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Individually-administered intelligence tests : an application of anchor test norming and equating procedures… Holmes, Barbara 1981

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INDIVIDUALLY-ADMINISTERED INTELLIGENCE TESTS: AN APPLICATION OF ANCHOR TEST NORMING AND EQUATING PROCEDURES IN BRITISH COLUMBIA BARBARA JOYCE HOLMES B.A., Queen's U n i v e r s i t y , 1964 M. S., U n i v e r s i t y of W i s c o n s i n , 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES Department of E d u c a t i o n a l P s y c h o l o g y We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1981 by DOCTOR OF EDUCATION i n B a r b a r a Joyce Holmes, 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of e ^ i — t T ^ The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date J^ipud ABSTRACT The purpose of the p r e s e n t s t u d y was t o s i m u l a t e t he Anchor T e s t Study f o r r e a d i n g achievement t e s t s u s i n g f i v e i n d i v i d u a l l y - a d m i n i s t e r e d i n t e l l i -gence t e s t s : The W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n — R e v i s e d (WISC-R), the Peabody P i c t u r e V o c a b u l a r y T e s t (PPVT), the S l o s s o n I n t e l l i g e n c e T e s t ( S I T ) , t he S t a n d a r d P r o g r e s s i v e M a t r i c e s (SPM), and the M i l l H i l l V o c a b u l a r y S c a l e (MHVS). Three major o b j e c t i v e s were adopted from t h e Anchor T e s t Study: t o p r e p a r e t a b l e s o f e q u i v a l e n t s c o r e v a l u e s f o r the c o n v e r s i o n of s c o r e s from one t e s t t o a n o t h e r ; t o compare l i n e a r and e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e s i n the d e r i v a t i o n of e q u i v a l e n t s c o r e s ; and t o de v e l o p p r o v i n c i a l l y r e p r e s e n t a t i v e norms f o r the f i v e t e s t s . The r a t i o n a l e f o r the p r e s e n t s t u d y was based on the f a c t t h a t i n t e l l i -gence t e s t s a r e commonly used i n t e r c h a n g e a b l y on the apparent a s s u m p t i o n t h a t an e q u i v a l e n c y r e l a t i o n s h i p e x i s t s among common purpose t e s t s . The p r i m a r y f o c u s of t h e p r e s e n t s t u d y was an e m p i r i c a l i n v e s t i g a t i o n of the v i a b i l i t y of t h i s use. I n a d d i t i o n , A merican and B r i t i s h n o r m - r e f e r e n c e d i n t e l l i g e n c e t e s t s are i n t e r p r e t e d i n B r i t i s h Columbia as i f the p o p u l a t i o n of c h i l d r e n t o whom the y a r e a p p l i e d i s i d e n t i c a l t o the p o p u l a t i o n of c h i l -d r en f o r whom each of the t e s t s was p r e p a r e d . An a n c i l l a r y f o c u s was the d e t e r m i n a t i o n of the r e l e v a n c e of e x i s t i n g norms f o r use i n B r i t i s h C o l u m b i a . A l l f i v e t e s t s were a d m i n i s t e r e d t o a s t r a t i f i e d random sample o f 340 c h i l d r e n at t h r e e age l e v e l s : 115 aged 1\ y e a r s , 117 aged 9^ y e a r s , and 108 aged \\\ y e a r s . The p o p u l a t i o n from w h i c h the sample was drawn i i c o n s i s t e d o f a l l n o n - N a t i v e I n d i a n , E n g l i s h - s p e a k i n g c h i l d r e n at t h e s e t h r e e age l e v e l s a t t e n d i n g p u b l i c and independent s c h o o l s i n B r i t i s h C o l u m b i a . T h i s p o p u l a t i o n was f u r t h e r r e s t r i c t e d t o e x c l u d e c h i l d r e n i n c l a s s e s f o r the p h y s i c a l l y h a n d i c a p p e d , e m o t i o n a l l y d i s t u r b e d , and t r a i n a b l e m e n t a l l y r e t a r d e d . The s t r a t i f i c a t i o n v a r i a b l e s employed were g e o g r a p h i c r e g i o n , community s i z e , s c h o o l s i z e , age, and sex. I n a d d i t i o n , i n f o r m a t i o n was c o l l e c t e d on a s i x t h v a r i a b l e , l e v e l of e d u c a t i o n of t h e head of the house-h o l d , t o p r o v i d e a d e s c r i p t i o n of the sample u s i n g a s o c i o e c o n o m i c i n d e x . The t e s t s were f i r s t s c o r e d u s i n g the norms t a b l e s i n t h e i r r e s p e c t i v e manuals. S t a t i s t i c a l t e s t s f o r d i f f e r e n c e s of means and v a r i a n c e s f o r the B.C. sample compared t o the o r i g i n a l s t a n d a r d i z a t i o n sample r e v e a l e d t h a t , i n most c a s e s , B.C. c h i l d r e n s c o r e d s i g n i f i c a n t l y h i g h e r and w i t h l e s s v a r i a b i l i t y (p < .05) . T h e r e f o r e , new norms t a b l e s were p r e p a r e d f o r each t e s t . These c o n s i s t e d of IQ c o n v e r s i o n t a b l e s f o r the WISC-R, PPVT, and SIT, and p e r c e n t i l e r a n k s a s s o c i a t e d w i t h raw s c o r e s f o r the SPM and MHVS. The re n o r m i n g p r o c e d u r e i n v o l v e d l o w e r i n g and s p r e a d i n g out the IQ s c o r e s c a l e s t o mean 100 and s t a n d a r d d e v i a t i o n 15. As a r e s u l t s t u d e n t s s c o r e d lower w i t h the B.C. tha n w i t h the p u b l i s h e d norms. T h i s Is most pronounced i n the lower s c o r e r a n g e s . I n the e q u a t i n g phase of the s t u d y , the e q u i v a l e n c e of each of the PPVT, SIT, SPM, and MHVS t o the three' WISC-R IQ s c a l e s was examined u s i n g b o t h p s y c h o l o g i c a l and s t a t i s t i c a l c r i t e r i a of e q u i v a l e n c e . P a i r s of t e s t s were d e f i n e d as n o m i n a l l y p a r a l l e l ( L o r d & N o v i c k , 1968) i f th e y were p s y c h o l -o g i c a l l y s i m i l a r i n terms of c o n t e n t and p u r p o s e , and s t a t i s t i c a l l y s i m i l a r as d e f i n e d by a d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c i e n t > .70. T h i r t e e n t e s t p a i r s were i d e n t i f i e d w h i c h s a t i s f i e d t he d u a l c r i t e r i a f o r e q u i v a l e n c y . i i i Both l i n e a r and e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e s were a p p l i e d t o t h e o b s e r v e d s c o r e d i s t r i b u t i o n s of t h e s e t e s t p a i r s . The a c c u r a c y of the r e s u l t s were judged by c o m p a r i s o n of the c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g a s s o c i a t e d w i t h the e q u a t i n g p r o c e d u r e s . These e r r o r s a v eraged 12 s c o r e p o i n t s and were s i m i l a r a c r o s s a l l p r o c e d u r e s . I t was c o n c l u d e d t h a t none of the t e s t p a i r s c o n s i d e r e d i n the s t u d y were e q u i v a l e n t , or p a r a l l e l , and t h a t , c o n s e q u e n t l y , t h e i r i n t e r c h a n g e a b l e use i s e r r o n e o u s . F u r t h e r , i t was c o n c l u d e d t h a t t e s t e q u i v a l e n c e r e q u i r e s a c l o s e c o r r e s p o n d e n c e of c o n t e n t i n terms of i t e m s i m i l a r i t y . W i t h o u t such c o r r e s p o n d e n c e , d i f f e r e n c e s between t e s t s r e n d e r e q u a t i n g i n a p p r o p r i a t e . R e s e a r c h S u p e r v i s o r : Dr. W. T. Rogers i v TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES i x LIST OF FIGURES x i ACKNOWLEDGMENT '• • x i i C h a p t e r I INTRODUCTION 1 The C h a l l e n g e t o S c h o o l P s y c h o l o g y 1 Background t o the Problem 3 The Anchor T e s t Study 4 I n t e r - T e s t Score C o n v e r s i o n s 6 E q u i v a l e n t S c o r e s » 6 Comparable S c o r e s 7 E q u a t i n g Methods 8 The P r o b l e m 9 D e l i m i t a t i o n s of the Study 11 N a t i v e I n d i a n s 11 E n g l i s h - S p e a k i n g C h i l d r e n 12 Handicapped C h i l d r e n 12 Age 13 O r g a n i z a t i o n o f the D i s s e r t a t i o n 13 I I REVIEW OF THE LITERATURE 14 J u s t i f i c a t i o n f o r E q u a t i n g 14 Wec h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n — R e v i s e d (WISC-R) 15 S l o s s o n I n t e l l i g e n c e T e s t ( S I T ) 17 Peabody P i c t u r e V o c a b u l a r y T e s t (PPVT) 19 S t a n d a r d P r o g r e s s i v e M a t r i c e s (SPM) 21 M i l l H i l l V o c a b u l a r y S c a l e (MHVS) 23 Summary 23 I n t e r - T e s t Score C o n v e r s i o n s 25 E q u a t i n g 27 P a r a l l e l Forms 27 N o m i n a l l y P a r a l l e l T e s t s 28 E q u a t i n g Methods 31 U n e q u a l l y R e l i a b l e T e s t s 37 Comparing 39 N o n p a r a l l e l T e s t s 39 v Methods 43 Summary 44 Renorming 44 I I I METHODOLOGY 48 Sample D e s i g n 48 Stage I : S c h o o l s 49 Stage I I : I n d i v i d u a l s 52 P o p u l a t i o n S i z e s 52 Sampling P r o c e d u r e s 54 Sample A l l o c a t i o n 54 P r e p a r a t i o n of the S c h o o l Sampling Frame 54 I d e n t i f i c a t i o n of S c h o o l s 60 P r e p a r a t i o n o f the Sampling Frames f o r I n d i v i d u a l s ... 61 T e s t i n g 62 T e s t s Used 62 T e s t e r s 63 T e s t i n g P r o c e d u r e s 63 S c o r i n g and Data P r e p a r a t i o n 64 M i l l H i l l V o c a b u l a r y S c a l e 65 DATA ANALYSIS 66 P r e l i m i n a r y A n a l y s e s 67 Order of A d m i n i s t r a t i o n 67 Goodness of F i t 67 D e t e r m i n a t i o n of Norm R e l e v a n c e 68 C e n t r a l Tendency 69 V a r i a n c e 69 P r e p a r a t i o n of B.C. Norms 70 Wec h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n — R e v i s e d 71 D e r i v a t i o n of S u b t e s t S c a l e d S c o r e s 71 D e r i v a t i o n of V e r b a l , P e r f o r m a n c e , and F u l l S c a l e IQ S c o r e s 76 Peabody P i c t u r e V o c a b u l a r y T e s t and S l o s s o n I n t e l l i g e n c e T e s t 77 S t a n d a r d P r o g r e s s i v e M a t r i c e s and M i l l H i l l V o c a b u l a r y S c a l e 78 S t a t i s t i c a l P r o p e r t i e s of the T e s t s 78 E q u a t i n g 80 D e t e r m i n a t i o n o f N o m i n a l l y P a r a l l e l T e s t P a i r s 81 Assignment of Tes t P a i r s t o E q u a t i n g Methods 82 L i n e a r E q u a t i n g ( E q u a l l y R e l i a b l e T e s t s ) 83 L i n e a r E q u a t i n g ( U n e q u a l l y R e l i a b l e T e s t s ) 86 E q u i p e r c e n t i l e E q u a t i n g 87 Summary . 88 v i IV RESULTS : 90 Rate of Response 90 R e p r e s e n t a t i v e n e s s of the Sample 91 R e s u l t s of P r e l i m i n a r y A n a l y s e s 96 Order E f f e c t 96 N o r m a l i t y 96 Comparison t o P u b l i s h e d Norms 99 Comparison o f WISC-R R e s u l t s t o "White" A m e r i c a n Norms ... 102 P r e p a r a t i o n of B.C. Norms 103 WISC-R S c a l e d S c o r e s 103 WISC-R IQ S c a l e s 108 PPVT and SIT IQ S c o r e s 108 S t a t i s t i c a l P r o p e r t i e s of the T e s t s 109 I n t e r p r e t a t i o n of the Norms I l l E q u a t i n g 114 I d e n t i f i c a t i o n o f N o m i n a l l y P a r a l l e l Test P a i r s 115 D e s i g n a t i o n of T e s t P a i r s t o E q u a t i n g Methods 116 A Comparative E x a m i n a t i o n o f E q u a t i n g P r o c e d u r e s 116 I . MHVS and WISC-R V e r b a l 116 I I . PPVT and WISC-R V e r b a l .° 127 E q u a t i n g R e s u l t s 135 V SUMMARY AND DISCUSSION 149 Summary 149 Norming 153 The B.C. Sc o r e s 153 Use of the New Norms 156 The C o m p a r a b i l i t y o f the New Norms -157 E q u a t i n g 157 The E q u a t a b i l i t y of N o m i n a l l y P a r a l l e l Test P a i r s 157 The Use and I n t e r p r e t a t i o n of I n t e l l i g e n c e T e s t s 160 L i m i t a t i o n s of the Study 160 Norming 160 E q u a t i n g 161 D i r e c t i o n s f o r F u r t h e r R e s e a r c h 161 REFERENCE NOTES 163 REFERENCES 164 APPENDIX A: L e t t e r s and Consent Forms 173 APPENDIX B: WISC-R Canadian S u b s t i t u t i o n Items 188 APPENDIX C: P r o j e c t Handbook 190 APPENDIX D: MHVS S c o r i n g Guides 200 v i i APPENDIX E: B r i t i s h Columbia Norms T a b l e s 213 APPENDIX F: ANOVA and Cochran's C • 250 APPENDIX G: G r a p h i c E q u i p e r c e n t i l e E q u a t i n g P r o c e d u r e : PPVT IQ t o WISC-R V e r b a l IQ Age 1\ 254 APPENDIX H: N o r m a l i z e d L i n e a r E q u a t i n g R e s u l t s 259 v i i i LIST OF TABLES T a b l e 1 WISC-R S u b t e s t s and S k i l l s Measured 16 2 P e a r s o n Product-Moment C o r r e l a t i o n C o e f f i c i e n t f o r PPVT IQs and Three WISC-R IQs 20 3 Content and S t r u c t u r e of the T e s t s 24 4 P s y c h o l o g i c a l l y and F u n c t i o n a l l y E q u i v a l e n t T e s t P a i r s as Suggested by t h e i r C o n t e n t , A u t h o r s ' C l a i m s , E m p i r i c a l V a l i d i t y , and P r a c t i t i o n e r s ' Use 24 5 R e l a t i o n s h i p between P a r a l l e l i s m and Type of Score C o n v e r s i o n - 44 6 P o p u l a t i o n S i z e S t r a t i f i e d by R e g i o n , Community S i z e , S c h o o l S i z e , and Age 53 7 P o p u l a t i o n P e r c e n t a g e s : R e g i o n by Age 54 8 P e r c e n t a g e of P o p u l a t i o n w i t h i n R e g i o n by Age 55 9 T a r g e t Sample A l l o c a t i o n : R e g i o n by Age 57 10 T a r g e t Sample A l l o c a t i o n w i t h i n R e g i o n 58 11 P r o p o r t i o n a l S c h o o l S i z e S ampling P r o c e d u r e R e g i o n #1, Community S i z e A, S c h o o l S i z e I I 59 12 Measures of C e n t r a l Tendency and V a r i a b i l i t y R e p o r t e d i n T e s t Manuals 68 13 Example of Computation of S c a l e d Score E q u i v a l e n t s of Raw S c o r e s WISC-R I n f o r m a t i o n S u b t e s t Age 11%, n=l08 72 14 Example of the G r a p h i c S c a l e d Score C o n v e r s i o n Approach WISC-R I n f o r m a t i o n S u b t e s t Age Ilk, n=l08 74 15 Form of R e l i a b i l i t y C o e f f i c i e n t Computed 79 16 Rates of Response f o r Each T e s t and Age 90 17 R a t e s of Response ( P e r c e n t a g e s ) f o r the T o t a l Sample D e s i g n .. 92 18 Sample P e r c e n t a g e s by Sex and Age 93 19 P o p u l a t i o n and Sample P e r c e n t a g e s by R e g i o n and Age 93 20 P o p u l a t i o n and Sample P e r c e n t a g e s by Community S i z e and Age .. 94 21 P o p u l a t i o n and Sample P e r c e n t a g e s by S c h o o l S i z e and Age 95 22 L e v e l of E d u c a t i o n of Head of Household P e r c e n t i n P o p u l a t i o n and Sample ( A H Ages Combined) 95 23 Summary of A n a l y s i s of V a r i a n c e f o r Order of T e s t A d m i n i s t r a t i o n 97 24 D V a l u e s f o r Kolmogorov-Smirnov T e s t s f o r Goodness of F i t ... 98 25 Means and S t a n d a r d D e v i a t i o n s f o r A l l T e s t s S c o r e d u s i n g P u b l i s h e d Norms T a b l e s 100 26 R e s u l t s of t T e s t s and x 2 T e s t s 101 27 t T e s t s f o r D i f f e r e n c e s i n Means between T o t a l B.C. Sample and American WISC-R "White" Sample (Mean=l02) 102 28 Comparison of R e s u l t s of A n a l y t i c a l and G r a p h i c S c a l e d S c o r e C o n v e r s i o n s A r i t h m e t i c S u b t e s t — A g e 9% 104 i x 29 Means and S t a n d a r d D e v i a t i o n s f o r WISC-R S c a l e d S c o r e s and Sums of S c a l e d S c o r e s B.C. Norms 107 30 Raw Scor e Means and S t a n d a r d D e v i a t i o n s f o r PPVT and SIT 108 31 I n t e r n a l C o n s i s t e n c y C o e f f i c i e n t s and S t a n d a r d E r r o r s of Measurement 110 32 P e r c e n t o f T o t a l Sample i n IQ C l a s s i f i c a t i o n C a t e g o r i e s f o r B.C. Norms and American Norms 113 33 Observed Score C o r r e l a t i o n C o e f f i c i e n t s C o r r e c t e d f o r A t t e n u a t i o n 115 34 Test P a i r s I d e n t i f i e d f o r E q u a t i n g Methods 117 35 Comparative Example of L i n e a r E q u a t i n g and E q u i p e r c e n t i l e E q u a t i n g f o r C o n v e r t i n g MHVS Raw S c o r e s t o WISC-R V e r b a l IQ S c o r e s (Age 11%) 118 36 S t a n d a r d E r r o r s of E q u a t i n g f o r MHVS Raw S c o r e s t o WISC-R V e r b a l IQ Sc o r e s (Age 11%) 120 37 D i s t r i b u t i o n s of MHVS Raw Sc o r e s and WISC-R V e r b a l IQ S c o r e s , Age 11% 123 38 E q u i p e r c e n t i l e P o i n t s f o r MHVS and WISC-R V e r b a l IQ from G r a p h i c P r o c e d u r e 125 39 Comparative Example of L i n e a r E q u a t i n g and E q u i p e r c e n t i l e E q u a t i n g f o r C o n v e r t i n g PPVT IQs t o WISC-R V e r b a l IQs (Age 7%) <129 40 S t a n d a r d E r r o r s of E q u a t i n g f o r PPVT IQ t o WISC-R V e r b a l IQ S c o r e s (Age 7%) 130 41 E q u i v a l e n t S c o r e s PPVT Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 9%) 138 42 E q u i v a l e n t S c o r e s PPVT Raw Sc o r e s to S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 11%) 139 43 E q u i v a l e n t S c o r e s SIT Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 7%) 140 44 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e S c o r e s (Age 7%) 141 45 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c ores (Age 9%) .142 46 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e S c o r e s (Age 9%) 143 47 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 11%) 144 48 E q u i v a l e n t S c o r e s SIT Raw S c o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e S c o r e s (Age 11%) 145 49 E q u i v a l e n t S c o r e s SPM Raw S c o r e s t o S t a n d a r d i z e d WISC-R Performance S c o r e s . ( A g e 11%) 146 50 E q u i v a l e n t S c o r e s MHVS Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 7%) 147 51 E q u i v a l e n t S c o r e s MHVS Raw Sc o r e s t o WISC-R S t a n d a r d i z e d V e r b a l S c o r e s (Age 9%) 148 x LIST OF FIGURES F i g u r e 1 B.C. R e g i o n a l G r o u p i n g s of S c h o o l D i s t r i c t s 50 2 Tes t A d m i n i s t r a t i o n Order ( s e c o n d s e s s i o n ) f o r each Age Group 64 3 R e l a t i v e C u m u l a t i v e F r e q u e n c i e s f o r the WISC-R I n f o r m a t i o n S u b t e s t , age 11% 75 4 I n t e r - t e s t Score C o n v e r s i o n Methods and P r o c e d u r e s used f o r Norming and E q u a t i n g 89 5 G r a p h i c Norming P r o c e d u r e — W I S C - R A r i t h m e t i c S u b t e s t , age 9k 106 6 Frequency D i s t r i b u t i o n s of WISC-R F u l l S c a l e IQ S c o r e d w i t h American and B. C. Norms (n=340) 112 7 S c a t t e r p l o t o f O b t a i n e d S c o r e s w i t h L i n e a r Observed Score and True Score E q u a t i n g C o n v e r s i o n L i n e s . MHVS t o WISC-R V e r b a l IQ, age Ilk 122 8 C u m u l a t i v e R e l a t i v e F r e q u e n c i e s f o r MHVS Raw Sc o r e s and WISC-R V e r b a l IQs, age Ilk 124 9 Hand-graphed E q u i p e r c e n t i l e E q u a t i n g C o n v e r s i o n L i n e . MHVS t o WISC-R V e r b a l IQ, age Ilk ••• 126 10 S c a t t e r p l o t of O b t a i n e d S c o r e s w i t h I n t e r p o l a t e d , L i n e a r C u r v e - f i t t i n g , and P o l y n o m i a l C u r v e - f i t t i n g C o n v e r s i o n L i n e s : A n a l y t i c a l E q u i p e r c e n t i l e E q u a t i n g P r o c e d u r e . MHVS t o WISC-R. V e r b a l IQ, age Ilk • 128 11 S c a t t e r p l o t of O b t a i n e d S c o r e s w i t h L i n e a r Observed Score and True Score E q u a t i n g C o n v e r s i o n L i n e s . PPVT IQ t o WISC-R V e r b a l IQ, age Ik - 131 12 S c a t t e r p l o t of O b t a i n e d S c o r e s w i t h I n t e r p o l a t e d , L i n e a r C u r v e - f i t t i n g , and P o l y n o m i a l C u r v e - f i t t i n g C o n v e r s i o n L i n e s : A n a l y t i c a l E q u i p e r c e n t i l e E q u a t i n g P r o c e d u r e . PPVT IQ t o WISC-R V e r b a l IQ, age Ik 133 x i ACKNOWLEDGMENT On the l a s t page among t h e s e many w r i t t e n , one i s overwhelmed by the r e c o l l e c t i o n of the h e l p and s u p p o r t of many and t h e r e f o r e humbly reduced t o the a d m i s s i o n : " I d i d i t w i t h the h e l p o f my f r i e n d s " The f a c t t h a t t h e i r names a r e not i n d i v i d u a l l y l i s t e d , does not d i m i n i s h the r e c o g n i t i o n o f t h e i r c o n t r i b u t i o n . F i n a n c i a l s u p p o r t f o r t h i s r e s e a r c h was p r o v i d e d t h r o u g h a g r a n t from the E d u c a t i o n a l R e s e a r c h I n s t i t u t e of B r i t i s h Columbia and a b u r s a r y from t h e Canadian A s s o c i a t i o n f o r E d u c a t i o n a l P s y c h o l o g y . I w i s h t o e x p r e s s my a p p r e c i a t i o n t o my r e s e a r c h s u p e r v i s o r , Dr. Todd Ro g e r s , who p r o v i d e d the m e t h o d o l o g i c a l e x p e r t i s e f o r the s t u d y and a model of the u n r e l e n t i n g p u r s u i t of e x c e l l e n c e . I a l s o w i s h t o thank my committee members, Dr. B u f f O l d r i d g e f o r h i s always generous s u p p o r t , a d v i c e , and g r a s s - r o o t s a s s i s t a n c e ; and Dr. J u l i Conry f o r h e r on-going e n t h u s i a s m and encouragement. To Dr s . D a v i d R o b i t a i l l e and R a l p h H a k s t i a n , t h e u n i v e r s i t y e x a m i n e r s , a word o f a p p r e c i a t i o n f o r t h e i r i n v o l v e m e n t and s t i m u l a t i n g q u e s t i o n s . And t o Dr. A l a n Kaufman, the e x t e r n a l examiner, a s p e c i a l t hanks f o r h i s time and v a l u e d comments. A l a r g e measure of i n d e b t e d n e s s goes t o the 44 s c h o o l p s y c h o l o g i s t s and p s y c h o m e t r i c i a n s a c r o s s the p r o v i n c e whose v o l u n t e e r t e s t i n g c o n t r i b u -t i o n s made t h i s s t u d y p o s s i b l e . The work i s d e d i c a t e d t o them. And thanks t o my g r a d u a t e s t u d e n t c o l l e a g u e s and f r i e n d s f o r t h e i r w i l l i n g x i i and m u l t i p l e c o n t r i b u t i o n s i n many s t a g e s of the p r o j e c t . A f i n a l word of a p p r e c i a t i o n goes t o the 340 c h i l d r e n i n p u b l i c and independent s c h o o l s t h r o u g h o u t B.C. who gave t h e i r time and e n e r g i e s t o h e l p i n g a l l of us t h r o u g h f i v e t e s t a d m i n i s t r a t i o n s . x i i i CHAPTER I INTRODUCTION The C h a l l e n g e t o S c h o o l P s y c h o l o g y C o n t r o v e r s y o v e r the use of s t a n d a r d i z e d t e s t s of i n t e l l i g e n c e f o r e d u c a t i o n a l d e c i s i o n - m a k i n g i s not new. The h i s t o r y of the t e s t i n g move-ment from the i n i t i a l e n t h u s i a s m f o r c l a s s i f i c a t i o n o f m e n t a l a b i l i t y to g r owing s k e p t i c i s m over the misuse and m i s i n t e r p r e t a t i o n o f such c l a s s -i f i c a t i o n i s w e l l documented (Cro n b a c h , 1975; Houts, 1976; Kamin, 1974, 1975; Marks, 1976-77). D u r i n g the l a s t two decades i n the U n i t e d S t a t e s the use of group i n t e l l i g e n c e t e s t s has been r e s t r i c t e d and i n some c a s e s a b o l i s h e d by l e g i s l a t i o n and l i t i g a t i o n ( s e e , f o r example, L o r e t a n [1965] and Mer c e r [ 1 9 7 9 ] ) . U n t i l v e r y r e c e n t l y i n d i v i d u a l l y - a d m i n i s t e r e d t e s t s of i n t e l l i -gence have remained r e l a t i v e l y f r e e from the c r i t i c i s m s of b i a s , m i s u s e , and m i s i n t e r p r e t a t i o n w h i c h have c h a r a c t e r i z e d the a t t a c k s a g a i n s t group t e s t s . However, i n O c t o b e r , 1979, a d i s t r i c t c o u r t i n C a l i f o r n i a e xtended j u d i c i a l c o n t r o l o f i n t e l l i g e n c e t e s t i n g t o i n c l u d e i n d i v i d u a l t e s t s on the grounds t h a t they t o o , were b i a s e d a g a i n s t m i n o r i t y group c h i l d r e n ( L a r r y P. v s . W i n s t o n R i l e s , 1979). T h e - c o u r t c h a r g e d the d e f e n -dants ( p s y c h o l o g i s t s and e d u c a t o r s ) w i t h the t a s k o f e n s u r i n g p r o p e r f u t u r e use of i n t e l l i g e n c e t e s t s by p r o v i d i n g d i f f e r e n t i a l norms f o r each d i s c r e t e group w i t h w h i c h t h e y a r e t o be used and v a l i d a t i o n f o r each s p e c i f i c purpose f o r w h i c h t h e y a re t o be a p p l i e d ( L a r r y P. v s . W i n s t o n R i l e s , 1 2 1979, p. 105). I t s h o u l d be n o t e d t h a t , beyond t h a t c o u r t ' s j u r i s d i c t i o n , d e f e n -d a n t s of s t a n d a r d i z e d t e s t s i n g e n e r a l have s t r e s s e d t he need f o r more i n f o r m e d i n t e r p r e t a t i o n and a p p l i c a t i o n of t e s t r e s u l t s ( A n a s t a s i , 1967, 1976; C l a r i z i o , 1979; Kaufman, 1979; Lennon, 1978; V i t r o , 1978). I t i s the t e s t p r a c t i t i o n e r s t h e m s e l v e s who a r e b e i n g c a l l e d t o t a s k : ". . . the p r i m a r y r e s p o n s i b i l i t y f o r the improvement of t e s t i n g c o n t i n u e s t o r e s t on the s h o u l d e r s of t e s t u s e r s " (APA, 1974, p. 7 ) . T h i s r e f e r s t o p r o f e s s i o n a l p s y c h o l o g i s t s and e d u c a t o r s who a r e q u a l i f i e d t o a d m i n i s t e r l e v e l B and l e v e l C t e s t s d e f i n e d as f o l l o w s : L e v e l B. T e s t s or a i d s w h i c h r e q u i r e some t e c h n i c a l knowledge of t e s t c o n s t r u c t i o n and use, and of s u p p o r t i n g s u b j e c t s such as s t a t i s t i c s , i n d i v i d u a l d i f f e r e n c e s , t he p y s c h o l o g y of a d j u s t m e n t , p e r s o n n e l p s y c h o l o g y , and g u i d a n c e . (Examples: g e n e r a l i n t e l l i -gence and' s p e c i a l a p t i t u d e t e s t s , i n t e r e s t i n v e n t o r i e s and p e r s o n -a l i t y s c r e e n i n g i n v e n t o r i e s . ) L e v e l C. T e s t s and a i d s w h i c h r e q u i r e s u b s t a n t i a l u n d e r s t a n d i n g of t e s t i n g s and s u p p o r t i n g p s y c h o l o g i c a l t o p i c s , t o g e t h e r w i t h s u p e r -v i s e d e x p e r i e n c e i n the use of t h e s e d e v i c e s . (Examples: c l i n i c a l t e s t s o f i n t e l l i g e n c e , and p e r s o n a l i t y t e s t s . ) . ( C r o n b a c h , 1970, p. 18) I n e d u c a t i o n a l s e t t i n g s , i n t e l l i g e n c e t e s t s o f the l e v e l B t y p e ( e . g . , group i n t e l l i g e n c e t e s t s , the Peabody P i c t u r e V o c a b u l a r y T e s t , and the S l o s s o n I n t e l l i g e n c e T e s t ) a re f r e q u e n t l y a d m i n i s t e r e d by t e a c h e r s and p r i n c i p a l s . L e v e l C t e s t i n g , however, i s the domain of the s c h o o l p s y c h o l -o g i s t . I n f a c t , s c h o o l p s y c h o l o g y as a p r o f e s s i o n grew out of the demand f o r t e s t e r s c a p a b l e o f a d m i n i s t e r i n g l e v e l C i n t e l l i g e n c e t e s t s . The r e s u l t i n g s y m b i o t i c r e l a t i o n s h i p between the two has r e s u l t e d i n a c h a l -l e n g e t o the c r e d i b i l i t y of the p r o f e s s i o n p a r a l l e l t o t h a t of the t e s t s t h e m s e l v e s (Brown, 1976-77; M e r c e r , 1977; S a r a s o n , 1977). Concern f o r the a p p r o p r i a t e n e s s o f t e s t use and i n t e r p r e t a t i o n , t h e r e f o r e , i s 3 a p r o f e s s i o n a l o b l i g a t i o n of the s c h o o l p s y c h o l o g i s t . The f a c t t h a t , i n r e c e n t y e a r s , t h i s p r o f e s s i o n a l o b l i g a t i o n has become a l e g a l mandate, s u b j e c t t o p u b l i c s c r u t i n y and j u d i c i a l i n v e s t i g a t i o n , makes i t a l l the more i m p e l l i n g . The r e s p o n s i b i l i t y of the s c h o o l p s y c h o l o g i s t , however, ex t e n d s beyond p e r s o n a l p r a c t i c e . As an " e x p e r t " i n t e s t t h e o r y and measurement i n the s c h o o l s t h e r e i s a f u r t h e r need t o ensure t h a t o t h e r t e s t u s e r s a r e a c c u r a t e i n t h e i r i n t e r p r e t a t i o n of t e s t r e s u l t s . I t i s toward t h i s aim t h a t the p r e s e n t d i s s e r t a t i o n was d i r e c t e d . Background t o the Problem I n 1922, E. L. T h o r n d i k e p o i n t e d out t h a t the development of i n c r e a s -i n g numbers of t e s t s of i n t e l l i g e n c e n e c e s s i t a t e d a means f o r t r a n s m i t t i n g "a s c o r e o b t a i n e d w i t h one t e s t i n t o the s c o r e t h a t i s e q u i v a l e n t t o i t i n some o t h e r t e s t " ( T h o r n d i k e , 1922, p . 2 9 ) . More r e c e n t l y , Lennon (1966a) c l a i m e d t h a t " i t ^ r s g e n e r a l l y a greed t h a t t h e r e i s need f o r d a t a t h a t w i l l p e r m i t c o n v e r s i o n of s c o r e s or IQ's d e r i v e d from one t e s t t o [ e q u i v a l e n t 3 measures d e r i v e d from o t h e r t e s t s " ( p . 168). The r a t i o n a l e f o r the c a l l f o r e q u i v a l e n t s c o r e c o n v e r s i o n s i s based on the d e s i r a b i l i t y of e s t a b l i s h i n g an e m p i r i c a l means f o r making comparisons among i n d i v i d u a l s or groups u s i n g common-purpose t e s t s c o r e s from d i f f e r e n t t e s t s o u r c e s . I t has been s u g g e s t e d t h a t one f a l l a c y i n the i n t e r p r e t a t i o n of i n t e l l i g e n c e t e s t s i s t h a t c omparisons of t h i s n a t u r e a r e o f t e n made on what may be an e r r o n e o u s a s s u m p t i o n of d i r e c t s c o r e c o r r e s p o n d e n c e between t e s t s w h i c h a r e seen as p s y c h o l o g i c a l l y e q u i v a l e n t . The b a s i c m i s u n d e r -s t a n d i n g u n d e r l y i n g t h i s p r a c t i c e has been termed the " j i n g l e f a l l a c y " : t e s t s w h i c h bear the same name measure the same t h i n g . T h i s has f o s t e r e d the n o t i o n t h a t t h e r e i s a common and t h e r e f o r e c o n s t a n t c o n c e p t u a l meaning 4 i n the n u m e r i c a l r e p r e s e n t a t i o n of IQ ( A n a s t a s i , 1976; E b e l , 1972, 1976; Newland, 1973). D e s p i t e the f a c t t h a t i t has been r e p e a t e d l y p o i n t e d out t h a t d i r e c t s c o r e e q u i v a l e n c e does not e x i s t from t e s t t o t e s t ( A n a s t a s i , 1976; Cronbach, 1970; S a t t l e r , 1974; S a l v i a & Y s s e l d y k e , 1978), t h e r e can be l i t t l e doubt from a p r a c t i t i o n e r ' s p o i n t of v i e w , t h a t IQ s c o r e s from v a r i o u s t e s t s of i n t e l l i g e n c e a r e used i n t e r c h a n g e a b l y f o r e d u c a t i o n a l purposes ( B a r r a t t , 1956; B i r k e m e y e r , 1964; R i t t e r , D u f f e y , & Fischman, .1973). The major f o c u s of the p r e s e n t s t u d y w a s . d i r e c t e d toward t h i s i s s u e . S p e c i f i c a l l y , the q u e s t i o n examined was whether i t was f e a s i b l e t o e s t a b l i s h f o r i n d i v i d u a l l y - a d m i n i s t e r e d i n t e l l i g e n c e t e s t s , the t y p e of s c o r e c o n v e r -s i o n s a d v o c a t e d by T h o r n d i k e (1922) and Lennon ( 1 9 6 6 a ) . A second f o c u s was on the development of p r o v i n c i a l l y r e p r e s e n t a t i v e norms as d i s c u s s e d i n a l a t e r s e c t i o n . The Anchor Te s t Study The Anchor T e s t Study (The N a t i o n a l T e s t E q u a t i n g Study i n Reading) a d d r e s s e d s i m i l a r i s s u e s . The s t u d y was u n d e r t a k e n i n r e s p o n s e t o the r e c o g -n i z e d need f o r s t a t i s t i c a l e q u i v a l e n c e among the e i g h t most w i d e l y used r e a d -i n g achievement t e s t s i n the U n i t e d S t a t e s ( L o r e t , Seder, B i a n c h i n i , & V a l e , 1974). I t had two major o b j e c t i v e s : t o p r o v i d e e q u i v a l e n c y t a b l e s f o r t r a n s -l a t i n g a s c o r e on any one of the t e s t s i n t o a s c o r e on any o t h e r t e s t , and t o p r o v i d e new n a t i o n a l norms f o r each of the t e s t s ( B i a n c h i n i & L o r e t , 1974, p . l ) . The s t u d y was named a f t e r the "anchor test';' norming t e c h n i q u e w h i c h i t a d o p t ed. T h i s t e c h n i q u e i n v o l v e d the i d e n t i f i c a t i o n o f one t e s t as the r e f e r e n c e s c a l e , or " a n c h o r , " t o w h i c h the s c o r e s of o t h e r s i m i l a r t e s t s a r e c o n v e r t e d or normed. The n o t i o n was f i r s t c o n c e p t u a l i z e d by C u r e t o n (1941) and l a t e r s u p p o r t e d by Lennon ( 1 9 6 6 b ) as a n a t i o n a l s o l u t i o n t o the need f o r a u n i f o r m system of u n i t s f o r a l l t e s t s . B o t h Lennon 5 and C u r e t o n a d v o c a t e d endorsement by a l l t e s t p u b l i s h e r s of a s t a n d a r d approach t o the norming of i n t e l l i g e n c e and achievement t e s t s i n r e f e r e n c e t o a s i n g l e g l o b a l anchor t e s t . The advantage of t h i s approach i s the c o m p a r a b i l i t y among t e s t s c o r e s y i e l d e d by the common norm p o p u l a t i o n . B r i e f l y , t he p r o c e d u r e used i n the Anchor T e s t Study was as f o l l o w s : one of the t e s t s , t he M e t r o p o l i t a n Achievement T e s t (MAT), was r e s t a n d a r d -i z e d d i r e c t l y on a n a t i o n a l l y r e p r e s e n t a t i v e sample of c h i l d r e n i n Grades 4, 5, and 6. F o l l o w i n g t h a t , e q u i v a l e n c y t a b l e s were e s t a b l i s h e d among a l l e i g h t t e s t s . F i n a l l y , norms were d e r i v e d f o r the seven non-MAT t e s t s , u s i n g the MAT as the r e f e r e n c e o r "a n c h o r " and r e a d i n g c o r r e s p o n d i n g norm v a l u e s from the e q u i v a l e n c e t a b l e s . Two p s y c h o m e t r i c q u e s t i o n s were examined i n t h i s p r o c e s s . The f i r s t d e a l t w i t h the t e c h n i c a l f e a s i b i l i t y of e q u a t i n g t e s t s w h i c h were not d e s i g n e d as p a r a l l e l , but w h i c h were s i m i l a r i n c o n t e n t and f u n c t i o n . The second c o n s i d e r e d the r e l a t i v e e f f i c i e n c y of the l i n e a r and e q u i p e r c e n t i l e methods f o r d e r i v i n g e q u i v a l e n t s c o r e s . I n the f o l l o w i n g s e c t i o n s , the c o n c e p t s and t e r m i n o l o g y a s s o c i a t e d w i t h s c o r e c o n v e r s i o n t y p e s and methods a r e b r i e f l y i n t r o d u c e d p r i o r t o a f o r m a l i z a t i o n of the r e s e a r c h p roblem. Each of t h e s e c o n c e p t s i s d i s -c u s s e d i n d e t a i l i n Chap t e r I I . 6 I n t e r - T e s t Score C o n v e r s i o n s Two t y p e s of i n t e r - t e s t s c o r e c o n v e r s i o n s a r e f a m i l i a r i n p s y c h o -m e t r i c l i t e r a t u r e : e q u i v a l e n c y c o n v e r s i o n s , based on t e s t e q u a t i n g p r o c e -d u r e s , and comparable s c o r e c o n v e r s i o n s , based on common s c a l i n g p r o c e -d u r e s . Both of t h e s e were examined i n terms of t h e i r t e c h n i c a l r e q u i r e -ments and t h e i r a p p l i c a b i l i t y t o the p r e s e n t s t u d y . E q u i v a l e n t S cores The t e c h n i c a l f e a s i b i l i t y of e q u a t i n g i s d e t e r m i n e d by the p a r a l l e l -ism of the t e s t s i n v o l v e d . A c c o r d i n g t o A n g o f f , e q u a t i n g , o r the d e r i v a t i o n of e q u i v a l e n t s c o r e s , c o n c e r n s i t s e l f w i t h t h e p r o b l e m of unique c o n v e r s i o n s w h i c h may be d e r i v e d o n l y a c r o s s t e s t forms t h a t are p a r a l l e l , t h a t i s forms t h a t measure, w i t h i n a c c e p t a b l e l i m i t s , the same p s y c h o l o g i c a l f u n c t i o n (1971, p. 563). I d e a l l y , p a r a l l e l i s m i s d e f i n e d i n the r e s t r i c t e d m a t h e m a t i c a l sense of c l a s s i c a l t r u e s c o r e t h e o r y (see C h a p t e r I I ) . Wesman (1958) p o i n t e d out t h a t " t h e s e c o n d i t i o n s are o r d i n a r i l y most c l o s e l y a p p r o x i m a t e d where p a r a l l e l forms of a t e s t have been c o n s t r u c t e d — f o r m s w h i c h are i n t e n d e d to be i n t e r c h a n g e a b l e " (p. 8 ) . F o r p r a c t i c a l p u r p o s e s , however, e q u i v -a l e n t s c o r e c o n v e r s i o n s may be d e s i r a b l e among t e s t s w h i c h were not s p e c -i f i c a l l y c o n s t r u c t e d i n t h i s manner ( F l a n a g a n , 1964; Lennon, 1966a; Marco, P e t e r s e n , & S t e w a r t , 1979). The e i g h t r e a d i n g achievement t e s t s i n the Anchor Te s t Study were such an example. I n t h a t s t u d y , b o t h h i g h c o n t e n t s i m i l a r i t y and h i g h d i s a t t e n u a t e d i n t e r c o r r e l a t i o n c o e f f i c i e n t s were c i t e d as e v i d e n c e of adequate p a r a l l e l i s m among the t e s t s t o j u s t i f y t h e i r t r e a t m e n t as p a r a l l e l ( L o r e t , e t a l . , 1974). I n the p r e s e n t s t u d y , the q u e s t i o n of t e c h n i c a l p a r a l l e l i s m was examined i n r e f e r e n c e t o t e s t s w h i c h a r e employed as f u n c t i o n a l l y p a r a l l e l but w h i c h a r e known not t o have a h i g h degree of c o n t e n t s i m i l a r i t y (as 7 w i l l be d i s c u s s e d i n Chap t e r I I ) . G i v e n t h i s , i t was not e x p e c t e d t h a t the t e s t s would s a t i s f y t he c l a s s i c a l c r i t e r i a f o r p a r a l l e l i s m . L o r d and N o v i c k ( 1 9 6 8 ) , however, have s u g g e s t e d an a p p l i c a t i o n of t e s t t h e o r y t o t e s t s w h i c h a r e i m p e r f e c t l y p a r a l l e l i n the c l a s s i c a l sense. They c o n s i d e r e d i t p s y c h o m e t r i c a l l y d e f e n s i b l e i n some ca s e s t o d e f i n e t r u e s c o r e i n terms of a " f a m i l y " o f t e s t s a l l m e asuring a common p s y c h o l o g i c a l f u n c t i o n r a t h e r t h a n i n terms of a s i n g l e t e s t . They i n t r o d u c e d the term n o m i n a l l y p a r a l l e l t o d e s c r i b e t e s t s w h i c h measure " i m p o r t a n t a s p e c t s or m a n i f e s t a t i o n s o f the p s y c h o l o g i c a l v a r i a b l e under s t u d y " ( p . 174) d e s p i t e the f a c t t h a t t h e r e may be some d i f f e r e n c e s among the t e s t s . Comparable S c o r e s U n l i k e the concept of e q u i v a l e n c e , w h i c h i s s p e c i f i c t o the t e s t s t h e m s e l v e s and, as has been shown, i s synonymous w i t h p a r a l l e l i s m , compar-a b i l i t y r e f e r s s o l e l y t o t e s t ' s c o r e s c a l e s . Comparable s c o r e s can be a c h i e v e d by s c a l i n g any t e s t s i n a common m e t r i c f o r a common r e f e r e n c e  group. The purpose of such common s c a l i n g i s t o a s s i g n the same n u m e r i c a l v a l u e t o s c o r e s o c c u p y i n g the same rank i n t h e i r r e s p e c t i v e d i s t r i b u t i o n s . T h i s can be done i r r e s p e c t i v e of t e s t c o n t e n t and c a r r i e s no i m p l i c a t i o n of the i n t e r c h a n g e a b i l i t y of t e s t s . A n g o f f (1971) d e s c r i b e d comparing as f o l l o w s : [Comparing] may be thought of q u i t e s i m p l y as the pro b l e m of " e q u a t i n g " t e s t s of d i f f e r e n t p s y c h o l o g i c a l f u n c t i o n . ( p . 