 .3016 .2303 .0492 .0664 .07 .0708 NT 20 .787 .6931 .5458 .3187 .7721 .667 .5064 .2749 .7406 .6133 .4359 .2147 MB 20 -.0074 -.0176 -.0277 -.039 -.0014 -.0045 -.0062 -.0109 -.0036 -.0064 -.0068 -.0098 RB 20 -.0077 -.0184 -.0281 -.0393 -.0098 -.0201 -.0307 -.0406 -.0117 -.0226 -.0308 -.0424 MD 20 -.0064 -.017 -.0272 -.0389 .0002 -.0036 -.0049 -.0102 -.0025 -.0052 -.006 -.0091 RD 20 -.0065 -.0175 -.0277 -.0391 -.0086 -.0192 -.0304 -.0406 -.0105 -.0214 -.0301 -.0421 OR 20 .7174 .8853 .9314 .9392 .9448 .95 .95 .95 .9412 .9496 .9499 .95 OS 20 .1145 .2818 .4348 .5478 .9394 .95 .95 .95 .9335 .9496 .9499 .9498 OF 20 -.005 -.0163 -.0266 -.0388 .0017 -.0022 -.0038 -.0092 -.0008 -.0031 -.0052 -.0085 CF 20 -.005 -.0163 -.0266 -.0388 .0017 -.0022 -.0038 -.0092 -.0008 -.0031 -.0052 -.0085 CS 20 .1555 .2839 .3213 .24 .0668 .0948 .1005 .0787 .041 .0582 .0698 .061 NT 40 .7915 .6939 .5408 .3166 .7754 .6708 .508 .2771 .7416 .6107 .4415 .7416 MB 40 -.0093 -.018 -.0283 -.0393 -.001 -.0003 -.0039 -.0038 -.0027 -.0039 -.0085 -.0101 RB 40 -.01 -.0196 -.0298 -.04 -.0111 -.0203 -.0299 -.0407 -.0111 -.0213 -.0322 -.042 MD 40 -.0086 -.0172 -.0279 -.039 .0002 .0008 -.0025 -.0027 -.0017 -.0025 -.0076 -.0096 RD 40 -.0094 -.0191 -.0292 -.0397 -.01 -.0195 -.0296 -.0405 -.0105 -.0212 -.0322 -.0419 OR 40 .8854 .9475 .9499 .95 .9446 .95 .95 .9499 .9408 .9496 .95 .9499 OS 40 .424 .7533 .8645 .9074 .9392 .9499 .95 .9499 .934 .9494 .9499 .9499 OF 40 -.0079 -.0169 -.0277 -.039 .0008 .0014 -.0016 -.0025 -.0009 -.0021 -.0074 -.0092 CF 40 -.0079 -.0169 -.0277 -.039 .0008 .0014 -.0016 -.0025 -.0009 -.0021 -.0074 -.0092 CS 40 .2371 .3964 .4213 .3292 .0163 .0308 .0367 .0346 .0406 .0637 .0681 .0651 173 Table 11.5 SEX f ° r tests on correlations with a preliminary omnibus test when P * to I, p = 10 across N:p x mNz x pNz (5 c rj t 0 5 = .00427, <5crjt .01 = .00562, i5 c r j t .001 = -00717) N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT 2 .0287 .0536 .0676 .0427 .3195 .4871 .43 .2386 .6864 .6198 .4467 .2154 MB 2 -.0358 -.0383 -.0418 -.0446 -.0206 -.0253 -.0335 -.0403 -.0111 -.0223 -.0313 -.0382 RB 2 -.0358 -.0383 -.0418 -.0446 -.0206 -.0257 -.0337 -.0403 -.0122 -.0238 -.0327 -.0397 MD 2 -.0357 -.0379 -.0416 -.0445 -.0201 -.0241 -.0328 -.04 -.0102 -.0216 -.0305 -.0378 RD 2 -.0358 -.0381 -.0417 -.0445 -.0204 -.0245 -.0331 -.0401 -.0114 -.0234 -.0326 -.0396 OR 2 .0287 .0579 .0919 .1193 .3437 .6324 .7608 .8176 .8276 .9377 .9466 .9477 OS 2 -.0269 -.0245 -.0237 -.026 .0785 .2043 .3138 .3887 .553 .7852 .8402 .8712 OF 2 -.0322 -.0355 -.039 -.0433 -.01 -.0137 -.024 -.0357 .0049 -.0095 -.0211 -.0346 CF 2 -.0322 -.0355 -.039 -.0433 -.01 -.0137 -.024 -.0357 .0049 -.0095 -.0211 -.0346 CS 2 .0107 .0086 .0035 -.0104 .1441 .2449 .2629 .1832 .26 .3598 .3509 .2492 NT 4 .0551 .1226 .1555 .115 .6085 .6518 .5055 .2745 .7452 .6188 .4507 .2227 MB 4 -.0355 -.0367 -.0397 -.0437 -.0128 -.0209 -.0298 -.0397 -.0076 -.0146 -.0224 -.0316 RB 4 -.0356 -.0367 -.0397 -.0438 -.0133 -.0217 -.0312 -.0402 -.0117 -.0226 -.0322 -.0419 MD 4 -.0352 -.0366 -.0396 -.0435 -.012 -.0203 -.0291 -.0392 -.0074 -.0139 -.022 -.0306 RD 4 -.0353 -.0366 -.0396 -.0435 -.0127 -.0213 -.0307 -.0399 -.011 -.0219 -.0319 -.0418 OR 4 .0561 .1362 .2181 .2848 .7014 .9114 .9389 .9444 .9385 .9494 .95 .9499 OS 4 -.0255 -.0136 -.0052 0 .3385 .6048 .7247 .7872 .9018 .9472 .9484 .9492 OF 4 -.0321 -.0344 -.0375 -.0423 -.0056 -.0145 -.0256 -.0377 1E-04 -.0079 -.0173 -.0271 CF 4 -.0321 -.0344 -.0375 -.0423 -.0056 -.0145 -.0256 -.0377 1E-04 -.0079 -.0173 -.0271 CS 4 .0224 .0403 .0396 .0151 .2271 .3685 .3925 .2853 .1713 .2309 .2307 .1686 NT 10 .1746 .3595 .3976 .2665 .777 .6763 .5051 .2747 .7434 .6213 .4401 .221 MB 10 -.0269 -.0262 -.0331 -.0399 -.0075 -.016 -.0231 -.0329 -.0033 -.0061 -.0088 -.0084 RB 10 -.0272 -.0263 -.0331 -.04 -.012 -.0215 -.0309 -.0395 -.0122 -.022 -.0318 -.0414 MD 10 -.0263 -.026 -.033 -.0396 -.0061 -.0148 -.0224 -.0324 -.0018 -.005 -.0081 -.0077 RD 10 -.0264 -.0261 -.0331 -.0397 -.0105 -.0206 -.0304 -.0394 -.011 -.0215 -.0315 -.0412 OR 10 .1795 .4236 .6135 .7218 .939 .95 .9499 .9499 .9396 .9496 .95 .9497 OS 10 .0022 .0563 .1157 .1698 .8842 .9454 .9481 .9493 .9318 .9493 .9499 .9497 OF 10 -.0255 -.0248 -.0323 -.0393 -.0035 -.0124 -.0201 -.0313 .0013 -.0025 -.0067 -.0063 CF 10 -.0255 -.0248 -.0323 -.0393 -.0035 -.0124 -.0201 -.0313 .0013 -.0025 -.0067 -.0063 CS 10 .0742 .1424 .1687 .1206 .1997 .2959 .3016 .2303 .0492 .0664 .07 .0708 NT 20 .4068 .6111 .5311 .3166 .7721 .667 .5064 .2749 .7406 .6133 .4359 .2147 MB 20 -.0164 -.0187 -.0278 -.039 -.0014 -.0045 -.0062 -.0109 -.0036 -.0064 -.0068 -.0098 RB 20 -.0167 -.0195 -.0282 -.0393 -.0098 -.0201 -.0307 -.0406 -.0117 -.0226 -.0308 -.0424 MD 20 -.0156 -.0181 -.0273 -.0389 .0002 -.0036 -.0049 -.0102 -.0025 -.0052 -.006 -.0091 RD 20 -.0157 -.0186 -.0278 -.0391 -.0086 -.0192 -.0304 -.0406 -.0105 -.0214 -.0301 -.0421 OR 20 .4363 .7918 .9037 .9324 .9448 .95 .95 .95 .9412 .9496 .9499 .95 OS 20 .1003 .2797 .4346 .5478 .9394 .95 .95 .95 .9335 .9496 .9499 .9498 OF 20 -.0143 -.0174 -.0267 -.0388 .0017 -.0022 -.0038 -.0092 -.0008 -.0031 -.0052 -.0085 CF 20 -.0143 -.0174 -.0267 -.0388 .0017 -.0022 -.0038 -.0092 -.0008 -.0031 -.0052 -.0085 CS 20 .1555 .2839 .3213 .24 .0668 .0948 .1005 .0787 .041 .0582 .0698 .061 NT 40 .7098 .6927 .5408 .3166 .7754 .6708 .508 .2771 .7416 .6107 .4415 .2183 MB 40 -.0101 -.018 -.0283 -.0393 -.001 -.0003 -.0039 -.0038 -.0027 -.0039 -.0085 -.0101 RB 40 -.0108 -.0196 -.0298 -.04 -.0111 -.0203 -.0299 -.0407 -.0111 -.0213 -.0322 -.042 MD 40 -.0094 -.0172 -.0279 -.039 .0002 .0008 -.0025 -.0027 -.0017 -.0025 -.0076 -.0096 RD 40 -.0102 -.0191 -.0292 -.0397 -.01 -.0195 -.0296 -.0405 -.0105 -.0212 -.0322 -.0419 OR 40- .8095 .9456 .9498 .95 .9446 .95 .95 .9499 .9408 .9496 .95 .9499 OS 40 .4205 .7533 .8645 .9074 .9392 .9499 .95 .9499 .934 .9494 .9499 .9499 OF 40 -.0087 -.0169 -.0277 -.039 .0008 .0014 -.0016 -.0025 -.0009 -.0021 -.0074 -.0092 CF 40 -.0087 -.0169 -.0277 -.039 .0008 .0014 -.0016 -.0025 -.0009 -.0021 -.0074 -.0092 CS 40 .2371 .3964 .4213 .3292 .0163 .0308 .0367 .0346 .0406 .0637 .0681 .0651 174 Table 12.1 Table of parametric measure of sensitivity obtained for tests of correlations with no preliminary omnibus test when P * I, p=5, N:p x mNz x pNz N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT MB RB MD RD OR OS OF CF CS .0687 .0200 .0225 .0156 .0188 .0037 .0320 .0077 .0077 .0252 .0555 .0320 .0315 .0345 .0316 .0238 .0129 .0087 .0087 .0206 .0630 .0788 .0778 .0813 .0795 .0291 .0362 .0521 .0521 .0539 .0600 .1375 .1362 .1332 .1312 .0329 .0655 .1034 .1034 .0699 .5263 .5146 .5178 .5157 .5169 .1462 .3845 5089 .5089 .4112 .5114 .4638 .4611 .4566 .4544 .1559 .3360 .4798 .4798 .4020 5329 .4758 .4690 .4750 .4673 .1709 .3045 .4926 .4926 .4874 5347 .4656 .4660 .4612 .4688 .1491 .2528 5013 .5013 .4824 1.1910 1.1348 1.1345 1.1329 1.1327 .4112 .7532 1.1528 1.1528 .8731 1.1925 1.0996 1.1034 1.1029 1.1055 .4390 .5936 1.1053 1.1053 .9773 1.2003 1.0948 1.0872 1.0968 1.0889 .4641 .5231 1.1151 1.1151 1.0319 1.2175 1.1260 1.1507 1.1329 1.1465 .4367 .3863 1.1330 1.1330 1.1811 NT MB RB MD RD OR OS OF CF CS .1751 .1883 .1891 .1887 .1904 .0477 .1539 .2008 .2008 .1037 .1822 .1839 .1841 .1835 .1816 .0562 .1685 .2115 .2115 .1434 .1763 .1972 .1968 .1957 .1938 .0454 .1588 .2113 .2113 .1846 .1529 .2083 .2092 .2091 .2090 .0515 .1279 .1981 .1981 .1794 .9834 1.0171 1.0175 1.0191 1.0208 .3279 .6888 1.0196 1.0196 .7745 .9776 1.0110 1.0126 1.0132 1.0142 .3529 .5711 1.0136 1.0136 .8441 .9779 1.0420 1.0331 1.0437 1.0319 .3400 .4658 1.0505 1.0505 .9079 .9665 1.0643 1.0595 1.0482 1.0518 .3013 .3540 1.0554 1.0554 .9407 2.0042 2.0074 2.0293 2.0115 2.0319 .9772 1.2426 2.0109 2.0109 1.6460 2.0073 1.9988 2.0218 1.9971 2.0202 1.0914 1.1005 1.9968 1.9968 1.7648 2.0163 2.0090 2.0411 2.0047 2.0383 1.0405 .9118 1.9987 1.9987 1.7749 2.0247 1.8590 2.0205 1.8606 2.0244 1.0980 .8376 1.8819 1.8819 1.9367 NT MB RB MD RD OR OS OF CF CS NT MB RB MD RD OR OS OF CF CS 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 .4086 .4608 .4620 .4692 .4684 .1044 .3453 .4748 .4748 .3568 .4063 .4717 .4767 .4751 .4807 .1027 .3219 .4800 .4800 .3818 .4033 .4637 .4628 .4694 .4699 .1085 .2914 .4772 .4772 .4201 .4084 .4729 .4751 .4701 .4692 .0984 .2700 .4657 .4657 .4156 1.8199 1.8797 1.8900 1.8798 1.8911 .8467 1.1706 1.8787 1.8787 15439 1.8309 1.8840 1.9131 1.8903 1.9162 .9099 .9900 1.8927 1.8927 1.6420 1.8265 1.8984 1.9209 1.9006 1.9264 .8878 .8183 1.8926 1.8926 1.6634 1.8410 1.8367 1.8946 1.8416 1.8877 .9630 .7601 1.8366 1.8366 1.7357 3.4834 3.5145 3.5505 3.5174 3.5517 2.5310 2.6802 3.5107 3.5107 2.9696 3.4828 3.5133 3.5565 3.5124 3.5606 2.8442 2.8006 3.5143 3.5143 3.0860 3.4876 3.4162 3.5652 3.4175 3.5671 2.6971 2.5010 3.4127 3.4127 3.1048 3.4956 3.3778 3.5302 3.3775 3.5251 2.8262 2.7951 3.3799 3.3799 3.2284 .6984 .7670 .7667 .7628 .7644 .2014 .5474 .7654 .7654 .5738 .6860 .7546 .7541 .7594 .7586 .1938 .4617 .7541 .7541 .6113 .6858 .7477 .7461 .7513 .7469 .1968 .3888 .7477 .7477 .6403 .6813 .7276 .7224 .7290 .7192 .1885 .3243 .7374 .7374 .6637 2.7591 2.8009 2.8271 2.7979 2.8301 1.7144 1.9085 2.7910 2.7910 2.4123 2.7628 2.7920 2.8282 2.7902 2.8305 1.9029 1.8542 2.7896 2.7896 2.5156 2.7529 2.7447 2.8186 2.7474 2.8243 1.9164 1.7233 2.7498 2.7498 2.5582 2.7440 2.6620 2.8061 2.6635 2.8102 2.0192 1.8591 2.6666 2.6666 2.5695 5.1234 5.1416 5.1853 5.1396 5.1865 4.3435 4.4516 5.1285 5.1285 4.5364 5.0156 5.1346 5.2183 5.1445 5.2131 4.4566 4.5916 5.1455 5.1455 4.6063 5.0718 5.0253 5.1878 5.0237 5.1823 4.0977 4.1754 5.0278 5.0278 4.4551 5.0799 4.9572 5.1783 4.9562 5.1760 3.7700 