Open Collections

A study of procedures to examine correlation pattern hypotheses under conditions of multivariate normality and nonnormality

University of British Columbia

A wide array of procedures have been proposed for testing correlation pattern. Many, but not all, of the statistical techniques available for testing correlation pattern are derived under the distributional condition of multivariate normality which does not always hold in the behavioral, educational and social sciences. Though a number of studies have explored the performance of structure analysis techniques under conditions of multivariate nonnormality, very little is known about the actual performance of many correlation structure analysis techniques under conditions of multivariate nonnormality. In addition, very little is known about the actual concurrent performance of tests of multivariate normality. The present investigation ascertains how tests of correlation pattern hypotheses and indicators of multivariate normality perform when data are from multivariate normal or nonnormal parent populations. This paper reviews and examines, using a Monte Carlo simulation study, the concurrent performance of different approaches to testing (1) correlation pattern hypotheses, including, (i) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques, (ii) NT and ADF correlation structure analysis techniques, (iii) correlation pattern specific techniques; (2) the distributional assumption of multivariate normality using statistics based on Mardia's measures of multivariate skewness and kurtosis. This paper also examines the performance characteristics of test procedures based on joint consideration of tests of multivariate normality and structure analysis techniques. Performance of the covariance and correlation structure analysis techniques, tests of multivariate normality, and joint test procedures was assessed across different types of correlation pattern models, numbers of variables, levels of skew and kurtosis, sample sizes, and nominal alpha levels, on the primary Neyman-Pearson criterion for an optimal test, according to which an optimal procedure (1) controls experimentwise Type I error rate at or below the nominal level, (2) maximizes power.

Thesis/Dissertation

application/pdf

2009-03-20

For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

http://hdl.handle.net/2429/6275

Psychology

University of British Columbia

UBCV

DSpace