590). [The d e r i v a t i o n of comparable s c o r e s i n v o l v e s ] the pro b l e m of nonunique c o n v e r s i o n s of s c o r e s a c r o s s n o n p a r a l l e l forms (p. 5 6 3 ) . As opposed t o t e s t e q u a t i n g , A n g o f f s t r e s s e d the b r o a d e r a p p l i c a t i o n of the concept of comparing ( i . e . , any two s c a l e s can be made comparable) and the n a r r o w e r i n t e r p r e t a t i o n of the c o n v e r t e d s c o r e s . S i n c e the s c o r e c o n v e r s i o n s a r e nonunique, t h e y a r e not g e n e r a l i z a b l e beyond t h e 8 group on w h i c h t h e y were e s t a b l i s h e d . L o r d (1950) p o i n t e d out t h a t " c o m p a r a b i l i t y may be e x p e c t e d t o h o l d a p p r o x i m a t e l y , however, w i t h r e s p e c t t o groups s u f f i c i e n t l y s i m i l a r t o the b a s i c group. O b v i o u s l y , the b a s i c group s h o u l d i n g e n e r a l be a r e p r e s e n t a t i v e sample o f p e r s o n s of the type f o r whom the t e s t s a r e i n t e n d e d " (p. 1 ) . The t e c h n i c a l c o n s i d e r a t i o n s i n the e s t a b l i s h m e n t of comparable s c o r e s , t h e r e f o r e , a r e f o c u s e d on the n a t u r e of the group used f o r e s t a b -l i s h i n g t he c o n v e r s i o n s r a t h e r t h a n on the n a t u r e of the t e s t s t h e m s e l v e s . E q u a t i n g Methods In t h e Anchor T e s t Study, two e q u a t i n g m e t h o d s — l i n e a r and e q u i -p e r c e n t i l e — w e r e a p p l i e d t o the d e r i v a t i o n of the e q u i v a l e n c y t a b l e s . These methods a r e g e n e r a t e d by d i f f e r e n t d e f i n i t i o n s of e q u i v a l e n c y : the e q u i p e r c e n t i l e method d e f i n e s as e q u i v a l e n t s c o r e s on two t e s t s c o r r e s -ponding t o e q u a l " p e r c e n t i l e r a n k s , w h i l e the l i n e a r method c o n s i d e r s s c o r e s c o r r e s p o n d i n g t o e q u a l s t a n d a r d - s c o r e d e v i a t e s as e q u i v a l e n t ( A n g o f f , 1971, p. 565). The l a t t e r p r o c e d u r e i n v o l v e s a l i n e a r t r a n s f o r m a t i o n f u n c t i o n o f the form Y = aX + b, w h i l e the former p r o c e d u r e i s an a r e a t r a n s f o r m a t i o n w h i c h s e r v e s t o s t r e t c h and compress one s c o r e d i s t r i b u t i o n t o conform t o the shape of the o t h e r . When t e s t s c o r e d i s t r i b u t i o n s a r e s i m i l a r beyond the f i r s t two moments, the l i n e a r method i s p r e f e r r e d , s i n c e i t i n v o l v e s an ad j u s t m e n t i n mean and s t a n d a r d d e v i a t i o n o n l y . When t e s t s c o r e d i s t r i b u t i o n s a r e d i s s i m i l a r , the e q u i p e r c e n t i l e method i s n e c e s s i t a t e d . T e s t forms w h i c h a r e s t r i c t l y p a r a l l e l can be assumed t o have i d e n -t i c a l raw s c o r e d i s t r i b u t i o n s and t h e r e f o r e t o s a t i s f y t he r e q u i r e m e n t s f o r l i n e a r e q u a t i n g . An a s s u m p t i o n o f p a r a l l e l i s m o f t e s t s such as t h a t made among the r e a d i n g achievement t e s t s i n the Anchor T e s t Study 9 l e a d s t o an h y p o t h e s i s of the v i a b i l i t y of a l i n e a r r e l a t i o n s h i p on w h i c h to base e q u a t i n g c o n v e r s i o n s . F u r t h e r , s i n c e l i n e a r and e q u i p e r c e n t i l e e q u a t i n g c l o s e l y a p p r o x i m a t e one a n o t h e r when s c o r e d i s t r i b u t i o n s a r e i d e n t i c a l , t he s c o r e c o n v e r s i o n s y i e l d e d by the two methods can be e x p e c t e d t o be s i m i l a r . The r e s u l t s of the Anchor Te s t S t u d y , however, f a i l e d t o s u p p o r t such e x p e c t a t i o n s . I t was found t h a t the l i n e a r e q u a t i n g method y i e l d e d some c o n v e r t e d s c o r e v a l u e s w h i c h f e l l o u t s i d e the c o r r e s -p o n d ing s c o r e ranges of the t e s t s ( B i a n c h i n i & L o r e t , 1974). T h e r e f o r e the r e p o r t e d e q u i v a l e n c y t a b l e s were produced u s i n g e q u i p e r c e n t i l e s c o r e c o n v e r s i o n s . The Problem The f u n c t i o n a l e q u i v a l e n c e o f i n t e l l i g e n c e t e s t s , d e f i n e d by the manner i n w h i c h t h e y a r e used i n common p r a c t i c e , was e s t a b l i s h e d e a r l i e r . The f i r s t purpose o f t h i s s t u d y was t o a s s e s s the v a l i d i t y of t h i s use. F i v e i n d i v i d u a l l y - a d m i n i s t e r e d i n t e l l i g e n c e t e s t s were c o n s i d e r e d : the We c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n - R e v i s e d (WISC-R), the Peabody P i c t u r e V o c a b u l a r y T e s t (PPVT), t h e S l o s s o n I n t e l l i g e n c e T e s t f o r C h i l d r e n and A d u l t s ( S I T ) , the S t a n d a r d P r o g r e s s i v e M a t r i c e s (SPM), and the M i l l H i l l V o c a b u l a r y S c a l e (MHVS). W i t h the e x c e p t i o n of the MHVS, a l l o f th e s e t e s t s a r e f r e q u e n t l y used i n s c h o o l s i n B r i t i s h C o l u m b i a , the p r o v -i n c e i n w h i c h the s t u d y was c o n d u c t e d . The WISC-R was chosen t o s e r v e as a n c h o r . I n a d d i t i o n t o b e i n g the most w i d e l y used i n d i v i d u a l i n t e l l i -gence t e s t (Beauchamp, Samuels, & G r i f f o r e , 1979; M e r c e r , 1979), i t has t r a d i t i o n a l l y s e r v e d as the c r i t e r i o n t e s t a g a i n s t w h i c h o t h e r measures of i n t e l l i g e n c e have been v a l i d a t e d ( B e r s o f f , 1980). The r e m a i n i n g t e s t s have the common advantage of r e q u i r i n g c o n s i d e r a b l y l e s s a d m i n i s t r a -t i o n time t h a n the WISC-R (10-30 m i n u t e s each compared t o 1-1% hours 10 f o r the WISC-R). F u r t h e r , t h e s e a r e l e v e l B t e s t s . As such, t h e y a r e more a c c e s s i b l e t h a n the WISC-R and a r e o f t e n used as a l t e r n a t i v e s t o i t . Thus, the i n t e r - t e s t r e l a t i o n s h i p s examined i n the p r e s e n t s t u d y were between the f o u r " s h o r t e r " t e s t s and the WISC-R. The d e f e n s i b i l i t y of s u b s t i t u t i n g t h e s e t e s t s f o r the WISC-R was c o n s i d e r e d f i r s t on l o g i c a l and t h e n on e m p i r i c a l grounds. The l o g i c a l a n a l y s i s c o n s i s t e d o f an e x a m i n a t i o n of the p s y c h o l o g i c a l p a r a l l e l i s m of t h e f o u r t e s t s t o the WISC-R. T h i s was o p e r a t i o n a l l y d e f i n e d i n terms o f the s i m i l a r i t y o f the p s y c h o l o g i c a l t r a i t measured. The e m p i r i c a l a n a l y s i s i n v o l v e d an i n v e s t i g a t i o n of the a p p l i c a b i l i t y of the e q u a t i n g methods used i n the Anchor T e s t Study t o the p a i r s of t e s t s i d e n t i f i e d as p s y c h o l o g i c a l l y e q u i v a l e n t . As w i t h t he Anchor T e s t Study, a p r e l i m i n a r y s t e p t o the a c t u a l e q u a t i n g was the d e t e r m i n a t i o n of the t e c h n i c a l , o r s t a t i s t i c a l , p a r a l l e l -ism of t h e t e s t s . G i v e n t h a t t he f i v e t e s t s i n the p r e s e n t s t u d y were a l l t e s t s o f i n t e l l i g e n c e as d e f i n e d by Lennon, t h e s e t e s t s t h a t p r o f e s s t o measure a more or l e s s g e n e r a l a b i l i t y , or a v e r y s m a l l number of such a b i l i t i e s , assumed t o u n d e r l i e o r c o n d i t i o n p erformance a c r o s s a c o n s i d e r a b l e range of t a s k s p r i m a r i l y i n t e l l e c t u a l i n c h a r a c t e r (1978, p. 1)> L o r d and N o v i c k ' s concept of n o m i n a l p a r a l l e l i s m was adopted. I n t h e absence o f s t a t i s t i c a l g u i d e l i n e s f o r d e f i n i n g n o m i n a l p a r a l l e l i s m , a d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c i e n t of a t l e a s t .70 between t e s t p a i r s ( r > .70) was s e l e c t e d . C o r r e l a t i o n s of t h i s magnitude a re commonly AI — found between WISC-R s c o r e s and s c o r e s on o t h e r t e s t s of i n t e l l i g e n c e ( S a t t l e r , 1974; W e c h s l e r , 1974). The r e q u i r e m e n t o f a l a r g e number of examinees on w h i c h t o base e q u i v a l e n c y c o n v e r s i o n s , a d d i t i o n a l l y p r o v i d e d the p o s s i b i l i t y o f r e n o r m i n g 11 the t e s t s and thus s i m u l a t i n g the Anchor Te s t Study i n b o t h i t s norming and e q u a t i n g a s p e c t s . T h e r e f o r e the scope of the p r e s e n t s t u d y was extended t o i n c l u d e the a d m i n i s t r a t i o n of the f i v e t e s t s t o a r e p r e s e n t a -t i v e sample of c h i l d r e n i n B r i t i s h C o l u m b i a and the development of p r o v i n -c i a l norms. The use of a common s t a n d a r d i z a t i o n sample and common s c a l -i n g p r o c e d u r e s e n s u r e d c o m p a r a b i l i t y among the t e s t s c o r e s . D e l i m i t a t i o n s of the Study N a t i v e I n d i a n s Problems of b i a s i n the use of s t a n d a r d i z e d i n t e l l i g e n c e t e s t s w i t h N a t i v e I n d i a n c h i l d r e n i n B r i t i s h Columbia have been r e c e n t l y summar-i z e d by More and O l d r i d g e ( 1 9 8 0 ) . S i m i l a r l y , Hawthorn (1971), i n A Survey  of the Contemporary I n d i a n s of Canada, s a i d : The m a t t e r of i n t e l l i g e n c e i s a s e r i o u s one. The t e s t s a r e known to be i n v a l i d f o r a l l p o p u l a t i o n s e x c e p t the one f o r w h i c h t h e y were s t a n d a r d i z e d , t h a t i s , E n g l i s h - s p e a k i n g White m i d d l e c l a s s e s of an urban group. . . . Even i f a t e a c h e r i s aware t h a t t e s t r e s u l t s may not be a c c u r a t e , i t would be d i f f i c u l t f o r him t o l o o k at a s e r i e s of below-normal s c o r e s on a c h i l d ' s PRC [Permanent Record Card] and not c o n c l u d e t h a t the c h i l d has low a b i l i t y . I f s c h o o l systems had adequate f a c i l i t i e s f o r slow l e a r n e r s , a l m o s t e v e r y I n d i a n c h i l d i n the c o u n t r y would be i n one oh the b a s i s of h i s i n t e l l i g e n c e and achievement t e s t s r e s u l t s . ( p . 144) Hawthorn recommended the a b o l i t i o n o f such t e s t s f o r I n d i a n s t u d e n t s . I n t e l l i g e n c e t e s t s c o r e means f o r N a t i v e I n d i a n C h i l d r e n i n B r i t i s h C olumbia ( F r a s e r , 1969; G o l d s t e i n , 1980) resemble t h o s e f o r c h i l d r e n from c u l t u r a l m i n o r i t y groups i n the U n i t e d S t a t e s (Kaufman & D o p p e l t , 1976; M e r c e r , 1979; R e s c h l y , i n p r e s s ) . M e r c e r (1979) s u g g e s t e d t h a t the b i m o d a l d i s t r i b u t i o n o f s c o r e s r e s u l t i n g from the s i g n i f i c a n t l y l ower mean s c o r e s of t h e s e nonwhite c h i l d r e n p r e c l u d e s t h e i r t r e a t m e n t as p a r t of the same s t a t i s t i c a l p o p u l a t i o n as w h i t e , m i d d l e - c l a s s c h i l d r e n . T h e r e f o r e , a n a t i o n a l norms group i n c l u d i n g the p r o p o r t i o n a l r e p r e s e n t a t i o n of such m i n o r i t y group c h i l d r e n i s i n a p p r o p r i a t e . A l t e r n a t e l y , M e r c e r a d v o c a t e d s e p a r a t e norms f o r m i n o r i t y groups ( 1 9 7 9 ) . The p o s i t i o n s t a t e -ment of the N a t i o n a l A s s o c i a t i o n of S c h o o l P s y c h o l o g i s t s (NASP, 1976) s i m i l a r l y s t a t e d , " A l l s t u d e n t i n f o r m a t i o n s h o u l d be i n t e r p r e t e d i n the c o n t e x t of the s t u d e n t ' s s o c i o - c u l t u r a l b a c k ground" (p. 1 ) . The use of subgroup o r d i f f e r e n t i a t e d norms f o r d i f f e r e n t - s c o r i n g groups has been recommended as p s y c h o m e t r i c a l l y d e s i r a b l e ( A n a s t a s i , 1976; A n g o f f , 1971) and, as mentioned e a r l i e r i n t h i s c h a p t e r , mandated as l e g a l l y b i n d i n g ( L a r r y P. v s . W i n s t o n R i l e s , 1979). B e a r i n g i n mind the arguments a g a i n s t i n c l u s i o n of N a t i v e I n d i a n c h i l d r e n i n a r e p r e s e n t a t i v e sample of the t o t a l p o p u l a t i o n and b e i n g r e s t r i c t e d by p r a c t i c a l c o n s i d e r a t i o n s of sample s i z e from r e p l i c a t i n g ' the norming p r o c e d u r e f o r a N a t i v e I n d i a n sample, t h e s e c h i l d r e n were e x c l u d e d from the s t u d y . E n g l i s h - S p e a k i n g C h i l d r e n The l a r g e l y v e r b a l n a t u r e of the c o n t e n t and i n s t r u c t i o n s of the t e s t s i n t h i s s t u d y n e c e s s i t a t e d , on l o g i c a l g rounds, t h e r e s t r i c t i o n o f the sample t o c h i l d r e n who were f l u e n t i n the use and comprehension of the E n g l i s h language. T h i s d i d n o f ' e x c l u d e c h i l d r e n f o r whom E n g l i s h i s a second language, as l o n g as f l u e n c y was a s s u r e d . Handicapped C h i l d r e n A l l c h i l d r e n e n r o l l e d i n c l a s s e s f o r the p h y s i c a l l y h a n d i c a p p e d , e m o t i o n a l l y d i s t u r b e d , or t r a i n a b l e m e n t a l l y r e t a r d e d were e x c l u d e d . T h i s i s c o n s i s t e n t w i t h sample r e s t r i c t i o n s p l a c e d on the o r i g i n a l s t a n d -a r d i z a t i o n of the WISC-R. (As w i l l be d e m o n s t r a t e d i n C h a p t e r I I I , t h i s was the model adopted f o r s a m p l i n g i n the p r e s e n t s t u d y . ) I t i s a l s o i n k e e p i n g w i t h c o n s c i e n t i o u s t e s t i n g p r a c t i c e s i n c e t h e s e c h i l d r e n u s u a l l y r e q u i r e s p e c i a l t e s t i n g p r o c e d u r e s . Age.-The sample was r e s t r i c t e d t o c h i l d r e n at t h r e e ages: 7%, 9%, and 11% y e a r s . These ages c o r r e s p o n d c l o s e l y t o grades 2, 4, and 6 and were c o n s i d e r e d b r o a d l y r e p r e s e n t a t i v e of c h i l d r e n a c r o s s the e l e m e n t a r y grades where r e q u e s t s f o r i n d i v i d u a l i n t e l l i g e n c e t e s t i n g a r e most common. O r g a n i z a t i o n of the D i s s e r t a t i o n The r e m a i n d e r of the d i s s e r t a t i o n c o n s i s t s of f o u r c h a p t e r s . I n C h a p t e r I I , the r e v i e w of the l i t e r a t u r e i s p r e s e n t e d . T h i s i s f o l -lowed by a d e t a i l e d o u t l i n e of the p r o c e d u r e s f o r d a t a c o l l e c t i o n and d a t a a n a l y s i s i n C h a p t e r I I I and the c o r r e s p o n d i n g r e s u l t s i n C h a p t e r IV. The f i n a l c h a p t e r c o n t a i n s a summary r e v i e w of the s t u d y and a d i s c u s s i o n of the f i n d i n g s . CHAPTER I I REVIEW OF THE LITERATURE The r e v i e w o f the l i t e r a t u r e i s p r e s e n t e d i n t h r e e major s e c t i o n s . F i r s t , t he p s y c h o l o g i c a l e q u i v a l e n c e o f the f i v e i n t e l l i g e n c e t e s t s c o n -s i d e r e d i n t h i s s t u d y i s examined t o e s t a b l i s h t he j u s t i f i c a t i o n f o r the e q u a t i n g phase. T h i s i s f o l l o w e d by a d i s c u s s i o n of the t e c h n i c a l c r i t e r i a and the methodology f o r i n t e r - t e s t 'score c o n v e r s i o n s . I n the f i n a l s e c t i o n , t h e r a t i o n a l e f o r i n c l u d i n g t he norming phase i s p r e s e n t e d . J u s t i f i c a t i o n f o r E q u a t i n g I n C h a p t e r I a d i s t i n c t i o n was made between f u n c t i o n a l and t e c h n i c a l e q u i v a l e n c e — t h e former based on a c t u a l p r a c t i c e and the l a t t e r on s t a t i s -t i c a l c r i t e r i a . The argument f o r the f u n c t i o n a l e q u i v a l e n c e of the f i v e t e s t s c o n s i d e r e d i n t h i s s t u d y was p r e s e n t e d i n terms of t h e i r common use i n e d u c a t i o n a l s e t t i n g s . The d e t e r m i n a t i o n of t e c h n i c a l e q u i v a l e n c e r e s t s on s t a t i s t i c a l i n d i c e s of the degree of p a r a l l e l i s m o f t e s t p a i r s . T h i s i s examined i n d e t a i l l a t e r i n t h i s c h a p t e r . The s u b j e c t of the p r e s e n t s e c t i o n i s the j u s t i f i c a t i o n f o r e q u a t i n g f o u r of the t e s t s (PPVT, SIT, SPM, MHVS) t o the WISC-R based on what may be c o n s i d e r e d t h e i r " p s y c h o l o g i c a l " e q u i v a l e n c e . T h i s i s o p e r a t i o n -a l l y d e f i n e d i n t h i s c o n t e x t as s i m i l a r i t y of the p s y c h o l o g i c a l t r a i t o r f u n c t i o n measured. The d i s c u s s i o n i n c l u d e s a co m p a r i s o n o f the hypo-t h e t i c a l c o n s t r u c t s u n d e r l y i n g the t e s t s i n s o f a r as t h e s e a r e r e f l e c t e d i n the s t a t e m e n t s o f purpose of t h e i r r e s p e c t i v e a u t h o r s and i n the 14 c o n t e n t and format o f the t e s t s t h e m s e l v e s . I n a d d i t i o n , the r e s u l t s of c o r r e l a t i o n a l and f a c t o r a n a l y t i c s t u d i e s a r e c i t e d as p r o v i d i n g e m p i r -i c a l e v i d e n c e of i n t e r - t e s t s i m i l a r i t i e s . The purpose of t h i s r e v i e w i s t o d e v e l o p a m a t r i x o f t e s t p a i r s w h i c h can be c o n s i d e r e d f u n c t i o n a l l y and p s y c h o l o g i c a l l y e q u i v a l e n t . T h i s w i l l p r o v i d e a framework f o r t h e f u r t h e r assessment of t e c h n i c a l e q u i v a l e n c e and the i d e n t i f i c a t i o n of t e s t p a i r s f o r e q u a t i n g . The d i s c u s s i o n i s o r g a n i z e d as f o l l o w s . F i r s t t he WISC-R, as anchor or r e f e r e n c e t e s t , i s d e s c r i b e d . S u b s e q u e n t l y , each of the o t h e r t e s t s i s examined f o r s i m i l a r i t y o f purpose and c o n t e n t t o the WISC-R. Wech s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n - R e v i s e d (WISC-R) The WISC-R i s a t e s t of " g l o b a l " i n t e l l i g e n c e w h i c h i s based on the c o n c e p t u a l i z a t i o n o f i n t e l l i g e n c e as a " m u l t i d i m e n s i o n a l and m u l t i -f a c e t e d e n t i t y r a t h e r t h a n an i n d e p e n d e n t , u n i q u e l y d e f i n e d t r a i t " ( W e c h s l e r , 1974, p. 5 ) . I n k e e p i n g w i t h t h i s m u l t i d i m e n s i o n a l n o t i o n , the t e s t a c t u a l l y c o n s i s t s of a s e t of t e n s u b t e s t s , each i n t e r n a l l y homogeneous' i n c o n t e n t and each " c o n s i d e r e d n e c e s s a r y f o r the f u l l e r a p p r a i s a l of i n t e l l i g e n c e " ( p . 9 ) . The s u b t e s t s , d e s c r i b e d i n T a b l e 1, a r e c l a s s i f i e d as me a s u r i n g e i t h e r v e r b a l or performance s k i l l s and ar e combined t o y i e l d t h r e e summary IQ s c o r e s : (1) the V e r b a l IQ com-p u t e d from the f i v e v e r b a l s u b t e s t s ; (2) the Performance IQ computed from the f i v e performance s u b t e s t s ; and (3) the F u l l S c a l e IQ d e r i v e d from a l l t e n s u b t e s t s . The r o b u s t n e s s of t h i s v e r b a l - p e r f o r m a n c e dichotomy has been w e l l s u b s t a n t i a t e d by f a c t o r a n a l y t i c s t u d i e s (Kaufman, 1975; R e s c h l y , 1978; S i l v e r s t e i n , 1977; Vance & W a l l b r o w n , 1978) and i s c o n s i s t e n t w i t h a c o n c e p t u a l d u a l i t y of s k i l l s u n d e r l y i n g i n t e l l i g e n c e w h i c h i s r e f l e c t e d 16 T a b l e 1 WISC-R S u b t e s t s and S k i l l s Measured* S u b t e s t s S k i l l s V e r b a l I n f o r m a t i o n S i m i l a r i t i e s A r i t h m e t i c V o c a b u l a r y Comprehension Performance P i c t u r e C o m p l e t i o n P i c t u r e Arrangement B l o c k D e s i g n O b j e c t Assembly Coding a c q u i r e d v e r b a l i n f o r m a t i o n v e r b a l c o n cept f o r m a t i o n , l o g i c a l t h i n k i n g r e a s o n i n g a b i l i t y , n u m e r i c a l a c c u r a c y i n m e n t a l a r i t h m e t i c word knowledge s o c i a l judgment, common sense v i s u a l a l e r t n e s s , v i s u a l o r g a n i z a t i o n , v i s u a l memory s e q u e n t i a l t h i n k i n g , n o n v e r b a l r e a s o n i n g p e r c e p t u a l o r g a n i z a t i o n , s p a t i a l v i s u a l i z a t i o n , v i s u a l - m o t o r c o o r d i n a t i o n p e r c e p t u a l o r g a n i z a t i o n v i s u a l - m o t o r c o o r d i n a t i o n , speed of me n t a l o p e r a t i o n , s h o r t - t e r m memory "Summarized from S a t t l e r (1974, pp. 175-187) i n o t h e r measures ( e . g . , C o g n i t i v e A b i l i t i e s T e s t , Kuhlmann-Anderson I n t e l l i g e n c e T e s t s , Henmon-Nelson T e s t s of M e n t a l A b i l i t y , C a l i f o r n i a T e s t of M e n t a l M a t u r i t y ) . H i e r a r c h i c a l f a c t o r s o l u t i o n s a l s o s u p p o r t the p r e s e n c e of a r e l a t i v e l y s t r o n g g e n e r a l (g) f a c t o r w h i c h i s c o n t r i -b u t e d t o by a l l s u b t e s t s ( W a l l b r o w n , 1979; Wa l l b r o w n , B l a h a , W a l l -brown, & E n g i n , 1975). The WISC-R, l i k e i t s p r e d e c e s s o r the WISC, s h a r e s s t a t u s among i n d i v i d u a l i n t e l l i g e n c e t e s t s w i t h the S t a n f o r d - B i n e t as one of the " s t a t e l y , r e v e r e d , and v e n e r a t e d d e v i c e s a g a i n s t w h i c h a l l o t h e r t e s t s [ a r e ] measured" ( B e r s o f f , 1980, p. 113). Re v i e w e r s a c c l a i m e d the WISC-R as an "even more v a l u a b l e t o o l than i t s h i g h l y p r a i s e d and w e l l - u s e d p r e d e -c e s s o r " ( K r i c h e r , 1978, p. 355) and " t h e i n s t r u m e n t of c h o i c e f o r the 17 p s y c h o l o g i c a l assessment of c h i l d r e n ' s i n t e l l i g e n c e " ( W h i t w o r t h , 1978, p. 3 5 1 ) . As p o i n t e d out i n Chap t e r I , however, i t i s time-consuming t o a d m i n i s t e r and i t s use i s r e s t r i c t e d t o p e r s o n s who have undergone e x t e n s i v e t r a i n i n g i n a d m i n i s t r a t i o n and i n t e r p r e t a t i o n . The c o m b i n a t i o n of i t s a c c e p t e d v a l i d i t y and i t s o b v i o u s c o s t have, s i n c e i t s i n c e p t i o n , p r e c i p i t a t e d "a c o n t i n u a l s e a r c h f o r a t e s t of m e n t a l a b i l i t y w h i c h would produce comparable r e s u l t s " ( C o v i n , 1977b, p. 259). S l o s s o n I n t e l l i g e n c e T e s t ( S I T ) The SIT has been a major c o n t e n d e r f o r the r o l e o f s h o r t - t e s t a l t e r n a t e t o b o t h the WISC-R and the S t a n f o r d - B i n e t , p r i m a r i l y because of i t s r e l a t i o n s h i p t o the l a t t e r . Many of the items i n the SIT were adapted d i r e c t l y from the S t a n f o r d -B i n e t and i n c l u d e , at l e a s t a t the lower age l e v e l s , i t e m s w h i c h c o u l d be c l a s s i f i e d as " p e r f o r m a n c e " t a s k s ( e . g . , d r a w i n g a c i r c l e ) . L i k e the S t a n f o r d - B i n e t however, i t i s e n t i r e l y v e r b a l a t the upper age l e v e l s ( i n c l u d i n g a l l t h r e e ages r e p r e s e n t e d i n t h i s s t u d y ) : t h a t i s , i t e m s are p r e s e n t e d v e r b a l l y and r e q u i r e spoken r e s p o n s e s . A l t h o u g h t h i s q u e s t i o n - a n s w e r mode i s u n i f o r m , the t e s t c o n t e n t i s d i v e r s e and "appears t o c o v e r a wide range of b e h a v i o r r e l e v a n t t o s u c c e s s f u l s c h o o l p e r f o r m -ance" ( L e s s l e r & G a l i n s k y , 1971). N i c h o l s o n (1970) a n a l y z e d the f u n c t i o n s of the SIT u s i n g S a t t l e r ' s (1965) c l a s s i f i c a t i o n schema and i d e n t i f i e d i t e m s of the f o l l o w i n g t y p e s : language, n u m e r i c a l r e a s o n i n g , c o n c e p t u a l t h i n k i n g , s o c i a l i n t e l l i g e n c e , memory, and v i s u a l - m o t o r . U s i n g a d i f f e r -ent c l a s s i f i c a t i o n a p p r o a c h , t h a t p r o p o s e d by V a l e t t ( 1 9 6 5 ) , Stone (1975) c a t e g o r i z e d SIT ite m s as me a s u r i n g i n f o r m a t i o n and comprehension, v o c a b u -l a r y and v e r b a l f l u e n c y , a r i t h m e t i c r e a s o n i n g , r e a s o n i n g , memory, and v i s u a l motor. Thus the SIT may be c o n s i d e r e d t o measure i n t e l l i g e n c e 18 i n a somewhat g e n e r a l , or v a r i e d , sense. S l o s s o n (1975) h i m s e l f o f f e r e d no s p e c i f i c c l a r i f i c a t i o n of t h e o r e t -i c a l i n t e n t , a l t h o u g h he d i d r e f e r t o IQ ( w i t h i m p l i e d g e n e r a l i t y ) as a "'rough' measure of an i n d i v i d u a l ' s c a p a c i t y t o r e a s o n , judge and r e t a i n knowledge" (1975, p. 2 4 ) . The s t a t e d purpose of the t e s t i s as an " i n d i -v i d u a l s c r e e n i n g i n s t r u m e n t " ( S l o s s o n , 1975, p. i i i ) w h i c h i s a c c e s s i b l e t o u n t r a i n e d t e s t e r s and w h i c h o f f e r s t he d u a l advantages of b r e v i t y and ease of a d m i n i s t r a t i o n . I n s e v e r a l papers p u b l i s h e d by the S l o s s o n E d u c a t i o n a l P u b l i s h i n g f i r m t h e r e a r e e x p l i c i t recommendations f o r the use of the SIT as a s u b s t i t u t e f o r one or b o t h of the WISC and the S t a n f o r d -B i n e t . P o i s s a n t (1967) e x p r e s s e d the hope t h a t the t i m e - s a y i n g ' SIT would-" r e p l a c e the use of the S t a n f o r d - B i n e t " i n r e t e s t i n g c h i l d r e n e n r o l l e d i n s p e c i a l e d u c a t i o n programs. She r e p o r t e d a c o r r e l a t i o n of .89 between the two t e s t s f o r a s m a l l sample of s l o w - l e a r n i n g c h i l d r e n . A r m s t r o n g and J ensen (1970) s i m i l a r l y s u g g e s t e d t h a t t h e SIT c o u l d be used as a " s u b s t i t u t e " ( p . 2) f o r the S t a n f o r d - B i n e t f o r s c r e e n i n g and r e t e s t i n g p u r p o s e s . I n a l a t e r s t u d y , A r m s t r o n g , J e n s e n , and Reyn o l d s (1974) made s i m i l a r c l a i m s f o r the r e l a t i o n s h i p between the SIT and the WISC. They t e s t e d 198 e l e m e n t a r y s c h o o l s t u d e n t s who had been r e f e r r e d f o r s p e c i a l c l a s s p l a c e m e n t . Based, on c o r r e l a t i o n s o f .93 and .90 r e s p e c t i v e l y , " t h e y c l a i m " e q u i v a l e n c e " o f SIT IQ's t o b o t h WISC V e r b a l and F u l l s c a l e IQs ( p . 2 ) . A l t h o u g h p r e v i o u s s t u d i e s i n v o l v i n g t h e S t a n f o r d - B i n e t a r e not d i r e c t l y r e l e v a n t t o the p r e s e n t r e s e a r c h , t h e y were i n c l u d e d t o emphasize th e f a c t t h a t c l a i m s f o r the " e q u i v a l e n c e " and " s u b s t i t u t a b i l i t y " (hence p a r a l l e l i s m ) o f the s h o r t , e a s y - t o - a d m i n i s t e r t e s t f o r the l o n g e r , p s y c h o l -o g i s t - a d m i n i s t e r e d t e s t s have been made. At the same t i m e , w a r n i n g s 19 a g a i n s t i n t e r c h a n g e a b i l i t y have been i s s u e d i n t h e M e n t a l Measurements Yearbook ( H i m e l s t e i n , 1972, p. 766); i n t r a i n i n g - o r i e n t e d t e x t b o o k s ( S a l v i a & Y s s e l d y k e , 1978, p. 241; S a t t l e r , 1974, p. 2 4 6 ) ; and i n a s e r i e s o f c o m p a r a t i v e s t u d i e s w i t h the WISC-R ( C o v i n , 1977a, 1977b; Lowrance & Ande r s o n , 1979; M a r t i n & K i d w e l l , 1977; M i z e , C a l l o w a y , & S m i t h , 1979). S t e w a r t and Jones ( 1 9 7 6 ) , i n a t e n - y e a r r e v i e w , summar-i z e d the c o r r e l a t i o n a l f i n d i n g s f o r the SIT and W e c h s l e r s c a l e s as f o l l o w s : (a) the h i g h e s t degree of r e l a t i o n s h i p i s between the SIT and the We c h s l e r v e r b a l s c a l e , and i n most s t u d i e s , t h e r e i s v i r t u a l l y an e q u a l degree of r e l a t i o n s h i p between the SIT and the W e c h s l e r F u l l S c a l e ; (b) t h e r e i s a lower and much more v a r i a b l e degree of r e l a -t i o n s h i p between the SIT and the W e c h s l e r Performance S c a l e ; and ( c ) w i t h samples of s u b j e c t s c h a r a c t e r i z e d by a wide range of IQ s c o r e s , the t y p i c a l c o r r e l a t i o n f a l l s i n the low .80s. (pp. 374-375) On the.-basis of the d i s c u s s i o n of t e s t c o n t e n t as b e i n g b o t h v e r b a l l y l o a d e d and d i v e r s e and on the e m p i r i c a l e v i d e n c e c i t e d above, the SIT appears d e f e n s i b l e as e i t h e r a v e r b a l o r a g e n e r a l t e s t of i n t e l l i g e n c e . Thus i t can be c o n s i d e r e d p s y c h o l o g i c a l l y e q u i v a l e n t t o b o t h the WISC-R V e r b a l and F u l l S c a l e s . Peabody P i c t u r e V o c a b u l a r y T e s t (PPVT) The PPVT has a l s o been c o n s i d e r e d as a p o s s i b l e s u b s t i t u t e f o r the WISC-R ( C o v i n , 1977b; M i z e , C a l l o w a y , & S m i t h , 1979). U n l i k e t h e WISC-R, however, t h i s t e s t has b o t h a s i n g l e format and c o n t e n t . I t r e q u i r e s the examinee t o s e l e c t from a s e t of f o u r p i c t u r e s the one p i c t u r e w h i c h d e f i n e s each s t i m u l u s word p r e s e n t e d by t h e examiner. I n the a u t h o r ' s words, the PPVT was d e s i g n e d " t o p r o v i d e an e s t i m a t e of a s u b j e c t ' s v e r b a l i n t e l l i g e n c e t h r o u g h m e a s u r i n g h i s h e a r i n g [ r e c e p t i v e ] v o c a b u l a r y " (Dunn, 1965, p. 2 5 ) . Dunn j u s t i f i e d t he c h o i c e of a v o c a b u l a r y f o r m a t f o r a t e s t o f i n t e l l i g e n c e on the b a s i s o f i t s p r o v e n c o n s t r u c t v a l i d i t y 20 (Terman & M e r r i l l , 1937; W e c h s l e r , 1949). He a l s o c l a r i f i e d i t s s p e c i f -i c i t y : one must concede t h a t the PPVT i s not p r o v i d i n g a comprehensive measure of i n t e l l e c t u a l f u n c t i o n i n g . I n s t e a d , by means of a s h o r t , r e s t r i c t e d sample of b e h a v i o r , i t a t t e m p t s t o p r o v i d e a u s e f u l p r e d i c t i o n o f s c h o o l s u c c e s s , e s p e c i a l l y i n the a r e a s w h i c h c a l l more h e a v i l y on v e r b a l i n t e l l i g e n c e . (Dunn, 1965, p. 33) At the same t i m e , however, he l a y s c l a i m t o the c o m p a r a b i l i t y o f PPVT IQs t o WISC IQs: " I n terms of c o m p a r a b i l i t y of s c o r e s , the PPVT and We c h s l e r I.Q. v a l u e s appear t o be v e r y s i m i l a r " (Dunn, 1965, pp. 33, 41 ) . A l t h o u g h i t would appear somewhat c o n t r a d i c t o r y t h a t the PPVT, w h i c h i s r e c o g n i z e d as a v e r b a l t e s t of i n t e l l i g e n c e , s h o u l d be c o n s i d e r e d i n r e l a t i o n t o the e n t i r e WISC-R, r e s e a r c h s t u d i e s t y p i c a l l y r e p o r t c o r r e -l a t i o n s between PPVT IQs and a l l t h r e e WISC-R IQs ( C o v i n , 1977b; M i z e , C a l l a w a y , & S m i t h , 1977; Richmond & Long, 1977; Vance, L e w i s , & De B e l l , 1979; Vance, P r i c h a r d , & W a l l b r o w n , 1978). The r e s u l t s o f t h e s e s t u d i e s , p r e s e n t e d i n T a b l e 2, unanimously show low c o r r e l a t i o n s between PPVT and WISC-R Performance IQs. T a b l e 2 P e a r s o n Product-Moment C o r r e l a t i o n C o e f f i c i e n t f o r PPVT IQs and Three WISC-R IQs M i z e e t Vance et Vance et C o v i n Richmond & a l . ( 1 9 7 7 ) a l . ( 1 9 7 9 ) a l . ( 1 9 7 8 ) (1977b) Long(1977) PPVT: WISC-R V e r b a l IQ .58 .43 .66 .57 .77 Performance IQ .41 .12 .50 .20 .32 F u l l S c a l e IQ .57 .40 .63 .43 .65 21 The tendency f o r c o r r e l a t i o n s w i t h F u l l S c a l e IQs t o approach the s i z e of c o r r e l a t i o n s w i t h V e r b a l IQs i s o b v i o u s and has been r e p o r t e d i n r e v i e w s o f s t u d i e s w i t h PPVT and WISC c o r r e l a t i o n s as w e l l . Dunn (1965) and S a t t l e r (1975) c i t e median c o r r e l a t i o n s c o e f f i c i e n t s of .67 and .66 r e s p e c t i v e l y f o r PPVT and WISC V e r b a l IQs and of .61 and .63 f o r PPVT and WISC F u l l S c a l e IQs. I t may be t h i s f a c t o r w h i c h encourages c o m p a r i s o n of the PPVT t o the e n t i r e WISC-R. A l l s t u d i e s , however, r e p o r t e d h i g h e s t c o r r e l a t i o n s o f PPVT IQs w i t h WISC and WISC-R V e r b a l IQs. T h i s , c o u p l e d w i t h the o b v i o u s v e r b a l c o n t e n t o f the PPVT and the a u t h o r ' s s t a t e m e n t s of i n t e n t , l e n d c r e d e n c e t o the l o g i c a l d e s i g n a t i o n of the PPVT as a s i n g u l a r l y v e r b a l measure of i n t e l l i g e n c e . S t a n d a r d P r o g r e s s i v e M a t r i c e s (SPM) The case f o r c a t e g o r i z a t i o n of the SPM i s not as c l e a r - c u t as f o r e i t h e r the SIT or PPVT. The t e s t c o n s i s t s o f 60 f i g u r a l d e s i g n s , or m a t r i c e s , each w i t h a m i s s i n g p o r t i o n . The t a s k f o r the examinee i s to s e l e c t , from s i x or e i g h t g i v e n a l t e r n a t i v e s , t he p i e c e w h i c h c o r r e c t l y c o m p l e t e s the p a t t e r n . Face v a l i d i t y as w e l l as the absence of e x p l i c i t v e r b a l c o n t e n t have r e s u l t e d i n t h e c o n s i d e r a t i o n o f the SPM as a non-v e r b a l , o r p e r f o r m a n c e - t y p e , t e s t . As a r e s u l t , t he t e s t has e n j o y e d some p o p u l a r i t y as a c u l t u r a l l y - u n b i a s e d and l a n g u a g e - f r e e measure of i n t e l l e c t u a l a b i l i t y ( A n a s t a s i , 1976; E l l e y & M a c A r t h u r , 1962). R e s u l t s from c o r r e l a t i o n a l s t u d i e s r e l a t i n g s c o r e s on P r o g r e s s i v e M a t r i c e s s c a l e s t o W e c h s l e r V e r b a l and Performance s c o r e s a r e , however, e q u i v o c a l . B i r k m e y e r (1964, 1965) and Burke and Bingham (1969) found h i g h e r c o r r e l a -t i o n s between M a t r i c e s and W e c h s l e r Performance s c o r e s t h a n between M a t r i c e s and W e c h s l e r V e r b a l s c o r e s f o r c h i l d r e n and a d u l t s . O t h e r s ( B a r r a t t , 1956; M a r t i n & W i e c h e r s , 1954; M e h r o t r a , 1968; S t a c e y & C a r l e t o n , 22 1955) though, f a i l e d t o f i n d a s t r o n g e r r e l a t i o n s h i p w i t h one s c a l e t h a n w i t h the o t h e r . I n f a c t , i n a l l of t h e s e l a t t e r s t u d i e s , the h i g h e s t c o r r e l a t i o n s were r e p o r t e d between M a t r i c e s and W e c h s l e r F u l l S c a l e s c o r e s . These f i n d i n g s cannot be c o n s i s t e n t l y a c c o u n t e d f o r by g r e a t e r v a r i a b i l i t y i n the F u l l S c a l e s c o r e s . C l a i m s t h a t the P r o g r e s s i v e M a t r i c e s t e s t s measure i n t e l l i g e n c e i n a more " g e n e r a l " t h a n s p e c i f i c sense have been p o s t u l a t e d s i n c e i t s i n t r o d u c t i o n . As summarized i n Burke's (1958) r e v i e w , Spearman h i m s e l f r e g a r d e d the 1938 P r o g r e s s i v e M a t r i c e s as the " b e s t of a l l " n o n v e r b a l t e s t of £ ( c i t e d i n B u r k e , 1958, p. 210). Vernon and P a r r y a l s o c o n s i d e r e d i t "an a l m o s t p e r f e c t g_ t e s t " ( c i t e d i n B u r k e , 1958, p. 210). More r e c e n t l y Bock (1973) p o s t u l a t e d s e m a n t i c components i n the P r o g r e s s i v e M a t r i c e s t e s t s . T h i s n o t i o n has been borne out i n f a c t o r a n a l y t i c s t u d i e s w h i c h show h i g h l o a d i n g s on a v e r b a l f a c t o r ( W i e d l & C a r l s o n , 1976) or on a s i n g l e g e n e r a l f a c t o r w h i c h i s i t s e l f h i g h l y v e r b a l (Burke & Bingham, 1969). Raven c o n s i d e r e d the SPM a t e s t of " o b s e r v a t i o n and c l e a r t h i n k i n g " w h i c h by i t s e l f w ould be m i s t a k e n l y d e s c r i b e d as a measure of g e n e r a l i n t e l l i g e n c e (1960, p. 2 ) . D e s p i t e h i s w a r n i n g , and as i n d i c a t e d by many of the s t u d i e s r e p o r t e d above, the SPM has become p o p u l a r i n N o r t h A m e r i c a f o r t h i s *very p u r p o s e . I t has a d d i t i o n a l l y , l i k e the SIT and PPVT, been s i n g l e d out as a c a n d i d a t e f o r WISC s u b s t i t u t e or a l t e r n a t e ( M a r t i n & W i e c h e r s , 1954; M e h r o t r a , 1968). D e s p i t e the f a c t t h a t some degree of r e l a t i o n s h p has been pr o p o s e d between the SPM and each of the t h r e e WISC-R s c a l e s , the s t r o n g e s t e v i d e n c e remains i n s u p p o r t of the SPM as a n o n v e r b a l measure. C e r t a i n l y i t e m c o n t e n t , r e s p o n s e f o r m a t , and a u t h o r ' s i n t e n t suggest t h i s . Thus 23 c o n s i d e r a t i o n of the SPM as p s y c h o l o g i c a l l y e q u i v a l e n t t o WISC-R P e r f o r m -ance i s propos e d . M i l l H i l l V o c a b u l a r y S c a l e (MHVS) The MHVS, O r a l D e f i n i t i o n s Form, c o n s i s t s o f two p a r a l l e l s e t s (A and B) of 44 words w h i c h a r e d e f i n e d o r a l l y by the examinee. T h i s t e s t was c o n s t r u c t e d by Raven f o r combined use w i t h the SPM " i n p l a c e of a s i n g l e t e s t o f ' g e n e r a l i n t e l l i g e n c e ' " (Raven, 1960, p. 3 ) , a r g u i n g t h a t : N o n - v e r b a l t e s t s a r e o f t e n m i s l e a d i n g l y d e s c r i b e d as t e s t s o f i n t e l -l i g e n c e when th e y sample o n l y c e r t a i n a s p e c t s of i n t e l l e c t u a l f u n c -t i o n i n g . The u n d e r l y i n g r e a s o n f o r the c r e a t i o n of v o c a b u l a r y s c a l e s t o be used t o g e t h e r w i t h RPM [Raven's P r o g r e s s i v e M a t r i c e s ] i s t h a t the v e r b a l and n o n - v e r b a l t e s t s a r e complementary. W h i l e RPM i s p r i m a r i l y a t e s t o f e d u c a t i o n , v o c a b u l a r y t e s t s r e p r e s e n t measures of r e p r o d u c t i o n , o r measures of a c q u i r e d i n f o r m a t i o n . (Raven, C o u r t , & Raven, 1976, p. G14) I n e f f e c t t h e n , Raven pr o p o s e d a dichotomous measurement i n s t r u m e n t h a v i n g • a v e r b a l and a n o n v e r b a l component. The o b v i o u s absence of r e f e r e n c e s t o the MHVS i n t e s t i n g t e x t s ( c f . A n a s t a s i , 1976; Cronbach, 1970; S a t t l e r , 1974) and i n the l i t e r a t u r e a t t e s t s t o the f a c t t h a t the s c a l e i s l i t t l e known and seldom used i n N o r t h A m e r i c a . C o n s e q u e n t l y , i t was i n t r o d u c e d i n the p r e s e n t s t u d y to e x p l o r e ' i t s v a l i d i t y as a v e r b a l measure of i n t e l l i g e n c e . Summary A summary of the c o n t e n t and f a c t o r i a l s t r u c t u r e s of the f i v e t e s t s i s p r e s e n t e d i n T a b l e 3. U s i n g the t h r e e WISC-R s c a l e s ( V e r b a l , P e r f o r m -ance, and F u l l S c a l e ) f o r r e f e r e n c e , t e s t s w h i c h a re p s y c h o l o g i c a l l y s i m i l a r t o t h e s e s c a l e s can be i d e n t i f i e d on the b a s i s of t h e i r c o n t e n t , a u t h o r ' s s t a t e m e n t of p u r p o s e , and/or the r e s u l t s from e m p i r i c a l v a l i d i t y s t u d i e s . These are i n d i c a t e d by the appearance of a C, A, or V r e s p e c t i v e l y i n T a b l e 4. The c o i n c i d e n c e of two or more of t h e s e 24 T a b l e 3 Content and S t r u c t u r e of the T e s t s Type of Measure V e r b a l N o n v e r b a l G e n e r a l WISC-R Y i e l d s V e r b a l IQ Y i e l d s Performance IQ Y i e l d s F u l l S c a l e IQ s c o r e — s u p p o r t e d s c o r e — s u p p o r t e d by s c o r e w h i c h combines by f a c t o r a n a l - f a c t o r a n a l y t i c V e r b a l and P e r f o r -y t i c s t u d i e s s t u d i e s mance. C o n s t i t u t e s a-measure o f g SIT V e r b a l f o r m a t . Item d i v e r s i t y sug-S i m i l a r t o S-B g e s t s a more g e n e r a l w h i c h has h i g h measure v e r b a l f a c t o r PPVT S t r i c t l y v e r b a l SPM Some s u g g e s t i o n O v e r t l y n o n v e r b a l . C o n s i d e r e d a measure of v e r b a l C o n s i d e r e d as such of g_ by some component s by Raven MHVS S t r i c t l y v e r b a l T a b l e 4 P s y c h o l o g i c a l l y and F u n c t i o n a l l y E q u i v a l e n t T e s t P a i r s as Suggested by t h e i r C ontent ( C ) , A u t h o r s ' C l a ims ( A ) , E m p i r i c a l V a l i d i t y ( V ) , and P r a c t i t i o n e r s ' Use (P) WISC-R V e r b a l P erformance F u l l S c a l e SIT PPVT SPM MHVS SPM & MHVS 25 s i m i l a r i t y f a c t o r s s u g g e s t s s t r o n g e v i d e n c e f o r the p s y c h o l o g i c a l e q u i v -a l e n c e of t e s t p a i r s . T h i s i s v i s u a l l y r e p r e s e n t e d by the s o l i d l i n e e n c l o s u r e s i n the body of the t a b l e . T e s t p a i r s h a v i n g weaker e v i d e n c e of p s y c h o l o g i c a l e q u i v a l e n c e a r e i l l u s t r a t e d w i t h a b r o k e n - l i n e e n c l o s u r e . F u n c t i o n a l l y e q u i v a l e n t t e s t p a i r s a r e a l s o r e p r e s e n t e d i n T a b l e 4 by the l e t t e r P. I t i s o b v i o u s from t h i s i l l u s t r a t i o n t h a t e v i d e n c e f o r the p s y c h o l o g i c a l e q u i v a l e n c e of the t e s t p a i r s c o n s i d e r e d i n t h i s s t u d y does not g e n e r a l l y s u b s t a n t i a t e the f u n c t i o n a l e q u i v a l e n c e w h i c h i s i m p l i e d i n t h e i r common use. The r e s e a r c h q u e s t i o n posed i n Ch a p t e r I c o n c e r n s the f u r t h e r s e a r c h o f e m p i r i c a l c o r r o b o r a t i o n o f the e q u i v a -l e n c e . I n the f o l l o w i n g s e c t i o n , t he c r i t e r i a f o r d e t e r m i n i n g t e c h n i c a l e q u i v a l e n c e and the methods f o r d e r i v i n g i n t e r - t e s t s c o r e c o n v e r s i o n s are p r e s e n t e d . I n t e r - T e s t Score C o n v e r s i o n s F o r p urposes o f c l a r i t y , t he d i s t i n c t i o n between e q u i v a l e n c e and c o m p a r a b i l i t y made i n Chapt e r I w i l l be m a i n t a i n e d t h r o u g h o u t t h i s d i s s e r -t a t i o n . However, s i n c e t h i s use of t e r m i n o l o g y i s not c o n s i s t e n t l y adhered t o i n the r e f e r e n c e s o u r c e s , a f u r t h e r note of c l a r i f i c a t i o n i s w a r r a n t e d . E q u a t i n g and comparing a r e r e f e r r e d t o as t y p e s of c o n v e r s i o n , where a c o n v e r s i o n i s an e m p i r i c a l t r a n s f o r m a t i o n o f the s c o r e s c a l e o f one t e s t so t h a t i t i s r e l a t e d t o t h e s c o r e s c a l e o f a n o t h e r t e s t i n some d e f i n e d manner. When t h i s t r a n s f o r m a t i o n y i e l d s an e q u i v a l e n c y r e l a t i o n -s h i p , the s c o r e v a l u e s on the two t e s t s have i d e n t i c a l meaning i n terms of the t r a i t b e i n g measured. Thus, e q u a l s c o r e v a l u e s r e p r e s e n t a q u a n t i -f i c a t i o n o f the same amount of the same t r a i t i r r e s p e c t i v e of the t e s t used. When a comparable r e l a t i o n s h i p i s e s t a b l i s h e d between two t e s t s , the same n u m e r i c a l s c o r e v a l u e s r e p r e s e n t the.same rank p o s i t i o n w i t h i n 26 a s p e c i f i e d group. T h i s i s a s c a l e r e l a t i o n s h i p o n l y and c a r r i e s no c o n n o t a t i o n r e g a r d i n g the e q u a l i t y of p o s s e s s i o n of the amount of the t r a i t o r t r a i t s b e i n g measured. A c l e a r example of the d i f f e r e n c e between the two, and one w h i c h e x i s t s w i t h i n the c o n t e x t o f t h i s s t u d y i s as f o l l o w s . The PPVT has two p a r a l l e l f orms: Form A and Form B. As such, i t does not m a t t e r w h i c h form i s used s i n c e t h e y y i e l d e q u i v a l e n t measures of v e r b a l i n t e l l i g e n c e t h rough r e c e p t i v e v o c a b u l a r y . An i n d i v i d u a l would be e x p e c t e d t o s c o r e s i m i l a r l y on b o t h t e s t forms. The WISC-R s u b t e s t s , on the o t h e r hand, a r e comparable t e s t s . Each s u b t e s t has uniq u e c o n t e n t and i s s c a l e d from 1-19 w i t h mean 10 and s t a n d a r d d e v i a t i o n 3. Thus a s c a l e d s c o r e of 12 has a c o n s t a n t meaning i n terms of rank a c r o s s a l l s u b t e s t s ( t h a t i s , a p e r c e n t i l e rank of 7 5 ) . However, an i n d i v i d u a l ' s s c o r e o f 11 on a g i v e n s u b t e s t cannot be c o n s i d e r e d p r e d i c t i v e of h e r s c o r e on any o t h e r s u b t e s t . C o m p a r a b i l i t y can be seen as the g e n e r i c r e l a t i o n s h i p , w h i c h a c c o u n t s f o r much of the i n t e r m i n g l i n g o f the terms i n the l i t e r a t u r e . A common d e f i n i t i o n of c o m p a r a b i l i t y i s t h a t the d i s t r i b u t i o n s of s c o r e s on two t e s t s have been made i d e n t i c a l f o r a g i v e n group ( A n g o f f , 1971; L o r d , 1950; F l a n a g a n , 1951). T h i s a p p l i e s t o e q u i v a l e n t as w e l l as t o compar-a b l e t e s t s ( a l t h o u g h , as w i l l be d i s c u s s e d i n the next s e c t i o n , t he r e s t r i c t e d r e f e r e n c e group n o t i o n i s not n e c e s s a r y f o r e q u i v a l e n t f o r m s ) . Thus e q u i v a l e n t s c o r e s share the c h a r a c t e r i s t i c s of comparable s c o r e s . E q u i v a l e n c e , however, i s a s p e c i f i c case of c o m p a r a b i l i t y w h i c h i s l i m i t e d by the a d d i t i o n a l r e q u i r e m e n t o f p a r a l l e l i s m o f the two t e s t s . 