3.8000 4.9641 4.9641 4.8626 NT MB RB MD RD OR OS OF CF CS 40 40 40 40 40 40 40 40 40 40 1.0862 1.1689 1.1773 1.1709 1.1783 .3903 .7843 1.1753 1.1753 .9239 1.0956 1.1843 1.1932 1.1813 1.1890 .3789 .6472 1.1838 1.1838 .9911 1.0920 1.1840 1.1844 1.1887 1.1868 .3666 .5067 1.1893 1.1893 1.0239 1.0944 1.2162 1.2142 1.2063 1.2143 .3721 .4177 1.2020 1.2020 1.0388 4.0432 4.0625 4.1135 4.0617 4.1107 3.0910 3.2491 4.0618 4.0618 3.5785 4.0181 4.0494 4.0987 4.0523 4.1007 3.3020 3.3635 4.0519 4.0519 3.6550 4.0375 3.9970 4.0769 3.9979 4.0783 3.3419 3.3025 3.9980 3.9980 3.6863 4.0356 3.9199 4.1187 3.9224 4.1175 3.3101 3.2529 3.9265 3.9265 3.8062 5.9044 6.7514 6.8288 6.7425 6.8205 4.9873 5.2322 6.7372 6.7372 6.2250 5.9020 6.6487 6.8305 6.6423 6.8216 4.4553 4.5945 6.6374 6.6374 6.4177 5.8928 6.4608 6.8189 6.4532 6.8108 4.0904 4.1737 6.4477 6.4477 6.1587 5.9171 6.1949 6.8373 6.1893 6.8271 3.7736 3.8010 6.1877 6.1877 6.0768 175 Table 12.2 Table of parametric measure of sensitivity obtained for tests of correlations with a preliminary omnibus test when P * I, p = 5, N:p x mNz x pNz N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT MB RB MD RD OR OS OF CF CS .0221 .0595 .0642 .0474 .0534 .0160 .0519 .0458 .0458 .0252 .0317 .0692 .0687 .0602 .0554 .0215 .0264 .0283 .0283 .0206 .0660 .1323 .1309 .1319 .1290 .0255 .0422 .0890 .0890 .0539 .0658 .1196 .1173 .1077 .1042 .0286 .0516 .1078 .1078 .0699 .3764 .4595 .4646 .4682 .4702 .1224 .2872 .4413 .4413 .4112 .4234 .4269 .4231 .4248 .4217 .1608 .2806 .4368 .4368 .4020 .5338 .4895 .4816 .4899 .4809 .1890 .2858 .5036 .5036 .4874 .5279 .4704 .4713 .4658 .4754 .1468 .2352 .5107 3107 .4824 .7996 1.0034 1.0023 1.0026 1.0015 .3118 .5764 .9850 .9850 .8731 1.0336 1.0771 1.0812 1.0809 1.0838 .4073 .5536 1.0772 1.0772 .9773 1.1850 1.1049 1.0984 1.1073 1.1004 .4561 .5143 1.1252 1.1252 1.0319 1.2463 1.1208 1.1456 1.1274 1.1409 .4242 .3816 1.1310 1.1310 1.1811 NT MB RB MD RD OR OS OF CF CS .0880 .1156 .1171 .1112 .1141 .0363 .0877 .1344 .1344 .1037 .1360 .1396 .1394 .1378 .1339 .0496 .1197 .1574 .1574 .1434 .1858 .1789 .1782 .1796 .1765 .0498 .1277 .1908 .1908 .1846 .1306 .1416 .1423 .1369 .1358 .0442 .0853 .1385 .1385 .1794 .7037 .9172 .9176 .9181 .9200 .2867 .5469 .9097 .9097 .7745 .8598 .9874 .9894 .9889 .9904 .3372 .5246 .9833 .9833 .8441 .9647 1.0438 1.0349 1.0478 1.0359 .3349 .4515 1.0543 1.0543 .9079 .9719 1.0684 1.0642 