27 E q u a t i n g P a r a l l e l Forms A n g o f f (1971) emphasizes t h a t s t r i c t adherence t o the concept o f e q u a t i n g i m p l i e s two r e s t r i c t i o n s . The f i r s t of t h e s e i s t h a t t h e two i n s t r u m e n t s i n q u e s t i o n be measures of the same c h a r a c t e r i s t i c ( p . 5 6 3 ) ; t h a t i s , t h e y a r e p a r a l l e l forms of the same t e s t . The second i s a c t u a l l y a c o r o l l a r y of the f i r s t and r e q u i r e s t h a t " t h e t r a n s f o r m a t i o n be i n d e p e n -dent o f the groups of i n d i v i d u a l s used t o d e v e l o p the c o n v e r s i o n " ( p . 563). Thus e q u a t i n g a p p l i e s t o p a r a l l e l t e s t forms and y i e l d s u n i q u e s c o r e t r a n s f o r m a t i o n s w h i c h a r e s u b s e q u e n t l y g e n e r a l i z a b l e t o any and a l l groups w i t h w h i c h the t e s t s may be used. The most r i g o r o u s d e f i n i t i o n of p a r a l l e l i s m comes from c l a s s i c a l t e s t t h e o r y : D i s t i n c t measurements X and X , a r e c a l l e d p a r a l l e l measurements g a g'a £  i f , f o r e v e r y s u b i e c t aeP, x = T , , and a(E ) = a(E , ). ga g'a ga g'a ( L o r d & N o v i c k , 1968, p. 48) T h i s d e f i n i t i o n s t a t e s t h a t measurement X f o r p e r s o n a on t e s t g_ and measurement X f o r p e r s o n a on t e s t g' are p a r a l l e l , i f f o r e v e r y member a of the p o p u l a t i o n (p, the t r u e s c o r e on g, T , e q u a l s the t r u e s c o r e — — ga on £' , x t^, and the s t a n d a r d e r r o r of measurement on j> e q u a l s the s t a n d a r d e r r o r of measurement on g'. L o r d and N o v i c k add: Thus p a r a l l e l measurements measure e x a c t l y the same t h i n g i n the same s c a l e and, i n a sense, measure i t e q u a l l y w e l l f o r a l l p e r s o n s . (p. 48) G u l l i k s e n (1950) p r o v i d e d a s e m a n t i c d e f i n i t i o n f o r p a r a l l e l i s m : from a common sense p o i n t o f v i e w , i t may be s a i d t h a t two t e s t s are " p a r a l l e l " when " i t makes no d i f f e r e n c e w h i c h t e s t you u s e . " I t i s c e r t a i n l y c l e a r t h a t , i f f o r some r e a s o n one t e s t i s b e t t e r t h a n the o t h e r f o r c e r t a i n p u r p o s e s , i t does make a d i f f e r e n c e w h i c h t e s t i s used, and the t e s t s c o u l d not be termed p a r a l l e l , ( p . I D 28 More s p e c i f i c a l l y , he o u t l i n e s two t y p e s o f c r i t e r i a f o r p a r a l l e l t e s t s . One of t h e s e he terms s t a t i s t i c a l and summarizes as f o l l o w s : " I n a d d i t i o n t o e q u a l means, v a r i a n c e s , and r e l i a b i l i t i e s , p a r a l l e l t e s t s s h o u l d have a p p r o x i m a t e l y e q u a l v a l i d i t i e s f o r any g i v e n c r i t e r i o n " ( p . 173). The o t h e r he r e f e r s t o as the p s y c h o l o g i c a l c r i t e r i o n . T h i s r e q u i r e s t h a t " t h e t e s t s s h o u l d c o n t a i n i t e m s d e a l i n g w i t h the same s u b j e c t m a t t e r , i t e m s of the same f o r m a t , e t c . I n o t h e r words, the t e s t s s h o u l d be p a r -a l l e l as f a r as p s y c h o l o g i c a l judgment i s c o n c e r n e d " (pp. 173-174). N o m i n a l l y P a r a l l e l T e s t s Marco, P e t e r s e n , and S t e w a r t (1979) q u a l i f y the s t r i c t p s y c h o m e t r i c r e q u i r e m e n t s f o r e q u a t i n g as " i d e a l . " They suggest t h a t t h e s e may be u n r e a l i s t i c i n a c t u a l t e s t i n g p r a c t i c e and t h a t " s c o r e s must sometimes be equated under l e s s - t h a n - q p t i m u m c o n d i t i o n s " ( p . 1 ) . A common adap-t a t i o n of p a r a l l e l - f o r m s t e s t e q u a t i n g i s w i t h t e s t s w h i c h , a l t h o u g h t h e y were not s p e c i f i c a l l y c o n s t r u c t e d as p a r a l l e l , a r e used f o r t h e same p u r -pose. I n such s i t u a t i o n s t he c r i t e r i a f o r p a r a l l e l i s m a r e r e l a x e d t o some e x t e n t . Wesman (1958) s a y s : A s s u m p t i o n s we can make w i t h r e g a r d t o c o n t e n t and r e l i a b i l i t y o f p a r a l l e l forms of one t e s t a r e not r e a d i l y a c c e p t a b l e when we a r e d e a l i n g w i t h two somewhat d i f f e r e n t t e s t s of the same g e n e r a l a b i l i t y . T h i s s i t u a t i o n i s one i n w h i c h the problem of e q u i v a l -ence f r e q u e n t l y a r i s e s . ( p . 8) He s u g g e s t s t h a t i n d e t e r m i n i n g the degree of e q u i v a l e n c e of s c o r e s i n t h e s e c i r c u m s t a n c e s , the s i z e of the c o r r e l a t i o n c o e f f i c i e n t i s of prime i m p o r t a n c e . The Anchor Te s t Study r e p r e s e n t s t h i s type o f a p p l i c a t i o n of e q u a t i n g methodology. A c c o r d i n g t o J a e g e r ( 1 9 7 3 ) , "The major q u e s t i o n t o be e x p l o r e d was the t e c h n i c a l f e a s i b i l i t y of e q u a t i n g t e s t s t h a t were not d e s i g n e d to be p a r a l l e l " ( p . 3 ) . I n t h a t s t u d y , the p s y c h o l o g i c a l c r i t e r i a were e v a l u a t e d by a p a n e l of e x p e r t s . They judged the t e s t s t o r e q u i r e many of the same s k i l l s and a b i l i t i e s but w i t h l e s s t h a n p e r f e c t o v e r l a p ( J a e g e r 1973). The s t a t i s t i c a l c r i t e r i o n was i n t e r p r e t e d s o l e l y i n terms o f i n t e r - t e s t c o r r e l a t i o n c o e f f i c i e n t s . When c o r r e c t e d f o r a t t e n u a t i o n , t h e y were found t o be u n i f o r m l y h i g h . "Of the 207 c o r r e c t e d i n t e r c o r r e -l a t i o n s o b t a i n e d i n the Anchor T e s t Study d a t a . . . only'.20 might be c o n s i d e r e d s i g n i f i c a n t l y below .95; and 20 were above .89" ( L o r e t e t a l . , 1974, p. 8 ) . L o r d and N o v i c k ' s (1968) n o t i o n of n o m i n a l l y p a r a l l e l t e s t s f o r m a l -i z e s t he r e l a x a t i o n o f the s t a t i s t i c a l r e s t r i c t i o n s imposed on s t r i c t l y p a r a l l e l t e s t s . They suggest t h a t t he term "does not i m p l y any mathe-m a t i c a l l y d e f i n e d degree of p a r a l l e l i s m i n any p a r t i c u l a r r e s p e c t " ( p . 174). N o m i n a l l y p a r a l l e l t e s t s a r e , r a t h e r , d e f i n e d i n terms o f f u n c -t i o n a l and p s y c h o l o g i c a l c r i t e r i a . They a r e c o n s i d e r e d a " f a m i l y " o f d i f f e r e n t measurements, each of w h i c h measures " i m p o r t a n t a s p e c t s o r mani-f e s t a t i o n s of the p s y c h o l o g i c a l v a r i a b l e under s t u d y " ( p . 174). I n an e a r l i e r p a p er, L o r d (1964) d e f i n e d as n o m i n a l l y p a r a l l e l "any s e t of t e s t forms t h a t a r e used i n t e r c h a n g e a b l y i n common p r a c t i c e , even though t h e y a r e not s t r i c t l y p a r a l l e l s t a t i s t i c a l l y " (p. 335). A p e r s o n ' s t r u e s c o r e i s t h e n d e f i n e d as the e x p e c t a t i o n of o b s e r v e d s c o r e s , o r of a w e i g h t e d e x p e c t a t i o n o f o b s e r v e d s c o r e s , .taken over a l l n o m i n a l l y p a r a l l e l t e s t s . L o r d and N o v i c k p r e s e n t t h i s as the g e n e r i c t r u e s c o r e s y m b o l i z e d by C and e x p r e s s e d a s : C = E E. Y ( p . 174) a g k gak 30 where a i s an examinee, g i s a g i v e n t e s t , and k i n d i c a t e s r e p e a t e d measurements f o r p e r s o n . a a c r o s s the p o p u l a t i o n of t e s t s n o m i n a l l y p a r a l l e l t o g Thus the g e n e r i c t r u e s c o r e " r e p r e s e n t s the s t a n d i n g of the examinee w i t h r e s p e c t t o the average of the t r a i t s measured by a l l the G t e s t f o r m s " ( L o r d & N o v i c k , 1968, p. 164). G e n e r i c t r u e - s c o r e t h e o r y d i f f e r s from c l a s s i c a l t h e o r y i n t h a t t h e r e a r e no a s s u m p t i o n s imposed c o n c e r n i n g the u n b i a s e d n e s s or n o n - c o r r e l a -t i o n of e r r o r s of measurement. L o r d and N o v i c k c l a i m t h a t w h i l e t h i s c o m p l i c a t e s g e n e r i c t r u e - s c o r e t h e o r y , i t a l s o makes i t " a p p l i c a b l e i n s i t u a t i o n s t h a t have t r o u b l e d p s y c h o m e t r i c i a n s " (p. 1 8 4 ) — s i t u a t i o n s i n w h i c h th o s e a s s u m p t i o n s a r e known t o be v i o l a t e d . Marks and L i n d s a y ( 1 9 7 2 ) , i n an e m p i r i c a l e x a m i n a t i o n of t e s t e q u a t i n g under l e s s - t h a n - o p t i m u m c o n d i t i o n s e n dorsed the n o t i o n ' of n o m i n a l l y p a r a l l e l t e s t forms as " q u i t e o b v i o u s l y the one most f r e q u e n t l y encoun-t e r e d i n t e s t i n g p r a c t i c e " ( p . 46).' They n o t e , however, t h a t the p r i c e of a t t e m p t i n g t o implement ' s t a t i s t i c a l r e l a x a t i o n s ' i s the absence of d e f i n i t i v e g u i d e l i n e s r e g a r d i n g how much l a t i t u d e can be t o l e r a t e d w i t h i n the e q u a t i n g model. As a r e s u l t , t e s t e q u a t o r s are f o r c e d t o r e l y on a d m i t t e d l y a r b i t r a r y " c h o i c e s based on i n d i v i d u a l judgment. Marks and L i n d s a y (1972) a t t e m p t e d t o c l a r i f y t h i s p r o b l e m by e x p l o r -i n g the e f f e c t s of f o u r p a r a m e t e r s — s a m p l e s i z e , t e s t l e n g t h , t e s t r e l i a b i l -i t y , and i n t e r t e s t c o r r e l a t i o n — o n the a c c u r a c y of t e s t e q u a t i n g . U s i n g a Monte C a r l o p r o c e d u r e , they p r oduced s i m u l a t e d s c o r e d i s t r i b u t i o n s f o r s p e c i f i e d v a l u e s of the f o u r p a r a m e t e r s . Then, u s i n g a r e g r e s s i o n 31 approach, they compared the r e l a t i v e s i z e s of the e r r o r s of e s t i m a t e a s s o c -i a t e d w i t h e s t i m a t i n g the t r u e s c o r e d i s t r i b u t i o n s of one t e s t form from the o b s e r v e d s c o r e d i s t r i b u t i o n s of the o t h e r t e s t form. ( I t w i l l be n o t e d i n the n e x t s e c t i o n t h a t the r e g r e s s i o n method i s a n o n - s t a n d a r d approach t o e q u a t i n g . Marks and L i n d s a y p o i n t o u t , however, t h a t the use of i d e n t i c a l l y - d i s t r i b u t e d p o p u l a t i o n d e n s i t i e s i n t h e i r s t u d y w o u l d y i e l d r e s u l t s q u i t e s i m i l a r t o o t h e r l i n e a r and c u r v i l i n e a r e q u a t i n g methods.) The r e s u l t s of the s t u d y i n d i c a t e d t h a t the most i m p o r t a n t f a c t o r s were sample s i z e and the e s t i m a t e d a s s o c i a t i o n between t r u e s c o r e d i s t r i -b u t i o n s . E x a m i n a t i o n of the i n t e r a c t i o n between t r u e s c o r e c o r r e l a t i o n s of .80, .90, and 1.0 and sample s i z e s of 100, 250, and 500 s u g g e s t e d t h a t w i t h l a r g e r sample s i z e s (n > 500) i n c r e a s i n g t e s t form d i s s i m i l a r i t y had r e l a t i v e l y l i t t l e e f f e c t . G r a p h i c r e p r e s e n t a t i o n of the i n t e r a c t i o n of t h e s e v a r i a b l e s i n d i c a t e d s h a r p l y i n c r e a s i n g e r r o r w i t h lower c o r r e l a -t i o n s . The a u t h o r s c o n c l u d e : I n p r a c t i c e and where the i n v e s t i g a t o r f e e l s u n c o m f o r t a b l e about the s i m i l a r i t y o f two or more t e s t forms i n terms of the d i m e n s i o n s measured or t h e i r l e n g t h , v e r y l a r g e samples of o b s e r v a t i o n s a r e i n d i c a t e d . C o n v e r s e l y , s m a l l sample s i z e s , say 250 o b s e r v a t i o n s or l e s s , s h o u l d be d i s c o u r a g e d under a n o m i n a l l y p a r a l l e l d e f i n i t i o n of t e s t e q u a t i n g . (Marks & L i n d s a y , 1972, p. 55) E q u a t i n g Methods F l a n a g a n (1951) p r e s e n t e d an h i s t o r i c a l r e v i e w of t e s t e q u a t i n g t e c h n o l o g y . One of the e a r l i e s t p r o c e d u r e s was t o c a l c u l a t e the means f o r the raw s c o r e d i s t r i b u t i o n s on two t e s t s . Any g i v e n s c o r e on one t e s t was t h e n " e q u a t e d " t o the c o r r e s p o n d i n g s c o r e on the o t h e r t e s t by a d d i n g or s u b t r a c t i n g a c o n s t a n t e q u a l t o the d i f f e r e n c e between the means. F l a n a g a n (p. 751) p o i n t s out the s h o r t c o m i n g s of t h i s approach s i n c e i t 32 assumes u n i f o r m i t y o f the d i f f e r e n c e between the s c o r e d i s t r i b u t i o n s beyond the f i r s t moment. A second method i n v o l v e d the use of r e g r e s s i o n p r o c e d u r e s t o compute the " b e s t e s t i m a t e " of a s c o r e on one t e s t form g i v e n the s c o r e on t h e second t e s t form. T h o r n d i k e (1922) s u g g e s t s , however, t h a t t h i s method i s s a t i s f a c t o r y as an e q u a t i n g approach o n l y when the two t e s t s a r e p e r f e c t l y p a r a l l e l and p e r f e c t l y r e l i a b l e , so t h a t t h e r e i s , i n e f f e c t , no r e g r e s s i o n . When t e s t s c o r r e l a t e i m p e r f e c t l y , the r e s u l t i n g r e g r e s s i o n l i n e w i l l not be unique f o r a l l g r o u p s , nor w i l l i t p r o v i d e i n v e r t i b l e s c o r e c o n v e r s i o n s . The former p r o b l e m v i o l a t e s t he r e q u i r e m e n t f o r u n i q u e n e s s ( A n g o f f , 1971, p. 563). The second v i o l a t e s a l o g i c a l c o n c e p t i o n of the e q u i v a l e n c y r e l a t i o n s h i p , namely t h a t the c o n v e r s i o n i s f i x e d and t h a t the r e s u l t i n g t a b l e of e q u i v a l e n t s c o r e v a l u e s can be r e a d i n e i t h e r d i r e c t i o n ( c f . Marco e t a l . , 1979). Both t h e l i n e a r and e q u i p e r c e n t i l e methods bear the " t r i e d and t r u e " stamp of decades of r e p r e s e n t a t i o n i n e q u a t i n g l i t e r a t u r e ( J a e g e r , 1980). As s t a t e d i n Chap t e r I , t h e s e were the two methods a p p l i e d i n the p r e s e n t s t u d y . The e q u i p e r c e n t i l e method d e r i v e s from a b a s i c d e f i n i t i o n of the e q u i v a l e n c y r e l a t i o n s h i p i n i t i a l l y s u g g e s t e d by L o r d (1950) and F l a n -agan (1951) and d e f i n e d by A n g o f f (1971) as f o l l o w s : Two s c o r e s , one on Form X and the o t h e r on Form Y (where X and Y measure the same f u n c t i o n w i t h the same degree of r e l i a b i l i t y ) , may be c o n s i d e r e d e q u i v a l e n t i f t h e i r c o r r e s p o n d i n g p e r c e n t i l e r a n k s i n any g i v e n group a r e e q u a l . ( p . 563) t h Thus f o r two c u m u l a t i v e p e r c e n t a g e d i s t r i b u t i o n s , P and P the j s c o r e A Y t h v a l u e on t e s t Y (Y.) i s e q u i v a l e n t t o the k s c o r e v a l u e on t e s t X (X, ) J k when P = P . T r a d i t i o n a l l y , t h i s has been a c c o m p l i s h e d u s i n g a hand-i . X J k g r a p h i n g t e c h n i q u e ( A n g o f f , 1971; F l a n a g a n , 1951). T h i s r e q u i r e s f i r s t , 33 the c o m p u t a t i o n of p e r c e n t i l e r a n k s f o r the raw s c o r e d i s t r i b u t i o n s on each t e s t . These a r e t h e n p l o t t e d and smoothed on a r i t h m e t i c p r o b a b i l i t y p aper. Next, f o r b o t h t e s t s , raw s c o r e s c o r r e s p o n d i n g t o s e l e c t e d p e r c e n -t i l e s a r e r e a d from the smoothed o g i v e s and p l o t t e d a g a i n s t each o t h e r on a r i t h m e t i c graph paper. F i n a l l y , a smoothed l i n e i s drawn c o n n e c t i n g t h e s e p o i n t s and i s extended t o c o v e r the f u l l range of p o s s i b l e t e s t s c o r e s . T h i s f i n a l c u r v e r e c o r d s the c o n v e r s i o n of s c o r e s from t e s t X t o t e s t Y. Problems a s s o c i a t e d w i t h t h i s p r o c e d u r e a r e t h a t i t i s t e d i o u s , n o n - a n a l y t i c a l , and v u l n e r a b l e t o e r r o r s i n hand-smoothing, p a r t i c u l a r l y i n the extremes of the s c o r e ranges where d a t a are s c a n t and/or e r r a t i c . I n an attempt t o a d d r e s s t h e s e d i f f i c u l t i e s and t o p r o v i d e an a n a l y t i c and v e r i f i a b l e approach t o e q u i p e r c e n t i l e e q u a t i n g , L i n d s a y and P r i c h a r d (1971) d e v e l o p e d a computer program w h i c h b o t h s i m u l a t e d the manual p r o c e -dure and p r o v i d e d f u n c t i o n a l e q u a t i o n s f o r p r e d i c t i n g e q uated s c o r e s on one t e s t from the o t h e r . From the d e f i n i t i o n on the p r e v i o u s page, i t can be seen t h a t e q u i -p e r c e n t i l e e q u a t i n g i n v o l v e s the d e t e r m i n a t i o n of p a i r s of raw s c o r e s t h a t c u t o f f e q u a l p r o p o r t i o n s of the two d i s t r i b u t i o n s . T h i s r e q u i r e s the e s t i m a t i o n of " m i s s i n g " raw s c o r e p o i n t s i n one d i s t r i b u t i o n t o c o r r e s -pond to e v e r y c u m u l a t i v e p e r c e n t a g e p o i n t i n the o t h e r d i s t r i b u t i o n and v i c e v e r s a . L i n d s a y and P r i c h a r d assumed t h a t " t h e b e s t e s t i m a t e of a ' m i s s i n g ' s c o r e p o i n t on one d i s t r i b u t i o n l i e s on a s t r a i g h t l i n e c o n -n e c t i n g two a d j a c e n t CPs [ c u m u l a t i v e p e r c e n t a g e s ] and t h e i r a s s o c i a t e d s c o r e p o i n t s " (p. 204). T h e i r p r o c e d u r e was d e r i v e d as f o l l o w s : F o r the t e s t s c o r e d i s t r i b u t i o n s X and Y, the raw s c o r e s X. and Y and t h e i r a s s o c i a t e d c u m u l a t i v e p e r c e n t a g e s P. and P can be 34 r e p r e s e n t e d as o r d e r e d p a i r s (X.,P.) and (Y ,P ). G i v e n t h a t an e q u i v a -l e n c y r e l a t i o n s h i p between and Y^ r e q u i r e s P^ = P , the e s t i m a t i o n p roblem i s t o f i n d the X a s s o c i a t e d w i t h the P on d i s t r i b u t i o n Y when n n P^ does not c o r r e s p o n d t o any X^. Then, from the assumed l i n e a r r e l a -t i o n s h i p , X n - xx' P n - PT |x2 - xj L P 2 - P J ( L i n d s a y & P r i c h a r d , 1971, p. 204) where ( X ^ P ^ and ( X 2 , P 2 ) are from d i s t r i b u t i o n X, and P^ 4 P i , P 2 . The method, w i t h a p p r o p r i a t e s u b s t i t u t i o n , i s s i m i l a r l y used t o s o l v e f o r Y . n T h i s s t e p of the computer program produces two d i s t r i b u t i o n s h a v i n g an e q u a l number of raw s c o r e p o i n t s and an i d e n t i c a l s e t of c u m u l a t i v e p e r c e n t a g e v a l u e s i n each. T h i s c o r r e s p o n d s t o the p r o d u c t i o n o f the f i r s t graph d e s c r i b e d i n the manual p r o c e d u r e . The next s t e p i n v o l v e s the g e n e r a t i o n of l i n e a r or p o l y n o m i a l r e g r e s s i o n e q u a t i o n s f o r f i t t i n g t he two d i s t r i b u t i o n s , and c o r r e s p o n d s t o the second graph i n the manual p r o c e d u r e . The p a r t i c u l a r advantages of the second s t e p a r e t h a t i t f a c i l i t a t e s a c c u r a t e e x t r a p o l a t i o n beyond the o b t a i n e d d a t a p o i n t s . The e q u i p e r c e n t i l e e q u a t i n g method can be a p p l i e d t o any p a i r o f p a r a l l e l measures. When the raw s c o r e d i s t r i b u t i o n s a r e d i s s i m i l a r , the 'procedure a d j u s t s the shape of the d i s t r i b u t i o n o f s c o r e s on one t e s t form t o c o r r e s p o n d t o t h a t of the o t h e r t e s t form. T h i s p r o v i d e s a c u r -v i l i n e a r t r a n s f o r m a t i o n o f s c o r e s w h i c h s e r v e s t o compensate f o r u n i n t e n -t i o n a l v a r i a t i o n s i n d i f f i c u l t y l e v e l between two t e s t s and y i e l d s , as 35 the d e f i n i t i o n of e q u i v a l e n c y s t a t e s , the same c o n v e r t e d s c o r e r e g a r d l e s s of the t e s t form t a k e n . I f the two raw s c o r e d i s t r i b u t i o n s a r e of the same shape, d i f f e r i n g i n none of t h e i r moments beyond the second, the same r e s u l t s can be a c h i e v e d by a l i n e a r t r a n s f o r m a t i o n w h i c h a d j u s t s o n l y t h e o r i g i n and t h e u n i t of measurement. The d e f i n i t i o n f o r l i n e a r e q u a t i n g s t a t e s t h a t : s c o r e s on two t e s t s a r e e q u i v a l e n t i f th e y c o r r e s p o n d s t o e q u a l s t a n d a r d - s c o r e d e v i a t e s , Y - M y X - M x where Sv ~ S v ( A n g o f f , 1971, p. 564) Y A M and M are the means and S and S the s t a n d a r d Y X Y A d e v i a t i o n s f o r t e s t forms X and Y. The terms can be r e a r r a n g e d so t h a t the e q u a t i o n t a k e s the f a m i l i a r l i n e a r t r a n s f o r m a t i o n form, Y = aX + b, where a = S /S and b = M - aM . I n I A Y A the p r e s e n t s t u d y , L o r d ' s (1950) n o t a t i o n was adopted. The l i n e a r e q u a t i o n i s shown a s : S X - S X -Y " = Y + X " Y - ( L o r d , 1950, p. 5) where Y" r e p r e s e n t s the Y s c o r e c o n v e r t e d t o the s c a l e of X, and the means f o r t e s t forms X and Y are r e p r e s e n t e d by X. and Y. r e s p e c t i v e l y . J a e g e r (1980) p o i n t e d out t h a t w i t h i m p e r f e c t l y p a r a l l e l t e s t s , the l i n e a r and e q u i p e r c e n t i l e methods w i l l produce d i f f e r e n t r e s u l t s and t h a t t h e s e d i f f e r e n c e s w i l l be most n o t i c e a b l e i n the t a i l s o f the s c o r e d i s t r i b u t i o n s . T h i s e f f e c t was r e p o r t e d f o r the Anchor Te s t Study. The moments ( t h e mean, v a r i a n c e , skewness, and k u r t o s i s ) o f the s c o r e d i s t r i b u t i o n s f o r t h e [ e i g h t ] t e s t s d i f f e r e d s u b s t a n t i a l l y . Thus, a l i n e a r t r a n s f o r m a t i o n based o n l y on the mean and v a r i a n c e of each d i s t r i b u t i o n was g e n e r a l l y i n a d e q u a t e , o f t e n y i e l d i n g e q u i v a l e n t s c o r e s w h i c h f e l l o u t s i d e t h e c o r r e s p o n d i n g raw s c o r e range o f the t e s t s . ( B i a n c h i n i & L o r e t , 1974, pp. 187-188) 36 Based on the i m p l a u s i b i l i t y of some of the l i n e a r e q u a t i n g r e s u l t s , t h i s method was r e j e c t e d i n f a v o r of the c u r v i l i n e a r a l t e r n a t i v e . The Anchor Te s t Study was a d m i t t e d l y a p i o n e e r i n g and e x p l o r a t o r y endeavor w i t h r e g a r d t o b o t h e q u a t i n g i m p e r f e c t l y p a r a l l e l t e s t s and com-p a r i n g l i n e a r and e q u i p e r c e n t i l e methods. As mentioned i n the p r e c e d i n g p a r a g r a p h , the r e s u l t s of t h a t c o m p a r i s o n were e v a l u a t e d on a l o g i c a l r a t h e r t h a n an e m p i r i c a l b a s i s . I n an e f f o r t t o p r o v i d e more s t r i n g e n t t o o l s f o r such c o m p a r i s o n s , J a e g e r (1980) e x p l o r e d a number of s t a t i s t i c a l i n d i c e s f o r j u d g i n g the adequacy of l i n e a r i t y f o r t e s t s h a v i n g somewhat n o n - i d e n t i c a l s c o r e d i s t r i b u t i o n s . He s u g g e s t e d t h a t the-crux of the p r a c t i c a l p r o b l e m was t h a t m e t h o d o l o g i s t s f a i l t o p r o v i d e s p e c i f i c g u i d e -l i n e s f o r d i s c r i m i n a t i n g "between s i t u a t i o n s where the l i n e a r e q u a t i n g method a d e q u a t e l y a d j u s t s f o r d i f f e r e n c e s between the s c o r e d i s t r i b u t i o n s o f two a p p r o x i m a t e l y p a r a l l e l t e s t forms, and s i t u a t i o n s where a more complex model i s needed" (p. 4 ) . The two major f i n d i n g s of h i s s t u d y were (1) t h a t a l i n e a r r e l a t i o n s h i p between t e s t s can b e s t be e n s u r e d i n the d e v e l o p m e n t a l s t a g e by b a l a n c i n g the i t e m d i f f i c u l t y d i s t r i b u t i o n s between t e s t s ( t h i s i s , by making the t e s t s as c l o s e l y p a r a l l e l as p o s s i b l e ) , and (2) t h a t t h e r e a r e , as w e l l , s t a t i s t i c a l means f o r d e t e r m i n i n g w h i c h method s h o u l d be used w i t h e x i s t i n g t e s t s . The f i r s t o f J a e g e r ' s i n d i c e s examines the s i m i l a r i t y o f the cumu-l a t i v e s c o r e d i s t r i b u t i o n s f o r t h e two t e s t s a f t e r one has been l i n e a r -e quated t o the o t h e r . I f t h e y a r e s i g n i f i c a n t l y d i f f e r e n t on the Kolmogorov-Smirnov two-sample t e s t , the need f o r e q u i p e r c e n t i l e e q u a t i n g i s i n d i c a t e d . A second approach c h e c k s f o r l i n e a r i t y of the r e s u l t s o f the e q u i p e r c e n t i l e method u s i n g l i n e a r and second- and t h i r d - o r d e r 2 p o l y n o m i a l r e g r e s s i o n a n a l y s e s and e x a m i n i n g the i n c r e m e n t s i n R . When R 2 f a i l s t o i n c r e a s e s i g n i f i c a n t l y i n the h i g h e r o r d e r a n a l y s e s , a l i n e a r r e l a t i o n s h i p i s a c c e p t e d . The f i n a l approach i n v o l v e s a d i r e c t c o m p a r i s o n of r e s u l t s a f t e r b o t h methods have been used. J a e g e r c r e a t e d a d i f f e r e n c e s c o r e ( e q u i p e r c e n t i l e equated s c o r e minus l i n e a r equated s c o r e ) f o r each raw s c o r e v a l u e on the c o n v e r t e d t e s t . He the n assumed t h a t i f t h e raw s c o r e d i s t r i b u t i o n s were s i m i l a r enough f o r the r e l a t i o n -s h i p t o be l i n e a r , t h e s e d i f f e r e n c e "scores " s h o u l d not be s y s t e m a t i c a l l y p r e d i c t a b l e from any f u n c t i o n of c o r r e s p o n d i n g raw s c o r e s " ( p . 14). He a g a i n used r e g r e s s i o n a n a l y s e s t o check t h i s a s s u m p t i o n . U n e q u a l l y R e l i a b l e T e s t s A l t h o u g h i t was not emphasized i n the p r e c e d i n g d i s c u s s i o n , d e f i n i -t i o n s of c o n v e r s i o n r e l a t i o n s h i p s i m p l y t r u e s c o r e components ( F l a n a g a n , 1951; L o r d , 1950). When t e s t s a r e e q u a l l y r e l i a b l e , o b s e r v e d s c o r e s can be used s i n c e the r e l a t i o n s h i p between t r u e and o b s e r v e d s c o r e s w i l l be a p p r o x i m a t e l y the same f o r b o t h forms. W i t h u n e q u a l l y r e l i a b l e t e s t s , however, t h e e r r o r components of the two t e s t s a r e d i f f e r e n t , r e s u l t i n g i n an u n s t a b l e r e l a t i o n s h i p between o b s e r v e d s c o r e s . I n t h i s c a s e , con-v e r s i o n s must be based on t r u e r a t h e r t h a n o b s e r v e d s c o r e s ( A n g o f f , 1971; F l a n a g a n , 1951, 1964; L o r d , 1950). A n g o f f (1971) p r o v i d e d a - l i h e a r c o n v e r s i o n e q u a t i o n f o r u n e q u a l l y r e l i a b l e t e s t s w h i c h i s s i m i l a r t o t h a t f o r l i n e a r e q u a t i n g , w i t h the e x c e p t i o n t h a t the v a r i a n c e components a r e d e r i v e d from e s t i m a t e d d i s t r i -b u t i o n s o f t r u e s c o r e s . The m a t h e m a t i c a l r e l a t i o n s h i p i s r e p r e s e n t e d by Y - M. X X - M. X ( A n g o f f , 1971, p. 571) 3'8 where M^ and M x are the means, S Y and the s t a n d a r d d e v i a t i o n s , and r ^ Y and r x x the r e l i a b i l i t i e s f o r t e s t s X and Y. U s i n g L o r d ' s (1950) n o t a t i o n a g a i n , t h e c o m p u t a t i o n a l f o r m u l a becomes V r Y Y V ' Y Y where the terms are d e f i n e d as t h e y were i n the l i n e a r e q u a t i n g f o r m u l a . The i n c l u s i o n of a d i s c u s s i o n of u n e q u a l l y r e l i a b l e t e s t s under t h e g e n e r a l h e a d i n g of " e q u a t i n g " i s somewhat m i s l e a d i n g and r e q u i r e s some q u a l i f i c a t i o n . I n t h e i r d i s c u s s i o n of n o m i n a l l y p a r a l l e l t e s t s , L o r d and N o v i c k (1968) p o i n t out the u n f a i r n e s s t o some examinees of the ' ' e q u i v a l e n t ' use of t e s t s h a v i n g - u n e q u a l r e l i a b i l i t i e s . When t h i s o c c u r s , a good examinee i s put a t a d i s a d v a n t a g e s i n c e i t i s e a s i e r f o r h e r t o o b t a i n a h i g h e r s c o r e on a r e l i a b l e t h a n an u n r e l i a b l e t e s t . T h i s s i t u a -t i o n can be seen t o v i o l a t e a b a s i c premise of e q u i v a l e n c y , namely, t h a t i t i s a m a t t e r of i n d i f f e r e n c e t o each examinee w h i c h t e s t she t a k e s ( c f . G u l l i k s e n , 1950; L o r d , 1977; Marco e t a l . , 1979; Wesman, 1958). S i n c e u n e q u a l l y r e l i a b l e t e s t s cannot be c o n s i d e r e d i n t e r c h a n g e a b l e , t h e y cannot t h e r e f o r e be equated i n any m e a n i n g f u l way ( A n g o f f , 1971; L o r d & N o v i c k , 1968). A n g o f f ( 1 9 7 1 ) , however, i n h i s compendium of e q u a t i n g methods and d e s i g n s , chose t o i n c l u d e the l i n e a r c o n v e r s i o n p r o c e d u r e u s i n g t r u e s c o r e s w h i l e a t the same ti m e e m p h a s i z i n g the n o n - i n t e r c h a n g e a b i l i t y of the t e s t s . These r e s t r i c t i o n s make the d i s t i n c t i o n s among e q u a t i n g p r o c e d u r e s b o t h c o n c e p t u a l l y awkward and d i f f i c u l t t o i n t e r p r e t . L i n e a r t r u e s c o r e e q u a t -i n g was i n c l u d e d i n the p r e s e n t s t u d y , however, because of r e p e a t e d r e f e r -ences t o the use of t r u e s c o r e s i n the l i t e r a t u r e ( e . g . , F l a n a g a n , 1950, 1964) and t o round out the m e t h o d o l o g i c a l e x a m i n a t i o n of e q u a t i n g p r o c e d u r e s . 39 Comparing N o n p a r a l l e l T e s t s A n g o f f ' s d e f i n i t i o n of comparing c i t e d i n Cha p t e r I (see p. 7) o u t l i n e s t h e o p p o s i t i o n a l f e a t u r e s between t h a t t y p e of c o n v e r s i o n and e q u a t i n g . I n f a c t , t e s t s t o be compared need not s a t i s f y any of the r e s t r i c t i v e c r i t e r i a f o r e q u a t i n g . The p r i c e of t h i s a p p a r e n t l a t i t u d e , however, i s t h a t comparable s c o r e s a r e l i m i t e d i n g e n e r a l i t y . The e f f e c t of d i f f e r e n c e s i n c o n t e n t f o r n o n p a r a l l e l t e s t s i s t h a t d i f f e r e n t r e l a t i o n -s h i p s between the t e s t s w i l l be e s t a b l i s h e d f o r d i f f e r e n t r e f e r e n c e groups ( A n g o f f , 1964, 1966, 1971; F l a n a g a n , 1964; L i n d q u i s t , 1964; L o r d , 1950). I n a d d i t i o n , t he a d o p t i o n of d i f f e r e n t d e f i n i t i o n s of c o m p a r a b i l i t y w i l l r e s u l t i n d i f f e r e n t s e t s of comparable v a l u e s (Angoff, 1964, 1966, 1971). For example, a d e f i n i t i o n of c o m p a r a b i l i t y based on e q u a l s t a n d a r d - s c o r e d e v i a t e s would y i e l d a d i f f e r e n t c o n v e r s i o n t h a n a d e f i n i t i o n of compar-a b i l i t y based on e q u a l p e r c e n t i l e s . I n c o n t r a s t t o t h i s , a l l methods or d e f i n i t i o n s of e q u i v a l e n c y f o r s t r i c t l y p a r a l l e l t e s t s w i l l l e a d t o the same c o n v e r s i o n ( A n g o f f , 1966). The d e f i n i t i o n o f c o m p a r a b i l i t y o f f e r e d e a r l i e r i n t h i s c h a p t e r r e q u i r e d t h a t the s c o r e d i s t r i b u t i o n on one t e s t be made i d e n t i c a l t o the s c o r e d i s t r i b u t i o n on a second t e s t . The fundamental d e f i n i t i o n c i t e d by A n g o f f (1971) was t h a t c e r t a i n agreed-upon moments of the d i s t r i b u t i o n of s c o r e s on the two t e s t s be i d e n t i c a l w i t h r e s p e c t t o a  p a r t i c u l a r ( s i n g l e ) group of examinees. ( p . 591) A n g o f f s u g g e s t e d f u r t h e r t h a t the "agreed-upon" moments f r e q u e n t l y i n c l u d e o n l y the mean and s t a n d a r d d e v i a t i o n . 40 P r o b a b l y the most common p r o c e d u r e of d e f i n i n g c o m p a r a b i l i t y i s s i m p l y t o a d m i n i s t e r the two or more t e s t s ( f r e q u e n t l y a b a t t e r y o f t e s t s ) t o a common b a s i c r e f e r e n c e group and t o s c a l e the t e s t s i n such a way t h a t the mean and s t a n d a r d d e v i a t i o n have the same n u m e r i c a l v a l u e s , r e s p e c t i v e l y , on each o f the v a r i o u s t e s t s . (pp. 590-591) The l a t t e r d e f i n i t i o n r e f l e c t s a p r i n c i p a l a p p l i c a t i o n of comparable s c o r e s c a l e s : t o p r o v i d e the means f o r p r o f i l e a n a l y s i s a c r o s s a b a t t e r y of t e s t s of d i f f e r e n t f u n c t i o n s . Many e d u c a t i o n a l and p s y c h o l o g i c a l t e s t s a r e s c a l e d i n t h i s manner ( e . g . , I l l i n o i s T e s t of P s y c h o l i n g u i s t i c A b i l i t i e s , Keymath, McCarthy S c a l e s of C h i l d r e n ' s A b i l i t i e s , WISC-R). A second a p p l i c a t i o n i n v o l v e s same-purpose but n o n p a r a l l e l t e s t s . As s u g g e s t e d i n Chapter!;, c o m p a r a b i l i t y among such t e s t s i s f r e q u e n t l y assumed when t e s t s have the same number s c a l e . I t i s now o b v i o u s t h a t the l a c k of u n i f o r m i t y i n s t a n d a r d i z a t i o n p r o c e d u r e s makes t h i s a s s u m p t i o n u n t e n a b l e . M i l l m a n and L i n d l o f (1964) r e p o r t a s t u d y w h i c h emphasizes t h i s f a c t . They a d m i n i s t e r e d the v o c a b u l a r y s u b t e s t s of t h r e e w i d e l y used achievement b a t t e r i e s ( t h e C a l i f o r n i a Achievement T e s t s , the Iowa T e s t s of B a s i c S k i l l s and the M e t r o p o l i t a n Achievement T e s t s ) t o each of 204 f i f t h - g r a d e s t u d e n t s . U s i n g the e q u i p e r c e n t i l e method, t h e y d e v e l o p e d a t a b l e of comparable p e r c e n t i l e r a n k s f o r the t e s t s . D i f f e r e n c e s among t h e s e r a n k i n g s were c i t e d as e v i d e n c e o f " t h e r i s k i n v o l v e d i n comparing d e r i v e d s c o r e s from d i f f e r e n t t e s t s s t a n d a r d i z e d on d i f f e r e n t p o p u l a t i o n s , as i s f r e q u e n t l y done when a measure of growth i n achievement or a c o m p a r i -son of a p t i t u d e and achievement i s made" (p. 136). Lennon's (1966) c o m p a r i s o n o f t h r e e i n t e l l i g e n c e t e s t s y i e l d e d s i m i l a r r e s u l t s . He examined the e q u i v a l e n c e among s c o r e s and IQs d e r i v e d from " t h r e e w i d e l y used m e n t a l a b i l i t y measures f o r secondary s c h o o l p u p i l s : Terman-McNemar T e s t o f M e n t a l A b i l i t y , O t i s Q u i c k - S c o r i n g M e n t a l A b i l i t y 41 T e s t s : Gamma T e s t , and P i n t n e r G e n e r a l A b i l i t y T e s t s : V e r b a l S e r i e s , Advanced T e s t " (p. 1 9 8 ) . The e q u a t i n g was based on d i s t r i b u t i o n s of s c o r e s f o r t h r e e groups of s t u d e n t s , one group p er t e s t , where the groups had been c l o s e l y matched w i t h r e s p e c t t o age, gr a d e , and achievement t e s t s c o r e s . A g r a p h i c e q u i p e r c e n t i l e p r o c e d u r e was used t o produce e q u i v a l -ency t a b l e s among the 1 t h r e e t e s t s . The adequacy of the r e s u l t s was judged by e x a m i n a t i o n o f t h e s e t a b l e s r a t h e r t h a n a c c o r d i n g t o any s t a t i s t i c a l c r i t e r i o n . Lennon p o i n t e d out from t h i s , t h a t a l t h o u g h t he d i f f e r e n c e s among IQs were not g r e a t , t h e y were, i n some c a s e s , l a r g e enough t o cause q u i t e d i f f e r e n t d e c i s i o n s t o be made about an i n d i v i d u a l depending on the t e s t used. H i s c o n c l u s i o n s i n c l u d e t he n e c e s s i t y of r e f e r e n c i n g any IQ t o i t s s p e c i f i c t e s t s o u r c e s i n c e s c o r e c o n s i s t e n c y a c r o s s t e s t s cannot be assumed. C o n s e q u e n t l y , where i n t e r - t e s t c o m parisons a r e d e s i r e d , t h e s e must be based on e m p i r i c a l l y - d e t e r m i n e d c o n v e r t e d s c o r e s r a t h e r t h a n on e x i s t i n g s c o r e s from d i f f e r e n t t e s t s . There a r e two i s s u e s r e g a r d i n g i n t e r - t e s t s c o r e c o n v e r s i o n s f o r n o n p a r a l l e l t e s t s w h i c h have r e c e i v e d c o n s i d e r a b l e a t t e n t i o n : 1) the t e c h n i c a l problems i n a c h i e v i n g p r e c i s i o n i n c o n v e r t e d s c o r e s , and 2 ) the p o t e n t i a l f o r m i s i n t e r p r e t a t i o n of the r e s u l t s ( A n g o f f , 1 9 6 4 , 1 9 6 6 , 1 9 7 1 ; F l a n a g a n , 1 9 6 4 ; Lennon, 1 9 6 4 ; L i n d q u i s t , 1 9 6 4 ) . The t e c h n i c a l problems a r i s e from the r e s t r i c t i o n s s t a t e d e a r l i e r , namely t h a t such c o n v e r s i o n s a r e a p p l i c a b l e o n l y t o the s p e c i f i c c o n d i t i o n s under w h i c h t h e y a r e d e r i v e d . As a r e s u l t , the e s t a b l i s h m e n t of an a p p r o p r i a t e r e f e r e n c e group becomes of prime i m p o r t a n c e . A n g o f f ( 1 9 6 4 , 1 9 6 6 , 1 9 7 1 ) o f f e r s t h r e e p o s s i b i l i -t i e s : n a t i o n a l norms g r o u p s , l o c a l norms g r o u p s , and d i f f e r e n t i a t e d norms gro u p s . The use of a f o u r t h type o f group on w h i c h t o base t a b l e s o f comparable s c o r e s — t h a t i s , on a "happenstance" group o f pe r s o n s f o r whom 42 s c o r e s a r e a v a i l a b l e on b o t h t e s t s — h a s been s t r o n g l y c r i t i c i z e d ( A n g o f f , 1 9 6 4 , 1 9 6 6 , 1 9 7 1 ; L i n d q u i s t , 1 9 6 4 ) . A n g o f f s u g g e s t e d t h a t when t e s t s a r e q u i t e s i m i l a r i n f u n c t i o n , " r o u g h " c o n v e r s i o n s can be based on t h e s c o r e s from t h e i r r e s p e c t i v e n a t i o n a l norms samples. I n e v i t a b l e d i f f e r -ences i n the s e l e c t i o n of t h e s e norms g r o u p s , however, v i o l a t e the p r e m i s e s f o r comparable s c o r e s . The M i l l m a n and L i n d l o f ( 1 9 6 4 ) and Lennon ( 1 9 6 6 ) s t u d i e s d i s c u s s e d e a r l i e r i l l u s t r a t e the inadequacy of t h i s a p p r oach. The most p r e c i s e and d e f e n s i b l e method i s t o base comparable s c o r e s on d i f f e r e n t i a t e d norms groups. "The p r o c e d u r e w i l l y i e l d a number of c o n -v e r s i o n t a b l e s , each based on, and a p p r o p r i a t e f o r , a d i f f e r e n t norms group. . . . The u s e r w i l l be f o r c e d t o choose t h e a p p r o p r i a t e t a b l e w i t h c a r e , k e e p i n g i n mind the group f o r w h i c h he i n t e n d s t o use i t and the purpose f o r w h i c h i t i s t o be a p p l i e d " ( A n g o f f , 1 9 7 1 , p. 5 9 6 ) . An example of d i f f e r e n t i a t e d norms group c o n v e r s i o n s would be the p r o v i s i o n of d i f f e r -ent t a b l e s f o r each age l e v e l c o v e r e d by the t e s t s . A n g o f f a l s o e n d o r s e d the l o c a l norms approach t o comparable s c o r e s p r o v i d e d a p p r o p r i a t e c a u t i o n s a r e t a k e n i n t h e s e l e c t i o n of the group and i n the a p p l i c a t i o n of the r e s u l t s . Problems of m i s i n t e r p r e t a t i o n of comparable s c o r e s a r i s e from t h e i r p o t e n t i a l c o n f u s i o n w i t h e q u i v a l e n t s c o r e s . A l l f o u r p a r t i c i p a n t s — A n g o f f , F l a n a g a n , Lennon, and L i n d q u i s t — i n a symposium e n t i t l e d "The E q u a t i n g of N o n - P a r a l l e l T e s t S c o r e s " p r e s e n t e d a t the 1 9 6 4 Annual M e e t i n g of the N a t i o n a l C o u n c i l on Measurement i n E d u c a t i o n , a d d r e s s e d t h i s c o n c e r n . Of the f o u r , L i n d q u i s t a l o n e t o t a l l y r e j e c t e d such c o n v e r s i o n s : No m a t t e r what p r e c a u t i o n s were t a k e n t o guard a g a i n s t m isuses and m i s i n t e r p r e t a t i o n s , the t o t a l e f f e c t would p r o b a b l y be i n c r e a s e d m i suses of the t e s t r e s u l t s , or a more w i d e s p r e a d f a i l u r e t o use the t e s t r e s u l t s i n the b e s t way p o s s i b l e . ( L i n d q u i s t , 1 9 6 4 , p. 5 ) 43 The o t h e r t h r e e emphasized t h a t w i t h c a r e f u l s e l e c t i o n and d e f i n i t i o n o f the r e f e r e n c e group, and w i t h the use of a p p r o p r i a t e c o n v e r s i o n p r o c e -d u r e s , s a t i s f a c t o r y and u s e f u l comparable s c o r e s c o u l d be p r o v i d e d ( A n g o f f , 1964; F l a n a g a n , 1964; Lennon, 1964). I n summary, w h i l e i t i s r e c o g n i z e d t h a t comparable s c o r e c o n v e r s i o n s r e q u i r e c a r e f u l i n t e r p r e t a t i o n g u i d e l i n e s , i t i s a l s o r e c o g n i z e d t h a t , when p r o p e r l y ' . c o n s t r u c t e d , such c o n v e r s i o n s can p r o v i d e v a l u a b l e i n f o r m a -t i o n t o t e s t u s e r s . A n g o f f (1968, 1971) i m p l i e d a j u s t i f i c a t i o n of e m p i r i c a l c o m p a r a b i l i t y on the grounds of p s y c h o m e t r i c s e l f - d e f e n s e . He c l a i m e d t h a t c omparisons a re made anyway, and t h a t , t h e r e f o r e , i t behooves us t o c o n s t r u c t a system w h i c h , w h i l e under the c i r c u m -s t a n c e s , cannot p o s s i b l y be w h o l l y s a t i s f a c t o r y , w i l l a t l e a s t r e p r e s e n t some improvement i n the s t a t u s quo and w i l l a v o i d some of i t s o b v i o u s i m p e r f e c t i o n s . ( A n g o f f , 1968, p. 13) Methods Both l i n e a r and e q u i p e r c e n t i l e c o n v e r s i o n methods can be used t o d e r i v e :.comparable s c o r e s between t e s t s ( A n g o f f , 1971). A g a i n , as w i t h e q u a t i n g , the use of a l i n e a r c o n v e r s i o n i s c o n t i n g e n t on the shapes of the raw s c o r e d i s t r i b u t i o n s of the t e s t s . Thus the e q u a t i o n s d e f i n i n g the b a s i c l i n e a r and e q u i p e r c e n t i l e r e l a t i o n s h i p s p r e s e n t e d e a r l i e r f o r e q u a t i n g a r e a p p l i c a b l e t o comparing. When, however, the t e s t s f o r w h i c h comparable s c o r e s a r e t o be d e r i v e d have been a d m i n i s t e r e d t o a common group of examinees, the s i m p l e s t p r o c e d u r e f o r e s t a b l i s h i n g c o m p a r a b i l i t y i s t o s c a l e the t e s t s so t h a t t h e y have e q u a l means and s t a n d a r d d e v i a -t i o n s ( A n g o f f , 1971). T h i s l a t t e r p r o c e d u r e was adopted i n the p r e s e n t s t u d y . 44 Summary A summary of the i n d i c e s of p s y c h o l o g i c a l e q u i v a l e n c e appeared i n T a b l e 4. I n T a b l e 5 the s t a t i s t i c a l i n d i c e s a s s o c i a t e d w i t h p a r a l l e l , n o m i n a l l y p a r a l l e l , and n o n p a r a l l e l t e s t s , as d e s c r i b e d i n t h i s c h a p t e r , are summarized and r e l a t e d t o the r e l e v a n t t y p e of s c o r e c o n v e r s i o n . T a b l e 5 R e l a t i o n s h i p between P a r a l l e l i s m and Type of S c o r e C o n v e r s i o n P a r a l l e l Forms N o m i n a l l y P a r a l l e l T e s t s N o n p a r a l l e l T e s t s Observed s c o r e e q u a t i n g v e r y h i g h i n t e r c o r r e l a t i o n s " e q u a l r e l i a b i l i t i e s m o d e r a t e l y h i g h i n t e r c o r r e l a t i o n s * e q u a l r e l i a b i l i t i e s True s c o r e equat i n g m o d e r a t e l y h i g h i n t e r c o r r e l a t i o n s * u n equal r e l i a b i l i t i e s Comparing low i n t e r -c o r r e l a t i o n s * * C o r r e c t e d f o r a t t e n t u a t i o n Renorming The m a j o r i t y of t e s t s used by s c h o o l p s y c h o l o g i s t s i n B r i t i s h C o l u m b i a , as e l s e w h e r e i n Canada, were c o n s t r u c t e d and s t a n d a r d i z e d i n o t h e r c o u n t r i e s . Such a d o p t i o n of e x i s t i n g t e s t s i n v o l v e s the i m p l i c i t a s s u m p t i o n t h a t the C a n adian p o p u l a t i o n t o w h i c h the t e s t s a r e a p p l i e d i s i d e n t i c a l t o the " f o r e i g n " p o p u l a t i o n f o r w h i c h the norms were p r e p a r e d . I n r e f e r e n c e t o the s p e c i f i c t e s t s i n c l u d e d i n the p r e s e n t s t u d y , use of the WISC-R i n B r i t i s h Columbia i n 1980 assumes the c o m p a r a b i l i t y of B r i t i s h Columbia s c h o o l c h i l d r e n t o a n a t i o n a l sample of A merican c h i l d r e n i n 1974 ( W e c h s l e r , 45 1974). S i m i l a r use of the PPVT assumes the c o m p a r a b i l i t y of B r i t i s h Columbia s c h o o l c h i l d r e n t o a sample of 4000 c h i l d r e n and a d o l e s c e n t s i n N a s h v i l l e , Tennessee i n 1958 (Dunn, 1965). The r e f e r e n c e group f o r the SIT i s v a g u e l y d e s c r i b e d as i n c l u d i n g c h i l d r e n and a d u l t s from v a r i o u s s c h o o l s and p r o f e s s i o n a l groups i n New York S t a t e who appear t o have been t e s t e d i n 1961 or 1962 ( S l o s s o n , 1975). F i n a l l y , use of the SPM or MHVS i n v o l v e s a c o m p a r i s o n w i t h a l l t h o s e c h i l d r e n l i v i n g i n C o l c h e s t e r , E n g l a n d i n 1943 whose surnames s t a r t e d w i t h the l e t t e r s A o r B (Raven, 1958)! To date t h e r e has been l i t t l e r e s e a r c h t o s u b s t a n t i a t e the a p p l i c a b i l -i t y of t h e s e t e s t s t o Canadian c h i l d r e n . Laycock (1960) i s c r i t i c a l of t h i s s i t u a t i o n : Canada . . . i s h a n d i c a p p e d by i t s r e l u c t a n c e t o spend s u b s t a n -t i a l amounts on e d u c a t i o n a l r e s e a r c h . As a r e s u l t i t has com-p a r a t i v e l y few data..of i t s own on w h i c h t o base the use of IQ t e s t s o r the s o l u t i o n of o t h e r e d u c a t i o n a l p r o b l e m s . (p. 236) S t u d i e s t h a t do e x i s t suggest t h a t f u r t h e r i n v e s t i g a t i o n w i t h Canadian c h i l d r e n i s r e q u i r e d . Beauchamp, Samuels, and G r i f f o r e (1979) a d m i n i s t e r e d two WISC-R s u b t e s t s — I n f o r m a t i o n and D i g i t S p a n — t o Canadian and A m e r i c a n c h i l d r e n t o compare d i f f e r e n c e s i n performance w h i c h c o u l d be a t t r i b u t e d to c r o s s - c u l t u r a l i n f l u e n c e s . T h e i r s u b j e c t s were s t u d e n t s i n two grade 3 c l a s s e s , one i n a r u r a l a r e a i n the p r o v i n c e of Quebec, and the o t h e r 45 m i l e s away, i n a r u r a l a r e a i n New York s t a t e . The a u t h o r s h y p o t h e s i z e d t h a t c u l t u r a l d i f f e r e n c e s would be r e f l e c t e d i n s c o r e s on the I n f o r m a t i o n s u b t e s t w h i c h c o n t a i n s items w i t h A merican c u l t u r e - s p e c i f i c b i a s . They f u r t h e r h y p o t h e s i z e d t h a t such d i f f e r e n c e s would not e x i s t on the D i g i t Span s u b t e s t w h i c h r e q u i r e s o n l y the r e p e t i t i o n of numbers. R e s u l t s of the s t u d y were e x a c t l y the o p p o s i t e of t h o s e e x p e c t e d . A l t h o u g h some s p e c i f i c q u e s t i o n s on the I n f o r m a t i o n s u b t e s t were answered c o r r e c t l y by a g r e a t e r p e r c e n t a g e of s t u d e n t s i n one c l a s s t h a n a n o t h e r , t h e r e was no s i g n i f i c a n t d i f f e r e n c e between mean s c a l e d s c o r e s f o r the two groups on t h a t s u b t e s t . There was a s i g n i f i c a n t mean s c o r e d i f f e r e n c e , however, on the D i g i t Span s u b t e s t w i t h Canadian c h i l d r e n s c o r i n g h i g h e r . The f a c t t h a t d i f f e r e n c e s were found and t h a t t h o s e were not p r e d i c t a b l e prompted the a u t h o r s t o a d v i s e c a u t i o u s i n t e r p r e t a t i o n of s c o r e s f o r Canadian c h i l d r e n . I n f a c t , t h e y p r o p o s e d the s t a n d a r d i z a t i o n o f the WISC-R i n Canada. P e t e r s ( 1 9 7 6 ) , i n a s i m i l a r v e i n , r e p o r t e d no e v i d e n c e of c o n c e r n f o r b i a s a g a i n s t Canadian s t u d e n t s i n WISC-R c o n t e n t . He d i d , however, f i n d mean IQ s c o r e s f o r c h i l d r e n i n a l a r g e c i t y i n S a s k a t -chewan t h a t were c o n s i s t e n t l y h i g h e r t h a n the Am e r i c a n s t a n d a r d i z a t i o n sample mean of 100. He r e p o r t e d average F u l l S c a l e IQ s c o r e s of 109.75, 106.58, and 103.41 f o r c h i l d r e n at ages 7%, 10%, and 13% r e s p e c t i v e l y . V a r i o u s s t u d i e s u s i n g group t e s t s of i n t e l l i g e n c e c o n f i r m a p a t t e r n of h i g h e r C a n adian s c o r e s . I n 1966, the s t a n d a r d i z a t i o n of the Canadian L o r g e - T h o r n d i k e I n t e l l i g e n c e T e s t y i e l d e d r e s u l t s w h i c h " c l e a r l y i n d i c a t e d the need f o r Canadian norms. The Canadian s t u d e n t s d i s p l a y e d b o t h a d i f f e r e n t average performance [ h i g h e r ] and a d i f f e r e n t amount of v a r i a b i l -i t y [more homogeneous] from the American s t u d e n t s " ( W r i g h t , T h o r n d i k e , & Hagen, 1972, p. 7 ) . Ke n n e t t (1972) r e p o r t e d an average IQ of 113.0 ( s t a n d a r d d e v i a t i o n = 9.7) f o r g i r l s and 110.7 ( s t a n d a r d d e v i a t i o n = 10.2) f o r boys a c r o s s f i v e s o c i o e c o n o m i c l e v e l s on the O t i s Q u i c k S c o r i n g M e n t a l A b i l i t y T e s t . O l d r i d g e (1968) d i s c u s s e d s i m i l a r r e s u l t s u s i n g the C a l i -f o r n i a T e s t o f M e n t a l M a t u r i t y and s u g g e s t e d : Those i n e d u c a t i o n who have been i n v o l v e d i n the i n t e l l e c t u a l and/or academic assessment of Canadian s c h o o l c h i l d r e n have o b s e r v e d the c o n s i s t e n t l y h i g h e r r a t i n g of t h e s e s t u d e n t s on Am e r i c a n t e s t s u s i n g A m erican norms. The h i g h e r academic achievement i s u s u a l l y e x p l a i n e d as b e i n g a f u n c t i o n o f the h i g h e r i n t e l l e c t u a l a b i l i t y (I.Q.) o f the Canadian g r o u p s . (p. 1) Herman (1979) r e p o r t e d t h a t e v i d e n c e from s e q u e n t i a l s t a n d a r d i z a t i o n of i n t e l l i g e n c e t e s t s i n the U n i t e d S t a t e s i n d i c a t e d b e t t e r performance t h e r e as w e l l . H i s paper would suggest t h a t h i g h e r IQ s c o r e s a r e a f u n c t i o n of time and may r e f l e c t g e n e r a l c u l t u r a l p r o g r e s s r a t h e r t h a n n a t i o n a l s u p e r i o r i t y . Whatever the r e a s o n s t h a t may be posed, t h e s t u d i e s c i t e d i n t h i s s e c t i o n p r o v i d e ample cause f o r q u e s t i o n i n g the adequacy of t h e e x i s t i n g norms t a b l e s f o r the t e s t s used i n t h e p r e s e n t s t u d y . As mentioned i n C h a p t e r I , the need f o r a l a r g e , r e p r e s e n t a t i v e sample on w h i c h t o base s c o r e c o n v e r s i o n s a l s o s a t i s f i e d the r e q u i r e m e n t s f o r an a p p r o p r i a t e norm-i n g sample. Thus t h i s s t u d y i n c l u d e d the d e t e r m i n a t i o n of the a p p l i c a b i l -i t y of the p u b l i s h e d " f o r e i g n " norms i n B r i t i s h C o l u m b i a . CHAPTER I I I METHODOLOGY There were two o b j e c t i v e s t o the p r e s e n t s t u d y : t o i n v e s t i g a t e the a p p l i c a t i o n of l i n e a r and e q u i p e r c e n t i l e e q u a t i n g t e c h n i q u e s t o t h o s e p a i r s o f t e s t s i d e n t i f i e d as p s y c h o l o g i c a l l y and t e c h n i c a l l y e q u i v a l e n t , and t o e s t a b l i s h comparable p r o v i n c i a l l y r e p r e s e n t a t i v e norms f o r ages 1\i 9%, and 11% y e a r s f o r each of the f i v e t e s t s . B r i e f l y , the p r o c e d u r e f o l l o w e d was t o a d m i n i s t e r a l l t e s t s t o each c h i l d i n the sample; t o e s t a b l i s h new norm t a b l e s f o r each t e s t ; and t o a p p l y e q u a t i n g p r o c e d u r e s t o the s e l e c t e d p a i r s of t e s t s . A complete d e s c r i p t i o n of the methodology i s p r e s e n t e d i n t h i s c h a p t e r . The sample d e s i g n and s a m p l i n g p r o c e d u r e s a r e d e s c r i b e d i n the f i r s t s e c t i o n . F o l l o w i n g t h a t , t he d a t a c o l l e c t i o n and p r e p a r a t i o n a r e d e s c r i b e d . I n the f i n a l s e c t i o n , the d a t a a n a l y s i s i s p r e s e n t e d under two h e a d i n g s : norming and e q u a t i n g . Sample D e s i g n A two-stage s t r a t i f i e d sample d e s i g n was used t o s e l e c t p r o b a b i l i t y samples, r e p r e s e n t a t i v e of the p o p u l a t i o n of i n t e r e s t i n the p r o v i n c e , f o r each of t h r e e age l e v e l s : 7%, 9%, and 11% y e a r s . The c h o i c e o f s t r a t i f i c a t i o n v a r i a b l e s was based on t h o s e i n c l u d e d i n the s t a n d a r d i z a t i o n of the WISC-R i n the U n i t e d S t a t e s i n 1973. At t h a t t i m e , the v a r i a b l e s used were age, sex, r a c e ( w h i t e - n o n w h i t e ) , g e o g r a p h i c r e g i o n , o c c u p a t i o n of head of h o u s e h o l d and u r b a n - r u r a l r e s i d e n c e ( W e c h s l e r , 1974). The w h i t e - n o n w h i t e v a r i a b l e was o m i t t e d from the p r e s e n t s t u d y : a p a r t from 48 49 the e x c l u s i o n of N a t i v e I n d i a n c h i l d r e n (see Chap t e r I ) , t h e r e was no attempt t o c l a s s i f y c h i l d r e n a c c o r d i n g t o r a c e . The v a r i a b l e , o c c u p a t i o n o f head of h o u s e h o l d , was r e p l a c e d by y e a r s o f s c h o o l i n g of head of h o u s e h o l d and was i n c l u d e d f o r d e s c r i p t i v e r a t h e r t h a n s e l e c t i o n p u rposes s i n c e p o p u l a t i o n f i g u r e s f o r t h i s v a r i a b l e were a v a i l a b l e o n l y f o r the p r o v i n c e as a whole (see p. 6 1 ) . I n summary, the s t r a t i f i c a t i o n v a r i a b l e s adopted from the o r i g i n a l WISC-R s t a n d a r d i z a t i o n were age, sex, g e o g r a p h i c r e g i o n s , and commun-i t y s i z e ( u r b a n - r u r a l ) . One f u r t h e r v a r i a b l e — s i z e of s c h o o l — w a s added t o t h e s e . T h i s v a r i a b l e has been used i n o t h e r s a m p l i n g d e s i g n s f o r t e s t s of i n t e l l e c t u a l a b i l i t y ( c f . W r i g h t , T h o r n d i k e , & Hagen, 1972). Stage I : S c h o o l s At the f i r s t s t a g e , the s a m p l i n g frame c o n s i s t e d of a l i s t of a l l 1 2 p u b l i c and independent s c h o o l s i n B r i t i s h Columbia i n wh i c h c h i l d r e n at one o r more of the t h r e e age l e v e l s were e n r o l l e d . D e t e r m i n a t i o n o f a s p e c i f i c age l e v e l was based on c o r r e s p o n d i n g grade l e v e l s , w i t h grades 2, 4, and 6 r e p r e s e n t i n g ages 1\, 9%, and W\ r e s p e c t i v e l y . A t o t a l of 1465 s c h o o l s — 1 3 1 2 p u b l i c and 153 i n d e p e n d e n t — w e r e i d e n t i f i e d and c a t e g o r i z e d a c c o r d i n g t o the Stage 1 s t r a t i f i c a t i o n v a r i a b l e s : g e o g r a p h i c r e g i o n , com-munity s i z e , and s i z e of s c h o o l . 3 G e o g r a p h i c r e g i o n . S e v e n t y - f o u r s c h o o l d i s t r i c t s i n t h e p r o v i n c e of B.C. were grouped i n t o t he s i x r e g i o n a l zones shown i n F i g u r e 1 and l i s t e d below: ''"Ministry o f E d u c a t i o n , Report on E d u c a t i o n 1976-1977, V i c t o r i a , B.C., 1978. 2 L i s t e d i n F e d e r a t i o n of Independent S c h o o l A s s o c i a t e s , B.C. I n d e -pendent S c h o o l s , 1978-1979. 3 The N i s h g a s c h o o l d i s t r i c t was e x c l u d e d from the s t u d y s i n c e i t e x c l u s i v e l y i n c o r p o r a t e s a N a t i v e I n d i a n p o p u l a t i o n . T h e r e f o r e , s c h o o l s i n a l l but one d i s t r i c t were i n c l u d e d i n the s a m p l i n g frame. 51 1. Okanagan 2. Metro 3. F r a s e r V a l l e y 4. Vancouver I s l a n d 5. Kootenay 6. N o r t h e r n These zones r e p r e s e n t a d m i n i s t r a t i v e u n i t s w i t h i n the B.C. s c h o o l system and have p r e v i o u s l y been used f o r sample s t r a t i f i c a t i o n p urposes i n educa-t i o n a l r e s e a r c h d e s i g n s f o r the p r o v i n c i a l l e a r n i n g assessment program (B.C. R e s e a r c h , Note 1 ) . Community s i z e . Three community s i z e s d e f i n e d i n terms of t o t a l p o p u l a t i o n , were used: A under 1,000 B 1,001-50,000 C over 50,000 The p r o p o r t i o n s of the p o p u l a t i o n of B.C. r e p r e s e n t e d i n t h e s e c a t e g o r i e s a c c o r d i n g t o 1971 census d a t a ( S t a t i s t i c s Canada, 1971) were: A - 25%, B - 25%, and C - 50%. S c h o o l s were a s s i g n e d t o community s i z e on the b a s i s of s c h o o l a d d r e s s and p o p u l a t i o n f i g u r e s from the S u r v e y s and Mapping B r a n c h , M i n i s t r y of the E n v i r o n m e n t , V i c t o r i a , B.C. (1978-1979). I n c a s e s where s c h o o l l o c a t i o n was u n s p e c i f i e d , the a d d r e s s was o b t a i n e d from the r e l e v a n t s c h o o l d i s t r i c t o f f i c e . S i z e of s c h o o l . S c h o o l s i z e was d e f i n e d by t o t a l s t u d e n t e n r o l l m e n t . Three c a t e g o r i e s of s c h o o l s i z e were d e t e r m i n e d : I . t o 150 I I . 151-300 I I I . o v er 300 C h o i c e of s c h o o l s i z e c a t e g o r i e s was d e t e r m i n e d t o ensure the adequate r e p r e s e n t a t i o n of a l l s i z e s of s c h o o l s i n the sample. 52 Stage I I : I n d i v i d u a l s The s a m p l i n g frame f o r i n d i v i d u a l s c o n s i s t e d of a l i s t of a l l non-N a t i v e I n d i a n , E n g l i s h - s p e a k i n g c h i l d r e n e n r o l l e d i n each s e l e c t e d s c h o o l . The l i s t s e x c l u d e d c h i l d r e n w i t h p h y s i c a l , e m o t i o n a l and m e n t a l h a n d i c a p s as o u t l i n e d i n C h a p t e r I . There were two s t r a t i f i c a t i o n v a r i a b l e s a t t h i s s t a g e : age and sex. Age. Three age groups were i n c l u d e d : 7%, 9%, and 11% y e a r s . Ages were d e f i n e d w i t h i n t h r e e months of the m i d y e a r ; thus 7% y e a r s spanned a 6-month range from 7 y e a r s 3 months t o 7 y e a r s 9 months. Ages 9% and 11% were s i m i l a r l y d e f i n e d . A l l c h i l d r e n whose ages c o r r e s p o n d e d t o t h e s e 6-month ranges a t the e s t i m a t e d time of t e s t i n g were l i s t e d . Sex. W i t h i n each age group the c h i l d r e n were c l a s s i f i e d by sex. P o p u l a t i o n S i z e s P o p u l a t i o n d a t a were based on the 1976-1977 s c h o o l y e a r e n r o l l m e n t f i g u r e s ( M i n i s t r y of E d u c a t i o n , 1978). These were the most r e c e n t d a t a a v a i l a b l e a t the time the sample was drawn. A l t h o u g h e n r o l l m e n t numbers have d e c l i n e d s i n c e t h a t t i m e , the r e d u c t i o n was judged t o be c o n s i s t e n t a c r o s s s c h o o l d i s t r i c t s (Rees, Note 2 ) . The f u l l sample d e s i g n i s shown i n T a b l e 6. E s t i m a t e s of the popu-l a t i o n s i z e i n each c e l l were c a l c u l a t e d i n d e p e n d e n t l y f o r ages 7%, 9%, and 11%. To do t h i s , age l e v e l s w i t h i n s c h o o l s were assumed t o have a one-to-one c o r r e s p o n d e n c e . w i t h grade l e v e l s . I t was f u r t h e r assumed t h a t c l a s s s i z e was c o n s t a n t a c r o s s g r a d e s . An e s t i m a t e of the number of c h i l d r e n a t each age l e v e l w i t h i n each s c h o o l was t h e n d e t e r m i n e d by d i v i d i n g the t o t a l s c h o o l e n r o l l m e n t by the number of g r a d e s . F o r example, i n a s c h o o l w i t h 320 c h i l d r e n and grades K-7 i t was e s t i m a t e d t h a t t h e r e were 40 c h i l d r e n at each l e v e l . 53 T a b l e 6 P o p u l a t i o n S i z e S t r a t i f i e d by R e g i o n , Community S i z e , S c h o o l S i z e , and Age Community S c h o o l R e g i o n S i z e S i z e 1 2 3 4 5 6 A I I I I I I 597 641 395 34 588 748 837 460 896 399 313 184 71 566 511 112 r- B <u oo < I I I I I I 245 826 1568 403 1439 3808 352 1027 1306 216 966 1219 287 684 1006 105 1045 1727 C 1 I I I I I 275 464 1473 810 2176 8000 — 148 885 2338 -86 193 1014 A " O N 0) oo < A I I I I I I .:• 524 641 395 34 477 787 918 335 896 559 294 184 95 566 511 112 B I I I I I I 223 897 1650 326 1439 3808 237 1027 1306 194 893 1219 220 744 1006 105 950 1904 C I I I I I I 249 464 1473 693 2090 8062 — 192 846 2338 -25 193 1014 A I 465 17 447 268 289 537 I I 641 - 737 837 190 511 I I I 395 - 918 484 95 112 B I 174 157 212 125 200 105 <y 00 I I 798 1211 1170 746 744 1018 < I I I 1625 3808 1382 1523 1439 2040 C I 77 402 — 147 25 I I 464 1401 - 821 - 193 I I I 1473 8062 — 2441 — 1014 Note. The p o p u l a t i o n s i z e s f o r each age l e v e l were c a l c u l a t e d by d i v i d i n g t o t a l e n r o l l m e n t per s c h o o l by number of grades w i t h i n t h e s c h o o l . The p r o c e d u r e i s d e s c r i b e d more f u l l y on page 52. 54 U s i n g the d a t a i n Ta b l e 6, p o p u l a t i o n p e r c e n t a g e s were c a l c u l a t e d as a b a s i s f o r d e t e r m i n i n g sample d i s p e r s i o n . Working i n d e p e n d e n t l y at each age l e v e l , p e r c e n t a g e s were f i r s t c a l c u l a t e d f o r each r e g i o n , as shown i n T a b l e 7, and t h e n w i t h i n each r e g i o n and age, f o r t h e r e m a i n i n g c e l l s of t he d e s i g n as shown i n T a b l e 8. T a b l e 7 P o p u l a t i o n P e r c e n t a g e s : R e g i o n by Age Reg i o n  1 2 3 4 5 6 Vancouver South G r e a t e r South I s l a n d & C e n t r a l Vancouver M a i n l a n d South Coast S o u t h e a s t N o r t h Age 1\ 14.9 38.4 11.2 17.3 5.9 12.3 Age 9% 15.1 38.2 11.0 17.3 5.9 12.5 Age \\\ 14.6 35.9 11.6 17.6 7.0 13.2 Note: The f a c t t h a t one row of the t a b l e does not t o t a l 100% i s due t o the e f f e c t o f r o u n d i n g each p e r c e n t t o the n e a r e s t t e n t h . S a mpling P r o c e d u r e s Sample A l l o c a t i o n The t a r g e t sample s i z e was e s t a b l i s h e d on the b a s i s of the f o l l o w i n g c o n s i d e r a t i o n s . 1. The Ame r i c a n s t a n d a r d i z a t i o n sample f o r the WISC-R i n c l u d e d 200 c h i l -d ren a t each age l e v e l . T h i s sample s i z e was a p p r o x i m a t e d as c l o s e l y as p o s s i b l e . 2. I t was n e c e s s a r y t o r e a l i z e many p r a c t i c a l c o n s t r a i n t s i n terms of f i n a n c i a l and p e r s o n n e l r e s o u r c e s . The scope of the s t u d y r e q u i r e d 55 T a b l e 8 P e r c e n t a l >e of P o p u l a t i o n w i t h i n R e g i o n by Age Community S c h o o l R e g i o n S i z e S i z e 1 2 3 4 5 6 A I 9.2 12.1 6.1 12.3 10.6 I I 9.9 - 15.4 11.9 7.2 9.5 H I 6.1 - . 17.2 5.3 2.8 2.1 r» B I 3.8 2.4 7.2 2.9 11.3 2.0 Age I I 12.7 8.6 21.1 12.8 26.9 19.5 Age I I I 24.2 22.8 26.9 16.2 39.5 32.2 C I 4.2 4.9 _ 2.0 1 . 6 I I 7.2 13.0 - 11.8 - 3.6 I I I 22.7 48.0 - 31.1 - 18.9 A I 8.0 10.0 4.5 11.6 10.5 I I 9.8 - 16.6 12.0 7.2 9.5 I I I 6.1 - 19.3 7.5 3.7 2.1 rW B 0) < I 3.4 2.0 5.0 2.6 8.6 2.0 I I 13.8 8.8 21.6 12.0 29.3 17.7 I I I 25.3 23.2 27.5 16.3 39.6 35.4 C I 3.8 4.2 _ 2.6 _ _ I I 7.1 12.7 - 11.3 — 3.6 I I I 22.6 49.0 - 31.3 - 18.8 A I 7.6 9.2 3.6 9.8 9.7 I I 10.5 - 15.2 1 1 . 3 6.4 9.2 I I I 6.5 - 18.9 6.6 3.2 2.0 B I—I I 2.8 1 . 0 4.4 1 . 7 6.8 1 . 9 I I 13.1 8.0 24.0 10.1 25.2 18.3 CD •oo < C I I I 26.6 25.3 28.4 20.6 48.7 36.7 1 _ 2.7 2.0 I I 7.6 9.3 - 11.1 — 3.5 I I I 24.1 53.5 — 33.0 — 18.2 Note: The f a c t t h a t some of the columns of the t a b l e do not t o t a l 100% i s due t o the e f f e c t of r o u n d i n g each p e r c e n t t o the n e a r e s t t e n t h . 56 e x t e n s i v e r e l i a n c e on the a v a i l a b i l i t y of v o l u n t e e r a s s i s t a n c e . I t was t h e r e f o r e d e s i r a b l e t o l i m i t the t e s t i n g b o t h i n terms of i n d i -v i d u a l and t o t a l p r o j e c t time commitment. 3. S i n c e sample s i z e i s d i r e c t l y r e l a t e d t o the p r e c i s i o n of the e s t i m a t i o n of p o p u l a t i o n p a r a m e t e r s , i t was n e c e s s a r y t o b a l a n c e the p r a c t i c a l need f o r s i z e r e s t r i c t i o n a g a i n s t the need f o r s t a t i s t i c a l r e l i a b i l i t y g a i n e d w i t h a l a r g e sample s i z e . T h i s l a t t e r need i s even g r e a t e r f o r the e q u a t i n g t h a n the norming r e q u i r e m e n t s i n the p r e s e n t s t u d y . A t a r g e t sample s i z e o f 180 s t u d e n t s (90 g i r l s and 90 boys) a t each l e v e l was e s t a b l i s h e d . G i v e n the f i x e d p o p u l a t i o n s t a n d a r d d e v i a t i o n of 15 f o r the WISC-R, t h i s s i z e y i e l d e d a s t a n d a r d e r r o r of the mean of 1.1 IQ p o i n t s , as i l l u s t r a t e d by the f o r m u l a : b t x - n - i - j m ~ ' Each t o t a l age sample was th e n a l l o c a t e d a c c o r d i n g t o the p o p u l a t i o n p e r c e n t a g e s shown i n T a b l e s 7 and 8. C o r r e s p o n d i n g t a r g e t sample s i z e s a r e shown i n T a b l e s 9 and 10. S i n c e the c e l l sample s i z e s were f a i r l y c o n s i s t e n t a c r o s s ages (as shown i n T a b l e 9 ) , i t was d e c i d e d t o t e s t one c h i l d a t each age l e v e l w i t h i n a s i n g l e s c h o o l . S c h o o l s were f i r s t s e l e c t e d on the b a s i s of sample a l l o c a t i o n f i g u r e s f o r age 7%. Where p o s s i b l e , the same s c h o o l was used f o r ages 9% and 11%. I n c a s e s where the sample s i z e was l a r g e r a t ages 9% and 11%, or where the age 7% s c h o o l c o n t a i n e d o n l y p r i m a r y g r a d e s , the s a m p l i n g p r o c e d u r e was r e p e a t e d at the o t h e r age l e v e l s f o r the p a r t i c u l a r c e l l i n q u e s t i o n . 57: T a b l e 9 Ta r g e t Sample A l l o c a t i o n : R e g i o n by Age Re; g i o n 1 2 3 4 5 6 Vancouver South G r e a t e r South I s l a n d & C e n t r a l Vancouver M a i n l a n d South Coast S o u t h e a s t N o r t h Age 1\ 14.9% 38.4% 11.2% 17.3% 5.9% 12.3% n=27 n=69 n=20 n=31 n = l l n=22 Age 9% 15.17. 38.2% 11.0% 17.3% 5.9% 12.5% n=27 n=69 n=20 n=31 n = l l n=23 Age 11% 14.6% 35.9% 11.6% 17.6% 7.0% 13.2% n=27 n=65 n=22 n=32 n=12 n-23 P r e p a r a t i o n of the S c h o o l Sampling Frame In o r d e r t o p r o v i d e f o r s a m p l i n g f l e x i b i l i t y i n s c h o o l s w i t h v e r y s m a l l e n r o l l m e n t s ( t h e r e were many r u r a l s c h o o l s w i t h 1--3 s t u d e n t s p e r a g e ) , " s u p e r s c h o o l s " . were c r e a t e d c o n s i s t i n g of the amalgamation of two or more s i m i l a r - s i z e s c h o o l s w i t h i n the same c e l l of the sample d e s i g n . S u p e r s c h o o l amalgamations were r e s t r i c t e d t o s c h o o l s w i t h i n the same s c h o o l d i s t r i c t and w i t h i n c l o s e g e o g r a p h i c p r o x i m i t y . The r u l e adopted f o r the e s t a b l i s h m e n t of " s u p e r s c h o o l s " was t h a t t h e r e would be no s c h o o l u n i t (a " s u p e r s c h o o l " i s c o n s i d e r e d one u n i t ) s m a l l e r t h a n 2n where n e q u a l l e d the sample a l l o c a t i o n f o r t h a t c e l l . When s a m p l i n g f o r i n d i v i d u a l s , a " s u p e r s c h o o l " was t r e a t e d as one s c h o o l u n i t w i t h a l l e l i g i b l e s t u d e n t s l i s t e d i n a s i n g l e s a m p l i n g frame. To ensure e q u a l s a m p l i n g p r o b a b i l i t y f o r each c h i l d i n the p o p u l a t i o n , the f o l l o w i n g p r o c e d u r e was used (as i l l u s t r a t e d i n T a b l e 11): 1. W i t h i n each c e l l , t he s c h o o l u n i t s were rank o r d e r e d from s m a l l e s t t o l a r g e s t a c c o r d i n g t o e n r o l l m e n t a t age 7%. 58 T a b l e 10 T a r g e t Sample A l l o c a t i o n w i t h i n R e gion Community S c h o o l R e g i o n S i z e S i z e 1 2 3 4 5 • 6 A A« oo < I I I I I I I I I I I I 2 3 2 1 4 7 1 6 16 2 3 4 1 4 5 2 4 2 1 4 5 1 1 1 3 4 2 2 4 7 C I I I I I I 1 2 6 4 9 33 1 3 10 - 1 4 A A™ * B oo < I I I I I I I I I I I I 2 3 2 1 4 7 1 6 16 2 3 4 1 4 5 2 4 2 1 4 5 1 1 1 3 4 3 2 1 1 4 8 C I I I I I I 1 2 6 3 9 34 1 3 10 _ 1 4 A I I I I I I 2 3 2 - 2 3 4 1 4 2 1 1 2 2 1 A n B r-l r-l 0) 00 I I I I I I I I I I I I . 1 4 7 2 7 1 5 16 2 6 35 1 5 6 1 3 7 1 4 11 1 3 6 1 4 9 1 4 T a b l e 11 P r o p o r t i o n a l S c h o o l S i z e Sampling P r o c e d u r e R e g i o n #1, Community S i z e A, S c h o o l S i z e I I n=3 per age f E n r o l l m e n t S c h o o l Code ( p e r age) c f cp cp x n 8913' 15 15 .023 .07 2716 21 36 .056 .17 1904 22 58 .090 .27 2209 22 80 .125 .38 2325 22 102 .159 .48 8921 22 124 .193 .58 2337 23 147 .229 .69 2604 24 171 .267 .80 2734* 24 195 .304 .91 2738 24 219 .342 1.03 8903 24 243 .379 1.14 8906 24 267 .417 1.25 1603 26 293 .457 1.37 2215* 27 320 .499 1.50 8919 27 347 .541 1.62 3004 28 375 .585 1.76 1510 30 405 .632 1.90 2739 31 436 .680 2.04 1401 32 468 .730 2.19 2207 32 500 .780 2.34 3005 33 533 .832 2.50 2305 35 568 .886 2.66 2432* 36 604 .942 2.83 2605 37 641 1.000 3.00 "'-Selected s c h o o l 60 2. C u m u l a t i v e f r e q u e n c i e s and c u m u l a t i v e p e r c e n t a g e s were c a l c u l a t e d f o r the r e s u l t i n g c e l l p o p u l a t i o n d i s t r i b u t i o n s . 3. The c u m u l a t i v e p e r c e n t a g e v a l u e was t h e n m u l t i p l i e d by n where n = s t u d e n t sample a l l o c a t i o n f o r t h a t c e l l . 4. The s c h o o l s w i t h i n a c e l l were d i v i d e d i n t o n s u b s t r a t a so t h a t e q u a l p r o p o r t i o n s of the c e l l s t u d e n t p o p u l a t i o n were r e p r e s e n t e d i n each s u b s t r a t u m . I d e n t i f i c a t i o n o f S c h o o l s For each s u b s t r a t a , a s i n g l e random number was drawn w i t h i n the range of c u m u l a t i v e f r e q u e n c y v a l u e s f o r t h a t s u b s t r a t u m ( i n the example, f o r the f i r s t s u b s t r a t u m , a random number between 0 and 200). C o n t i n u i n g w i t h the e x a m p l e ' i n T a b l e 11, the f i r s t random number drawn was 180. S i n c e the 180th s t u d e n t was e n r o l l e d i n the s c h o o l coded as #2734, i t became the s e l e c t e d s c h o o l f o r t h i s s u b s t r a t u m . One s c h o o l from each of the o t h e r s u b s t r a t a was s i m i l a r l y i d e n t i f i e d . P r e p a r a t i o n of the Sampling Frames f o r I n d i v i d u a l s Consent f o r p a r t i c i p a t i o n i n the s t u d y was r e q u e s t e d s e q u e n t i a l l y from d i s t r i c t s u p e r i n t e n d e n t s and s c h o o l p r i n c i p a l s . Samples of a l l l e t -t e r s a r e i n c l u d e d i n Appendix A. C o n s e n t i n g p r i n c i p a l s were asked t o p r o v i d e c l a s s l i s t s i n c l u d i n g the names and b i r t h d a t e s of a l l c h i l d r e n w i t h the e x c e p t i o n of t h o s e d e s c r i b e d i n the d e l i m i t a t i o n s • s e c t i o n of Chap-t e r I . The c l a s s l i s t s were sent t o the r e s e a r c h e r who t h e n p r e p a r e d the s a m p l i n g frame a c c o r d i n g t o the age-range s p e c i f i c a t i o n s and s t r a t i f i e d by sex. E q u a l numbers of boys and g i r l s were a s s i g n e d t o each c e l l when the sample s i z e f o r t h a t c e l l was even. When c e l l sample s i z e was odd, the sex of the "odd" p e r s o n was d e t e r m i n e d randomly and the female-male quota of the n e x t a d j a c e n t c e l l ( w i t h i n r e g i o n ) was s t r u c t u r e d t o b a l a n c e the numbers. I d e n t i f i c a t i o n o f I n d i v i d u a l s W i t h i n s c h o o l s , a random sample of s t u d e n t s , s t r a t i f i e d by age and sex, was s e l e c t e d . S tudent names p l u s p a r e n t l e t t e r s and c o n s e n t forms were r e t u r n e d t o t h e p r i n c i p a l s and were s u b s e q u e n t l y sent t o p a r e n t s d i r e c t l y from the s c h o o l s . T e s t i n g was c o n t i n g e n t on the r e t u r n of the s i g n e d p a r e n t c o n s e n t forms. I n o r d e r t o a l l o w a more complete assessment of t h e r e p r e s e n t a t i v e -ness of the sample, p a r e n t s were r e q u e s t e d t o p r o v i d e i n f o r m a t i o n on a s o c i o - e c o n o m i c v a r i a b l e : the l e v e l of e d u c a t i o n , i n y e a r s , of the head of the h o u s e h o l d (see p a r e n t c o n s e n t form, Appendix A ) . T h o r n d i k e (1951) found t h i s v a r i a b l e t o c o r r e l a t e most h i g h l y w i t h c h i l d r e n s ' i n t e l l i g e n c e i n a s t u d y of community p r e d i c t o r s of i n t e l l i g e n c e and academic a c h i e v e -ment. At the time t h i s s t u d y was c o n d u c t e d , census d a t a on w h i c h p o p u l a -t i o n p r o p o r t i o n s were based were a v a i l a b l e on a p r o v i n c i a l b a s i s o n l y . ^ T h e r e f o r e , the r e p r e s e n t a t i v e n e s s of the sample on t h i s v a r i a b l e was d e t e r -mined i n r e f e r e n c e t o p r o v i n c e - w i d e d a t a . The f o l l o w i n g c a t e g o r i e s , condensed from 1976 census d a t a , were used: I . Grade 8 and below I I . Grades 9-10 I I I . Grades 11-13 IV. P o s t - s e c o n d a r y , n o n - u n i v e r s i t y V. P o s t - s e c o n d a r y , i n c l u d i n g u n i v e r s i t y F o r f u t u r e r e s e a r c h , t h i s d a t a w i l l be a v a i l a b l e f o r s c h o o l d i s t r i c t s from Data S e r v i c e s , M i n i s t r y of E d u c a t i o n . 