1.0506 1.0551 .3000 .3457 1.0524 1.0524 .9407 1.5624 1.8917 1.9144 1.8930 1.9140 .8272 1.0926 1.8759 1.8759 1.6460 1.9456 1.9910 2.0141 1.9891 2.0122 1.0554 1.0879 1.9874 1.9874 1.7648 1.9974 2.0087 2.0413 2.0044 2.0384 1.0137 .9093 1.9976 1.9976 1.7749 2.0267 1.8588 2.0204 1.8604 2.0243 1.0829 .8373 1.8817 1.8817 1.9367 NT MB RB MD RD OR OS OF CF CS NT MB RB MD RD OR OS OF CF CS 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 .3091 .4227 .4232 .4311 .4282 .1344 .2743 .4368 .4368 .3568 .3549 .4797 .4863 .4781 .4853 .1231 .2811 .4821 .4821 .3818 .3830 .4605 .4596 .4663 .4671 .1336 .2619 .4827 .4827 .4201 .3818 .4976 .5017 .5044 .5040 .1205 .2482 .4948 .4948 .4156 1.4240 1.7721 1.7828 1.7703 1.7819 .7502 1.0446 1.7619 1.7619 1.5439 1.7565 1.8748 1.9044 1.8809 1.9071 .8815 .9773 1.8824 1.8824 1.6420 1.8113 1.8957 1.9181 1.8977 1.9234 .8671 .8154 1.8894 1.8894 1.6634 1.8407 1.8389 1.8978 1.8437 1.8908 .9475 .7597 1.8385 1.8385 1.7357 3.3794 3.5063 3.5427 3.5088 3.5437 2.4770 2.6503 3.5015 3.5015 2.9696 3.4828 3.5133 3.5565 3.5124 3.5606 2.8442 2.8006 3.5143 3.5143 3.0860 3.4872 3.4162 3.5652 3.4175 3.5671 2.6971 2.5010 3.4127 3.4127 3.1048 3.4956 3.3778 3.5302 3.3775 3.5251 2.8262 2.7951 3.3799 3.3799 3.2284 .5235 .6741 .6731 .6724 .6744 .1940 .4325 .6769 .6769 .5738 .5878 .7141 .7134 .7208 .7198 .2094 .4065 .7168 .7168 .6113 .6428 .7384 .7369 .7424 .7376 .2090 .3626 .7376 .7376 .6403 .6481 .7079 .7021 .7124 .7015 .1861 .3057 .7220 .7220 .6637 2.4710 2.7526 2.7794 2.7488 2.7816 1.5948 1.8293 2.7402 2.7402 2.4123 2.7534 2.7913 2.8275 2.7895 2.8298 1.8925 1.8521 2.7889 2.7889 2.5156 2.7516 2.7446 2.8185 2.7473 2.8242 1.9098 1.7229 2.7497 2.7497 2.5582 2.7440 2.6620 2.8061 2.6635 2.8102 2.0192 1.8591 2.6666 2.6666 2.5695 5.1234 5.1416 5.1853 5.1396 5.1865 4.3435 4.4516 5.1285 5.1285 4.5364 5.0156 5.1346 5.2183 5.1445 5.2131 4.4566 4.5916 5.1455 5.1455 4.6063 5.0718 5.0253 5.1878 5.0237 5.1823 4.0977 4.1754 5.0278 5.0278 4.4551 5.0799 4.9572 5.1783 4.9562 5.1760 3.7700 3.8000 4.9641 4.9641 4.8626 NT MB RB MD RD OR OS OF CF CS 40 40 40 40 40 40 40 40 40 40 .8241 1.0662 1.0764 1.0686 1.0777 .3551 .6591 1.0716 1.0716 .9239 .9671 1.1483 1.1579 1.1433 1.1516 .3774 .6049 1.1440 1.1440 .9911 1.0433 1.1704 1.1709 1.1763 1.1743 .3622 .4922 1.1760 1.1760 1.0239 1.0650 1.2079 1.2057 1.1974 1.2053 .3668 .4118 1.1926 1.1926 1.0388 3.9711 4.0582 4.1094 4.0573 4.1066 