62 T e s t i n g T e s t s Used The f o l l o w i n g f i v e t e s t s were used: W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n - R e v i s e d (WISC-R) S l o s s o n I n t e l l i g e n c e T e s t f o r C h i l d r e n and A d u l t s ( S I T ) Peabody P i c t u r e V o c a b u l a r y T e s t , Form A (PPVT) S t a n d a r d P r o g r e s s i v e M a t r i c e s , S e t s A, B, C, D, and E (SPM) M i l l H i l l V o c a b u l a r y S c a l e (MHVS) A l t e r a t i o n s were made t o item s i n the WISC-R and the MHVS; the o t h e r t e s t s were a d m i n i s t e r e d w i t h o u t change. On the WISC-R, s i x item s i n the I n f o r m a t i o n s u b t e s t and one i t e m i n the Comprehension s u b t e s t were reworded to " C a n a d i a n i z e " U . S . - s p e c i f i c c o n t e n t . The r e w o r d i n g s adopted were recommended by P. E. Vernon (1974, 1976, 1977) on the b a s i s t h a t t h e i r use w i t h Canadian c h i l d r e n y i e l d e d s u b t e s t pass p e r c e n t a g e s s i m i l a r t o those f o r the American s t a n d a r d i z a t i o n sample. The a l t e r n a t e items a r e . p r e s e n t e d i n Appendix B. In t he MHVS, the f i r s t 20 words i n each s e t were checked f o r f r e q u e n c y of o c c u r r e n c e i n c h i l d r e n ' s t e x t b o o k s p u b l i s h e d i n the U n i t e d S t a t e s ( C a r r o l l , D a v i e s , & Richman, 1971). An a r b i t r a r y f r e q u e n c y v a l u e o f two or l e s s was chosen as the b a s i s f o r r e j e c t i n g a word as "uncommon" and t h e r e f o r e u n l i k e l y t o be i n the v o c a b u l a r y r e p e r t o i r e o f s c h o o l age c h i l -d r e n . One word i n each s e t was i d e n t i f i e d i n t h i s manner and r e p l a c e d w i t h i t s synonym from the synonym l i s t p r o v i d e d i n the Guide (Raven, 1958). In Set A the word " d r e s s " was s u b s t i t u t e d f o r " f r o c k " and i n Set B the word " q u a r r e l " was s u b s t i t u t e d f o r " s q u a b b l e . " 63 T e s t e r s I n a l l c a s e s , the WISC-R was a d m i n i s t e r e d by " l e v e l C" (C r o n b a c h , 1970, p. 18) t e s t e r s . G e n e r a l l y , the same p e r s o n a d m i n i s t e r e d a l l t e s t s t o a g i v e n s t u d e n t . I n some s i t u a t i o n s , t he non-WISC-R t e s t s were admin-i s t e r e d by a l e a r n i n g a s s i s t a n c e t e a c h e r o r a f i r s t - y e a r g r a d u a t e s t u d e n t i n s c h o o l p s y c h o l o g y , t r a i n e d t o " l e v e l B" (Cron b a c h , 1970, p. 18) t e s t i n g competence. The t e s t i n g was com p l e t e d by 54 v o l u n t e e r s , many of whom were p r a c t i c i n g s c h o o l p s y c h o l o g i s t s i n the c o o p e r a t i n g s c h o o l d i s t r i c t s , and f i v e p a i d r e s e a r c h a s s i s t a n t s . T e s t i n g P r o c e d u r e s Each t e s t a d m i n i s t r a t o r was s u p p l i e d w i t h a p r o j e c t Handbook (see Appendix C) p r o v i d i n g s t a n d a r d i z a t i o n i n f o r m a t i o n r e g a r d i n g t e s t i n g p r o c e -dures s p e c i f i c t o t h i s s t u d y . The i n d i v i d u a l t e s t a d m i n i s t r a t i o n p r o c e -dures were t h o s e d e s c r i b e d i n the r e s p e c t i v e t e s t manuals w i t h the f o l l o w i n g a l t e r a t i o n s : 1. Only 10 WISC-R s u b t e s t s were g i v e n : Mazes and D i g i t Span were not a d m i n i s t e r e d . 2. The " C a n a d i a n " it e m s were s u b s t i t u t e d f o r the o r i g i n a l t e s t i t e m s on the WISC-R. 3. For the MHVS, the o r a l d e f i n i t i o n s p r o c e d u r e s were used (Raven, 1958, p. 2 9 ) . C h i l d r e n were t e s t e d i n two s e s s i o n s . The WISC-R was a d m i n i s t e r e d i n t he f i r s t s e s s i o n and the r e m a i n i n g t e s t s , i n c o u n t e r b a l a n c e d o r d e r (as shown i n F i g u r e 2) i n the second. I n d i v i d u a l t e s t packages were p r e p a r e d c o n s i s t i n g of t h r e e p a r t s : 1. the r e q u e s t f o r s u b j e c t p a r t i c i p a t i o n form ( s e e Appendix A ) ; 2. the WISC-R p r o t o c o l s w i t h Canadian s u b s t i t u t i o n i t e m s on a s e p a r a t e 64 1, 2, 3 n=30 2, 1, 3 n=30 3, 1, 2 n=30 1, 3, 2 n=30 2, 3, 1 n=30 3, 2, 1 n=30 F i g u r e 2 . T e s t a d m i n i s t r a t i o n o r d e r ( s e c o n d s e s s i o n ) f o r each age group. 1 = PPVT; 2 = SIT; 3 = SPM + MHVS page; and 3. the r e m a i n i n g t e s t s numbered and s t a p l e d t o g e t h e r i n one of the a s s i g n e d sequences. E q u a l numbers of packages were p r e p a r e d f o r each sequence; t e s t sequence was randomly a s s i g n e d a c r o s s a l l s u b j e c t s . A l l t e s t i n g was com p l e t e d between May 1 and December 1 7 , 1 9 7 9 . P r e c e d i n g each t e s t i n g s e s s i o n , s t u d e n t consent f o r p a r t i c i p a t i o n was s e c u r e d . A s t u d e n t code number, b i r t h d a t e , and sex were r e c o r d e d on each t e s t form. T h i s p r o c e d u r e a l l o w e d i d e n t i f i c a t i o n of each s t u d e n t i n terms of each of the s t r a t i f i c a t i o n v a r i a b l e s . S u b j e c t anonymity was g u a r a n t e e d by the absence of s t u d e n t names on any l i s t s or i n any r e c o r d s . S c o r i n g and Data P r e p a r a t i o n Completed t e s t p r o t o c o l s were r e t u r n e d t o U.B.C. To ensure c o n s i s -t e n c y a l l t e s t s were s c o r e d by the r e s e a r c h e r f o l l o w i n g t he d i r e c t i o n s g i v e n i n the r e s p e c t i v e manuals. The e x c e p t i o n t o t h i s was the M i l l H i l l V o c a b u l a r y S c a l e : the s c o r i n g p r o c e d u r e s used f o r t h a t t e s t a r e d e s c r i b e d i n d e t a i l i n the f o l l o w i n g s e c t i o n . Second p a r t y v e r i f i c a t i o n of a 1 0 % random sample of t e s t s r e v e a l e d a . 5 7 % e r r o r r a t e f o r the WISC-R. F o r a l l o t h e r t e s t s , the e r r o r r a t e was 0 % . The d a t a were the n coded w i t h 2 0 % random v e r i f i c a t i o n and keypunched w i t h 1 0 0 7 o v e r i f i c a t i o n . 65 • M i l l H i l l V o c a b u l a r y S c a l e I t was n e c e s s a r y t o c o n s t r u c t s c o r i n g g u i d e s f o r the MHVS s i n c e e x i s t i n g " c r i t e r i a f o r m a r k i n g " were i n c o m p l e t e and p o s s i b l y o b s o l e t e . The MHVS Guide (Raven, 1958) o f f e r s s c o r i n g o u t l i n e s f o r o n l y e v e r y f i f t h word on S e t s A and B, u s i n g c r i t e r i a e s t a b l i s h e d p r i o r t o the s t a n d a r d i z a -t i o n o f the t e s t i n E n g l a n d i n 1943-1944 (Raven, 1958; Raven & Walshaw, 1944). A d d i t i o n a l s c o r i n g c r i t e r i a a r e a v a i l a b l e f o r the f i r s t 40 words of the MHVS (words 1-20 from each o f Set A and Set B) as the y appear i n the C r i c h t o n V o c a b u l a r y S c a l e (Raven, 1954). S i n c e t h e s e c r i t e r i a were e s t a b l i s h e d i n E n g l a n d i n 1949, i t was f e l t t h a t they s h o u l d be examined f o r a p p l i c a b i l i t y t o c u r r e n t Canadian usage. The s c o r i n g g u i d e l i n e s d e v e l o p e d f o r the p r e s e n t s t u d y were based on Canadian S e n i o r D i c t i o n a r y ( A v i s , D r y s d a l e , Gregg, & S c a r g i l l , 1979) d e f i n i t i o n s p l u s meanings commonly g i v e n by c h i l d r e n i n the sample. F o r each word i n b o t h s e t s , e v e r y q u a l i t a t i v e l y unique meaning was r e c o r d e d and a t a l l y was k e p t of the f r e q u e n c y of o c c u r r e n c e f o r the e n t i r e sample. The l i s t of meanings f o r each word was then d i v i d e d i n t o a c c e p t a b l e and u n a c c e p t a b l e r e s p o n s e s f o l l o w i n g the g e n e r a l s c o r i n g p r i n c i p l e s f o r the WISC-R V o c a b u l a r y T e s t ( W e c h s l e r , 1974, pp. 161-162). I n almost a l l c a s e s , t h i s p r o c e d u r e r e s u l t e d i n o b v i o u s c a t e g o r i z a t i o n s and y i e l d e d c r i t e r i a s i m i l a r t o the o r i g i n a l w i t h some r e w o r d i n g s and a d d i t i o n s of ph r a s e s a c c o r d i n g t o c u r r e n t use. There were two pr o b l e m s , however, f o r wh i c h o u t s i d e e x p e r t i s e was sought. One of t h e s e was the q u e s t i o n o f a c c e p t a b i l i t y of s l a n g e x p r e s s i o n s ( e . g . , " r i g h t on," as the meaning f o r " p r e c i s e " ) . The o t h e r c o n c e r n e d t he r e v e r s e p o l a r i z a t i o n of an o r i g i n a l l y u n a c c e p t a b l e response t o a c u r r e n t l y a c c e p t a b l e one. I n the l a t t e r c a s e , one d e f i n i t i o n was i n v o l v e d : t he res p o n s e "mean" t o the s t i m u l u s word " c r u e l " ( S e t B ) . I n the s c o r i n g c r i t e r i a f o r the C r i c h t o n V o c a b u l a r y S c a l e , t he d e f i n i t i o n "mean" was l i s t e d as an u n a c c e p t a b l e r e s p o n s e (Raven, 1954, p. 6 ) . Moreover, t h a t p a r t i c u l a r d e f i n i t i o n was not i n c l u d e d i n the r e s o u r c e d i c t i o n a r y used. I t was, however, g i v e n as a synonym f o r c r u e l by 76% of the p r e s e n t sample. The q u e s t i o n s o f a c c e p t a b i l i t y of common usage and of c o l l o q u i a l i s m s were r e f e r r e d t o a l i n g u i s t . Such i s s u e s a r e commonly r e s o l v e d on an i n d i v i d u a l b a s i s i n r e f e r e n c e t o the i n t e n t i o n of the g i v e n t e s t ( R a l s t a n , N o t e . 3 ) . When the purpose o f the t e s t i s t o measure the v e r n a c u l a r (com-m u n i c a t i o n s ) c h a r a c t e r i s t i c s o f language, common u s a g e — i n c l u d i n g s l a n g — i s a c c e p t a b l e . A c c o r d i n g t o Raven, the aim of the MHVS " i s t o r e c o r d a p e r s o n ' s p r e s e n t r e c a l l of a c q u i r e d i n f o r m a t i o n and a b i l i t y f o r v e r b a l c ommunication" (1958, p. 4 ) . T h i s s t a t e d i n t e n t was judged t o be com-p a t i b l e w i t h t he c r i t e r i o n s t a t e d above. T h e r e f o r e s l a n g e x p r e s s i o n s or c o l l o q u i a l i s m s and commonly g i v e n meanings were c o n s i d e r e d a c c e p t a b l e . The complete s c o r i n g g u i d e s f o r the MHVS as used i n the p r e s e n t s t u d y a r e i n c l u d e d i n Appendix D. DATA ANALYSIS The d a t a a n a l y s i s c o n s i s t e d of two phases: norming and e q u a t i n g . In the norming phase of the s t u d y , t e s t s c o r e s f o r t he B.C. sample were f i r s t compared t o p u b l i s h e d t e s t d a t a t o d e t e r m i n e the a p p l i c a b i l i t y of e x i s t i n g norms. I n Chapt e r IV, the need f o r re n o r m i n g was e s t a b -l i s h e d . The p r e p a r a t i o n o f new norms and the c o m p u t a t i o n o f the s t a t i s -t i c a l p r o p e r t i e s of the renormed t e s t s c o n s t i t u t e d t he rem a i n d e r of t h i s phase. The e q u a t i n g phase i n v o l v e d t he a p p l i c a t i o n of t e s t e q u a t i n g t e c h n i q u e s •67' t o the p a i r s of t e s t s s e l e c t e d on the b a s i s of t h e i r c h a r a c t e r i s t i c s as o u t l i n e d i n T a b l e s 4 and 5. The d e t e r m i n a t i o n of r e l e v a n t t e s t p a i r s f o r i n c l u s i o n i n t h i s a n a l y s i s and the d e s c r i p t i o n of t h e a c t u a l p r o c e d u r e s used a r e i n c l u d e d i n the f i n a l s e c t i o n of t h i s c h a p t e r . P r e l i m i n a r y A n a l y s e s Two p r e l i m i n a r y a n a l y s e s were ru n u s i n g raw s c o r e d a t a from a l l f i v e t e s t s . The f i r s t o f t h e s e was t o d e t e r m i n e the independence of t e s t r e s u l t s from the o r d e r i n w h i c h the t e s t s were a d m i n i s t e r e d . The second was t o d e t e r m i n e the goodness of f i t of the B.C. d a t a t o the t h e o r e t i c a l normal d i s t r i b u t i o n t o judge the adequacy of the a s s u m p t i o n of normal d i s t r i -b u t i o n of i n t e l l i g e n c e t e s t s c o r e s i n : t h e p o p u l a t i o n . Order of A d m i n i s t r a t i o n For each t e s t , a one-way, f i x e d e f f e c t s a n a l y s i s of v a r i a n c e was run w i t h o r d e r of a d m i n i s t r a t i o n as the independent v a r i a b l e . The s i x sequences shown i n F i g u r e 2 were used as s i x l e v e l s of the f a c t o r , o r d e r . The n u l l h y p o t h e s i s t e s t e d was t h a t o r d e r of t e s t a d m i n i s t r a t i o n had no e f f e c t on t e s t s c o r e s . As shown i n Chapter.'.IV, the r e s u l t s c o n f i r m e d the n u l l h y p o t h e s i s . Goodness of F i t The d i s t r i b u t i o n s of raw s c o r e s on the t e n WISC-R s u b t e s t s , the PPVT, the SIT, the SPM, and the MHVS were a n a l y z e d f o r goodness of f i t t o the t h e o r e t i c a l normal d i s t r i b u t i o n e m p l o y i n g the Kolmogorov-Smirnov t e s t ( S i e g e l , 1956). As shown i n C h a p t e r IV, the K-S s t a t i s t i c showed n o n - s i g n i f i c a n t d e p a r t u r e s from n o r m a l i t y f o r a l l t e s t s . 68 D e t e r m i n a t i o n of Norm Re l e v a n c e IQ s c o r e s were d e r i v e d f o r each c h i l d on the WISC-R, PPVT, and SIT u s i n g t he p r o c e d u r e s and s c o r e c o n v e r s i o n t a b l e s i n the r e s p e c t i v e t e s t manuals. For the SPM and MHVS, the raw s c o r e was used s i n c e no s c a l e d s c o r e c o n v e r s i o n s were p r o v i d e d by t h e i r a u t h o r (Raven, 1958, 1960). To a s s e s s t he a p p l i c a b i l i t y of the use of the e x i s t i n g norms f o r each t e s t w i t h B. C. c h i l d r e n , measures of c e n t r a l tendency and v a r i a b i l i t y were com-pu t e d and compared t o the p u b l i s h e d norm d a t a . The p u b l i s h e d v a l u e s used i n t h e s e c omparisons a r e shown i n T a b l e 12. Ta b l e 12 Measures of C e n t r a l Tendency and V a r i a b i l i t y R e p o r t e d i n T e s t Manuals (b) (a) S t a n d a r d Mean IQ D e v i a t i o n WISC-R 100 15 PPVT 100 15 SIT 100 16 Median Raw Score SPM 7%. 17 9% 24 11% 35 MHVS 7% 16 9% 22 11% 28 ,69 C e n t r a l Tendency Each t e s t was t r e a t e d s e p a r a t e l y s i n c e the u n i t of i n t e r e s t was the i n d i v i d u a l t e s t and s i n c e the t e s t s a r e not a d m i n i s t e r e d i n c o m b i n a t i o n r e g u l a r p r a c t i c e . A c c o r d i n g l y the one sample t t e s t was used t o t e s t f o r d i f f e r e n c e s i n means between the B.C. sample and the p u b l i s h e d means: X. - a t = S v//n~ ( G l a s s & S t a n l e y , 1970, p. 293) A where X. i s the B.C. mean a i s the p u b l i s h e d mean S i s the B.C. s t a n d a r d d e v i a t i o n , and X n i s the sample s i z e The p u b l i s h e d median raw s c o r e v a l u e s were s u b s t i t u t e d f o r a f o r t h e SPM and MHVS s i n c e i t was assumed t h a t the s c o r e d i s t r i b u t i o n s 7 f o r the o r i g i n a l s t a n d a r d i z a t i o n samples were s y m m e t r i c a l and c o n s e q u e n t l y t h a t the mean and median were e q u a l . V a r i a n c e The t e s t s t a t i s t i c used f o r a s s e s s i n g c o r r e s p o n d i n g d i f f e r e n c e s i n v a r i a n c e was: ( n - l ) S y 2 2 _ X b ( G l a s s &:Stanley, 1970, p. 301) where S v 2 i s the B.C. v a r i a n c e , and X b i s the p u b l i s h e d v a r i a n c e S i n c e df > 30, the v a l u e of the t e s t s t a t i s t i c was ^con v e r t e d t o a s t a n d a r d normal d e v i a t e z = /2x 2 - /2df - 1 ( G l a s s & S t a n l e y , 1970, p. 520) f o r h y p o t h e s i s t e s t i n g p u r p o s e s . The r e s u l t s of t h e s e two t e s t s r e v e a l e d t h a t , i n m o s t e a s e s , t h e s c o r e s f o r t he B.C. sample were s i g n i f i c a n t l y d i f f e r e n t from the p u b l i s h e d norm 70 -v a l u e s (see C h a p t e r I V ) . T h e r e f o r e i t was n e c e s s a r y t o renorm the t e s t s f o r B.C. P r e p a r a t i o n of B.C. Norms I n t h i s s e c t i o n t he norming p r o c e d u r e s a r e d e s c r i b e d f o r each t e s t i n d i v i d u a l l y . IQ c o n v e r s i o n t a b l e s w i t h mean 100 and s t a n d a r d d e v i a t i o n 15 were p r e p a r e d f o r t h r e e t e s t s : t he WISC-R, PPVT, and SIT. The r e s u l t -i n g IQ s c a l e s a r e comparable i n the.:sense d e s c r i b e d i n C h a p t e r s I and I I . That i s , the t e s t s were a d m i n i s t e r e d t o the same group and s c a l e d " i n such a way t h a t t he mean and s t a n d a r d d e v i a t i o n have the same n u m e r i c a l v a l u e s , r e s p e c t i v e l y , on each of the v a r i o u s t e s t s " ( A n g o f f , 1971, p. 590). T h e r e -f o r e , a g i v e n IQ s c o r e v a l u e has a c o n s t a n t meaning on a l l t e s t s i n terms of r e l a t i v e p o s i t i o n w i t h i n the p o p u l a t i o n r e p r e s e n t e d by the B.C. s t a n d a r d -i z a t i o n sample. Fo r the WISC-R and the PPVT d e v i a t i o n IQ t a b l e s were c o n s t r u c t e d f o l l o w i n g t he p r o c e d u r e s used i n the p r e p a r a t i o n of the r e s p e c t i v e p u b l i s h e d norms. The PPVT s c a l i n g p r o c e d u r e was a p p l i e d t o SIT s c o r e s as w e l l . T h i s r e p r e s e n t s . a change i n m e t r i c f o r t he SIT s i n c e t he p u b l i s h e d norms i n c l u d e m e n t a l age and r a t i o IQ c a l c u l a t i o n s . N o r m a t i v e d a t a f o r t h e SPM arid MHVS were p r e p a r e d as p e r c e n t i l e r a n k s a s s o c i a t e d w i t h t h e raw s c o r e d i s t r i b u t i o n s . IQ s c o r e c o n v e r s i o n s were not p r o v i d e d f o r t h e s e t e s t s s i n c e i t was f e a r e d t h a t t h e y would be misu s e d . S p e c i f i c a l l y , s i n c e o n l y the SPM i s commonly used ( t h e MHVS i s v i r t u a l l y unknown i n B.C.), i t i s l i k e l y t h a t the p r o v i s i o n of IQ s c o r e c o n v e r s i o n s would r e s u l t i n the i s o l a t e d r e p o r t i n g of SPM IQs. S i n c e such usage would be i n v i o l a t i o n of Raven's i n t e n t (see C h a p t e r I I ) , t he s c o r e s on t h e s e two t e s t s were r e p o r t e d as i n the o r i g i n a l t e s t manuals (Raven, 1958, 1960). A l l norm t a b l e s a r e i n c l u d e d i n Appendix E. •71 W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n - R e v i s e d I n a c c o r d a n c e w i t h the p r o c e d u r e s r e p o r t e d f o r the WISC-R (Herman, Note 4; M a t a r a z z o , ., 1972 ; W e c h s l e r , 1974), t a b l e s of n o r m a l i z e d s c a l e d s c o r e e q u i v a l e n t s (mean 10, s t a n d a r d d e v i a t i o n 3) of raw s c o r e s were p r e -p a r e d f o r each of the t e n s u b t e s t s f o r each age group. IQ e q u i v a l e n t s (mean 100, s t a n d a r d d e v i a t i o n 15) were the n p r e p a r e d f o r t h r e e sums of s c a l e d s c o r e s : V e r b a l , P e r f o r m a n c e , and F u l l S c a l e . These p r o c e d u r e s a r e d e s c r i b e d i n d e t a i l i n t h i s s e c t i o n . I n a d d i t i o n , an a l t e r n a t e norming method employ i n g a g r a p h i n g t e c h n i q u e ( A n g o f f , 1971) was a p p l i e d t o the s u b t e s t s c o r e s f o r c o m p a r a t i v e p u r p o s e s . D e r i v a t i o n of S u b t e s t S c a l e d S c o r e s 1. The p u b l i s h e r s ' method. The p r o c e d u r e s f o l l o w e d f o r n o r m a l i z i n g the o b s e r v e d s c o r e d i s t r i b u t i o n s and t r a n s f o r m i n g them t o s c a l e d s c o r e s were t h o s e used by the P s y c h o l o g i c a l C o r p o r a t i o n f o r the W e c h s l e r t e s t s (Herman, Note 4 ) . The s t e p s are d e s c r i b e d below and an a c t u a l example of the c a l c u l a t i o n s i s p r e s e n t e d i n T a b l e 13. ( i ) The f r e q u e n c y d i s t r i b u t i o n of raw s c o r e s was r e c o r d e d w i t h e v e r y raw s c o r e r e p r e s e n t e d . T h i s c o r r e s p o n d s t o the f i r s t two columns of T a b l e 13. ( i i ) The v a l u e f was computed f o r each s c o r e . T h i s v a l u e i s the f r e -quency f o r a s c o r e p l u s the f r e q u e n c y f o r the s c o r e i m m e d i a t e l y above. ( i i i ) The f i r s t and l a s t f r e q u e n c i e s were p a r t i t i o n e d o f f as i l l u s t r a t e d , ( i v ) The q v a l u e s f o r the f i r s t and l a s t f r e q u e n c i e s ( i . e . , t h o s e above and below the p a r t i t i o n s ) were computed as f / n . (v) The r e m a i n i n g q v a l u e s were c a l c u l a t e d by c u m u l a t i v e l y d i v i d i n g the f' v a l u e s by 2n from the top down. Thus, f o r raw s c o r e 24, T a b l e 13 Example of Computation of S c a l e d Score E q u i v a l e n t s of Raw Sc o r e s WISC-R I n f o r m a t i o n S u b t e s t Age 11%, n=108 T o t a l Raw Score f f q x SS 30 29 28 27 26 1 1 .009 2.70 18.0 25 2 3 .018 2.46 17.4 24 0 2 .028 1.91 15.7 23 3 3 .042 1.73 15.2 22 0 3 .056 1.59 14.8 21 7 7 .088 1.35 14.0 20 8 15 .157 1.01 13-0 19 12 20 .250 .67 12.0 18 12 24 .361 .36 11.1 17 7 19 .449 .13 10.4 16 10 17 .528 .07 9.8 15 6 16 .602 .26 9.2 14 14 20 .694 .51 8.5 13 10 24 .806 .86 7.4 12 4 14 .870 1.13 6.6 11 6 10 .917 1.38 5.9 10 4 10 .963 1.79- 4.6 9 1 5:' .986 2.20 3.4 8 0 1 .991 2.37 2.9 7 1 1 .009 2. 70 1.9 6 — 1 — — — 5 4 3 73 the c u m u l a t i v e f' i s 6. The q v a l u e was c a l c u l a t e d as 6/216. ( v i ) The x v a l u e s r e c o r d e d i n column 5 of T a b l e 13 were r e a d from the normal c u r v e t a b l e i n K e l l e y ( 1 9 2 4 ) . For the f i r s t and l a s t raw s c o r e s r e p r e s e n t e d i n the f r e q u e n c y d i s t r i b u t i o n ( i . e . , t h o s e w i t h p a r t i t i o n e d - o f f q v a l u e s ) the t a b l e s were e n t e r e d w i t h q v a l u e s and the c o r r e s p o n d i n g X v a l u e s were r e a d . For the remaining'. q v v a l u e s l e s s t h a n .500, the t a b l e s were e n t e r e d w i t h q and c o r r e s -ponding z / q v a l u e s were r e c o r d e d . F o r q v a l u e s g r e a t e r than .500, q was c o n s i d e r e d as p when e n t e r i n g the t a b l e s ; z / q v a l u e s were r e c o r d e d . ( v i i ) A l i n e was drawn a c r o s s the l a s t t h r e e columns above the f i r s t q t h a t exceeds .500. The s c a l e d s c o r e s above t h i s l i n e were com-p u t e d as SS = 10 + 3X. Below the l i n e , s c a l e d s c o r e s were computed as SS = 10 - 3X. The s c a l e d s c o r e range 1 t o 19 was adopted from the WISC-R. F o r many of the t e s t s , i t was n e c e s s a r y t o e x t r a p o l a t e and smooth s c o r e s i n the extreme t a i l s of d i s t r i b u t i o n s . T h i s was .done i n a manner t o p r e s e r v e the form of the d i s t r i b u t i o n and t o p r o v i d e a p r o g r e s s i o n of s c a l e d s c o r e s from age t o age. 2. A g r a p h i c method. Because of the a r b i t r a r i n e s s of smoothing s c o r e s i n the t a i l s of the d i s t r i b u t i o n s u s i n g the f i r s t a p p r o a c h , an a l t e r n a t e method based on a g r a p h i n g t e c h n i q u e was employed i n the hope t h a t i t would f a c i l i t a t e the e x t r a p o l a t i o n p r o c e d u r e . T h i s method was d e s c r i b e d by A n g o f f (1971, pp. 515-518) and i n v o l v e d the f o l l o w i n g s t e p s (as i l l u s t r a t e d i n T a b l e 14 and F i g u r e 3 ) : ( i ) The f r e q u e n c y d i s t r i b u t i o n of a s e t of raw s c o r e s f o r a t e s t i s p r e p a r e d . 74 T a b l e 14 Example of the G r a p h i c S c a l e d Score C o n v e r s i o n Approach WISC-R I n f o r m a t i o n S u b t e s t Age 11%, n=108 C u m u l a t i v e P e r c e n t i l e Raw Frequency Frequency P e r c e n t Rank ( f r o m Normal S c a l e d S c o r e s D i s t r i b u t i o n D i s t r i b u t i o n Below F i g - 3) D e v i a t e Score 30 99.86 2.99 19.0 29 99.74 2.8 18.4 28 99.57 2.63 17.9 27 99.25 2.43 17.3 26 1 108 99.07 98.73 2.24 16.7 25 2 107 97.22 97.75 2.0 16.0 24 96.3 1.79 15.4 23 3 105 94.44 94.3 1.58 14.7 22 91.45 1.37 14.1 21 7 102 87.96 87.5 1.15 13.4 20 8 95 80.56 82. 0.92 12.8 19 12 87 69.44 74.75 0.67 12.0 18 12 75 58.33 65.8 0.41 11.2 17 7 63 51.85 55.5 0.14 10.4 16 10 56 42.59 44.5 -0.14 9.6 15 6 46 37.04 33.0 -0.44 8.7 14 14 40 24.07 23.5 -0.72 7.8 13 10 26 14.82 15.0 -1.04 6.9 12 4 16 11.11 9.0 -1.34 6.0 11 6 12 5.56 5.0 -1.65 5.0 10 4 6 1.85 2.4 -1.98 4.1 9 1 2 .93 .95 -2.35 3.0 8 .325 -2.73 1.8 7 1 1 .078 < 3.00 1.0 6 5 4 3 2 1 > ON 99 U J 98 => o 95 U J cr 90 L L 80 U J > 70 60 < 50 _ J ZD 40 30 no 20 U J 10 > 5 < 2 - J U J 1 CC 10 15 2 0 2 5 RAW SCORE Figure 3 . Relative cumulative frequencies for the WISC-R Information subtest, age 11%. 76 ( i i ) R e l a t i v e c u m u l a t i v e f r e q u e n c i e s ( p e r c e n t below each s c o r e v a l u e ) are computed. These are p l o t t e d and smoothed on a r i t h m e t i c graph p a p e r . ( i i i ) New p e r c e n t i l e rank v a l u e s a r e r e a d from the smoothed c u r v e and c o r r e s p o n d i n g normal d e v i a t e s ( z ) a r e d e t e r m i n e d u s i n g a t a b l e of a r e a s of the u n i t normal d i s t r i b u t i o n , ( i v ) F i n a l l y , the v a l u e s a r e t r a n s f o r m e d t o a s c a l e h a v i n g the d e s i r e d mean and s t a n d a r d d e v i a t i o n , i n t h i s case 10 and 3 r e s p e c t i v e l y . D e r i v a t i o n of V e r b a l , P e r f o r m a n c e , and F u l l S c a l e IQ S c o r e s Three sums of s c a l e d s c o r e s ( V e r b a l , P e r f o r m a n c e , and F u l l S c a l e ) were o b t a i n e d f o r each c h i l d . The V e r b a l Score and Performance Score are the sums of the f i v e v e r b a l s u b t e s t s c a l e d s c o r e s and the f i v e p e r -formance s u b t e s t s s c a l e d scores' r e s p e c t i v e l y . The F u l l S c a l e Score i s the sum of a l l t e n s u b t e s t s c o r e s . F o r each age group, the means and s t a n d a r d d e v i a t i o n s were computed s e p a r a t e l y f o r each sum of s c a l e d s c o r e s . As found w i t h the American s t a n d a r d i z a t i o n sample ( W e c h s l e r , 1974, p. 23) and as r e v e a l e d i n T a b l e 30 ( C h a p t e r IV) f o r the B.C. sample, t h e s e d a t a were s i m i l a r a c r o s s ages. T h e r e f o r e , the r e s p e c t i v e sums of s c a l e d s c o r e s f o r a l l age groups combined were used as a b a s i s f o r c o n s t r u c t i n g the t h r e e c o r r e s p o n d i n g IQ t a b l e s . For each IQ s c a l e , the mean and s t a n d a r d d e v i a t i o n were s e t e q u a l t o 100 and 15 r e s p e c t i v e l y . The c o n v e r s i o n from sums of s c a l e d s c o r e s t o e q u i v a l e n t IQ v a l u e s was a c c o m p l i s h e d u s i n g the f o l l o w i n g f o r m u l a : IQ = ^ (X. - X . ) + 100 ( M a t a r a z z o , 1972, p. 509) bx 1 where S = s t a n d a r d d e v i a t i o n f o r a l l age groups combined f o r the approp-A r i a t e sum of s c a l e d s c o r e s 77 = any sum of s c a l e d s c o r e s X. = mean f o r a l l age groups combined f o r the a p p r o p r i a t e sum of s c a l e d s c o r e s . As i n the WISC-R Manual, f o r the V e r b a l and Performance S c a l e s , IQs were extended t o 3 2/3 s t a n d a r d d e v i a t i o n s on e i t h e r s i d e o f the mean, and range from 45 t o 155. F o r the F u l l S c a l e , IQs were extended t o 4 s t a n d a r d d e v i a t i o n s on e i t h e r s i d e o f the mean, and range from 40 t o 160. The p e r c e n t i l e r a n k s p u b l i s h e d i n the WISC-R Manual ( W e c h s l e r , 1974, p. 25) may be a p p l i e d t o the B.C. WISC-R norms. T h e r e f o r e new p e r c e n t i l e r a n k s were not c a l c u l a t e d . Peabody P i c t u r e V o c a b u l a r y T e s t and S l o s s o n I n t e l l i g e n c e T e s t The raw s c o r e s c a l e s f o r b o t h the PPVT and SIT were c o n v e r t e d t o IQ e q u i v a l e n t s f o l l o w i n g the p r o c e d u r e r e p o r t e d i n the PPVT Manual (Dunn, 1965, pp. 28-29). The c o n v e r s i o n f o r m u l a was i d e n t i c a l t o t h a t used i n the d e r i v a t i o n of the WISG-R IQs. U n l i k e the WISC-R, however, the PPVT and SIT IQ c o n v e r s i o n s were c a l c u l a t e d i n d e p e n d e n t l y f o r each age l e v e l . Thus the means and s t a n d a r d d e v i a t i o n s e n t e r e d i n t o t he e q u a t i o n were computed f o r each age s e p a r a t e l y . The IQs were extended t o 4 s t a n d a r d d e v i a t i o n s on e i t h e r s i d e of the mean, r a n g i n g from 40 t o 160. P e r c e n t i l e r a n k s a s s o c i a t e d w i t h the s c o r e d i s t r i b u t i o n s f o r the PPVT and SIT were d e r i v e d u s i n g the f o r m u l a : % i l e = + c f ) (Dunn, 1965, p. 29) where n = number of ca s e s i n d i s t r i b u t i o n , f = f r e q u e n c y o f a s c o r e , and c f = c u m u l a t i v e f r e q u e n c y o f a s c o r e . 78 S t a n d a r d P r o g r e s s i v e M a t r i c e s and M i l l H i l l V o c a b u l a r y S c a l e I n the p r e p a r a t i o n o f the norms and i n a l l f u t u r e c a l c u l a t i o n s , the MHVS s c o r e r e p r e s e n t s t he t o t a l s c o r e on S e t s A and B. No r m a t i v e i n f o r m a t i o n f o r the SPM and MHVS was p r e p a r e d as raw s c o r e d i s t r i b u t i o n s w i t h c o r r e s p o n d i n g p e r c e n t i l e r a n k s f o r each age group, c a l c u l a t e d as shown above. T h i s i s c o n s i s t e n t w i t h t he p u b l i s h e d norm d a t a f o r t h e s e two t e s t s (Raven, 1958, 1960). S t a t i s t i c a l P r o p e r t i e s of the T e s t s As a f i n a l s t e p i n the norming phase, i n t e r n a l - c o n s i s t e n c y r e l i a b i l -i t y c o e f f i c i e n t s and s t a n d a r d e r r o r s o f measurement f o r each t e s t were c a l c u l a t e d as d e s c r i b e d below. The i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t s used and the i t e m components i n c l u d e d i n t h e i r c a l c u l a t i o n s a r e summarized i n T a b l e 15. W i t h t he e x c e p t i o n o f the WISC-R IQ S c a l e s , a l l c o e f f i c i e n t s a r e s p l i t - h a l f c o r r e l a -t i o n s c o r r e c t e d by the Spearman-Brown f o r m u l a . Items were e x c l u d e d from the c a l c u l a t i o n s as not e d i n o r d e r t o y i e l d s p l i t t e s t h a l v e s w i t h e q u a l t o t a l s c o r e s . Coding i s a speeded t e s t f o r w h i c h s p l i t - h a l f t e c h n i q u e s are i n a p p r o p r i a t e . L i m i t a t i o n s on time and a v a i l a b i l i t y of t e s t e r s p r e -c l u d e d the p o s s i b i l i t y of g e t t i n g ; . a t e s t - r e t e s t r e l i a b i l i t y c o e f f i c i e n t f o r Coding ( c f . W e c h s l e r , 1974); t h e r e f o r e r e l i a b i l i t y e s t i m a t e s f o r t h i s s u b t e s t a r e not a v a i l a b l e . Some of the WISC-R s u b t e s t s , as w e l l as t he PPVT and the SIT have v a r i a b l e b a s a l l e v e l s below w h i c h items a r e s c o r e d as c o r r e c t a l t h o u g h t h e y a r e not i n f a c t i n c l u d e d i n the q u e s t i o n i n g . To a v o i d a r t i f i c i a l l y i n f l a t i n g i n t e r n a l c o n s i s t e n c y e s t i m a t e s by i n c l u d i n g t h e s e i t e m s , t o t a l "odd" s c o r e and t o t a l "even" s c o r e were c a l c u l a t e d on the b a s i s o f item s a c t u a l l y p r e s e n t e d ; t h a t i s a l l i t e m s w i t h i n the b a s a l t o c e i l i n g range. T h i s was not n e c e s s a r y w i t h t he WISC-R T e s t Table 15 Form of R e l i a b i l i t y C o e f f i c i e n t Computed R e l i a b i l i t y C o e f f i c i e n t Components WISC-R I n f o r m a t i o n S i m i l a r i t i e s A r i t h m e t i c V o c a b u l a r y Comprehension P i c t u r e C o m p l e t i o n P i c t u r e Arrangement B l o c k D e s i g n O b j e c t Assembly Coding V e r b a l IQ Performance IQ F u l l S c a l e IQ PPVT SIT SPM MHVS s p l i t - h a l f (odd v s . s p l i t - h a l f (odd v s . s p l i t - h a l f (odd v s . s p l i t - h a l f (odd v s . s p l i t - h a l f (odd v s . s p l i t - h a l f (odd vs. s p l i t - h a l f (odd vs. s p l i t - h a l f (odd vs. s p l i t - h a l f (odd vs. none even i t e m s ) , Spearman-Brown c o r r e c t i o n even i t e m s ) , Spearman-Brown c o r r e c t i o n Spearman-Brown c o r r e c t i o n Spearman-Brown c o r r e c t i o n Spearman-Brown c o r r e c t i o n even i t e m s ) , even i t e m s ) , even i t e m s ) , even i t e m s ) , Spearman-Brown c o r r e c t i o n even i t e m s ) , Spearman-Brown c o r r e c t i o n even i t e m s ) , Spearman-Brown c o r r e c t i o n even i t e m s ) , Spearman-Brown c o r r e c t i o n r e l i a b i l i t y o f a c o m p o s i t e group of t e s t s ( G u i l f o r d , 1954) r e l i a b i l i t y of a composite group of t e s t s ( G u i l f o r d , 1954) r e l i a b i l i t y of a c o m p o s i t e group of t e s t s ( G u i l f o r d , 1954) s p l i t - h a l f (odd v s . even i t e m s ) , Spearman-Brown c o r r e c t i o n s p l i t - h a l f (odd v s . even i t e m s ) , Spearman-Brown c o r r e c t i o n s p l i t - h a l f (odd v s . even items*), Spearman-Brown c o r r e c t i o n s p l i t - h a l f ( S e t A v s . Set B ) , -Spearman-Brown c o r r e c t i o n b a s a l i t e m t o c e i l i n g i t e m i t e m #1 t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m 1 b a s a l i t e m t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m 2 a l l i t e m s 3 5 v e r b a l t e s t s 4 performance t e s t s 9 t e s t s b a s a l i t e m t o c e i l i n g i t e m b a s a l i t e m t o c e i l i n g i t e m a l l items i t e m #1 t o c e i l i n g i t e m , b o t h s e t s E x c l u d i n g item #17; 2 e x c l u d i n g item #1; E x c l u d i n g s c o r e of 9 on item #4; s c o r e d as 8. 80 S i m i l a r i t i e s and O b j e c t Assembly s u b t e s t s or w i t h the SPM and MHVS s i n c e , f o r each of t h e s e , the b a s a l i t e m i s f i x e d a t i t e m #1 f o r a l l ages. The c o e f f i c i e n t s f o r the WISC-R IQ S c a l e s were o b t a i n e d from the f o r m u l a f o r the r e l i a b i l i t y o f a composite group o f t e s t s ( G u i l f o r d , 1954, p. 3 9 3 ) . As i n d i c a t e d i n T a b l e 15, t h e s e a r e based on s u b t e s t c o m b i n a t i o n s e x c l u d i n g C o d i n g . S t a n d a r d e r r o r s of measurement were c a l c u l a t e d f o r a l l t e s t s u s i n g the f o r m u l a : S E M = S X ^ " rXX where S = s t a n d a r d d e v i a t i o n , and X r = r e l i a b i l i t y c o e f f i c i e n t . XX These were d e r i v e d u s i n g s c a l e d s c o r e u n i t s f o r the WISC-R s u b t e s t s ; IQ u n i t s f o r the WISC-R IQ s c a l e s , the PPVT, and the SIT; and raw s c o r e u n i t s f o r the SPM and MHVS. E q u a t i n g The purpose of the e q u a t i n g phase of the stu d y was t o e x p l o r e e m p i r -i c a l l y t he e q u i v a l e n c e of f o u r t e s t s — P P V T , SIT, SPM, M H V S — t o the WISC-R. The method adopted was t o a p p l y t e s t e q u a t i n g p r o c e d u r e s t o p a i r s of p s y c h o l o g i c a l l y and t e c h n i c a l l y e q u i v a l e n t t e s t s and t o examine the a c c u r -acy of the c o n v e r t e d s c o r e s . As d i s c u s s e d i n C h a p t e r s I and I I , the o p e r a t i o n a l d e f i n i t i o n of t e c h n i c a l e q u i v a l e n c e used i n t h i s s t u d y was based on the concept of n o m i n a l p a r a l l e l i s m ( L o r d , 1964; L o r d & N o v i c k , 1968). Two t e s t s were c o n s i d e r e d n o m i n a l l y p a r a l l e l i f th e y measured the same p s y c h o l o g i c a l f u n c t i o n , were used i n t e r c h a n g e a b l y , and had a d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c i e n t of a t l e a s t .70. The f i r s t s t e p i n the e q u a t i n g phase o f the a n a l y s i s was t o de t e r m i n e i f the t e s t p a i r s i d e n t i f i e d as p s y c h o l o g i c a l l y e q u i v a l e n t i n Chapter n 81 f u r t h e r s a t i s f i e d t he s t a t i s t i c a l c r i t e r i o n f o r e q u a t i n g . These t e s t s were the n a s s i g n e d t o o b s e r v e d s c o r e o r t r u e s c o r e e q u a t i n g methods on the b a s i s of the s i m i l a r i t y of t h e i r r e l i a b i l i t y c o e f f i c i e n t s . A summary of t e s t c h a r a c t e r i s t i c s and e q u a t i n g methods was p r e s e n t e d i n Ta b l e 5 and i s d e s c r i b e d i n d e t a i l i n the f o l l o w i n g s e c t i o n s . D e t e r m i n a t i o n of N o m i n a l l y P a r a l l e l T e s t P a i r s B o t h A n g o f f (1971) and L o r d (1950) s t r e s s the use of raw s c o r e s i n e q u a t i n g p r o c e d u r e s . S i n c e WISC-R s c o r e s a r e commonly used o n l y i n s c a l e d s c o r e and IQ s c o r e form, i t was n e c e s s a r y t o c r e a t e a new type of WISC-R s c o r e c o r r e s p o n d i n g t o raw s c o r e r a t h e r t h a n n o r m a l i z e d s c o r e d i s t r i b u t i o n s . The WISC-R components of i n t e r e s t i n the e q u a t i n g phase a re the summary V e r b a l , P e r f o r m a n c e , and F u l l S c a l e s c o r e s . I t w i l l be r e c a l l e d t h a t , i n the norming p r o c e d u r e s , t h e s e summary s c o r e s were a d d i t i v e c o m b i n a t i o n s of s c a l e d s c o r e s on groups of s u b t e s t s . To d e r i v e c o r r e s p o n d i n g raw s c o r e c o m b i n a t i o n s , however, a d i r e c t summing of s u b t e s t raw s c o r e s i s not p o s s i b l e s i n c e t h e y a r e i n d i f f e r e n t m e t r i c s . T h e r e f o r e i t was n e c e s s a r y t o r e s c a l e the s u b t e s t s t o p r o v i d e e q u a l s c o r e i n t e r v a l s . To a c c o m p l i s h t h i s , s c o r e s on each s u b t e s t were t r a n s f o r m e d t o s t a n d a r d ( z ) s c o r e s w i t h mean 0, s t a n d a r d d e v i a t i o n 1. A V e r b a l s c o r e was c r e a t e d f o r each i n d i v i d u a l c o n s i s t i n g of t h e sum of z - s c o r e s f o r the f i v e v e r b a l t e s t s . S i m i l a r l y , a Performance s c o r e was c r e a t e d as t h e sum of z - s c o r e s f o r t he f i v e p erformance t e s t s . The F u l l S c a l e s c o r e s c o n s i s t e d o f the sum of z - s c o r e s on a l l 10 t e s t s . These summary g r o u p i n g s c o r r e s p o n d t o the s u b t e s t c o m b i n a t i o n s f o r the V e r b a l , P e r f o r m a n c e , and F u l l S c a l e IQs. To a v o i d w o r k i n g w i t h n e g a t i v e numbers, the t h r e e summary s c o r e s were i n t u r n c o n v e r t e d t o s t a n d a r d i z e d s c o r e s w i t h mean 100 and s t a n d a r d d e v i a t i o n .15. These a re r e f e r r e d t o i n the f o l l o w i n g d i s c u s s i o n as " s t a n d a r d i z e d " 82 t o d i s t i n g u i s h them from IQ s c o r e s . Product-moment c o r r e l a t i o n c o e f f i c i e n t s were c a l c u l a t e d f o r a l l p a i r -i n g s of the t h r e e WISC-R s t a n d a r d i z e d s c o r e s ( V e r b a l , P e r f o r m a n c e , and F u l l S c a l e ) w i t h the raw s c o r e s of the r e m a i n i n g f o u r t e s t s . These were c o r r e c t e d f o r a t t e n u a t i o n u s i n g the f o r m u l a r /Vr- r where r and r XY AA Y.Y XX YY are i n t e r n a l c o n s i s t e n c y measures and r i s the c o r r e l a t i o n between.the A Y t e s t s . As d i s c u s s e d p r e v i o u s l y , n o m i n a l l y p a r a l l e l t e s t p a i r s were s t a t i s -t i c a l l y d e f i n e d as t h o s e h a v i n g d i s a t t e n u a t e d c o r r e l a t i o n s of .70 or more. E x a m i n a t i o n of the c o r r e c t e d c o r r e l a t i o n c o e f f i c i e n t s i n T a b l e 3 3 ( C h a p t e r IV) shows t h a t , w i t h the e x c e p t i o n of the SPM, the s t a t i s t i c a l e v i d e n c e of p a r a l l e l i s m c o r r e s p o n d s t o the p s y c h o l o g i c a l e v i d e n c e summarized i n T a b l e 4. S i n c e the s t r i c t l y v e r b a l t e s t s , PPVT and MHVS, were c o n s i d e r e d l o g i c a l l y " e q u a t a b l e " o n l y t o the WISC-R V e r b a l S c a l e , no attempt was made t o equate v e r b a l t e s t s c o r e s t o WISC-R F u l l S c a l e s c o r e s . The a s t e r i s k s i n T a b l e 33 ( C h a p t e r IV) i n d i c a t e t e s t p a i r s i d e n t i f i e d f o r e q u a t i n g as j o i n t l y d e t e r m i n e d by the p s y c h o l o g i c a l and s t a t i s t i c a l c r i t e r i a d e v e l o p e d f o r t h i s s t u d y . Assignment of Test P a i r s t o E q u a t i n g Methods I n C h a p t e r I I I , t h r e e e q u a t i n g methods were i d e n t i f i e d based on A n g o f f ' s (1971) work: l i n e a r o b s e r v e d s c o r e e q u a t i n g , l i n e a r t r u e s c o r e e q u a t i n g ; and e q u i p e r c e n t i l e e q u a t i n g . A d i s t i n c t i o n was made between the a p p l i c a b i l i t y of o b s e r v e d s c o r e and t r u e s c o r e e q u a t i n g methods on the b a s i s o f the s i m i l a r i t y o f the t e s t s ' r e l i a b i l i t y c o e f f i c i e n t s . N o m i n a l l y p a r a l l e l t e s t s w i t h e q u a l , o r almo s t e q u a l , r e l i a b i l i t i e s can be equated u s i n g o b s e r v e d s c o r e s . When the r e l i a b i l i t i e s a r e u n e q u a l , p r o c e d u r e s based on t r u e s c o r e d i s t r i b u t i o n s must be used. 83 There are no s p e c i f i c g u i d e l i n e s r e g a r d i n g the t o l e r a n c e of e q u a t i n g p r o c e d u r e s from e x a c t e q u a l i t y of r e l i a b i l i t i e s . Marks and L i n d s a y (1972) used t e s t p a i r s w i t h as l a r g e as a .20 d i s c r e p a n c y between r e l i a b i l i t y c o e f f i c i e n t s and found n o n - s i g n i f i c a n t e f f e c t s f o r r e l i a b i l i t y on s i z e of e q u a t i n g e r r o r . A much more c o n s e r v a t i v e d i f f e r e n c e (> .06) was adopted i n the p r e s e n t study t o ensure the i n c l u s i o n of the t r u e s c o r e e q u a t i n g method. E x a m i n a t i o n o f the r e l i a b i l i t y c o e f f i c i e n t s i n T a b l e 31 ( C h a p t e r IV) r e s u l t e d i n the f u r t h e r s u b d i v i s i o n of the p r e v i o u s l y i d e n t i -f i e d n o m i n a l l y p a r a l l e l t e s t p a i r s i n t o t h o s e w i t h " e q u a l " and " u n e q u a l " r e l i a b i l i t i e s . T h i s s t e p c o r r e s p o n d e d t o the assignment of t e s t p a i r s to o b s e r v e d s c o r e and t r u e s c o r e e q u a t i n g methods as shown i n T a b l e ( C h a p t e r I V ) . L i n e a r E q u a t i n g ( E q u a l l y R e l i a b l e T e s t s ) The use of a l i n e a r t r a n s f o r m a t i o n f o r the purpose of e q u a t i n g two t e s t s i s p r e d i c a t e d on the f o l l o w i n g a s s u m p t i o n s : 1. the t e s t s a r e ( n o m i n a l l y ) p a r a l l e l , 2. the t e s t s a r e e q u a l l y r e l i a b l e , and 3. the s c o r e d i s t r i b u t i o n s of the t e s t s a r e i d e n t i c a l ( c f . A n g o f f , 1971). I n the p r e s e n t s t u d y , s p e c i f i c t e s t p a i r s w h i c h s a t i s f i e d the f i r s t two a s s u m p t i o n s were s e l e c t e d f o r e q u a t i n g . F u r t h e r , s i n c e a l l t e s t s c o r e d i s t r i b u t i o n s were shown not t o d e p a r t s i g n i f i c a n t l y from n o r m a l i t y the t e s t p a i r s s e l e c t e d on the b a s i s of assumptions 1 and 2 were a d d i t i o n a l l y c o n s i d e r e d t o s a t i s f y a s s u m p t i o n 3. W i t h i n the g e n e r a l l i n e a r method, the r e l e v a n t p r o c e d u r e f o r the c a l c u l a t i o n o f c o n v e r t e d s c o r e s i s d e t e r m i n e d by the n a t u r e of the d a t a c o l l e c t i o n d e s i g n . I n the p r e s e n t s t u d y , the s u b j e c t s were s e l e c t e d randomly and a l l t e s t s were a d m i n i s t e r e d t o a l l s u b j e c t s i n c o u n t e r b a l a n c e d 84 o r d e r . T h i s d e s i g n s a t i s f i e s the r e q u i r e m e n t s f o r L o r d ' s Case I model (1950, pp. 4-8) p r o v i d e d a f o u r t h a s s u m p t i o n can be met, namely: 4. the t e s t r e s u l t s a r e u n a f f e c t e d by the o r d e r of a d m i n i s t r a t i o n of the t e s t s . I t was p o i n t e d out e a r l i e r t h a t the s c o r e s from the f i v e t e s t s i n t h i s s t u d y were not s i g n i f i c a n t l y a f f e c t e d by the o r d e r of t e s t i n g . T h e r e f o r e , L o r d ' s Case I l i n e a r e q u a t i n g model was adopted. T h i s c o r r e s p o n d s t o A n g o f f ' s v a r i a n t of D e s i g n s I and I I (1971, p. 5 7 5 ) . A p p l y i n g L o r d ' s b a s i c l i n e a r model f o r a c o n v e r t e d s c o r e SX - s x -Y* = — Y + X. - — Y. ( L o r d , 1950, p. 5) bY b Y and s u b s t i t u t i n g the terms Y. f o r the s c o r e of i n d i v i d u a l i on t e s t t s i t - -( t = PPVT, SIT, MHVS) and X. f o r the s c o r e of I n d i v i d u a l i on t e s t 1W w (w = WISC- R) the l i n e a r e q u a t i n g f o r m u l a becomes S. . S w — w — Y*. = -T— Y. + X. — Y. i t S i t w S t t t where X. , Y. , S , and S are the means and s t a n d a r d d e v i a t i o n s of the w t w t s c o r e s on t e s t s w and t . Two e r r o r measures were e s t i m a t e d c o r r e s p o n d i n g t o the two used i n the Anchor Test Study ( B i a n c h i n i & L o r e t , 1974; J a e g e r , 1973). The equat-i n g e r r o r (S ^) r e f l e c t s " t he degree t o w h i c h the e q u a t i n g r e s u l t s would v a r y i f the same e q u a t i n g p r o c e d u r e and method were a p p l i e d t o d i f f e r e n t r e p r e s e n t a t i v e sample of p u p i l s " ( J a e g e r , 1973, p. 7 ) . The f o r m u l a used was ! (1 + r ) + 2 Sv.„ = / S 2 (1 - r ) — — ( c f . L o r d , 1950, p. 7) Y" J w wt n v 85 where n s i z e o f sample, r u n c o r r e c t e d c o r r e l a t i o n between s c o r e s on test'.w and wt t e s t t , and Y. - Y. i t z . i t S t The o t h e r e r r o r measure, c a l l e d t he c o n d i t i o n a l mean-root-square e r r o r o f e q u a t i n g , i s an e s t i m a t e of "the degree t o w h i c h a s c o r e r e a d from the e q u a t i n g t a b l e s would d i f f e r from the s c o r e a p u p i l would have e a r n e d , had he been g i v e n the equated t e s t " ( J a e g e r , 1973, p. 7 ) . The c o n d i t i o n a l root-mean-square e r r o r of e q u a t i n g was computed as These f o r m u l a s were a p p l i e d t o a l l t e s t p a i r s i d e n t i f i e d f o r l i n e a r o b s e r v e d s c o r e e q u a t i n g (see T a b l e 34, Ch a p t e r I V ) . The s c o r e v a l u e s e n t e r e d i n t o t he e q u a t i o n s were raw s c o r e s f o r the PPVT, SIT,and MHVS, and s t a n d a r d i z e d s c o r e s f o r the WISC-R. E x a m i n a t i o n o f t h e i n d i c e s o f skewness and k u r t o s i s f o r the raw s c o r e d i s t r i b u t i o n s of t h e s e t e s t s r e v e a l e d t h a t , a l t h o u g h each i n d i v i d u a l d i s t r i -b u t i o n d i d not d i f f e r s i g n i f i c a n t l y from n o r m a l i t y , f o r any g i v e n t e s t p a i r t he d i s t r i b u t i o n s were not e x a c t l y i d e n t i c a l . T h e r e f o r e , t o i n s u r e t h a t t he r e s u l t s of the l i n e a r c o n v e r s i o n s r e f l e c t e d t he i n f l u e n c e of t e s t p a r a m e t e r s w h i c h were not confounded w i t h a n o m a l i e s i n the s c o r e d i s t r i b u -t i o n s , t h e d i s t r i b u t i o n s o f i s c o r e s on a l l t e s t s i d e n t i f i e d f o r o b s e r v e d s c o r e e q u a t i n g were n o r m a l i z e d i n the manner d e s c r i b e d f o r the WISC-R sub-t e s t s , and the e q u a t i n g p r o c e d u r e s were r e a p p l i e d t o t h e s e s c o r e s . ( c f . B i a n c h i n i & L o r e t , 1974, p. 158) 86 L i n e a r E q u a t i n g ( U n e q u a l l y R e l i a b l e T e s t s ) A n g o f f (1971) p r e s e n t e d a l i n e a r t r u e s c o r e e q u a t i n g p r o c e d u r e w h i c h i s a p p l i c a b l e under the same d a t a c o l l e c t i o n c o n d i t i o n s as the p r e v i o u s l y d i s c u s s e d o b s e r v e d s c o r e p r o c e d u r e but w h i c h i s based on a reduced s e t of a s s u m p t i o n s . S i n c e the r e s t r i c t i o n c o n c e r n i n g e q u a l r e l i a b i l i t i e s i s not r e q u i r e d , the a s s u m p t i o n s u n d e r l y i n g the analogous "Case I " t r u e s c o r e method a r e : 1. the t e s t s are ( n o m i n a l l y ) p a r a l l e l , 2. the s c o r e d i s t r i b u t i o n s of the t e s t s are i d e n t i c a l , and 3. the t e s t r e s u l t s a r e u n a f f e c t e d by the o r d e r of a d m i n i s t r a t i o n of the t e s t s (pp. 565-569, 571-573). C o n v e r s i o n f o r m u l a e f o r t e s t s h a v i n g u n e q u a l r e l i a b i l i t i e s r e q u i r e t r u e s c o r e s r a t h e r t h a n o b s e r v e d s c o r e s (see C h a p t e r I I ) . T h e r e f o r e , v a r i a n c e e s t i m a t e s of h y p o t h e t i c a l t r u e s c o r e d i s t r i b u t i o n s were used i n p l a c e of the v a r i o u s components i n the e q u a t i n g f o r m u l a s . The l i n e a r t r u e s c o r e c o n v e r s i o n f o r m u l a used was: i t : I t w t Y YY Y YY The e q u a t i o n f o r the s t a n d a r d e r r o r of e q u a t i n g was: S /s * (1 + rXY> + 2 V = / S X r X X ( 1 - r X Y } n where n = number of c a s e s r = u n c o r r e c t e d c o r r e l a t i o n between s c o r e s on t e s t w and t e s t t AI —* — Z Y = Y i t " Y - t / S Y / r Y Y The c o n d i t i o n a l root-mean-square e r r o r of e q u a t i n g was computed as shown f o r the l i n e a r o b s e r v e d s c o r e p r o c e d u r e . 87 4 These f o r m u l a e were a p p l i e d t o the IQ s c o r e s (B.C. normed) of a l l t e s t p a i r s w h i c h were i d e n t i f i e d as h a v i n g unequal r e l i a b i l i t i e s . I t w i l l be n o t e d t h a t t h i s e q u a t i n g p r o c e d u r e was a p p l i e d t o IQ s c o r e s r a t h e r t h a n o b s e r v e d s c o r e s . A g a i n , t h i s i s i n k e e p i n g w i t h A n g o f f ' s (1971) use. S i n c e t h e r e i s a v e r y c l o s e c o r r e s p o n d e n c e between WISC-R s t a n d a r d -i z e d and WISC-R IQ s c o r e s , however, e s s e n t i a l l y the same r e s u l t s would be a c h i e v e d r e g a r d l e s s of the m e t r i c used. E q u i p e r c e n t i l e E q u a t i n g As d e s c r i b e d i n Ch a p t e r I I , e q u i p e r c e n t i l e e q u a t i n g i n v o l v e s the i d e n t i f i c a t i o n of c o r r e s p o n d i n g p e r c e n t i l e s f o r two s c o r e d i s t r i b u t i o n s and the assignment of e q u i v a l e n c e t o t h e i r a s s o c i a t e d s c o r e v a l u e s . Two p r o c e d u r e s , h a n d - g r a p h i n g and c o m p u t e r i z e d , were used and t h e i r r e s u l t s compared. The s t e p s i n v o l v e d i n each a r e d e t a i l e d i n t h e f o l l o w i n g s e c t i o n s . Hand-graphing ( A n g o f f , 1971, pp. 571-575; F l a n a g a n , 1951, pp. 727-730). 1. A t a b l e of r e l a t i v e c u m u l a t i v e f r e q u e n c i e s ( i . e . , p e r c e n t a g e s o f ca s e s 7 '.  f a l l i n g below each i n t e r v a l ) was computed f o r each d i s t r i b u t i o n . 2. These v a l u e s were p l o t t e d and smoothed on a r i t h m e t i c p r o b a b i l i t y p a p e r . 3. Score v a l u e s f o r g i v e n p e r c e n t i l e s were r e a d from the smoothed o g i v e s and r e c o r d e d . 4. These v a l u e s were p l o t t e d a g a i n s t each o t h e r on a r i t h m e t i c graph paper. 5. A smoothed l i n e was drawn c o n n e c t i n g t h e s e p o i n t s and was extended t o c o v e r the f u l l range of p o s s i b l e t e s t s c o r e s . 6. A t a b l e o f e q u i v a l e n t s c o r e v a l u e s was p r e p a r e d from t h i s f i n a l c u r v e . 4 S i n c e IQ s c o r e s a r e not r e p o r t e d f o r the MHVS, raw s c o r e s from t h i s t e s t were used i n the c o n v e r s i o n s . 88 The h a n d - g r a p h i n g e q u i p e r c e n t i l e method was a p p l i e d t o two t e s t e q u a t -i n g p a i r s i n t h e p r e s e n t s t u d y . For i l l u s t r a t i v e p u r p o s e s , t h e s e i n c l u d e d p a i r s of t e s t s h a v i n g the h i g h e s t and the l o w e s t i n t e r c o r r e l a t i o n s . From T.able 33, t h e s e p a i r s were i d e n t i f i e d as WISC-R V e r b a l : PPVT, age 7%; and WISC-R V e r b a l : MHVS, age 11%. Computer a n a l o g u e . The c o m p u t e r i z e d e q u i p e r c e n t i l e program d e v e l o p e d by L i n d s a y and P r i c h a r d (1971) was a p p l i e d t o b o t h the o b s e r v e d and n o r m a l -i z e d IQ s c o r e d i s t r i b u t i o n s of a l l t e s t p a i r s used i n l i n e a r e q u a t i n g . T h i s program i n v o l v e d t h r e e d i s t i n c t r o u t i n e s . 1. The i n t e r p o l a t i o n p r o c e d u r e w h i c h y i e l d e d two d i s t r i b u t i o n s w i t h matched c u m u l a t i v e p e r c e n t a g e v a l u e s and raw s c o r e p o i n t s . 2. The c u r v e - f i t t i n g p r o c e d u r e w h i c h p r o v i d e d l i n e a r and h i g h e r - o r d e r e q u a t i o n s ( t o the f i f t h p o l y n o m i a l ) f o r f i t t i n g t he two i n t e r p o l a t e d d i s t r i b u t i o n s . 3. The p l o t t i n g p r o c e d u r e w h i c h produced graphs of the a c t u a l smoothed ( i n t e r p o l a t e d ) d i s t r i b u t i o n s and of the e s t i m a t e d d i s t r i b u t i o n s u s i n g b o t h l i n e a r and c u r v i l i n e a r p r e d i c t i o n f u n c t i o n s . As a r e s u l t , c o mparisons were made p o s s i b l e between c o n v e r t e d s c o r e s produced by the l i n e a r and e q u i p e r c e n t i l e e q u a t i n g methods and between the g r a p h i c and a n a l y t i c a l e q u i p e r c e n t i l e p r o c e d u r e s . Summary At the c o n c l u s i o n of C h a p t e r ' I I , the t h r e e i n t e r t e s t s c o r e c o n v e r s i o n methods i d e n t i f i e d f o r use i n t h i s s t u d y were summarized a c c o r d i n g t o the c r i t e r i a o f p a r a l l e l i s m of the t e s t s i n v o l v e d . F i g u r e 4 p r e s e n t s an extended o u t l i n e i n c o r p o r a t i n g the methods and p r o c e d u r e s f o r each c o n v e r -s i o n type as d e s c r i b e d i n the p r e s e n t c h a p t e r . The r e s u l t s of a l l a n a l -yses a r e p r e s e n t e d i n Chap t e r IV. EQUATING NORMING T e s t P a i r C h a r a c t e r i s t i c s n o m i n a l l y p a r a l l e l ( r - > -70) e q u a l l y r e l i a b l e ( r = r ) U X X YY n o m i n a l l y p a r a l l e l XY .70) u n e q u a l l y r e l i a b l e ( r / r ) U X X F YY n o n p a r a l l e l ( r X Y < . 7 0 ) C o n v e r s i o n T y p e S h a p e o f D i s t r i b u t i o n s C o n v e r s i o n M e t h o d P r o c e d u r e OBSERVED SCORE EQUATING , I 1 "I same s h a p e d i f f e r e n t s h a p e LINEAR E Q U I P E R C E N T I L E \ / no s e q u e n c e e f f e c t TRUE SCORE EQUATING COMPARING L o r d ' s ( 1 9 5 0 ) C a s e I A. G r a p h i c ( A n g o f f , 1 9 7 1 ; Flanagan, 1 9 5 1 ) LINEAR A n g o f f ( 1 9 7 1 ) sx s x S x / r x x Y*. = — Y. + X. - — Y. B. A n a l y t i c a l ( L i n d s a y Y* = • =-X t S Y X t W Y t 6 P r i c h a r d , 1 9 7 1 ) S / r Y. + X. i t common s c a l i n g X. = 100 S x = 15 F i g u r e 4. I n t e r - t e s t s c o r e c o n v e r s i o n m e t h o d s a n d p r o c e d u r e s u s e d f o r n o r m i n g and e q u a t i n g . CHAPTER IV RESULTS The o r g a n i z a t i o n of t h i s c h a p t e r p a r a l l e l s t h a t of Ch a p t e r I I I . The c h a r a c t e r i s t i c s of the o b t a i n e d samples a r e r e p o r t e d f i r s t , f o l l o w e d i n t u r n , by the r e s u l t s of the norming and e q u a t i n g phases of the a n a l y s e s . Rate of Response The t a r g e t sample s i z e f o r t h i s s t u d y was 180 c h i l d r e n at each of the t h r e e age l e v e l s . The a c t u a l number of s t u d e n t s t e s t e d t o g e t h e r w i t h the number of u s a b l e t e s t s a r e shown i n Ta b l e 16 f o r each age l e v e l . As T a b l e 16 Rates of Response f o r Each T e s t and Ag Tar g e t Number of % # % Age Sample S i z e S t u d e n t s T e s t e d T e s t e d T e s t U s a b l e U s a b l e ih 180 115 63.9 WISC-R 115 100.0 PPVT 114 99.1 SIT 108 93.9 SPM 99 86.1 MHVS 114 99.1 180 117 65.0 WISC-R 117 100.0 PPVT 113 96.6 SIT 111 94.9 SPM 108 92.3 MHVS 103 88.0 Ilk 180 108 60.0 WISC-R 108 100.0 PPVT 104 96.3 SIT 100 92.6 SPM 106 98.2 MHVS 105 • 97.2 90 91 seen i n t h i s t a b l e , WISC-R s c o r e s were o b t a i n e d f o r each c h i l d t e s t e d . F o r a few s t u d e n t s , however, s c o r e s were not a v a i l a b l e on the r e m a i n i n g f o u r t e s t s . For some of t h e s e c h i l d r e n , t e s t i n g was not com p l e t e d because of a b s e n t e e i s m . For the r e m a i n i n g , t e s t p r o t o c o l s were c o n s i d e r e d u n s c o r -a b l e due t o e r r o r s i n a d m i n i s t r a t i o n . I n T a b l e 17 the r a t e of res p o n s e i s shown f o r each c e l l i n the sample d e s i g n , based on the t o t a l r e t u r n s at each age l e v e l . The r a t e of res p o n s e i s c a l c u l a t e d as the p e r c e n t a g e of the t a r g e t sample (see Ta b l e 10, Ch a p t e r I I I ) r e p r e s e n t e d i n the a c t u a l sample. R e p r e s e n t a t i v e n e s s of the Sample I n T a b l e s 18 t h r o u g h 22 the sample i s d e s c r i b e d i n terms o f the r e m a i n -i n g f o u r s t r a t i f i c a t i o n v a r i a b l e s and the s o c i o e c o n o m i c v a r i a b l e ( e d u c a t i o n ) f o r the WISC-R samples. The p e r c e n t a g e s r e p o r t e d f o r the v a r i a b l e sex are based on the t a r g e t sample g o a l of e q u a l numbers of g i r l s and boys a t each age l e v e l . F or each of the o t h e r v a r i a b l e s , t he t a b l e s show the p e r -c e n t a g e s , based on 1976-1977 s c h o o l e n r o l l m e n t d a t a o r 1976 census d a t a (as o u t l i n e d i n Chap t e r I I I ) , t h a t c o n s t i t u t e d the p o p u l a t i o n , and the p e r -c e n t a g e s t h a t were o b t a i n e d i n the sample. From T a b l e 19, i t can be seen t h a t the r e l a t i v e p r o p o r t i o n s of c h i l -d ren t e s t e d i n each g e o g r a p h i c r e g i o n c o r r e s p o n d c l o s e l y t o the p o p u l a t i o n p r o p o r t i o n s . The Metro and Kootenay r e g i o n s a r e s l i g h t l y o v e r r e p r e s e n t e d w h i l e the Okanagan and F r a s e r V a l l e y r e g i o n s a r e somewhat u n d e r r e p r e s e n t e d . 92 T a b l e 17 Rates of Response ( P e r c e n t a g e s ) f o r the T o t a l Sample D e s i g n Community S c h o o l R e g i o n  S i z e S i z e 1 2 3 4 5 6 A I I I I I I 50.0 33.3 50.0 -50.0 33.3 50.0 50.0 50.0 0.0 100.0 100.0 50.0 100.0 Age B I I I I I I 100.0 75.0 42.9 100.0 50.0 50.0 0.0 25.0 80.0 0.0 75.0 80.0 100.0 100.0 75.0 100.0 50.0 100.0 C I I I I I I 100.0 0.0 66.7 175.0 88.9 63.6 -0.0 66.7 70.0 - 0.0 50.0 A I I I I I I 100.0 33.3 50.0 - 50.0 33.3 50.0 100.0 50.0 0.0-100.0 100.0 33.3 100.0 0.0 A N ON 01 00 < B I I I I I I 100.0 75.0 42.9 100.0 50.0 50.0 0.0 25.0 80.0 0.0 75.0 80.0 100.0 100.0 75.0 0.0 50.0 75.0 C I I I I I I 0.0 0.0 66.7 233.0 88.9 61.8 -0.0 66.7 90.0 : 0.0 75.0 A I I I I I I 50.0 33.3 0.0 - 50.0 33.3 50.0 100.0 50.0 0.0 100.0 100.0 50.0 100.0 0.0 Age 11 B I I I I I I 100.0 75.0 57.1 100.0 60.0 50.0 0.0 20.0 83.3 0.0 100.0 57.1 100.0 100.0 50.0 100.0 50.0 88.9 C I I I I I I 0.0 42.9 200.0 83.3 60.0 — 0.0 50.0 63.6 — 0.0 25.0 T a b l e 18 Sample P e r c e n t a g e s by Sex and Age Sex  Age Female Male 7% 47.8 52.2 9h 53.8 46.2 llh 47.2 52.8 T a b l e 19 P o p u l a t i o n and Sample P e r c e n t a g e s by Region and Age R e g i o n P o p u l a t i o n Sample 1. Okanagan Ih 14.9 13.0 9h 15.1 12.8 11% 14.6 12.0 2. Metro Ih 38.4 41.7 9h 38.2 40.2 11% 35.9 38.9 3. F r a s e r V a l l e y 7% 11.2 7.8 9% 11.0 8.6 11% 11.6 9.3 4. Vancouver I s l a n d 7% 17.3 16.5 9% 17.3 18.8 11% 17.6 17.6 5. Kootenay 7% 5.9 7.8 9% 5.9 7.8 11% 7.0 8.3 6. N o r t h e r n 7% 12.3 13.0 9% 12.5 12.0 11% 13.2 13.9 94 T a b l e 20 P o p u l a t i o n and Sample P e r c e n t a g e s by Community S i z e and Age Community S i z e P o p u l a t i o n Sample A — u n d e r 1,000 Ih 16.9 13.0 9h 17.0 14.8 llh 16.6 13.0 B — 1 , 0 0 1 to 50,000 ih 42.0 41.7 9h 42.1 40.2 llh 44.1 47.2 C — o v e r 50,000 ih 41.1 45.2 9h 40.9 45.3 llh 39.4 39.8 T a b l e 20 shows a s l i g h t sample b i a s toward s c h o o l s l o c a t e d i n l a r g e urban r a t h e r t h a n r u r a l a r e a s . T h i s i s i n k e e p i n g w i t h the i n f l a t e d r e p r e -s e n t a t i o n of the Metro r e g i o n d i s c u s s e d f o r T a b l e 19. Any t r e n d toward the d i s p r o p o r t i o n a t e i n c l u s i o n of l a r g e u n i t s w h i c h might be s u s p e c t e d from the d a t a t o t h i s p o i n t , however, i s d i s p r o v e d i n T a b l e 21. More of t h e c h i l d r e n t e s t e d were e n r o l l e d i n s m a l l s c h o o l s t h a n was e x p e c t e d from the t a r g e t sample a l l o c a t i o n based on t h e s e p o p u l a t i o n p e r c e n t a g e s . As was seen i n T a b l e 17, t h i s p r o p o r t i o n i s a t t r i b u t e d t o the t e s t i n g of more c h i l -d r e n i n s m a l l s c h o o l s i n the Metro r e g i o n than a n t i c i p a t e d . The p e r c e n t a g e s shown i n T a b l e 22 f o r l e v e l of e d u c a t i o n of head of h o u s e h o l d were d e r i v e d f o r the e n t i r e p r o v i n c e . As mentioned p r e v i o u s l y , i t was not p o s s i b l e t o s t r a t i f y on t h i s v a r i a b l e . C l a s s i f i c a t i o n a c c o r d -i n g t o l e v e l of e d u c a t i o n was r e q u e s t e d from p a r e n t s a f t e r the sample had been drawn (see P a r e n t Consent Form, Appendix A ) . As shown, a much l a r g e r T a b l e 21 P o p u l a t i o n and Sample P e r c e n t a g e s by School-S i z e and Age • S c h o o l S i z e P o p u l a t i o n Sample I t o 150 7% 9% 11% I I 151 t o 300 7% 9% 11% I I I o v er 300 7% 9% 12.6 10.9 8.7 29.2 29.1 27.4 58.2 60.0 63.9 14.7 14.5 12.0 27.8 26.5 26.8 57.4 60.0 61.1 T a b l e 22 L e v e l o f E d u c a t i o n of Head of Household P e r c e n t i n P o p u l a t i o n and Sample ( A l l Ages Combined) E d u c a t i o n Completed P o p u l a t i o n Sample (n=258) Grade 8 and below 13.3 Grades 9 t o 10 16.0 Grades 11 t o 13 27.0 P o s t - s e c o n d a r y , n o n - u n i v e r s i t y 20.0 P o s t - s e c o n d a r y , i n c l u d i n g u n i v e r s i t y 23.6 10.5 18.6 38.0 15.9 17.0 Note: The number of p a r e n t s who responded t o t h i s c a t e g o r i z a t i o n was 258. 96 t h a n e x p e c t e d p e r c e n t a g e r e p o r t e d the h i g h e s t l e v e l of s c h o o l i n g c o m p l e t e d to be s e n i o r secondary (grades 11 t o 13). I n summary, a l t h o u g h the o b t a i n e d sample s i z e was l e s s t h a n the t a r g e t s i z e on w h i c h the a l l o c a t i o n s were based, the sample was d i s p e r s e d i n b a s i c -a l l y the same r e l a t i v e p r o p o r t i o n s f o r a l l s t r a t i f i c a t i o n v a r i a b l e s . R e s u l t s of P r e l i m i n a r y A n a l y s e s Order E f f e c t The r e s u l t s o f a n a l y s e s of v a r i a n c e t o d e t e r m i n e i f o r d e r of t e s t a d m i n i s t r a t i o n had an e f f e c t on t e s t performance are summarized i n T a b l e 23. An a l p h a l e v e l o f .25 was s e l e c t e d s i n c e i t was more i m p o r t a n t t o p r o t e c t a g a i n s t a Type I I t h a n a Type I e r r o r . Three s i g n i f i c a n t F r a t i o s were found. However, w i t h 12 t e s t s , the number of s i g n i f i c a n t f i n d i n g s by chance a l o n e i s 3 ( 1 2 x . 2 5 ) . As seen i n T a b l e 23, the s i g n i f i c a n t r e s u l t s were not l i m i t e d t o one t e s t or age l e v e l . Thus i t was c o n c l u d e d t h a t the r e s u l t s were c o n s i s t e n t w i t h what would be e x p e c t e d by chance and t h a t t h e r e was no s y s t e m a t i c e f f e c t a t t r i b u t a b l e t o o r d e r . N o r m a l i t y The r e s u l t s o f the Kolmogorov-Smirnov (K-S) one-sample goodness of f i t t e s t s a r e summarized i n T a b l e 24. The t a b l e r e p o r t s D v a l u e s f o r the p o i n t at w h i c h the r e l a t i v e c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s of the t h e o r -e t i c a l normal and the o b s e r v e d d i s t r i b u t i o n s show the g r e a t e s t d i v e r g e n c e . F o r D < K-S(a) i t i s c o n c l u d e d t h a t t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between the two d i s t r i b u t i o n s a t a l e v e l of s i g n i f i c a n c e of a. A g a i n , t o reduce the chance of a Type I I e r r o r , an a l p h a l e v e l of .20 was adopted. T h i s i s the l o w e s t s i g n i f i c a n c e l e v e l r e p o r t e d by S i e g e l ( 1 9 5 6 ) . W i t h 45 t e s t s (as shown i n T a b l e 2 4 ) , the e x p e c t e d number of s i g n i f i c a n t r e s u l t s by chance i s 9. However, o n l y one of the t e s t s c o r e d i s t r i b u t i o n s was T a b l e 23 Summary of A n a l y s i s of V a r i a n c e f o r Order of T e s t A d m i n i s t r a t i o n T e s t Source SS df MS F PPVT Order 100. 934 5 20. 187 0 .266 Re s i d u a l . 8182. 121 108 75. 76 SIT Order 152. 284 5 30. 457 1 .004 R e s i d u a l 3094. 473 102 30. 338 SPM Order 337. 273 5 67. 455 1 .307 R e s i d u a l 4800. 758 93 51. 621 MHVS Order 128. 171 5 25. 634 1 .603' R e s i d u a l 1727. 438 108 15. 995 PPVT Order 531. 039 5 106. 208 1 .296 R e s i d u a l 8768. 102 107 81. 945 SIT Order 205. 454 5 41. 091 0 .607 R e s i d u a l 5961. 504 105 56. 776 SPM Order 691. 859 5 138. 372 2 . 252' R e s i d u a l 6268. 281 102 61. 454 MHVS Order 22. 535 5 4. 507 0 . 148 R e s i d u a l 3261. 435 107 30. 481 PPVT Order 447. 293 5 89.459 0. 834 R e s i d u a l 10509. 203 98 107.237 SIT Order 105. 089 5 21.018 0. 198 Res i d u a l 9954. 492 94 105.899 SPM Order 249. 115 5 49.823 1. 175 oo < R e s i d u a l 4238. 758 100 42.388 MHVS Order 282. 376 5 56.475 1. 462* R e s i d u a l 3825. 003 99 38.636 *p < .25 T a b l e 24 D V a l u e s f o r Kolmogorov-Smirnov T e s t s f o r Goodness of F i t 1\ 9% 11% WISC-R In f o r m a t i o n 0. 020 0. 044 0. 055 S i m i l a r i t i e s 0. 024 0. 074 . 0. 062 A r i t h m e t i c 0. 040 0. 03 7 0. 079 V o c a b u l a r y 0. 031 0. 044 0. 054 Comprehension 0. 043 0. 030 0. 029 P i c t u r e C o m p l e t i o n 0. 026 0. 031 0. 069 P i c t u r e Arrangement 0. 048 0. 034 0. 107 B l o c k D e s i g n .0. 053 0. 044 0. 034 O b j e c t Assembly 0. 040 0. 068 0. 034 Coding 0. 127* 0. 066 0. 048 PPVT 0.102 0.058 0.063 SIT 0.036 0.055 0.040 SPM 0.098 0.051 0.031 MHVS: A 0.052 0.073 0.062 B 0.015 0.062 0.074 *D > K-S(.20) 99 found t o d i f f e r s i g n i f i c a n t l y from n o r m a l i t y f o r a = .20. Thus the h y p o t h e s i s of n o r m a l l y d i s t r i b u t e d i n t e l l i g e n c e t e s t s c o r e s i n the p o p u l a -t i o n was a c c e p t e d . Comparison t o P u b l i s h e d Norms The means and s t a n d a r d d e v i a t i o n s of the t e s t s s c o r e d u s i n g t he pub-l i s h e d norms t a b l e s i n t h e i r r e s p e c t i v e manuals a r e shown- i n T a b l e 25. These were compared t o the c o r r e s p o n d i n g v a l u e s r e p o r t e d i n the t e s t manuals (as shown i n Chapt e r I I I , T a b l e 1 2 ) . The r e s u l t s of t t e s t s f o r d i f f e r -ences i n means and x 2 t e s t s f o r d i f f e r e n c e s i n v a r i a n c e a r e shown i n T a b l e 26. S i g n i f i c a n t mean s c o r e d i f f e r e n c e s f o r t he B. C. sample were found f o r a l l t e s t s e x c e p t t he WISC-R V e r b a l IQ at age 11% and the MHVS at ages 7% and 11%. I t w i l l be r e c a l l e d t h a t the MHVS s c o r i n g p r o c e d u r e was e s t a -l i s h e d u s i n g t he re s p o n s e s from t h i s group of c h i l d r e n r a t h e r t h a n t he o r i g i n a l C o l c h e s t e r s t a n d a r d i z a t i o n sample. T h e r e f o r e t he MHVS means r e p o r t e d i n T a b l e 29 are based on r e s t a n d a r d i z e d s c o r e s f o r t he B.C. sample. The r e s u l t s suggest t h a t , when s c o r e d f o r contemporary usage, B. C. 7% and 11% y e a r o l d s can d e f i n e , on the a v e r a g e , a p p r o x i m a t e l y t he same number of words on the MHVS as c o u l d t he o r i g i n a l r e f e r e n c e group. The f a c t t h a t the 9% y e a r o l d s s c o r e d s i g n i f i c a n t l y h i g h e r may p o s s i b l y be a t t r i b u t e d t o a v e r b a l l y p r e c o c i o u s group whose WISC-R V o c a b u l a r y s u b t e s t and PPVT s c o r e s a l s o i n d i c a t e a h i g h e r l e v e l of performance t h a n f o r t he o t h e r age grou p s . S i g n i f i c a n t d i f f e r e n c e s i n v a r i a n c e were a l s o found f o r 8 of the 15 comparisons made. I n each c a s e , t he v a r i a n c e f o r t he B.C. sample was l e s s t h a n f o r t he o r i g i n a l s t a n d a r d i z a t i o n sample. 100 T a b l e 25 Means and S t a n d a r d D e v i a t i o n s f o r A l l T e s t s S c o r e d u s i n g P u b l i s h e d Norms T a b l e s Age Mean 1\ S.D. 9 Mean h S. D. 11 Mean h S. D. WISC-R In f o r m a t i o n 10.722 (2.553) 10.641 ( 2 . 778) 9.880 ( 2 . 611) S i m i l a r i t i e s 11.168 (2.982) 11.243 ( 2 . 998) 10.870 ( 3 . 293) A r i t h m e t i c 10.826 (2.894) 11.216 ( 2 . 427) 11.259 ( 2 . 552) V o c a b u l a r y 10.719 (2.783) 11.128 (2 . 355) 9.917. ( 2 . 376) Comprehension 11.158 (2.965) 10.880 (2 . 516) 9.824 ( 2 . 437) P i c t u r e C o m p l e t i o n 11.339 (2.309) 10.897 (2 . 513) 10.704 ( 2 . 503) P i c t u r e Arrangement 12.035 (3.267) 11.897 (2 . 836) 11.157 ( 2 . 721) B l o c k D e s i g n 11.504 (3.360) 11.761 (2 . 996) 11.654 ( 2 . 921) O b j e c t Assembly 11.851 (2.652) 11.643 (2 . 998) 11.759 ( 3 . 057) Coding 10.491 (2.841) 10.282 (2 . 834) 10.393 (2 . 867) V e r b a l IQ 106.078 (13.785) 106.009 (12. 465) 101.685 (12. 694) Performance IQ 109.922 (13.114) 108.855 (12. 711) 107.685 (13. 531) F u l l S c a l e IQ 108.157 (12.351) 107.889 (12. 756) 104.796 (12. 884) PPVT IQ 106.526 (15.251) 112.708 (14. 3 4 8 ) s 110.490 (14. 991) SIT IQ 114.954 (11.905) 112.523 (12. 676) 109.480 (15. 418) SPM (raw) 21.172 (7.241) 31.583 (8. 065) 37.575 (6. 538) MHVS (raw) 15.412 (4.052) 23.549 ( 5 . 415) 28.410; (6 . 284). T a b l e 26 R e s u l t s of t T e s t s and x 2 T e s t s T e s t t z a WISC-R V e r b a l IQ 4. 73* - 1 . 19 WISC-R Performance IQ 8.11* - 1 . 86 WISC-R F u l l S c a l e IQ 7.08* -2. 63* PPVT IQ 4.57* 0. 28 SIT IQ 13.05* -3 . 71* SPM 5.73* - b MHVS -1.55 - b WISC-R V e r b a l IQ 5.21* -2. 54* WISC-R Performance IQ 7.54* -2. 29* WISC-R F u l l S c a l e IQ 6.69** -2. 25* PPVT IQ 9.42* -0. 62 • SIT IQ 10.41* -3 . 05* SPM 9.77* -MHVS 3.04* -WISC-R V e r b a l IQ 1.38 -2. 22* WISC-R Performance IQ 5.90* - 1 . 40 WISC-R F u l l S c a l e IQ 3.87* -2. 03* PPVT IQ 7.14* 0. 03 SIT IQ 6.15* -0. 48 SPM 4.06* -MHVS 0.67 — *p < .05 a z = /2T2" - /2 d f - l f o r df > 30 ^There i s no measure of v a r i a b i l i t y r e p o r t e d i n the t e s t manuals f o r the SPM and MHVS. 102 Comparison of WISC-R R e s u l t s t o "White" American Norms The A merican WISC-R s t a n d a r d i z a t i o n sample i n c l u d e d b l a c k c h i l d r e n i n the same p r o p o r t i o n as i n the p o p u l a t i o n f o r the age range t e s t e d . S e p a r a t e a n a l y s e s f o r b l a c k and w h i t e c h i l d r e n r e v e a l e d t h a t the former s c o r e d one s t a n d a r d d e v i a t i o n below the l a t t e r (Kaufman & D o p p e l t , 1976). As p o i n t e d out i n Chapter I , N a t i v e I n d i a n c h i l d r e n i n B.C. have been shown to s c o r e i n a s i m i l a r manner ( G o l d s t e i n , 1980). I t may t h e r e f o r e be h y p o t h e s i z e d t h a t the e x c l u s i o n of N a t i v e I n d i a n c h i l d r e n from the B.C. sample s e r v e d t o i n f l a t e the IQ s c o r e s o b t a i n e d . To check t h i s , t t e s t s f o r d i f f e r e n c e s i n means were a p p l i e d t o B.C. sample means and WISC-R " w h i t e " means. Kaufman and D o p p e l t (1976) r e p o r t e d t h e l a t t e r t o be 102 f o r each of the t h r e e WISC-R IQ s c a l e s c a l c u l a t e d a c r o s s a l l age g r o u p s . The r e s u l t s of t h e s e t t e s t s a r e g i v e n i n T a b l e 27. U s i n g mean 102, s i g n i f i c a n t d i f f e r e n c e s were s t i l l found f o r e i g h t of the n i n e means. T a b l e 27 t T e s t s f o r D i f f e r e n c e s i n Means between T o t a l B.C. Sample and A merican WISC-R "White" Sample (mean=l02) 1\ 9h I l k WISC-R V e r b a l IQ 3.17* 3.48* -0.26 WISC-R Performance IQ 6.48* 5.83* 4.37* WISC-R F u l l S c a l e IQ 5.35* 4.99* 2.26* *p < .05 103 P r e p a r a t i o n of B.C. Norms G i v e n the d i f f e r e n c e s n o t e d i n the p r e v i o u s s e c t i o n , B.C. norms were p r e p a r e d f o r a l l f i v e t e s t s . The r e s u l t s of r e n o r m i n g a r e d i s c u s s e d below. A l l norms t a b l e s a r e i n c l u d e d i n Appendix E. WISC-R S c a l e d Scores Two p r o c e d u r e s , d e s c r i b e d i n C h a p t e r I I I , were compared f o r p r o d u c i n g n o r m a l i z e d s c a l e d s c o r e c o n v e r s i o n s f o r WISC-R s u b t e s t raw s c o r e s . For c l a r i t y i n the f o l l o w i n g d i s c u s s i o n , t h e s e a r e r e f e r r e d t o as " a n a l y t i c a l " ( i . e . , the p u b l i s h e r ' s method) and " g r a p h i c " ( A n g o f f , 1971). The o b j e c t i v e i n e i t h e r case was t o produce c o n v e r s i o n t a b l e s r e l a t i n g raw s c o r e v a l u e s f o r each s u b t e s t t o s c a l e d s c o r e s h a v i n g range 1-19, mean 10, and s t a n d a r d d e v i a t i o n 3. An example of the r e s u l t s of the two p r o c e d u r e s are shown i n T a b l e 28 f o r the A r i t h m e t i c s u b t e s t a t age 9%. The raw s c o r e t o s c a l e d s c o r e c o n v e r s i o n s a s s o c i a t e d w i t h the a n a l y t i c a l p r o c e d u r e a r e l i s t e d i n column 2 and t h o s e a s s o c i a t e d w i t h the g r a p h i c p r o c e d u r e are l i s t e d i n column 3. Use of the a n a l y t i c a l p r o c e d u r e i s r e l a t i v e l y non time-consuming and e s s e n t i a l l y v e r i f i a b l e . The d i r e c t raw s c o r e t o s c a l e d s c o r e c o n v e r -s i o n s , however, a r e l i m i t e d by the range of raw s c o r e s o b t a i n e d i n the p a r t i c u l a r sample. F o r the s u b t e s t i l l u s t r a t e d , the t o t a l raw s c o r e range i s 1-18. The o b t a i n e d s c o r e range f o r the B.C. sample was 7-17. T h i s l e a v e s 'gaps' i n the extremes of the d i s t r i b u t i o n s and n e c e s s i t a t e s e x t r a p -o l a t i o n of the raw s c o r e s t o c o r r e s p o n d t o the s c a l e d s c o r e range of 1-19. The r u l e of thumb adopted f o r t h i s was t o e x t e n d the s c o r e s i n a manner t h a t e n s u r e d a p r o g r e s s i o n from age t o age ( W e c h s l e r , 1974, p. 2 1 ) . Thus, i n g e n e r a l , i n c r e a s i n g l y h i g h e r raw s c o r e v a l u e s were a s s o c i a t e d w i t h any g i v e n s c a l e d s c o r e as age i n c r e a s e d . T a b l e 28 Comparison of R e s u l t s of A n a l y t i c a l and G r a p h i c S c a l e d Score C o n v e r s i o n s A r i t h m e t i c S u b t e s t — A g e 9% Raw S c o r e s  S c a l e d S c o res A n a l y t i c a l G r a p h i c 1 0-2 5 2 3-4 6 3 5-6 7 4 7 8 5 8 9 6 9 10 7 10 _ 8 11 11 9 - 12 10 12 -11 - 13 12 13 -13 - 14 14 14 15 15 - -16 15 16 17 16 17 18 17 18 19 18 Mean 10.05 9.21 S t a n d a r d D e v i a t i o n 2.95 3.04 105 The g r a p h i c approach was a t t e m p t e d i n the hope t h a t the shape of the graph wouLd d i c t a t e the s o l u t i o n f o r e x t r a p o l a t i o n t h e r e b y r e d u c i n g any a r b i t r a r i n e s s i n the p r o c e d u r e . The graph produced f o r the A r i t h -m e t i c s u b t e s t , age 9%, i n shown i n F i g u r e 5. G u i d e l i n e s f o r the p o s i t i o n -i n g and smoothing of the c u r v e were o f f e r e d by A n g o f f : The smoothed c u r v e s h o u l d i n g e n e r a l sweep t h r o u g h the p o i n t s i n such a way as t o e q u a l i z e the d i v e r g e n c e s of the p o i n t s on e i t h e r s i d e of the l i n e . (1971, p. 516) The p o s i t i o n i n g of the t a i l s of the c u r v e , however, remains s p e c u l a t i v e and s u b j e c t t o c o n s i d e r a b l e v a r i a b i l i t y . To judge the e f f i c i e n c y o f t h i s p r o c e d u r e , the mean and s t a n d a r d d e v i a t i o n of the s c a l e d s c o r e s were c a l c u -l a t e d and compared t o the c o r r e s p o n d i n g v a l u e s f o r the a n a l y t i c a l p r o c e d u r e . These are shown below the r e l e v a n t columns i n T a b l e 28. The r e s u l t s shown f o r t h i s example a r e i n d i c a t i v e of tho s e found a c r o s s s u b t e s t s and age l e v e l s and r e v e a l a c o n s i s t e n t g r a p h e r b i a s toward low s c o r e s . The t e d i o u s n e s s and time-consuming r e q u i r e m e n t s of r e - g r a p h i n g c o u p l e d w i t h the f a i l u r e of the p r o c e d u r e t o f i x the c o n v e r s i o n l i n e f o r extreme s c o r e s r e s u l t e d i n the r e j e c t i o n of t h i s p r o c e d u r e i n f a v o r of the a n a l y t i c a l method. As a r e s u l t , the WISC-R s u b t e s t s c a l e d s c o r e s were d e r i v e d a c c o r d -i n g t o t h e p r o c e d u r e s used by the p u b l i s h e r , P s y c h o l o g i c a l C o r p o r a t i o n . R e f e r e n c e t o T a b l e 29 shows t h a t the d e s i r e d mean and s t a n d a r d d e v i a t i o n • were a c h i e v e d w i t h t h i s a p p roach. The complete c o n v e r s i o n t a b l e s f o r a l l s u b t e s t s a r e i n c l u d e d i n Appen-d i x E. The means and s t a n d a r d d e v i a t i o n s f o r the B.C. sample when s c o r e d u s i n g t h e s e t a b l e s a r e p r e s e n t e d i n T a b l e 29. 107 T a b l e 29 Means and S t a n d a r d D e v i a t i o n s f o r WISC-R S c a l e d S c o r e s and Sums of S c a l e d S c o r e s B r i t i s h Columbia Norms ik 9k nk Mean S.D. Mean S.D. Mean S.D. V e r b a l S u b t e s t s I n f o r m a t i o n 10. .05 2. .92 10. 10 3, ,09 9. ,92 3, .00 S i m i l a r i t i e s 10. .04 3. ,09 10. 03 3, .03 9. .92 2, .91 A r i t h m e t i c 9. .96 2. ,88 10. 05 2, .92 9. ,97 2, .98 V o c a b u l a r y 10. .14 2. ,90 10. 09 2. .91 10. ,03 2, .97 Comprehension 9. .97 2. ,87 10. 08 3, .05 9. ,96 3, .00 Performance S u b t e s t s P i c t u r e C o m p l e t i o n 10.29 2.99 10. 20 3.08 9. 84 2 .84 P i c t u r e Arrangement 9.96 3.01 10. 02 3.05 9. 98 3 .01 B l o c k D e s i g n 10.15 2.85 9. 94 3.09 9. 98 3 .07 O b j e c t Assembly 10.05 2.97 9. 96 3.00 9. 97 2 .95 Coding 10.12 2.99 9. 98 3.06 10. 