3.0478 3.2243 4.0574 4.0574 3.5785 4.0181 4.0494 4.0987 4.0523 4.1007 3.3020 3.3635 4.0519 4.0519 3.6550 4.0375 3.9970 4.0769 3.9979 4.0783 3.3419 3.3025 3.9980 3.9980 3.6863 4.0356 3.9199 4.1187 3.9224 4.1175 3.3101 3.2529 3.9265 3.9265 3.8062 5.9044 6.7514 6.8288 6.7425 6.8205 4.9873 5.2322 6.7372 6.7372 6.2250 5.9020 6.6487 6.8305 6.6423 6.8216 4.4553 4.5945 6.6374 6.6374 6.4177 5.8928 6.4608 6.8189 6.4532 6.8108 4.0904 4.1737 6.4477 6.4477 6.1587 5.9171 6.1949 6.8373 6.1893 6.8271 3.7736 3.8010 6.1877 6.1877 6.0768 176 Table 12.3 Table of parametric measure of sensitivity obtained for tests of correlations with no preliminary omnibus test when P * I, p = 10, N:p x mNz x pNz N:p 1-2 1-4 1-6 1-8 3-2 3-4 3-6 3-8 5-2 5-4 5-6 5-8 NT MB RB MD RD OR OS OF CF CS .1702 .2395 .2380 .2462 .2477 .0498 .1867 .2246 .2246 .1741 .1752 .2372 .2372 .2344 .2357 .0429 .1597 .2296 .2296 .2277 .1757 .2320 .2320 .2341 .2346 .0438 .1355 .2327 .2327 .2369 .1852 .1917 .1917 .1928 .1909 .0379 .1078 .2091 .2091 .2087 .9870 1.0106 1.0072 1.0101 1.0094 .3315 .5413 1.0043 1.0043 .9183 .9926 1.0422 1.0431 1.0357 1.0358 .3385 .3592 1.0416 1.0416 .9687 .9900 1.0374 1.0345 1.0347 1.0322 .3046 .2515 1.0171 1.0171 .9826 1.0002 1.0019 .9929 1.0021 .9953 .2691 .1788 1.0083 1.0083 .9864 2.0123 1.9953 1.9915 1.9967 1.9921 1.0927 1.0328 2.0132 2.0132 1.8289 2.0172 2.0423 2.0305 2.0425 2.0338 1.1562 .8616 2.0379 2.0379 1.9104 2.0223 2.0308 2.0061 2.0266 2.0125 1.0624 .6666 2.0101 2.0101 1.9345 2.0289 1.9739 1.9526 1.9715 1.9583 .9643 .5269 1.9937 1.9937 1.9141 NT MB RB MD RD OR OS OF CF CS .3303 .4122 .4130 .4134 .4142 .0688 .3019 .3995 .3995 .3384 .3262 .4061 .4061 .4100 .4105 .0653 .2480 .4123 .4123 .3720 .3275 .4089 .4073 .4156 .4134 .0699 .2013 .4167 .4167 .3995 .3290 .3673 .3691 .3698 .3688 .0668 .1546 .3699 .3699 .4026 15837 1.6492 1.6461 1.6501 1.6487 .7235 .7961 1.6545 1.6545 1.4990 1.5881 1.6662 1.6599 1.6667 1.6629 .7481 .5740 1.6648 1.6648 1.5359 15899 1.6662 1.6636 1.6621 1.6633 .7066 .4320 1.6692 1.6692 1.5396 1.5899 1.6702 1.6519 1.6637 1.6503 .6723 .3427 1.6786 1.6786 1.5333 3.0678 3.1122 3.1154 3.1167 3.1163 2.2758 2.1464 3.1204 3.1204 2.8395 3.0664 3.1206 3.1342 3.1216 3.1350 2.3634 2.2743 3.1225 3.1225 2.9161 3.0622 3.0975 3.1242 3.1022 3.1274 2.1795 1.9452 3.1039 3.1039 2.9339 3.0684 3.0595 3.1563 3.0534 3.1608 2.0714 1.8398 3.0551 3.0551 2.9110 NT MB RB MD RD OR