00 3 .04 Sums of S c a l e d S c o r e s V e r b a l S c o r e 50.16 10.74 50.35 11.45 49.80 11.48 Performance Score 50.57 9.23 50.09 9.71 49.78 10.03 F u l l S c a l e S c o r e 100.73 16.81 100.44 19.05 99.57 19.01 Mean S.D. A l l Ages Combined: VS 50.10 11.19 PS 50.16 9.64 FSS 100.26 18.26 108 WISC-R IQ S c a l e s To check the apparent s i m i l a r i t y of means and s t a n d a r d d e v i a t i o n s f o r s u b t e s t s and sums of s c a l e d s c o r e s a c r o s s age l e v e l s , one way f i x e d e f f e c t s a n a l y s e s of v a r i a n c e and Cochran's t e s t f o r homogeneity of v a r i a n c e (Winer, 1971) were used. The r e s u l t s a r e summarized i n Appendix F. I n no case were s i g n i f i c a n t d i f f e r e n c e s found f o r a = .05. T h e r e f o r e the P s y c h o l o g i c a l C o r p o r a t i o n p r o c e d u r e d e s c r i b e d i n C h a p t e r I I I was adopted ( c f . W e c h s l e r , 1974). The means and s t a n d a r d d e v i a t i o n s f o r the sums of s c a l e d s c o r e s f o r a l l age groups combined, as shown i n T a b l e 29, were used as the b a s i s f o r c o n s t r u c t i n g IQs. PPVT and SIT IQ S c o r e s IQ C o n v e r s i o n t a b l e s f o r the PPVT and SIT were c o n s t r u c t e d s e p a r a t e l y a t each age l e v e l u s i n g the a p p r o p r i a t e raw s c o r e means and s t a n d a r d d e v i a -t i o n s i n the c o n v e r s i o n e q u a t i o n i n Cha p t e r I I I . These v a l u e s are shown i n T a b l e 30. Ta b l e 30 Raw Score Means and S t a n d a r d D e v i a t i o n s f o r PPVT and. SIT 7% 9k 11% Mean S.D. Mean S.D. Mean S.D. PPVT 68.16 (8.56) 82.41 (9.11) 91.12 (10.31) SIT 106.45 (5.51) 118.19 (7.49) 129.23 . ( 1 0 . 0 8 ) 109 S t a t i s t i c a l P r o p e r t i e s of the T e s t s The i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t s and a s s o c i a t e d s t a n d a r d e r r o r s of measurement f o r each t e s t a r e r e p o r t e d i n T a b l e 31.- The c o e f f i c i e n t s were c a l c u l a t e d f o l l o w i n g t he p r o c e d u r e s i d e n t i f i e d i n T a b l e 15, Ch a p t e r I I I . The s t a n d a r d e r r o r s o f measurement a r e i n s c a l e d s c o r e u n i t s f o r the WISC-R s u b t e s t s ; i n IQ u n i t s f o r the t h r e e WISC-R IQ s c a l e s , the PPVT and the SIT; and i n raw s c o r e u n i t s f o r the SPM and MHVS. Comparison of t h e s e d a t a w i t h the c o r r e s p o n d i n g p u b l i s h e d d a t a show t h a t , f o r the WISC-R ( c f . W e c h s l e r , 1974, p. 2 8 ) , the B.C. r e l i a b i l i t y c o e f f i c i e n t s a r e g e n e r a l l y lower as would be e x p e c t e d from the red u c e d v a r i a b i l i t y i n the B.C. sample. The s t a n d a r d e r r o r s o f measurement, i n t u r n , a r e s l i g h t l y h i g h e r f o r the B.C. sample ( c f . W e c h s l e r , 1974, p. 3 0 ) . The B.C. r e l i a b i l i t y c o e f f i c i e n t s a r e a l s o lower t h a n the r e l i a b i l i t y of .97 r e p o r t e d f o r the SIT ( S l o s s o n , 1977, p . v . ) . However, the l a t t e r was based on a t e s t - r e t e s t p r o c e d u r e u s i n g a group w i t h v e r y h i g h v a r i a b i l i t y . The f i n d i n g s were r e v e r s e d f o r the PPVT ( c f . Dunn, 1965, p. 3 0 ) . H i g h e r r e l i a b i l i t i e s and lower s t a n d a r d e r r o r s o f e s t i m a t e were found f o r the B.C. sample. A l t h o u g h the v a r i a b i l i t y was comparable f o r the PPVT s t a n d -a r d i z a t i o n sample and the B. C. sample, the o r i g i n a l PPVT r e l i a b i l i t y c o e f -f i c i e n t was c a l c u l a t e d u s i n g the p a r a l l e l form method w h i c h i s known t o y i e l d l o wer c o e f f i c i e n t s t h a n o t h e r methods. T a b l e 31 I n t e r n a l C o n s i s t e n c y C o e f f i c i e n t s and S t a n d a r d E r r o r s of Measurement 7% 11% rxx M r -XX M rxx M WISC-R I n f o r m a t i o n .69 1 .63 .68 1 .75 .86 1. .12 S i m i l a r i t i e s .68 1 .75 .77 1 .46 .80 1. .30 A r i t h m e t i c .72 1 .52 .65 1 .72 .70 1. .63 V o c a b u l a r y .59 1 .86 .75 1 .46 .82 1. .26 Comprehens i o n .66 1 .68 .98 .43 .71 1. .62 P i c t u r e C o m p l e t i o n .61 1 .87 .68 1 .74 .67 1. .63 P i c t u r e Arrangement .75 1 .51 .55 2 .05 .44 2. .30 B l o c k D e s i g n .85 1 .10 .81 1 .35 .77 1. ,47 O b j e c t Assembly .63 1 .81 .67 1 .72 .62 1. .82 Coding - - - - - -Verbal. IQ .86 5 .39 .93 4 .07 .93 4. .08 Performance IQ .88 4 .98 .83 6 .23 .82 6. .61 F u l l S c a l e IQ .86 5 .16 .88 5 .41 .87 5. ,63 PPVT .88 5 .20 .87 5 .41 .87 5, .41 SIT .78 7 .04 .79 6 .87 .88 5, .20 SPM .89 2 .40 .92 2 .28 .83 2. .70 MHVS .76 1 .98 .83 2 .23 .88 2, ,18 I l l i n t e r p r e t a t i o n of the Norms The re n o r m i n g p r o c e d u r e s f o r the WISC-R, PPVT, and SIT i n v o l v e d the r e - a l i g n m e n t of the IQ s c a l e s f o r t h e s e t h r e e t e s t s t o mean 100 and s t a n d -a r d d e v i a t i o n 15. S i n c e the B. C. sample s c o r e d h i g h e r and w i t h l e s s v a r i -a b i l i t y t h a n the A merican s t a n d a r d i z a t i o n samples u s i n g A merican norms, the e f f e c t of r e s c a l i n g was t o lower and s p r e a d out the IQ s c o r e s c a l e s . The r e s u l t of t h i s p r o c e d u r e i s t h a t below average s t u d e n t s w i l l s c o r e lower w i t h B. C. than American norms, w h i l e s t u d e n t s who a r e much above average w i l l s c o r e the same or even h i g h e r w i t h B.C. norms. The e f f e c t s of the r e s c a l i n g p r o c e s s are shown g r a p h i c a l l y i n F i g u r e 6. The c u r v e s were c o n s t r u c t e d from the a c t u a l d i s t r i b u t i o n s of WISC-R F u l l S c a l e IQ s c o r e s p o o l e d a c r o s s a l l age groups f o r the'340 c h i l d r e n t e s t e d . The peaked c u r v e shows the d i s t r i b u t i o n of IQs when the t e s t s were s c o r e d u s i n g A m erican norms. The more s y m m e t r i c a l c u r v e shows the d i s t r i b u t i o n of IQs f o r the same t e s t s s c o r e d u s i n g the new B.C. norms. The e f f e c t of renorming on any g i v e n s c o r e v a l u e can be a p p r e c i a t e d by i m a g i n i n g the peaked c u r v e t o be s t r e t c h e d and compressed i n t o the shape of the second c u r v e . The more pronounced e f f e c t on the s c o r e changes f o r below average th a n above average c h i l d r e n can be seen from t h i s diagram. One of the immediate q u e s t i o n s t h a t a r i s e s i s the e f f e c t of t h i s l o w e r i n g of s c o r e s on the way c h i l d r e n a r e c l a s s i f i e d f o r e d u c a t i o n a l p u r -p o s e s . T a b l e 32 shows the IQ s c o r e ranges and c l a s s i f i c a t i o n c a t e g o r i e s r e p o r t e d i n the manuals . f o r the WISC-R, PPVT, and SIT r e s p e c t i v e l y . The p e r c e n t a g e s of the B. C. sample f a l l i n g w i t h i n each c l a s s i f i c a t i o n a r e g i v e n f o r the t e s t s s c o r e d w i t h A merican norms and w i t h B.C. norms. The p e r c e n t r e p r e s e n t e d i n each c a t e g o r y f o r B.C.-scored t e s t s c o r r e s p o n d s t o the p e r -c e n t e x p e c t e d based on the normal c u r v e d i s t r i b u t i o n . For a l l t h r e e 113 T a b l e 32 P e r c e n t of T o t a l Sample i n IQ C l a s s i f i c a t i o n C a t e g o r i e s f o r B.C. Norms and American Norms IQ C l a s s i f i c a t i o n A m e rican Norms B.C. Norms T h e o r e t i c a l Normal WISC-R (n=340) 130 and above 120-129 110-119 90-109 80-89 70-79 69 and below Ver y S u p e r i o r 4.1 S u p e r i o r 12.4 Hig h Average ( B r i g h t ) 25.3 Average 50.6 Low Average ( D u l l ) 6.2 B o r d e r l i n e _ 1.2 M e n t a l l y D e f i c i e n t .3 2.6 7.4 15.9 49.7 15.3 7.4 1.8 2.2 6.7 16.1 50.0 16.1 6.7 2.2 PPVT (n=331) 125 and above 110-124 90-109 75-89 Below 75 Very R a p i d L e a r n e r R a p i d L e a r n e r Average L e a r n e r Slow L e a r n e r V e r y Slow L e a r n e r 16.9 31.4 43.8 6.0 1.8 4.2 19.6 47.4 24.5 4.2 SIT (n=319) 140 and above 120-139 110-119 90-109 80-89 70-79 50-69 20-49 0-19 Very S u p e r i o r 2.2 S u p e r i o r 27.6 B r i g h t 28.5 Average 37.6 D u l l 3.1 B o r d e r l i n e .6 M i l d R e t a r d a t i o n .3 Moderate R e t a r d a t i o n -Severe R e t a r d a t i o n -.3 9.1 18.5 47.0 18.8 5.0 .6 .6 from WISC-R Manual ( W e c h s l e r , 1974, p. 26) 'from PPVT Manual (Dunn, 1965, p. 11) 'from SIT Manual ( S l o s s o n , 1977, i n s i d e f r o n t c o v e r ) 114 t e s t s , the s h i f t t o lower c l a s s i f i c a t i o n s i s o b v i o u s and pronounced. I n a c t u a l numbers, u s i n g WISC-R F u l l S c a l e IQs, f i v e t i m e s as many c h i l d r e n s c o r e 70 and below u s i n g B.C. norms tha n u s i n g A merican norms. Fo r t h e SIT, t h i s number i s almost seven t i m e s as many. Fo r t h e below 75 c l a s s -i f i c a t i o n on the PPVT, a l i t t l e more tha n t w i c e as many c h i l d r e n a r e i n -c l u d e d when s c o r e d w i t h B.C. as opposed to American norms. As seen i n t h i s s e c t i o n , the IQ t e s t s (WISC-R, PPVT, SIT) were r e -s c a l e d t o conform w i t h c o n v e n t i o n a l use and i n t e r p r e t a t i o n : t h a t i s , w i t h mean 100 and s t a n d a r d d e v i a t i o n 15. The e f f e c t of t h e s e a d j u s t m e n t s i s a l o w e r i n g of the s c o r e v a l u e a s s i g n e d t o a g i v e n l e v e l of p e r f o r m a n c e . The i m p l i c a t i o n s of t h e s e r e s u l t s are d i s c u s s e d i n C h a p t e r V. One f u r t h e r set of t a b l e s was p r e p a r e d f o l l o w i n g d i s c u s s i o n s w i t h p r a c t i t i o n e r s c o n c e r n i n g the u s e f u l n e s s of the - r e s u l t s of the s t u d y . The p e r c e n t i l e r a n k s of IQ s c o r e s c o r r e s p o n d i n g t o s e l e c t e d s t a n d a r d d e v i a t i o n s were c a l c u l a t e d f o r the B.C. sample u s i n g the p u b l i s h e d norms. These a r e i n c l u d e d w i t h the norms t a b l e s i n Appendix E. E q u a t i n g T h i s s e c t i o n i s o r g a n i z e d as f o l l o w s . F i r s t , n o m i n a l l y p a r a l l e l t e s t p a i r s a r e i d e n t i f i e d and a s s i g n e d t o o b s e r v e d s c o r e and t r u e s c o r e e q u a t i n g methods. F o l l o w i n g t h i s , t h e r e i s a c o m p a r a t i v e e x a m i n a t i o n of the outcomes of a p p l y i n g a l l f o u r p r o c e d u r e s — l i n e a r o b s e r v e d s c o r e e q u a t i n g , l i n e a r t r u e s c o r e e q u a t i n g , g r a p h i c e q u i p e r c e n t i l e e q u a t i n g , and a n a l y t i c a l e q u i p e r c e n t i l e e q u a t i n g — t o two p a i r s of s c o r e s . The p a i r s chosen f o r t h i s i l l u s t r a t i o n were: 1) WISC-R V e r b a l and PPVT, age 7%, and WISC-R V e r b a l and MHVS, age 11%. These r e p r e s e n t t e s t p a i r s h a v i n g low ( c o r r e c t e d r = .68) and h i g h ( c o r r e c t e d r = .92) d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c -XY XY i e n t s r e s p e c t i v e l y . A l t h o u g h t h i s format n e c e s s i t a t e s some d i s c u s s i o n 115 i n o r d e r t o i n t e r p r e t and a s s e s s t he s i g n i f i c a n c e o f the r e s u l t s , a more g e n e r a l d i s c u s s i o n of the a p p l i c a b i l i t y and s u i t a b i l i t y of e q u a t i n g t h e s e i n t e l l i g e n c e t e s t s i s r e s e r v e d f o r Chap t e r V. F i n a l l y , the e q u i v a l e n c y t a b l e s r e s u l t i n g from the e q u a t i n g p r o c e d u r e s a r e p r e s e n t e d . I d e n t i f i c a t i o n o f N o m i n a l l y P a r a l l e l T e s t P a i r s The m a t r i x of c o r r e l a t i o n c o e f f i c i e n t s , c o r r e c t e d f o r a t t e n u a t i o n , i s p r e s e n t e d i n Ta b l e 33,. The c o e f f i c i e n t s were computed u s i n g s t a n d a r d i z e d T a b l e 33 Observed Score C o r r e l a t i o n C o e f f i c i e n t s C o r r e c t e d f o r A t t e n u a t i o n WISC-R  S t a n d a r d i z e d S t a n d a r d i z e d S t a n d a r d i z e d Raw Score V e r b a l Score Performance Score F u l l S c a l e Score Age 7% PPVT .68* .35 .62 SIT .94* .40 .79* SPM .34 .50 .48 MHVS .88* .38 .74 Age 9% PPVT . 72* .52 .69 SIT .76* .67 . 80* SPM .46 .60 .58 MHVS .82* .43 .70 Age 11% PPVT .78* .46 .71 SIT .92* .67 .89* SPM .52 .68* .67 MHVS .92* .59 .86 N o m i n a l l y p a r a l l e l t e s t p a i r s WISC-R s c o r e s and raw s c o r e s f o r the o t h e r f o u r t e s t s . The s t a t i s t i c a l c r i t e r i o n f o r n o m i n a l p a r a l l e l i s m was d e f i n e d as c o r r e c t e d r > .70. A p p l i c a t i o n of t h i s c r i t e r i o n t o a l l t e s t p a i r s i d e n t i f i e d as p s y c h o l o g i c -a l l y p a r a l l e l a d d i t i o n a l l y s a t i s f i e d t he c r i t e r i o n f o r s t a t i s t i c a l p a r a l -l e l i s m ( w i t h t he e x c e p t i o n of t h e SPM and WISC-R Performance a t ages 7% and 9%). Thus the 13 p a i r s of t e s t s i n d i c a t e d by the a s t e r i s k s i n T a b l e 33 were s e l e c t e d f o r e q u a t i n g . I t -was n o t e d i n Chapt e r I I I t h a t t he l i n e a r t r u e s c o r e e q u a t i n g p r o c e -dure was based on c o n v e r t e d IQ s c o r e s r a t h e r t h a n on o b s e r v e d s c o r e s . I n t h a t c h a p t e r i t was f u r t h e r p o i n t e d out t h a t t h e r e was a c l o s e c o r r e s -pondence between WISC-R s t a n d a r d i z e d and WISC-R IQ s c o r e s . S i m i l a r l y , t h e c o r r e l a t i o n c o e f f i c i e n t s computed u s i n g o b s e r v e d s c o r e s and IQ s c o r e s are v i r t u a l l y i d e n t i c a l . T h e r e f o r e t he s t a t i s t i c a l e v i d e n c e of nom i n a l p a r a l l e l i s m p r e s e n t e d i n T a b l e 33 a p p l i e s t o b o t h o b s e r v e d s c o r e and IQ s c o r e d i s t r i b u t i o n s . D e s i g n a t i o n of Test P a i r s t o E q u a t i n g Methods As d i s c u s s e d i n Chapt e r I I I , the c r i t i c a l d i f f e r e n c e v a l u e f o r the d e t e r m i n a t i o n of e q u a l l y r e l i a b l e t e s t s was s e t a t .06. Test p a i r s h a v i n g r e l i a b i l i t i e s d i f f e r i n g by no more tha n .06 were a s s i g n e d t o ob s e r v e d s c o r e e q u a t i n g methods ( b o t h l i n e a r and e q u i p e r c e n t i l e ) , w h i l e t e s t s whose r e l i -a b i l i t i e s d i f f e r e d by more tha n .06 were a s s i g n e d t o t h e l i n e a r t r u e s c o r e e q u a t i n g method. These d e s i g n a t i o n s a r e shown i n T a b l e 34. A Comparative E x a m i n a t i o n o f E q u a t i n g P r o c e d u r e s T. MHVS and WISC-R V e r b a l • Ta b l e 35 c o n s i s t s of a s e r i e s o f " e q u i v a l e n t " s c o r e v a l u e s f o r the MHVS and WISC-R V e r b a l IQ (B.C. normed) at age 11% w h i c h were produced by the d i f f e r e n t e q u a t i n g p r o c e d u r e s . I t w i l l be n o t e d t h a t t he c o n v e r t e d IQ 117 T a b l e 34 Test P a i r s I d e n t i f i e d f o r E q u a t i n g Methods D i s a t t e n u a t e d Age C o r r e l a t i o n R e l i a b i l i t y T est P a i r L e v e l C o e f f i c i e n t C o e f f i c i e n t s Observed Score E q u a t i n g ( L i n e a r and E q u i p e r c e n t i l e ) WISC-R V e r b a l : PPVT .68 .86, .88 9h .72 .93, .87 .78 .93, .87 WISC-R V e r b a l : SIT llh .92 • 93, .88 WISC-R F u l l S c a l e : SIT nh .89 .87, .88 WISC-R Perf o r m a n c e : SPM nh .68 .82, .83 WISC-R V e r b a l : MHVS nh .92 .93, .88 True Score E q u a t i n g ( L i n e a r ) WISC-R V e r b a l : SIT ih .94 .86, .78 9h .76 .93, .79 WISC-R F u l l S c a l e : SIT -.7% ..'.79 .,'8'6, .78 9h .80 .88, .79 WISC-R V e r b a l : MHVS ih .88 .86, .76 9h .82 .93, .83 aWISC-R r e l i a b i l i t y l i s t e d f i r s t 118 T a b l e 35 Comparative Example of L i n e a r E q u a t i n g and E q u i p e r c e n t i l e E q u a t i n g f o r C o n v e r t i n g MHVS Raw Sc o r e s t o WISC-R V e r b a l IQ Sc o r e s (Age Ilk) r x y = .92, r x x = .93, r y y = .88 L i n e a r E q u a t i n g E q u i p e r c e n t i l e E q u a t i n g  MHVS Observed A n a l y t i c a l  Raw Score True Score I n t e r p o l a t e d C u r v e - F i t t i n g S c o r e s Y* Y* G r a p h i c S c o r e s L i n e a r P o l y n o m i a l (1) (56.5) 49.00 35.78 48.89 7 46.95 45.50 63.0 62.00 49.99 61.49 13 61.69 60.65 69.3 64.00 64.20 65.58/ 15 66.61 65.70 71.7 66.00 68.94 68.57 16 69.06 68.22 72.8 72.00 71.31 70.35 18 73.98 73.27 75.4 74.00 76.04 74.35 19 76.94 75.80 77.0 78.60 78.41 76.50 20 78.89 78.32 78.6 79.20 80.78 78.73 21 81.35 80.85 80.3 81.00 83.15 81.00 22 83.81 83.37 82.5 85.25 85.52 83.31 23 86.26 85.90 84.6 86.50 87.89 85.64 24 88.72 88.42 86.8 87.50 90.26 87.99 25 91.18 90.95 89.2 88.67 92.63 90.36 26 93.64 93.47 91.5 92.60 94.99 92.78 27 96.09 96.00 93.9 93.83 97.36 95.25 28 98.55 98.52 96.8 96.50 99.73 97.79 29 101.01 101.05 99.5 99.50 102.10 100.41 30 103.46 103.57 102.6 101.67 104.47 103.15 31 105.92 106.10 105.7 108.00 106.84 106.00 32 108.38 108.62 108.8 109.00 109.21 108.98 33 110.83 111.15 111.8 112.50 111.58 112.06 34': 113.29 113.67 114.7 117.00 113.94 115.23 35 115.75 116.20 117.5 119.50 116.31 118.44 36 118.20 118.72 120.3 123.00 118.68 121.60 38 123.12 123.77 125.5 125.00 123.42 127.29 39 125.58 126.30 128.0 128.00 125.79 129.47 40 128.03 128.82 130.3 131.00 128.16 130.88 41 130.49 13.1.35 132.9 133.00 130.53.' 131.20 Y.=28.41 RMS Q = 8.87 RMS T = 9.62 RMS G = 9.13 RMS]. = 9.47 RMS L 9.40 RMS p = 9.24 119 v a l u e s a r e r e p o r t e d t o two d e c i m a l p l a c e s . S i n c e the purpose o f t h i s p a r t of the s t u d y was t o examine the e f f i c a c y of e q u a t i n g p r o c e d u r e s , i t was d e s i r a b l e t o r e t a i n p r e c i s i o n t o the second d e c i m a l p o i n t . I n the p r e p a r -a t i o n o f e q u i v a l e n c y t a b l e s f o r p r a c t i t i o n e r s ' use, however, t h e s e w o u l d be rounded t o the n e a r e s t whole number ( c f . L o r e t et a l . , 1974). I n t he f i r s t column the raw s c o r e v a l u e s f o r the MHVS a r e l i s t e d . The o b t a i n e d s c o r e range on t h i s t e s t was 7-41: the v a l u e 1 shown i n p a r e n t h e s e s was d e r i v e d from the a n a l y t i c a l e q u i p e r c e n t i l e p r o c e d u r e and i s d e s c r i b e d i n the s e c t i o n f o r t h a t p r o c e d u r e . The n e x t two columns c o n t a i n the r e s u l t s o f l i n e a r e q u a t i n g : t he con -v e r t e d WISC-R s c o r e s from the ob s e r v e d s c o r e and t r u e s c o r e p r o c e d u r e s a r e shown i n t h e columns l a b e l l e d Y*^ and Y* r e s p e c t i v e l y . The r e s u l t s of the e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e s a r e shown i n columns 4 t o 7. The c o n v e r t e d s c o r e s from the h a n d - g r a p h i n g p r o c e d u r e a r e l i s t e d f i r s t (column 4 ) , f o l l o w e d by the r e s u l t s from the c o m p u t e r i z e d a n a l y t i c a l program (columns 5-7). Column 5 shows the i n t e r p o l a t e d s c o r e s , and columns 6 and 7 the con -v e r t e d s c o r e s r e s u l t i n g from the l i n e a r and p o l y n o m i a l c u r v e - f i t t i n g p r o c e -d u r e s . Below the t a b l e , t he f o l l o w i n g s t a t i s t i c s a r e p r e s e n t e d t o a i d i n the i n t e r p r e t a t i o n o f the r e s u l t s : Y. = mean of the MHVS raw s c o r e s RMS = c o n d i t i o n a l root-mean-square e r r o r of e q u a t i n g . The s u b s c r i p t s 0, T, G, I , L, and P i n d i c a t e the co r r e s p o n d e n c e of t h e s e e r r o r s to t he o b s e r v e d s c o r e , t r u e s c o r e , g r a p h i c , i n t e r p o l a t e d , l i n e a r c u r v e - f i t t i n g , and p o l y n o m i a l c u r v e - f i t t i n g columns r e s p e c t i v e l y . The s t a n d a r d e r r o r s of e q u a t i n g f o r the two l i n e a r p r o c e d u r e s were o m i t t e d from T a b l e 35 because o f space l i m i t a t i o n s . They a r e shown i n T a b l e 36. 120 T a b l e 36 S t a n d a r d E r r o r s of E q u a t i n g f o r MHVS Raw S c o r e s to WISC-R V e r b a l IQ S c o r e s (Age 11%) M H V S SY * S Y * Raw S c o r e s 0 T 7 3.15 3.28 13 2.36 2.44 15 2.10 2.17 16 1.98 2.04 18 1.73 1. 78 19 1.62 1.66 20 1.50 1.54 21 1.40 1.42 22 1.29 1.31 23 1.20 1.21 24 1.12 1.12 25 1.04 1.04 26 .99 .98 27 .95 .92 28 .93 .91 29 .93 .92 30 .96 .94 31 1.00 .99 32 1.06 1.05 33 1.31 1.14 34 1.22 1.23 35 1.31 1.33 36 1.42 1.44 38 1.64 1.68 39 1.76 1.81 40 1.88 1.93 41 2.00 2.06 121 L i n e a r e q u a t i n g . As shown i n Ta b l e 35, column 2, the c o n v e r t e d v a l u e s f o r t he l i n e a r o b s e r v e d s c o r e p r o c e d u r e ranged from 46.95 t o 130.49. The a c t u a l o b t a i n e d s c o r e range was 49 t o 133. Taken a c r o s s t he a c t u a l s c o r e s , the c o n d i t i o n a l root-mean-square e r r o r was 8.87. The c o r r e s p o n d i n g e r r o r f o r t he l i n e a r t r u e s c o r e p r o c e d u r e was s l i g h t l y l a r g e r : 9.62. The e x t e n t o f t he d i s c r e p a n c i e s between o b s e r v e d and c o n v e r t e d s c o r e s a r e shown more f u l l y i n F i g u r e 7. T h i s diagram shows a s c a t t e r p l o t of the o b t a i n e d s c o r e s w i t h b o t h l i n e a r c o n v e r s i o n l i n e s superimposed on i t . D i s c r e p a n c i e s between an o b s e r v e d WISC-R V e r b a l IQ and the c o r r e s p o n d i n g equated v a l u e f o r a g i v e n MHVS raw s c o r e a r e r e p r e s e n t e d by the l e n g t h of the v e r t i c a l segment between an o b s e r v e d s c o r e p o i n t ( r e p r e s e n t e d by a c l o s e d c i r c l e ) and the c o n v e r s i o n l i n e ( e . g . , see v e r t i c a l segment A ) . G r a p h i c e q u i p e r c e n t i l e e q u a t i n g . The c o n v e r t e d s c o r e s l i s t e d i n the column of T a b l e 35 l a b e l l e d " G r a p h i c " were d e r i v e d f o l l o w i n g t he s t e p s o u t -l i n e d i n Chapt e r I I I and i l l u s t r a t e d on the f o l l o w i n g pages. T a b l e 37 shows the p r e p a r a t i o n of the r e l a t i v e c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s f o r the two t e s t s . The graphs of t h e s e v a l u e s a r e p i c t u r e d i n F i g u r e 8, and e q u i -p e r c e n t i l e p o i n t s c o r r e s p o n d i n g t o s e l e c t e d p e r c e n t i l e s from t he o g i v e s a r e r e c o r d e d i n T a b l e 38. The a c t u a l c o n v e r s i o n l i n e r e p r e s e n t s t he smoothed graph of the e q u i p e r c e n t i l e p o i n t s p l o t t e d a g a i n s t each o t h e r ( F i g u r e 9 ) . The f i n a l e q u i v a l e n t v a l u e s f o r c o n v e r t i n g MHVS raw s c o r e s t o WISC-R V e r b a l IQs, r e p o r t e d i n column 4, T a b l e 35, were r e a d from the graph i n F i g u r e 9. As shown, the c o n v e r t e d s c o r e s c o r r e s p o n d i n g t o the o b t a i n e d MHVS s c o r e s ranged from 63.0 t o 132.9. The root-mean-square e r r o r of e q u a t i n g was 9.13. 0. 10 20 30 40 50 MHVS RAW SCORE F i g u r e 7. S c a t t e r p l o t of o b t a i n e d s c o r e s w i t h l i n e a r o b s e r v e d s c o r e and t r u e s c o r e e q u a t i n g c o n v e r s i o n l i n e s . MHVS t o WISC-R V e r b a l IQ, age 11.%. 123 T a b l e 37 D i s t r i b u t i o n s o f MHVS Raw Sc o r e s and WISC-R V e r b a l IQ S c o r e s , Age 11% MHVS Raw C u m u l a t i v e % Score Frequency Frequency Below 41 1 105 99.0 40 1 104 98.1 39 1 103 97.2 38 2 102 95.2 36 4 100 91.4 35 6 96 85.7 34 5 90 81.0 33 8 85 73.3 32 4 77 69.5 31 16 73 63.8 30 4 67 60.0 29 7 63 43.8 28 4 46 40.0 27 7 42 33.3 26 7 35 26.7 25 5 28 21.9 24 2 23 20.0 23 4 21 16.2 22 4 17 12.4 21 3 13 9.5 20 1 10 8.6 19 3 9 5.7 18 1 6 4.8 16 1 5 3.8 15 1 4 2.9 13 1 3 1.9 7 2 2 WISC-R V e r b a l C u m u l a t i v e % IQ Frequency Frequency Below 133 1 105 99.0 131 1 104 98.1 128 1 103 97.1 125 1 102 96.2 124 1 101 95.2 123 1 100 94.3 121 4 99 90.5 119 5 95 85.7 117 1 90 84.8 115 2 89 82.9 113 4 87 79.0 112 5 83 74.3 111 1 78 73.3 109 4 77 69.5 108 2 73 67.6 107 3 71 64.8 105 5 68 60.0 104 4 63 56.2 103 3 59 53.3 101 1 56 52.4 100 4 .55 48.6 99 3 51 45.7 97 4 48 41.9 96 1 44 41.0 94 6 43 35.2 93 5 37 30.5 92 1 32 29.5 90 1 31 28.6 89 6 30 22.9 88 4 24 19.0 86 4 20 15.2 85 1 16 14.3 84 1 15 13.3 82 1 14 12.4 81 5 13 7.6 78 1 8 6.7 76 2 7 4.8 72 1 5 3.8 66 2 4 1.9 62 1 2 1.0 49 1 1 124 MHVS RAW SCORE 10 20 30 40 50 i 1 1 1 1 1 ' l l l 1 L I 1 60 70 80 90 100 110 120 130 WISC-R VERBAL IQ F i g u r e 8. C u m u l a t i v e r e l a t i v e f r e q u e n c i e s f o r MHVS raw s c o r e s and WISC-R V e r b a l IQs, age 11%. T a b l e 38 E q u i p e r c e n t i l e P o i n t s f o r MHVS and WISC-R V e r b a l IQ from G r a p h i c P r o c e d u r e P e r c e n t i l e WISC-R Rank MHVS V e r b a l 0.5 6.5 62.5 0.7 8.0 64.0 1.0 9.5 65.7 1.4 11.3 67.5 1.8 12.6 68.8 2.0 13.2 69.5 3 15.0 71.8 4 16.8 73.6 5 17.8 75.3 8 20.0 .78'. 7 12 22.0 82.2 17 23.5 85.5 20 24.3 87.2 24 25.2 89.4 30 26.4 92.3 34 27.0 94.2 40 28.0 96.8 46 29.0 99.5 50 29.5 101.0 54 30.0 102.6 60 31.0 105.0 66 31.7 107.5 70 32.3 109.2 74 32.8 111.0 78 33.5 112.8 82 34.2 115.5 85 34.8 116.8 88 35.5 118.4 90 36.0 119.8 93 37.0 122.2 95 37.7 124.3 97 39.0 127.3 98 39.8 129.5 98.4 40.3 130.5 98.8 40.8 132.0 1 2 6 I | I I I 1 1 10 20 30 40 50 MHVS RAW SCORE F i g u r e 9 . Hand-graphed e q u i p e r c e n t i l e e q u a t i n g c o n v e r s i o n l i n e . MHVS t o WISC-R V e r b a l IQ, age 11%. 127 A n a l y t i c a l e q u i p e r c e n t i l e e q u a t i n g . As d e s c r i b e d i n C h a p t e r s I I and I I I , t he f i r s t s t e p of the a n a l y t i c a l p r o c e d u r e was t o produce i n t e r p o l a t e d d i s t r i b u t i o n s f o r b o t h MHVS raw s c o r e s and WISC-R V e r b a l IQ s c o r e s . The c o n v e r t e d v a l u e s r e p o r t e d i n T a b l e 35 c o r r e s p o n d o n l y t o the o b t a i n e d MHVS s c o r e s w i t h one e x c e p t i o n : t he s c o r e of 1, shown i n p a r e n t h e s e s , was p r o -duced by the i n t e r p o l a t i o n p r o c e d u r e t o c o r r e s p o n d t o the o b t a i n e d WISC-R V e r b a l IQ of 49. The second s t e p of the p r o c e d u r e , c u r v e - f i t t i n g , r e p r e s e n t e d an attempt t o f i t a r e g r e s s i o n l i n e t o the i n t e r p o l a t e d s c o r e d i s t r i b u t i o n s u s i n g b o t h a l i n e a r and a p o l y n o m i a l f u n c t i o n a l e q u a t i o n . The b i v a r i a t e i n t e r p o l a t e d s c o r e d i s t r i b u t i o n and the l i n e a r and p o l y n o m i a l r e g r e s s i o n l i n e s a r e shown i n F i g u r e 10. The root-mean-square e r r o r s c o r r e s p o n d i n g t o each of th e s e were 9.47, 9.40, and 9.24 r e s p e c t i v e l y . As i n F i g u r e 7, the d i s c r e p a n c y between an o b s e r v e d and a c o n v e r t e d s c o r e i s i n d i c a t e d by the l e n g t h of the v e r t i c a l segment A. The c o n d i t i o n a l root-mean-square e r r o r s o f e q u a t i n g (RSM and RSM ) J-J L were d e r i v e d from the l i n e a r and p o l y n o m i a l r e g r e s s i o n e q u a t i o n s , respect -', t i v e l y , g e n e r a t e d by the c u r v e - f i t t i n g p r o c e d u r e s . These r e p r e s e n t a d i f -f e r e n t t y p e of e r r o r e s t i m a t e t h a n t h a t r e p o r t e d by L i n d s a y and P r i c h a r d (1971) as w i l l be d i s c u s s e d i n a l a t e r s e c t i o n . I I . PPVT and WISC-R V e r b a l The r e s u l t s o f the second example, i n w h i c h each of the e q u a t i n g p r o c e -dures was a p p l i e d t o PPVT IQ and WISC-R V e r b a l IQ s c o r e s a t age 11%, a r e p r e s e n t e d i n T a b l e s 39 and 40. These t a b l e s a r e i d e n t i c a l i n format t o T a b l e s 35 and 36 f o r the f i r s t example. F i g u r e 11 shows a s c a t t e r p l o t o f the o b t a i n e d s c o r e s used i n the l i n e a r e q u a t i n g p r o c e d u r e s and i n c l u d e s t he two l i n e a r c o n v e r s i o n l i n e s produced by the ob s e r v e d s c o r e and t r u e s c o r e 128 130 h 40 Interpolated Scores •— Linear — Polynomial F i g u r e 10. 10 20 30 40 50 MHVS RAW SCORE S c a t t e r p l o t o f o b t a i n e d s c o r e s w i t h i n t e r p o l a t e d , l i n e a r c u r v e - f i t t i n g , and p o l y n o m i a l c u r v e - f i t t i n g c o n v e r s i o n l i n e s : a n a l y t i c a l e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e . MHVS to WISC-R V e r b a l IQ, age 11%. 129 T a b l e 39 Comparative Example of L i n e a r E q u a t i n g and E q u i p e r c e n t i l e E q u a t i n g f o r C o n v e r t i n g PPVT IQs t o WISC-R V e r b a l IQs (Age 7k) RXY = - 6 8 ' RXX = - 8 6 ' RXY = - 8 8 ' L i n e a r E q u a t i n g E q u i p e r c e n t i l e E q u a t i n g Observed A n a l y t i c a l PPVT Score True Score I n t e r p o l a t e d Curve- - F i t t i n g IQ Y * o Y* T G r a p h i c S c o r e s L i n e a r P o l y n o m i a l 70 71.19 71.52 (<70.0) 70.00 71.36 71.12 75 76.24 76.51 73.0 71.33 76.25 69.43 77 77.92 78.18 74.6 72.67 77.88 71.53 79 79.61 79.84 76.0 76.00 79.51 74.24 80 81.29 81.51 76.8 76.50 81.14 77.29 82 82.98 83.17 78.7 80.25 82.77 80.45 84 84.66 84.84 81.5 81.00 84.41 83.56 86 86.34 86.50 85.4 85.50 86.04 86.50 87 88.03 88.16 87.5 88.00 87.67 89.19 89 89.71 89.83 91.0 93.67 89.30 91.62 91 91.39 91.49 93.7 95.20 90.93 93.77 93 93.08 93.16 96.4 96.60 92.56 95.66 94 94.76 94.82 97.6 99.00 94.20 97.34 96 96.44 96.49 99.7 99.67 95.82 98.83 98 98.13 98.15 101.4 99.83 97.46 100.18 100 99.81 99.82 102.8 101.29 99.08 101.45 101 101.50 101.48 103.6 101.57 100.72 102.68 103 103.18 103.14 104.8 102.43 102.35 103.92 105 104.86 104.81 106.0 104.67 103.98 105.18 107 106.55 106.47 107.3 107.14 105.61 106.52 108 108.23 108.14 108.0 107.86 107.24 107.92 110 109.91 109.80 109.4 109.50 108.88 109.42 112 111.60 111.46 111.0 111.50 110.51 110.99 114 113.28 113.13 112.6 112.75 112.14 112.61 115 114.96 114.79 113.4 113.00 113.77 114.26 117 116.65 116.46 115.0 115.00 115.40 115.91 119 118.33 118.12 116.7 119.00 117.03 117.52 121 120.02 119.79 118.4 120.50 118.67 119.07 124 123.38 123.12 121.0 122.00 121.93 121.78 128 126.75 126.44 124.7 123.50 125.18 123.90 130 128.43 128.11 126.6 124.00 126.82 124.75 133 ' 131.80 131.44 129.7 126.33 130.08 126.35 135 133.48 133.10 131.6 127.67 131.71 127.32 137 135.17 134.77 133.8 129.00 133.34 128.65 Y.=100 .00 RMSQ = RMS m = T RMS G = RMS = RMS = Li RMS p = 13.08 13.00 13.18 12.94 12.89 12.90 T a b l e 40 S t a n d a r d E r r o r s of E q u a t i n g f o r PPVT t o WISC -R V e r b a l IQ S c o r e s (Age 7k) PPVT IQs T 7:0 •2.50 2.53 75 2.18 2.19 77 2.07 2.08 79 1.97 1.98 80 1.87 1.87 82 1.78 1.77 84 1.69 1.68 86 1.60 1.59 87 1.52 1.50 89 1.45 1.43 91 1.39 1.36 93 1.33 1.30 94 1.29 1.25 96 1.25 1.21 98 1.23 1.19 100 1.22' 1.18 101 1.23 1.18 103 1.24 1.20 105 1.28 1.23 107 1.32 1.28 108 1.37 1.34 110 1.43 1.40 112 1.50 1.48 114 1.58 1.56 115 1.66 1.65 117 1.75 1.74 119 1.84 1.84 121 1.94 1.94 124 2.14 2.16 128 2.36 2.38 130 . 2.47 2.50 133 2.69 2.73 135 2.81 2.85 137 2.92 2.97 131 150 140 • Obtained Scores — Observed Score Equating — — True Score Equating 80 90 100 110 PPVT IQ 120 130 F i g u r e 11. S c a t t e r p l o t of o b t a i n e d s c o r e s w i t h l i n e a r o b s e r v e d s c o r e and t r u e s c o r e e q u a t i n g c o n v e r s i o n l i n e s . PPVT IQ t o WISC-R V e r b a l IQ, age 1\. 132 methods. The root-mean-square e r r o r s c o r r e s p o n d i n g t o t h e s e a r e 13.08 and 13.00 r e s p e c t i v e l y . These are somewhat l a r g e r t h a n the e r r o r s a s s o c i a t e d w i t h the l i n e a r e q u a t i n g p r o c e d u r e s i n the p r e v i o u s example. I t s h o u l d be n o t e d , however, t h a t the c o r r e l a t i o n i n t h i s example i s l o w e r . The t a b l e s and graphs i l l u s t r a t i n g the g r a p h i c e q u i p e r c e n t i l e p r o c e d u r e f o r t h e s e t e s t s appear i n Appendix G. A graph of the i n t e r p o l a t e d s c o r e d i s t r i b u t i o n i s i l l u s t r a t e d i n F i g u r e 12, t o g e t h e r w i t h the l i n e a r and p o l y -n o m i a l r e g r e s s i o n l i n e s r e s u l t i n g from the a n a l y t i c a l p r o c e d u r e . The mean-r o o t - s q u a r e e r r o r s c o r r e s p o n d i n g t o the t h r e e s c o r e d i s t r i b u t i o n s r e p r e s e n t e d i n F i g u r e 12 a r e 12.94, 12.89, and 12.90 r e s p e c t i v e l y . Summary. The c h a r a c t e r i s t i c s of the e q u a t i n g methods and p r o c e d u r e s w h i c h were demonstrated i n the examples i n t h i s s e c t i o n are summarized below. 1. L i n e a r Observed Score v s . L i n e a r True Score E q u a t i n g The c o n v e r t e d WISC-R s c o r e d i s t r i b u t i o n s r e s u l t i n g from the a p p l i c a t i o n of the o b s e r v e d and t r u e s c o r e l i n e a r p r o c e d u r e s are v e r y s i m i l a r . L i k e w i s e the d i s t r i b u t i o n s of the s t a n d a r d e r r o r s of e q u a t i n g and the s i z e of the c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g a s s o c i a t e d w i t h t h e two p r o -cedures are s i m i l a r . Thus no o b v i o u s advantages a r e a c c r u e d by u s i n g the t r u e s c o r e p r o c e d u r e , a t l e a s t f o r the range of d i s c r e p a n c i e s between the r e l i a b i l i t y c o e f f i c i e n t s r e p o r t e d i n the p r e s e n t s t u d y . 2. S t a n d a r d E r r o r s of E q u a t i n g The s t a n d a r d e r r o r s of e q u a t i n g a s s o c i a t e d w i t h the l i n e a r p r o c e d u r e s show a g r e a t e r p r e c i s i o n of c o n v e r t e d s c o r e s c l o s e r t o t h e mean. The i n c r e a s e i n the s i z e of the s t a n d a r d e r r o r s i n the extremes of the d i s t r i b u -t i o n s i n d i c a t e s more i n s t a b i l i t y of c o n v e r t e d s c o r e s i n t h o s e a r e a s . 133 150 140 Interpolated Scores Linear Polynomial 90 100 PPVT 110 IQ 120 130 F i g u r e 12. S c a t t e r p l o t o f o b t a i n e d s c o r e s w i t h i n t e r p o l a t e d , l i n e a r c u r v e - f i t t i n g , and p o l y n o m i a l c u r v e - f i t t i n g c o n v e r s i o n l i n e s : a n a l y t i c a l e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e . PPVT IQ t o WISC-R V e r b a l IQ, age 1\. 134 3. G r a p h i c v s . I n t e r p o l a t e d E q u i p e r c e n t i l e E q u a t i n g The a n a l y t i c a l p r o c e d u r e was i n c l u d e d i n the p r e s e n t s t u d y f o r compar-i s o n w i t h the t r a d i t i o n a l h a n d - g r a p h i n g p r o c e d u r e . T h i s c o m p a r i s o n i n v o l v e s o n l y columns 4 and 5 i n T a b l e s 35 and 39 ( i . e . , t h o s e columns l a b e l l e d " g r a p h i c " and " i n t e r p o l a t e d s c o r e s " ) . As can be seen, t h e s e two s c o r e d i s t r i b u t i o n s a r e v e r y s i m i l a r . A g a i n , d i f f e r e n c e s a r e most e v i d e n t i n the extremes of the d i s t r i b u t i o n s where d a t a f o r g r a p h i n g a re s c a n t . D e s p i t e t h e s e d i f f e r e n c e s , however, e x a m i n a t i o n o f the c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g r e v e a l s t h a t the two p r o c e d u r e s a r e comparable. 4. The C u r v e - F i t t i n g P r o c e d u r e s C u r v e - f i t t i n g , t h r o u g h the a p p l i c a t i o n of l i n e a r and p o l y n o m i a l r e g r e s -s i o n p r o c e d u r e s , was i n c l u d e d by L i n d s a y and P r i c h a r d (1971) as a f u r t h e r e f f o r t t o d e f i n e the shape of the c o n v e r s i o n l i n e . As can be seen by com-p a r i n g columns 5, 6, and 7, the d i s t r i b u t i o n s of p r e d i c t e d s c o r e s a re s i m i l a r to the d i s t r i b u t i o n of i n t e r p o l a t e d s c o r e s . T h i s i s r e f l e c t e d i n the s i z e of t he r e s p e c t i v e root-mean-square e r r o r s . 5. L i n e a r v s . E q u i p e r c e n t i l e E q u a t i n g The l i n e a r and e q u i p e r c e n t i l e c o n v e r s i o n p r o c e d u r e s produced v e r y s i m -i l a r r e s u l t s i n the c e n t r a l a r e a s of the d i s t r i b u t i o n s . D i f f e r e n c e s i n c o n v e r t e d s c o r e v a l u e s a re most pronounced i n the extremes. However, the c o n d i t i o n a l root-mean-square e r r o r s a re of s i m i l a r magnitude f o r b o t h l i n e a r and e q u i p e r c e n t i l e p r o c e d u r e s . A f u r t h e r comment on c u r v e - f i t t i n g . I n t h e i r a n a l y t i c a l p r o c e d u r e , L i n d s a y and P r i c h a r d (1971) r e l i e d on the s t a n d a r d e r r o r of e s t i m a t e from the r e g r e s s i o n p r o c e d u r e as a measure of e q u a t i n g e r r o r . T h i s , however, i s m i s l e a d i n g . By d e f i n i t i o n , t he e q u a l - p e r c e n t i l e ( i . e . , i n t e r p o l a t e d ) s c o r e d i s t r i b u t i o n s a r e h i g h l y c o r r e l a t e d . U s i n g the f i r s t example g i v e n 135 2 i n t h i s s e c t i o n f o r i l l u s t r a t i o n , the v a l u e of R ( c o e f f i c i e n t of d e t e r -m i n a t i o n ) a s s o c i a t e d w i t h the i n t e r p o l a t e d s c o r e s i s .9719. C o n s e q u e n t l y , a r e g r e s s i o n e q u a t i o n can be found w h i c h w i l l a c c u r a t e l y r e p r o d u c e the c o n -v e r s i o n l i n e . The s t a n d a r d e r r o r s of e s t i m a t e a s s o c i a t e d w i t h the l i n e a r and p o l y n o m i a l r e g r e s s i o n e q u a t i o n s f o r t h i s example are 1.48 and 1.42 r e s p e c -t i v e l y . These v a l u e s however, a r e i n d i c e s of the a c c u r a c y of f i t of the p r e d i c t e d l i n e s t o the e q u a l - p e r c e n t i l e l i n e and s h o u l d not be c o n s t r u e d as a measure of e q u i v a l e n c y . The a p p r o p r i a t e measure i s the d i s c r e p a n c y between the o b s e r v e d s c o r e s and the c o n v e r t e d s c o r e s , as i s r e p o r t e d i n the c o n d i t i o n a l root-mean-square e r r o r of e q u a t i n g . The c o r r e s p o n d i n g v a l u e s f o r t h i s measure a r e 9.40 and 9.24. E q u a t i n g R e s u l t s The t e s t p a i r s i d e n t i f i e d f o r e q u a t i n g were l i s t e d i n T a b l e 34. W i t h the e x c e p t i o n of the two p a i r s used as examples, the t a b l e s of e q u i v a l e n t s c o r e v a l u e s f o r each of t h e s e t e s t p a i r s a r e p r e s e n t e d i n t h i s s e c t i o n . S i n c e the o b s e r v e d s c o r e and t r u e s c o r e p r o c e d u r e s were found t o be v i r t u a l l y i d e n t i c a l , the t r u e s c o r e method was e x c l u d e d , and b o t h l i n e a r and e q u i p e r -c e n t i l e p r o c e d u r e s were a p p l i e d t o a l l t e s t p a i r s . As s t a t e d i n Chapter I I I , the g r a p h i c e q u i p e r c e n t i l e p r o c e d u r e was a p p l i e d t o o n l y the t e s t p a i r s i n the two examples. Because of the c l o s e r e l a t i o n between the g r a p h i c and i n t e r p o l a t e d p r o c e d u r e s , t h e r e was no advantage i n p r o d u c i n g the g r a p h i c c o n v e r t e d s c o r e s as w e l l . F i n a l l y , t h e t h i r d s t e p of t h e a n a l y t i c a l e q u i -p e r c e n t i l e program, namely the g r a p h i c r e p r e s e n t a t i o n of the g o o d n e s s - o f -f i t of the c u r v e — f i t t i n g p r o c e d u r e was o m i t t e d . To t e s t the adequacy of the a s s u m p t i o n of i d e n t i c a l t e s t s c o r e d i s t r i -b u t i o n s , the l i n e a r e q u a t i n g p r o c e d u r e was r e a p p l i e d t o t h e n o r m a l i z e d d i s -t r i b u t i o n s of the t e s t p a i r s i d e n t i f i e d as h a v i n g e q u a l r e l i a b i l i t i e s . 136 T h i s r e s u l t e d i n no improvement i n p r e c i s i o n of e q u a t i n g as i n d i c a t e d by the e r r o r e s t i m a t e s . The t a b l e s r e p o r t i n g t h e s e e q u i v a l e n t s c o r e v a l u e s appear i n Appendix H. The e q u a t i n g r e s u l t s a r e p r e s e n t e d i n T a b l e s 41 t o 51. I n each c a s e , the o b t a i n e d s c o r e s f o r the t e s t t o be equated a r e l i s t e d i n column 1, the l i n e a r equated s c o r e s (Y*) and t h e i r a s s o c i a t e d s t a n d a r d e r r o r s (S ^) i n columns 2 and 3 r e s p e c t i v e l y , and the r e s u l t s o f the a n a l y t i c a l e q u i p e r c e n t i l e program i n columns 4, 5, and 6. The c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g , RMS , RMS , and RMS , are i n t e r p r e t e d as th e y \J LJ IT were i n the p r e v i o u s examples and appear below the columns t o w h i c h t h e y a p p l y . The r e s u l t s a r e p r e s e n t e d i n the f o l l o w i n g o r d e r : PPVT t o WISC-R V e r b a l , SIT t o WISC-R V e r b a l and F u l l S c a l e , SPM t o WISC-R P e r f o r m a n c e , and MHVS t o WISC-R V e r b a l . The r e s u l t s shown.in T a b l e s 41 t o 51, i n c l u d e d a t the end of t h i s c h a p t e r , s u b s t a n t i a t e t h o s e summarized f o r the two examples g i v e n e a r l i e r . As shown by the c o n d i t i o n a l root-mean-square e r r o r s , t h e r e was v e r y l i t t l e d i f f e r e n c e between the l i n e a r and e q u i p e r c e n t i l e p r o c e d u r e s . C o n s e q u e n t l y , t h e r e i s no p r e f e r e n c e f o r one method over the o t h e r i n terms o f the a c c u r a c y of the c o n v e r t e d s c o r e s i n r e l a t i o n t o the o b t a i n e d s c o r e s . The s i z e of the root-mean-square e r r o r s can be judged b o t h i n c o m p a r i -son t o t h o s e found f o r the Anchor T e s t Study, and i n a p r a c t i c a l sense as t h e y p e r t a i n t o t e s t i n t e r p r e t a t i o n . I n r e f e r e n c e t o the f o r m e r , L i n n (1975) r e p o r t e d t h a t " t he e s t i m a t e d e r r o r f o r a l l t e s t s was g e n e r a l l y l e s s t h a n one raw s c o r e p o i n t ( s u b s t a n t i a l l y l e s s i n most c a s e s ) " ( p . 207). I n the p r e s e n t s t u d y , the mean c o n d i t i o n a l root-mean-square e r r o r s of 137 e q u a t i n g t a k e n a c r o s s a l l 13 t e s t p a i r s were 11.46, 11.34, 11.48, and 12.56 f o r l i n e a r e q u a t i n g , i n t e r p o l a t e d s c o r e s , l i n e a r c u r v e - f i t t i n g , and p o l y -n o m i a l c u r v e - f i t t i n g r e s p e c t i v e l y . I n r e f e r e n c e t o s c o r e i n t e r p r e t a t i o n , t h i s s u g g e s t s t h a t a d i s c r e p a n c y of as much as + 12 s c o r e p o i n t s would be e x p e c t e d between an o b s e r v e d and a c o n v e r t e d s c o r e v a l u e . The c l o s e c o r r e s -pondence between s t a n d a r d i z e d WISC-R s c o r e s and WISC- R IQs was r e f e r r e d t o i n C h a p t e r s I I I and IV. T h e r e f o r e , a l t h o u g h the r e s u l t s r e p o r t e d here a r e i n t h e s t a n d a r d i z e d s c o r e m e t r i c , t h e y would be v i r t u a l l y i d e n t i c a l f o r IQ s c o r e s . U s i n g the o b t a i n e d WISC-R s c o r e s as c r i t e r i a of the a c c u r a c y o f c o n v e r -s i o n , d i s c r e p a n c i e s of + 12 s c o r e p o i n t s can be seen t o f l u c t u a t e a c r o s s two o r t h r e e o f the WISC-R i n t e l l i g e n c e c l a s s i f i c a t i o n s . D e v i a t i o n s of t h i s magnitude a re i n t o l e r a b l e f o r s c o r e s on w h i c h e d u c a t i o n a l d e c i s i o n s are based. T h e r e f o r e the e r r o r s were i n t e r p r e t e d as i n d i c e s o f the non-e q u a t a b i l i t y o f t h e t e s t p a i r s i n t h i s s t u d y . T h i s f i n d i n g and i t s i m p l i -c a t i o n s a r e d i s c u s s e d i n the f i n a l c h a p t e r . 138 T a b l e 41 E q u i v a l e n t S c o r e s PPVT Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 9%) RXY = - ? 2 ' RXX = - 9 3 ' RYY = - 8 7 L i n e a r E q u a t i n g E q u i p e r c e n t i l e E q u a t i n g  PPVT I n t e r p o l a t e d C u r v e - F i t t i n g Raw S c o r e s Y* S .^ S c o r e s L i n e a r P o l y n o m i a l 51 48.30 3.88 59 61.47 3.00 62 66.41 2.68 63 68.05 2.57 65 71.34 2.36 67 74.64 2.16 69 77.93 1.97 70 79.57 1.88 71 81.22 1.79 73 84.52 1.62 74 86.16 1.54 75 87.81 1.47 76 89.45 1.40 77 91.10 1.34 78 92.75 1.29 79 94.39 1.25 80 96.04 1.21 81 97.68 1.19 82 99.33 1.18 83 100.98 1.18 84 102.62 1.19 85 104.27 1.22 86 105.91 1.25 87 107.56 1.30 88 109.21 1.35 89 110.85 1.41 90 112.50 1.48 91 114.14 1.55 92 115.79 1.63 93 117.44 1.72 94 119.08 1.80 95 120.73 1.90 96 122.37 1.99 97 124.02 2.08 98 125.67 2.18 99 127.31 2.28 101 130.60 2.49 Y.=82.41 RMSQ = 12.65 58.85 49.28 58.28 75.87 62.42 75.89 75.97 67.35 76.73 76.95 68.99 76.90 77.18 72.27 77.34 77.85 75.56 78.11 79.66 78.84 79.36 79.95 80.48 80.19 80.35 82.13 81.16 80.54 85.41 83.52 85.57 87.05 84.89 86.93 88.70 86.38 88.81 90.34 87.97 90.76 91.98 89.65 91.38 93.62 91.41 92.21 95.26 93.22 93.22 96.91 95.08 96.12 98.55 96.97 98.58 100.19 98.88 101.92 101.83 100.78 102.70 103.48 102.68 104.11 105.12 104.56 105.90 106.76 106.42 108.71 108.40 108.25 109.92 110.05 110.05 111.20 111.69 111.83 112.68 113.33 113.61 118.12 114.97 115.38 119.07 116.61 117.18 119.22 118.26 119.03 119.29 119.90 120.97 121.03 121.54 123.02 126.58 123.18 125.25 128.07 124.83 127.70 130.04 126.47 130.44 131.09 128.11 133.54 145.07 131.39 141.15 RMSj = R M S L = RMS p = 12.10 12.65 12.21 •139 T a b l e 42 E q u i v a l e n t S c o r e s PPVT Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 11%) rXY = ' 7 8 ' rXX = * 9 3 ' rYY = - 8 7 PPVT Raw Scores L i n e a r E q u a t i n g Y* S_„ E q u i p e r c e n t i l e E q u a t i n g  I n t e r p o l a t e d C u r v e — F i t t i n g S c o r e s L i n e a r P o l y n o m i a l 57 50.40 3.60 43.55 50.08 44.79 64 60.51 2.94 65.56 62.84 65.34 75 76.57 1.97 66.67 78.18 74.01 77 79.48 1.81 75.10 80.97 76.94 78 80.93 1.73 77.73 82.36 78.58 80 83.84 1.58 81.54 85.15. 82.15 81 85.29 1.51 86.54 86.55 84.04 82 86.75 1.45 89.24 87.94 85.98 83 88.20 1.38 89.71 89.34 87.95 84 89.66 1.33 89.72 90.73 89.92 8-5 91.11 1.28 89. 79 92''. 13' 91.89 86 92.56 1.23 91.49 93.52 93.84 87 94.02 1.19 94.67 94.92 95.74 88 95.47 1.16 97.27 96.31 97.60 89 96.92 1.14 100.53 97.70 99.38 90 98.38 1.13 102.21 99.10 101.10 91 99.83 1.12 103.55 100.49 102.73 92 101.29 1.12 105.26 101.89 104.29 93 102.74 1.14 105.56 103.28 105.75 95 105.65 1.19 106.53 106.07 108.43 96 107.10 1.22 108.33 107.47 109.65 97 108.56 1.27 110.48 108.86 110.80 98 110.01 1.32 110.92 110.26 111.90 99 111.46 1.37 112.31 111.65 112.94 100 112.92 1.43 113.21 113.04 113.94 101 114.37 1.50 116.83 114.44 114.91 102 115.83 1.56 117.09 115.83 115.87 103 117.28 1.64 118.41 117.23 116.83 105 120.19 1.79 119.22 120.02 118.78 106 121.64 1.87 120.72'. 121.41 119.79 107 123.10 1.95 121.13 122.81 120.84 108 124.55 2.03 121.78 124.20 121.92 109 126.00 2.12 121.84 125.59 123.03 110 127.46 2.20 122.46 126.99 124.17 112 130.37 2.38 125.41 129.78 126.44 113 131.82 2.46 : 128.49 131.17 127.53 119 140.54 "•3..;02 130.69 139.54 130.26 =91.12 RMS Q = RMS = 'RMS = RMS p = 11.43 10.92 11.24 11.19 140 T a b l e 43 E q u i v a l e n t S c o r e s SIT Raw S c o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 1\) RXY = ' 9 4 ' RXX = ' 8 6 ' RYY = * 7 8 SIT Raw S c o r e s L i n e a r E q u a t i n g Y* S Y" E q u i p e r c e n t i l e E q u a t i n g I n t e r p o l a t e d S c o r e s C u r v e - F i t t i n g L i n e a r P o l y n o m i a l 88 49.80 3.24 65.87 50.00 65.87 94 66.12 2.30 72.42 69.44 72.41 96 71.56 2.00 73.29 72.22 72.08 97 74.28 1.86 74.26 75.00 72.80 98 77.00 1.72 75.31 77.77 74.54 99 79.72 1.58 75.95 80.55 77.12 100 82.44 1.46 78.80 83.33 80.34 101 85.16 1.34 80.35 86.11 83.97 102 87.88 1.23 89.52 88.88 87.76 103 90.60 1.14 93.49 91.66 91.54 104 93.32 1.06 97.34 94.44 95.12 105 96.04 1.01 98.34 97.22 98.42 106 98.76 0.98 100.57 99.99 101.38 107 101.48 0.98 102.52 102.77 104.03 108 104.20 1.01 106.30 105.55 106.44 109 106.92 1.07 109.15 108.32 108.72 110 109.64 1.14 111.42 111.10 111.00 111 112.36 1.24 112.75 113.88 113.43 112 115.08 1.35 117.98 116.66 116.13 113 117.80 1.47 118.67 119.43 119.13 114 120.52 1.60 122.90 122.21 122.38 115 123.24 1.73 125.46 124.99 125.70 116 125.96 1.87 126.72 127.77 128.67 118 131.40 2:: 16 132.51 133.32 130.65 Y.=106.45 RMSQ = 10.19 RMS]. = 10.28 RMS = Li 10.34 RMS p = 12.18 141 T a b l e 44 E q u i v a l e n t S c o r e s SIT Raw S c o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e Scores (Age 1\) RXY = ' 7 9 ' RXX = - 8 6 ' RYY = * 7 8 L i n e a r E q u a t i n g SIT Raw S c o r e s Y* S v E q u i p e r c e n t i l e E q u a t i n g I n t e r p o l a t e d S c o r e s C u r v e - F i t t i n g L i n e a r P o l y n o m i a l 88 49.80 3.87 62.96 49.36 62.82 94 66.12 2.76 68.62 66.13 68.80 96 71.56 2.41 71.27 71.72 71.57 97 74.28 2.24 73.37 74.52 73.66 98 77.00 2.07 76.12 77.31 76.15 99 79.72 1.91 78.71 80.11 78.95 100 82.44 1.76 81.70 82.90 81.96 101 85.16 1.62 84.23 85.70 85.07 102 87.88 1.50 87.62 88.49 88.20 103 90.60 1.39 93.21 91.29 91.28 104 93.32 1.30 95.79 94.08 94.24 105 96.04 1.24 97.29 96.88 97.07 106 98.76 1.21 98.03 99.67 99.76 107 101.48 1.21 102.56 102.47 102.35 108 104.20 1.25 104.84 105.26 104.88 109 106.92 1.31 106.71 108.06 107.43 110 109.64 1.40 108.57 110.85 110.06 111 112.36 1.51 112.52 113.65 112.85 112 115.08 1.64 117.52 116.45 115.87 113 117.80 1.78 118.49 119.24 119.15 114 120.52 1.93 123.21. 122.04 122.68 115 123.24 2.09 126.64 124.83 126.40 116 125.96 2.25 127.50 127.63 130.14 118 131.40 2.60 137.99 133.22 136.54 Y.=106.45 RMSQ = 12.63 RMS]. = 12.58 RMS = J-j 12.84 RMS p = 17.14 142 T a b l e 45 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R V e r b a l Scores (Age 9%) rXY = ' 7 6 ' rXX = > 9 3 ' rYY = - 7 9 Li-near-i-Equat i n g E q u i p e r c e n t i l e E q u a t i n g SIT Raw Scores Y* I n t e r p o l a t e d S c o r e s C u r v e - F i t t i n g L i n e a r P o l y n o m i a l 90 43.62 4.24 58.85 45.56 58.64 105 73.62 2.25 75.86 75.05 75.94 107 77.62 2.01 76.95 78.98 78.90 108 79.62 1.89 79.66 80.95 80.59 109 81.62 1.78 80.54 82.92 82.38 110 83.62 1.68 83.32 84.88 84.24 111 85.62 1.58 85.77 86.85 86.17 112 87.62 1.49 90.42 88.81 88.14 113 89.62 1.41 91.11. 90.78 90.14 114 91.62 1.34 93.21 92.74 92.14 115 93.62 1.28 95.56 94.71 94.13 116 95.62 1.23 96.12 96.68 96.12 117 97.62 1.20 96.60 98.64 98.10 118 99.62 1.19 98.58 100.61 100.06 119 101.62 1.20 101.61 102.57 102.02 120 103.62 1.22 102.70 • 104.54 103.98 121 105.62 1.26 105.33 106.51 105.95 122 107.62 1.31 107.58 108.47 107.94 123 109.62 1.38 109.18 110.44 109.97 124 111.62 1.46 111.20 112.40 112.06 125 113.62 1.54 117.74 114.37 114.20 126 115.62 1.64 119.29 116.33 116.41 127 117.62 1.74 119.79 118.30 118170 128 119.62 1.85 121.03 120.27 121.06' 129 121.62 1.96 121.22 122.23 123.49 130 123.62 2.08 125.86 124.20 125.96 131 125.62 2.20 128.07 126.16 128.43 133 129.62 2.45 130.04 130.10 133.18 135 133.62 2.71 145.07 134.03 137.12 :118.19 RMS 0 = RMS I = RMS = RMS p = 12.53' 12.11 12.46 14.08 143 T a b l e 46 E q u i v a l e n t S c o res SIT Raw S c o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e S c o r e s (Age 9%) RXY = " 8 ° ' RXX = ' 8 6 ' RYY = ' 7 6 L i n e a r E q u a t i n g E q u i p e r c e n t i l e E q u a t i n g  SIT I n t e r p o l a t e d C u r v e - F i t t i n g  Raw Scores Y* S ^ S c o r e s L i n e a r P o l y n o m i a l 90 43.62 4.14 59.41 46.42 59.79 105 73.62 2.19 69.05 75.46 72.90 107 77.62 1.96 76.36 79.33 77.07 108 79.62 1.85 78.24 81.27 79.35 109 81.62 1.74 81.86 83.21 81.70 110 83.62 1.64 82.75 85.14 84.08 111 85.62 1.54 85.55 87.08 86.45 112 87.62 1.45 90.64 89.02 88.78 113 89.62 1.37 91.11 90.95 91.04 114 91.62 1.30 94.67 92.89 93.22 115 93.62 1.24 97.00 94.83 95.31 116 95.62 1.20 97.47 96.76 97.31 117 97.62 1.17 97.75 98.70 99.21 118 99.62 1.16 99.55 100.63 101.04 119 101.62 1.16 101.79 102.57 102.81 120 103.62 1.18 103.31 104.51 104.55 121 105.62 1.22 106.01 106.44 106.28 122 107.62 1.28 109.46 108.38 108.04 123 109.62 1.34 110.87 110.32 109.85 124 111.63 1.42 112.34 112.25 111.75 125 113.62 1.50 114.02 114.19 113.74 126 115.62 1.60 115.87 116.13 115.85 127 117.62 1.70 119.66 118.06 118.08 128 119.62 1.80 121.41 120.00 120.40 129 121.62 1.92 121.54 121.94 122.79 130 123.62 2.03 124.59 123.87 125.19 131 125.62 2.15 128.29 125.81 127.51 133 129.62 2.39 129.21 129.68 131.39 135 133.62 2.64 136.78 133.55 132.97 Y.=118.19 RMSQ = 12.14 RMSj = 9.79 RMS = 11.97 RMS p = 17.,83 144 Ta b l e 47 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 11%) rXY = - 9 2 ' rXX = - 9 3 ' rYY = ' 8 8 PPVT Raw Sc o r e s L i n e a r E q u a t i n g Y* S..... E q u i p e r c e n t i l e E q u a t i n g I n t e r p o l a t e d S c o r e s C u r v e - F i t t i n g L i n e a r P o l y n o m i a l 93 46.09 3.13 43.55 47.51 43.57 109 69.90 1.89 62.02 70.91 59.18 112 74.36 1.68 65.56 75.29 70.43 113 75.85 1.61 73.26 76.76 73.59 114 77.34 1.54 77.73 78.22 76.47 116 80.31 1.40 81.61 81.14 81.40 117 81.80 1.34 83.84 82.60 83.49 118 83.29 1.28 84.14 84.07 85.37 119 84.78 1.22 88.70 85.53 87.06 120 86.27 1.16 89.02 86.99 88.60 121 87.75 1.11 90.10 88.45 90.01 122 89.24 1.06 90.76 89.92 91.32 123 90.73 1.02 91.28 91.38 92.58 124 92.22 .98 92.74 92.84 93.79 125 93.71 .94 95.37 94.30 9 4..$'9 126 95.19 .92 95.88 95.76 96.20 127 96.68 .89 97.27 97.23 97.44 128 98.17 .88 98.99 98.69 98.71 129 99.66 .88 100.65 100.15 100.05 130 101.15 .88 101.05 101.61 101.44 131 1G2>. 63 .89 103.39 103.08 102.89 132 104.12 .90 104.94 104.54 104.41 133 105.61 .93 105.42 106.00 105.98 134 107.10 .96 107.58 107.46 107.60 135 108.59 1.00 109.03 108.93 109.25 136 110.07 1.04 110.46 110.39 110.92 137 111.56 1.09 112.14 111.85 112.59 138 113.05 1.14 115.33 113.31 114.24 139 114.54 1.19 116.08 114.77 115.85 140 116.03 1.25 117.10 116.24 117.39 141 117.51 1.31 120.72 117.70 118.85 144 121.98 1.51 121.13 122.09 122.55 145 123.47 1.57 122.46 • 123.55 123.50 150 130.91 1.93 125.42 130.86," 126.32 151 132.39 2.07 128.49 132.32 126.67 156 139.83 2.32 130.69 139.63 131.23 Y.=129.23 RMS Q = 8.78 RMS]. = 9.00 RMS .= 8.72 RMS p = 9.26 145 T a b l e 48 E q u i v a l e n t S c o r e s SIT Raw Sc o r e s t o S t a n d a r d i z e d WISC-R F u l l S c a l e Scores (Age 11%) rXY = ' 8 9 ' rXX = - 8 7' rYY = - 8 8 SIT Raw Sc o r e s L i n e a r E q u a t i n g Y* S„, E q u i p e r c e n t i l e E q u a t i n g I n t e r p o l a t e d S c o r e s C u r v e - F i t t i n g L i n e a r P o l y n o m i a l 93' 46.09 3'-. 5.1 •3'4.46 47.50 34.50 109 69.89 2.13 61.98 70.93 59.99 112 74.36 1.88 68.51 75.32 71.09 113 75.85 1.80 75.92 76.79 74.23 114 77.33 1.73 76.41 78.25 77.08 116 80.31 1.58 78.49 79.72 79.66 117 81.80 1.51 79.87 81.18 81.99 118 83.29 1.44 84.70 82.65 84.07 119 84.77 1.37 84.76 84.11 85.95 120 86.26 1.31 88.92 87.04 89.16 121 87.75 1.25 92.49 88.50 90.56 122 89.24 1.20 92.89 89.97 91.85 123 90.73 1.15 93.56 91.43 93.07 124 92.21 1.10 94.71 92.90 94.24 125 93.70 1.07 96.07 94.36 95.39 126 95.19 1.03 96.49 95.82 96.53 127 96.68 1.01 97.96 97.29 97.69 128 98.17 1.00 98.94 98.75 98.89 129 99.65 .99 99.38 100.22 100.13 130 101.14 .99 99.74 101.69 101.43 131 102.63 1.00 101.24 103.15 102.79 132 104.12 1.02 104.1.7 104.61 104.22 133 105.61 1.05 106.25 106.08 105.70 134 107.09 1.09 107.86 107.54 107.25 135 108.58 1.13 109.31 109.01 108.84 136 110.07 1.17 109.61 110.47 110.47 137 111.56 1.23 111.60 111.94 112.12 138 113.05 1.27 114.94 113.40 113.78 139 114.53 1.34 116.09 114.86 115.42 140 116.02 1.41 116.79 116.33 117.04 141 117.51 1.48 119.86 117.79 118.60 144 121.97 1.69 120.65 122.19 122.77 145 123.46 1.77 123.01 123.65 123.93 150 130.90 2.17 127.45 130.97 127.63 151 132.39 2.25 129.06 132.44 128.00 156 139.83 2.68 129.73 139.76 130.02 Y.=129.23 RMSQ = 9.91 RMS.,. = 9.79 RMS = L i 9.85 RMS p = 10.62 146 T a b l e 49 E q u i v a l e n t S c o r e s SPM Raw Sc o r e s t o S t a n d a r d i z e d WISC-R Performance S c o r e s (Age 11%) r x y = .68, r x x = .82, r y y = .83 SPM Raw Sc o r e s L i n e a r E q u a t i n g I n t e r p o l a t e d S c o r e s E q u i p e r c e n t i l e E q u a t i n g C u r v e - F i t t i n g L i n e a r - P o l y n o m i a l 15 48.21 4.38 40.05 49.08 40.07 20 59.68 3.52 68.81 60.59 68.52 24 68.85 2.85 70.46 69.80 71.11 26 73.44 2.53 71.93 74.41 73.41 27 75.74 2.38 75.99 76.71 75.14 28 78.03 2.23 77.97 79.01 7.21 29 80.32 2.09 78.32 81.31 79.59 30 82.62 1.95 80.71 83.62 82.21 31 84.91 1.82 85.45 85.92 84.99 32 87.21 1.71 86.49 88.22 87.86 33 89.50 1.60 89.94 90.52 90.73 34 91.79 1.51 93.98 92.82 93.54 35 94.09 1.44 97.90 95.13 96.23 36 96.38 1.39 98.62 97.43 98.77 37 98.68 1.37 101.15 99.73 101.14 38 100.97 1.36 103.50 102.04 103.33 39 103.26 1.39 104.57 104.34 105.37 40 105.56 1.43 106.22 106.64 107.28 41 107.85 1.50 108.04 108.95 109.12 42 110.15 1.59 111.61 111.25 110.93 43 112.44 1.69 114.73 113.55 112.78 45 117.03 1.93 117.87 118.15 116.83 46 119.32 2.07 118.08 120.46 119.11 47 121.62 2.21 119.47 122.76 121.58 48 123.91 2.36 125.04 125.06 124.22 49 126.21 2.51 127.39 127.36 126.95 53 135.38 3.15 134.78 136.57 134.78 Y.=37.57 RMS Q = 14.11 RMS]. = 14.37 RMS = Ju 14.15 RMS P 14.28 147 T a b l e 50 E q u i v a l e n t S c o r e s MHVS Raw Sc o r e s t o S t a n d a r d i z e d WISC-R V e r b a l S c o r e s (Age 7%) = .86, r„„ = .76 XY XX YY L i n e a r E q u a t i n g E q u i p e r c e n t i l e E q u a t i n g MHVS Raw Sc o r e s Y * I n t e r p o l a t e d S c o r e s C u r v e -L i n e a r F i t t i n g P o l y n o m i a l 5 61.46 2.76 65.87 63.03 66.34 7 68.86 2.32 71.77 70.43 71.05 8 72.56 2.10 74.26 74.12 74.16 9 76.26 1.90 78.32 77.82 77.56 10 79.96 1.70 79.27 81.52 81.12 11 83.67 1.52 84.41 85.22 84.78 12 87.37 1.36 89.86 88.92 88.49 13 91.07 1.22 92.94 92.63 92.24 14 94.77 1.12 95.48 96.32 96.03 15 98.48 1.08 99.99 100.02 99.86 16 102.18 1.08 102.59 103.72 103.73 17 105.88 1.14 106.93 107.42 107.66 18 109.58 1.24 112.41 111.12 111.62 19 113.28 1.38 116.95 114.82 115.59 20 116.98 1.55 118.09 118.52 119.48 21 120.69 1.73 124.70 122.22 123.21 22 124.39 1.93 126.60 125.92 126.61 23 128.09 2.14 129.28 129.62 129.49 24 131.79 2.35 131.13 133.32 131.59 26 139.20 2.80 132.51 140.72 132.01 Y.=15.41 RMS 0 = 11.44 RMS]. = 11.50 RMS = L i 11.54 RMS p = 11.44 148 T a b l e 51 E q u i v a l e n t S c o r e s MHVS Raw Sc o r e s t o WISC-R S t a n d a r d i z e d V e r b a l S c o r e s (Age 9%) RXY = * 8 2 ' RXX = ' 9 3 ' RYY = ' 8 3 . . _ . E q u i p e r c e n t i l e E q u a t i n g L i n e a r E q u a t i n g 3 — s -MHVS 3 a I n t e r p o l a t e d C u r v e - Fi.t.f.ing Raw Sc o r e s Y* S ^ Sc o r e s L i n e a r P o l y n o m i a l 6 51.39 3.34 58.85 53.63 58.83 9 59.70 2.84 75.86 61.83 75.72 12 68.01 2.34 75.97 70.03 77.33 14 73.55 2.02 77.18 75.50 78.33 15 76.32 1.87 79.66 78.24 79.47 16 79.09 1.73 79.95 80.97 81.08 17 81.86 1.59 81.54 83.70 83.10 18 84.63 1.46 86.93 86.44 85.44 19 87.40 1.34 88.52 89.17 88.02 20 90.17 1.24 90.77 91.91 90.72 21 92.94 1.15 92.63 94.64 93.47 22 95.71 1.09 95.56 97.38 96.20 23 98.48 1.06 99.67 100.11 98.90 24 101.25 1.06 102.39 " .102.85 101.55 25 104.02 1.09 104.08 105.58 104.21 26 106.79 1.14 106.87 108.31 106.93 27 109.56 1.23 109.66 111.05 109.81 28 112.33 1.33 111.95 113.78 112.94 29 115.10 1.44 117.74 116.52 116.41 30 117.87 1.57 • 119.79 119.25 120.28 31 120.64 1.71 126.58 121.98 124.58 32 123.41 1.86 128.07 124.72 129.24 33 126.18 2.01 131.09 127.45 134.12 34 128.95 2.16 145.07 130.19 138.94 Y.=23.55 RMSQ = 11.22 RMS I = 10.83 RMS = L i 11.19 RMS p = 10.93 CHAPTER V SUMMARY AND DISCUSSION I n t h i s f i n a l c h a p t e r the p u r p o s e s , p r o c e d u r e s , and r e s u l t s o f the stud y a r e summarized. The major f i n d i n g s and t h e i r i m p l i c a t i o n s a r e t h e n d i s c u s s e d and an o r i e n t a t i o n f o r f u r t h e r r e s e a r c h i s s u g g e s t e d . Summary The p r e s e n t s t u d y a d d r e s s e d two i s s u e s c o n c e r n i n g the a p p r o p r i a t e use and i n t e r p r e t a t i o n of i n d i v i d u a l l y - a d m i n i s t e r e d t e s t s of i n t e l l i g e n c e . One i s s u e c o n c e r n e d the i n t e r c h a n g e a b l e use of i n t e l l i g e n c e t e s t s f o r the same purposes i n e d u c a t i o n a l s e t t i n g s . The second i s s u e c o n c e r n e d the a p p r o p r i a t e n e s s of i n t e r p r e t i n g t e s t r e s u l t s i n B r i t i s h C olumbia u s i n g f o r e i g n norms. Three major o b j e c t i v e s were adopted from the Anchor T e s t Study i n Rea d i n g . These were: the p r e p a r a t i o n o f a s e t of e q u i v a l e n c y t a b l e s f o r t r a n s l a t i n g s c o r e s on one t e s t t o s c o r e s on a n o t h e r t e s t ; t he com p a r i s o n of l i n e a r and e q u i p e r c e n t i l e e q u a t i n g methods f o r the development of the e q u i v a l e n c y ' t a b l e s ; and the development o f new norms. Four i n d i v i d u a l l y - a d m i n i s t e r e d i n t e l l i g e n c e t e s t s were s e l e c t e d on the b a s i s of t h e i r r e g u l a r use i n s c h o o l s : the Wech s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n — R e v i s e d (WISC-R), the Peabody P i c t u r e V o c a b u l a r y Test (PPVT), the S l o s s o n I n t e l l i g e n c e T e s t ( S I T ) , and the S t a n d a r d P r o g r e s s i v e M a t r i c e s (SPM). A f i f t h t e s t , t he M i l l H i l l V o c a b u l a r y S c a l e (MHVS) was a l s o i n c l u d e d . A l t h o u g h the MHVS i s l i t t l e known i n B. C , i t was d e v e l o p e d 149 150 f o r j o i n t use w i t h the SPM (Raven, 1960). The s p e c i f i c r e s e a r c h q u e s t i o n s posed were whether the PPVT, SIT, SPM, and MHVS c o u l d l e g i t i m a t e l y be used as a l t e r n a t i v e s t o the WISC-R, and whether e x i s t i n g norms f o r a l l f i v e t e s t s were a p p r o p r i a t e i n B.C. Three t e c h n i c a l i s s u e s were examined. The f i r s t of t h e s e was the d i s t i n c t i o n between e q u i v a l e n c e and c o m p a r a b i l i t y . E q u i v a l e n c e d e f i n e s a s p e c i f i c r e l a t i o n s h i p between t e s t s based on t h e i r p a r a l l e l i s m and i n t e r -c h a n g e a b i l i t y . C o r r e s p o n d i n g l y , t e s t e q u a t i n g i s the p r o c e s s of i d e n t i f y i n g p a i r s of s c o r e v a l u e s between t e s t s w h i c h have i d e n t i c a l q u a l i t a t i v e and q u a n t i t a t i v e meaning. C o m p a r a b i l i t y , on the o t h e r hand, d e f i n e s a common rank p o s i t i o n o f s c o r e v a l u e s f o r a g i v e n r e f e r e n c e group. Comparing, t h e n , i s the p r o c e s s o f s c a l i n g t e s t s i n a manner t h a t a s s o c i a t e s a g i v e n s c o r e v a l u e w i t h a g i v e n rank p o s i t i o n a c r o s s t e s t s f o r a g i v e n p o p u l a t i o n . The c o m p a r a b i l i t y of IQ s c o r e s i s i m p l i e d i n common usage when a con-s t a n t meaning i s a s s o c i a t e d w i t h mean 100 and s t a n d a r d d e v i a t i o n 15 o r 16. The f a c t t h a t IQ s c a l e s a r e d e r i v e d u s i n g d i f f e r e n t s t a n d a r d i z a t i o n groups and p r o c e d u r e s f o r d i f f e r e n t t e s t s , however, v i o l a t e s the c o n d i t i o n s of c o m p a r a b i l i t y . A d d i t i o n a l l y , the e q u i v a l e n c e of IQ t e s t s i s i m p l i e d i n common usage when t h e y a r e used i n t e r c h a n g e a b l y f o r the same p u r p o s e . W i t h the i n t r o d u c t i o n o f the n o t i o n o f comparable s c o r e s , the m e t h o d o l o g i c a l o r i e n t a t i o n of the s t u d y was extended t o i n c l u d e the development of compar-a b l e s c o r e s c a l e s f o r a l l f i v e t e s t s as w e l l as the p r e p a r a t i o n of e q u i v a l -ency t a b l e s among t e s t s where the l a t t e r were f e a s i b l e as d e t e r m i n e d by p s y c h o l o g i c a l and s t a t i s t i c a l c r i t e r i a . The second t e c h n i c a l i s s u e c o n c e r n e d the v i a b i l i t y of c o n s i d e r i n g as p a r a l l e l , and t h e r e f o r e e q u a t a b l e , the WISC-R and each of the o t h e r t e s t s . The concept of no m i n a l p a r a l l e l i s m ( L o r d , 1964; L o r d & N o v i c k , 151 1968) was adopted as c o m p a t i b l e w i t h the n a t u r e and use of the t e s t s c o n -s i d e r e d i n t h i s s t u d y . The c r i t e r i a e s t a b l i s h e d f o r no m i n a l p a r a l l e l i s m were p s y c h o l o g i c a l s i m i l a r i t y i n terms of c o n t e n t and purpose and s t a t i s t i c a l s i m i l a r i t y as d e f i n e d by d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c i e n t s o f a t l e a s t . 70. The t h i r d i s s u e c o n c e r n e d the a p p l i c a b i l i t y of f o u r e q u a t i n g m e t h o d s — l i n e a r o b s e r v e d s c o r e , l i n e a r t r u e s c o r e , g r a p h i c e q u i p e r c e n t i l e , and a n a l -y t i c a l e q u i p e r c e n t i l e — t o n o m i n a l l y p a r a l l e l t e s t s . T h i s r e p r e s e n t e d an e x t e n s i o n of p r e v i o u s e q u a t i n g a p p l i c a t i o n s and a l l o w e d an e x p l o r a t i o n o f the r o b u s t n e s s of l i n e a r and e q u i p e r c e n t i l e e q u a t i n g methods t o t e s t s w h i c h were not s t r i c t l y p a r a l l e l i n the c l a s s i c a l sense. The p o p u l a t i o n i d e n t i f i e d f o r t h e s t u d y was a l l n o n - N a t i v e I n d i a n , E n g l i s h - s p e a k i n g c h i l d r e n at t h r e e age l e v e l s — 7 % y e a r s , 9% y e a r s , and 11% y e a r s — a t t e n d i n g p u b l i c and independent s c h o o l s i n B r i t i s h C olumbia. The p o p u l a t i o n was f u r t h e r r e s t r i c t e d t o e x c l u d e c h i l d r e n e n r o l l e d i n c l a s s e s f o r the p h y s i c a l l y h a n d i c a p p e d , e m o t i o n a l l y d i s t u r b e d , or t r a i n a b l e m e n t a l l y r e t a r d e d . A s t r a t i f i e d s a m p l i n g d e s i g n was used e m p l o y i n g f i v e s t r a t i f i c a -t i o n v a r i a b l e s : g e o g r a p h i c r e g i o n , community s i z e , s i z e o f s c h o o l , age, and sex. A random sample of 180 c h i l d r e n was i d e n t i f i e d a t each of t h r e e age l e v e l s t o p r o p o r t i o n a t e l y r e p r e s e n t t h e p o p u l a t i o n d e s c r i b e d a c c o r d i n g to t h e s e v a r i a b l e s . The a c t u a l number of s t u d e n t s t e s t e d was 63 per c e n t of t h i s t a r g e t sample: they were shown, however, t o m a i n t a i n the r e p r e s e n t -a t i v e n e s s of the t a r g e t sample i n terms of the s t r a t i f i c a t i o n v a r i a b l e s . A l l f i v e t e s t s were a d m i n i s t e r e d t o each c h i l d , w i t h a C a n a d i a n i z e d v e r s i o n of the WISC-R g i v e n i n one t e s t i n g s e s s i o n , and the o t h e r f o u r t e s t s g i v e n i n c o u n t e r b a l a n c e d o r d e r i n a second s e s s i o n . The t e s t s were f i r s t s c o r e d u s i n g the norms t a b l e s and p r o c e d u r e s i n t h e i r r e s p e c t i v e manuals. 152 S t a t i s t i c a l t e s t s f o r d i f f e r e n c e s of means and v a r i a n c e s f o r the B.C. sample compared t o the o r i g i n a l s t a n d a r d i z a t i o n samples r e v e a l e d t h a t , i n g e n e r a l , B.C. c h i l d r e n s c o r e d s i g n i f i c a n t l y h i g h e r and w i t h l e s s v a r i a b i l i t y (p < .05). T h e r e f o r e , new norms t a b l e s were p r e p a r e d f o r the c o n v e r s i o n of raw t e s t s c o r e s t o IQs' and c o r r e s p o n d i n g p e r c e n t i l e r a n k s f o r the WISC-R, PPVT, and SIT. I n k e e p i n g w i t h the o r i g i n a l format of the SPM and MHVS i n t e r -p r e t a t i o n a l i n f o r m a t i o n , raw s c o r e s and p e r c e n t i l e r a n k s o n l y were r e p o r t e d . The B. C. r e s c a l i n g p r o c e d u r e s i n v o l v e d l o w e r i n g and s p r e a d i n g out the s c o r e s c a l e s t o conform t o c o n v e n t i o n a l use and i n t e r p r e t a t i o n . The r e s u l t i s t h a t below average s t u d e n t s s c o r e lower w i t h t he B.C. than the p u b l i s h e d norms, w h i l e s t u d e n t s who are much above average s c o r e t he same or even h i g h e r w i t h B.C. norms. Both l i n e a r and e q u i p e r c e n t i l e e q u a t i n g p r o c e d u r e s were a p p l i e d t o the o b s e r v e d s c o r e d i s t r i b u t i o n s of the f o l l o w i n g t e s t p a i r s i d e n t i f i e d as n o m i n a l l y p a r a l l e l : PPVT WISC -R V e r b a l , ages ih, 9%, and nh SIT WISC -R V e r b a l , ages ih, 9%, and nh SIT WISC -R F u l l S c a l e , ages ih, 9h, and 11% SPM WISC -R P e r f o r m a n c e , age nh MHVS WISC -R V e r b a l , ages ih, 9%, and 11% The a c c u r a c y o f the r e s u l t s were judged by comparison of t h e c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g a s s o c i a t e d w i t h the e q u a t i n g p r o c e d u r e s . These e r r o r s averaged 12 s c o r e p o i n t s and were s i m i l a r a c r o s s a l l p r o c e -d u r e s . 153 I n k e e p i n g w i t h the o r g a n i z a t i o n of C h a p t e r s I I I and IV, the r e s u l t s o f the norming p o r t i o n of the s t u d y a r e d i s c u s s e d f i r s t , f o l l o w e d by the r e s u l t s of e q u a t i n g . Norming The B.C. Sc o r e s A c o n c e r n w h i c h has been f r e q u e n t l y e x p r e s s e d by p r a c t i t i o n e r s t o whom the r e s u l t s were p r e s e n t e d i s t h a t the e x c l u s i o n of N a t i v e I n d i a n and l o w - s c o r i n g c h i l d r e n had a s p u r i o u s e f f e c t on s c o r e s and t h a t the r e s u l t i n g d i s t r i b u t i o n s a r e " t oo h i g h . " However, the r e p r e s e n t a t i v e n e s s of the sample f o r t he p o p u l a t i o n d e f i n e d was s u b s t a n t i a t e d i n Chap t e r IV. The e x c l u s i o n of o t h e r groups o f c h i l d r e n such as t h o s e n o n - f l u e n t i n E n g l i s h o r e m o t i o n a l l y d i s t u r b e d i s c o n s i s t e n t w i t h the American WISC-R s t a n d a r d i z a t i o n p r o c e d u r e s . No c h i l d r e n were e x c l u d e d on the b a s i s of l e a r n i n g d i s a b i l i t i e s , low academic p e r f o r m a n c e , or d i s c i p l i n a r y p r o b l e m s . P e r s o n a l communication w i t h many p r i n c i p a l s c o n f i r m e d t h a t any e x c l u s i o n s made a c c o r d i n g t o the d e l i m i t a t i o n s i n C hapter I were r e s t r i c t e d t o extreme c a s e s . An a l t e r n a t e h y p o t h e s i s t o t h a t o f s a m p l i n g b i a s toward h i g h s c o r e s , i s t h a t c h i l d r e n i n B.C., and perhaps i n Canada, p e r f o r m a t a h i g h e r l e v e l as d e f i n e d by IQ s c o r e s . C e r t a i n l y s u p p o r t f o r the g e n e r a l i z a b i l i t y of h i g h IQ s c o r i n g p a t t e r n s was p r o v i d e d by s t u d i e s r e f e r e n c e d i n Chap t e r I I i n w h i c h group i n t e l l i g e n c e t e s t s were used (Kenneth, 1972; O l d r i d g e , 1968; W r i g h t et a l . , 1972). More d i r e c t l y r e l e v a n t , P e t e r s (1976) r e p o r t e d mean WISC-R s c o r e s f o r a sample-of 7%, 10%, and 13% y e a r o l d s i n a c i t y i n Sas-katchewan t h a t c l o s e l y resemble t h o s e found i n the p r e s e n t s t u d y . The mean WISC-R f u l l S c a l e IQ s c o r e s f o r h i s sample of 100 c h i l d r e n at each age l e v e l were 109.75, 106.58, and 103.41 r e s p e c t i v e l y . The c o r r e s p o n d i n g s c o r e s f o r 7%, 9%, and 11% y e a r o l d s i n t h e B.C. sample were 108.16, 107.89, 154 and 104.80. A t h i r d h y p o t h e s i s f o r the h i g h e r s c o r e s i s t h a t i n t e l l i g e n c e , i n g e n e r a l , i s i n c r e a s i n g over t i m e . T h e r e f o r e r e n o r m i n g e f f o r t s would be e x p e c t e d t o n e c e s s i t a t e a l o w e r i n g o f the s c o r e s c a l e s t o m a i n t a i n t he mean IQ a t 100. Doppelt and Kaufman (1977) compared s c o r e s on ite m s common t o b o t h t e s t s u s i n g the 1949 WISC sample and the 1974 WISC-R sample. U s i n g r e g r e s s i o n e q u a t i o n s , they e s t i m a t e d WISC IQs f o r the WISC-R s t a n d a r d i z a t i o n sample at each age l e v e l . They found t h a t t he o b t a i n e d WISC-R IQs were lower t h a n the e s t i m a t e d WISC IQs by 4 t o 8 p o i n t s f o r c h i l d r e n from 6% t o 11% y e a r s o l d and by 2 t o 3 p o i n t s f o r o l d e r c h i l d r e n , w i t h the g r e a t e s t d i s c r e p a n c i e s o c c u r r i n g f o r the l o w e s t s c o r i n g c h i l d r e n . Herman (1977) r e p o r t e d a c o n s i s t e n t t r e n d toward the l o w e r i n g of IQ s c a l e s i n s e q u e n t i a l s t a n d a r d i z a t i o n s of i n t e l l i g e n c e t e s t s i n the U n i t e d S t a t e s . He c o n c l u d e d t h e r e f o r e t h a t v a r i a t i o n s i n s a m p l i n g c o u l d not account f o r the d i f f e r e n c e s , and s u g g e s t e d i n s t e a d t h a t i n t e l l i g e n c e i s i n c r e a s i n g . One p o s s i b l e e x p l a n a t i o n f o r t h i s , and one w h i c h i s c o n s i s t e n t w i t h t he f i n d i n g of ' l a r g e r d i f f e r e n c e s f o r younger c h i l d r e n , i s the g r e a t e r emphasis p l a c e d on e n v i r o n m e n t a l e n r i c h m e n t f o r p r e - s c h o o l and p r i m a r y c h i l d r e n ( T h o r n d i k e , 1977). A n o t h e r might be i n c r e a s i n g t e s t - w i s e n e s s of c h i l d r e n i n g e n e r a l ( c f . Beauchamp e t a l . , 1979; Herman, 1979). The B r i t i s h Columbia sample was t e s t e d i n 1980. I f i n f a c t , i n t e l l i -gence as measured by i n t e l l i g e n c e t e s t s , i s i n c r e a s i n g , t h i s a l o n e may account f o r the B.C. d i f f e r e n c e s and be independent o f n a t i o n a l i t y . One i n t e r e s t i n g o b s e r v a t i o n i n the p r e s e n t s t u d y w h i c h was a l s o n o t e d i n the Dop p e l t and Kaufman paper, i s t h a t g r e a t e r i n c r e a s e s were found i n P e r f o r -mance t h a n V e r b a l IQs (see T a b l e 25, C h a p t e r I V ) . I t i s p o s s i b l e t h a t a g e n e r a l f a m i l i a r i t y w i t h games and the i n c r e a s i n g a c c e p t a b i l i t y of such 155 games i n s c h o o l s e t t i n g s may c o n t r i b u t e t o the h i g h e r s c o r e s . A n o t h e r h y p o t h e s i s f o r the h i g h e r B.C. s c o r e s on the WISC-R i s t h a t the C a n a d i a n i z e d items p r o v i d e d an advantage. T h i s however, seems u n l i k e l y s i n c e Vernon's (1977) r a t i o n a l e f o r the s u b s t i t u t i o n s was t o match A m e r i c a n pass p e r c e n t a g e s f o r Canadian examinees on item s f o r w h i c h Canadian pass p e r c e n t a g e s were o t h e r w i s e d e p r e s s e d . E x a m i n a t i o n o f the' C a n a d i a n i z e d c o n t e n t (see Appendix B) does not i n d i c a t e any o b v i o u s e a s i n e s s of i t e m s . I n f a c t , the c o n t r a r y might be s p e c u l a t e d . I n p a r t i c u l a r , t he i t e m , "Name t h r e e oceans t h a t b o r d e r Canada" was n o t e d t o be d i f f i c u l t s i n c e the a c c e p -t a b l e r e s p o n s e had t o i n c l u d e m e n t i o n of the A r c t i c ocean. The r e s u l t s of the P e t e r s ' (1976) s t u d y r e f u t e the n o t i o n of an e a s i e r C a n a d i a n i z e d v e r s i o n . He a d m i n i s t e r e d the WISC-R w i t h o u t any changes and found v e r y s i m i l a r s c o r e s t o those r e p o r t e d i n t h i s s t u d y . P e t e r s ' mean I n f o r m a t i o n s u b t e s t s c o r e s were 11.05, 10.08, and 9.92 f o r ages 7%, 10%, and 13%. The c o r r e s p o n d i n g means i n t h i s s t u d y were 10.72, 10.64, and 9.88 f o r ages 7%, 9%, and 11%. A l i m i t a t i o n n o t e d f o r the p r e s e n t s t u d y i s bhab b o t h A merican and Canadian items were not a d m i n i s t e r e d and the r e s u l t s compared. C o n s i d e r -i n g the r e s u l t s of P e t e r s ' s t u d y , one would be i n c l i n e d t o suggest t h a t the B.C. WISC-R norms are a p p l i c a b l e r e g a r d l e s s o f whether the Canadian ite m s a r e used o r n o t . T h i s i s not a d v i s e d , however, u n l e s s f u r t h e r r e s e a r c h c o n f i r m s the s i m i l a r i t y o f s c o r e s . For most of the s u b s t i t u t i o n i t e m s , a case can be made f o r the f a c e - v a l u e d e s i r a b i l i t y o f the Canadian w o r d i n g s . Canadian t e s t e r s have, f o r y e a r s , been making s u b s t i t u t i o n s i n f o r m a l l y and i n c o n s i s t e n t l y ( c f . P e t e r s , 1976; Spreen & T r y k , 1970), based on the b e l i e f s t h a t some item s were A m e r i c a n - b i a s e d and t h a t C a nadian c h i l d r e n s h o u l d be o r i e n t e d toward Canadian c u l t u r e . Thus the a d o p t i o n o f Vernon's items 156 a r e recommended s i n c e they a r e e m p i r i c a l l y - b a s e d . Use of the New Norms A c o n c e r n r e g a r d i n g the r e n o r m i n g r e s u l t s i s the q u e s t i o n of r e c e p -t i v i t y of both p r a c t i t i o n e r s and l a y p e r s o n s t o the n o t i o n of l o w e r i n g IQ. The q u e s t i o n i s not p e r c e i v e d t o o c c u r at the l e v e l of the c o n c e p t u a l sound-ness of r e s c a l i n g . The c o n v e n t i o n a l i n t e r p r e t a t i o n of IQ assumes a r e f e r -ence v a l u e of the mean e q u a l t o 100. M a t a r a z z o (1972) summarized the d e s i r -a b i l i t y o f e n d o r s i n g t h i s c o n c e p t u a l c o n s t a n c y , s a y i n g t h a t i t i s o b v i o u s l y a m a t t e r of common sense t o s e l e c t a v a l u e f o r i t as would be i n l i n e w i t h t h e o r d e r of n u m e r i c a l v a l u e s of IQ's now i n g e n e r a l use. (p. 104) The i n t e r p r e t a t i o n a d d i t i o n a l l y assumes a normal d i s t r i b u t i o n of s c o r e s around the mean so t h a t p e r c e n t i l e r a n k s a s s o c i a t e d w i t h g i v e n s c o r e s are known. From a p r a c t i t i o n e r ' s p o i n t of v i e w , a s s u r a n c e t h a t t h i s a p p l i c a -t i o n of t e s t r e s u l t s i s a c c u r a t e has v e r y o b v i o u s j u s t i f i c a t i o n . I t i s a t the p r a c t i c a l l e v e l t h a t problems may o c c u r . I n an e d u c a t i o n a l m i l i e u of w o r k i n g f a m i l i a r i t y w i t h t e s t r e s u l t s from e x i s t i n g norms, the i n c a u t i o u s i n t r o d u c t i o n of a new norms r e f e r e n c e s c a l e c o u l d have m i s l e a d i n g and e r r o n e o u s i m p a c t . I n p a r t i c u l a r , the r e - t e s t i n g of c h i l d r e n u s i n g the same t e s t but d i f f e r e n t norms, or the comparing of c h i l d r e n on the b a s i s of s c o r e s d e r i v e d from d i f f e r e n t norms t a b l e s would be u n f o r t u n a t e and w o u l d , i n f a c t , c o n t r i b u t e t o t h e v e r y t y p e of c o m p a r a t i v e m i s u s e o f s c o r e s t h a t t h i s s t u d y s e t out t o r e c t i f y . The onus of the r e s p o n s i b i l i t y f o r e n s u r i n g c o r r e c t use comes back t o the p r o f e s s i o n a l t e s t e r . Any s c o r e r e p o r t i n g based on B.C. norms r e q u i r e s c a r e f u l r e f e r e n c e and c l a r i f i c a t i o n . The r e s u l t s of the s t u d y w h i c h may prove of most p r a c t i c a l v a l u e t o t e s t e r s a r e t h o s e they s u g g e s t e d , namely the p e r c e n t i l e r a n k s a s s o c i a t e d w i t h s e l e c t e d s t a n d a r d d e v i a t i o n s . S i n c e the t r e n d i s away from r e p o r t i n g 157 a c t u a l n u m e r i c a l s c o r e r e s u l t s , t h e s e v a l u e s may be more u s e f u l . They a t l e a s t would s e r v e t o a v o i d the e m o t i o n a l l y - l a d e n impact on l a y p e r s o n s of l o w e r i n g a c t u a l s c o r e s . The C o m p a r a b i l i t y of the New Norms The IQ s c o r e s c a l e s f o r the WISC-R, PPVT, and SIT are comparable i n the sense d e s c r i b e d i n Chapter I I ; t h a t i s , a g i v e n s c o r e v a l u e r e p r e s e n t s a c o n s t a n t rank p o s i t i o n a c r o s s t e s t s f o r t h e p o p u l a t i o n d e f i n e d i n t h i s s t u d y . I t was n o t e d e a r l i e r t h a t the p r a c t i c e of a s s i g n i n g a common s c o r e t o d i f f e r e n t t e s t s of i n t e l l i g e n c e f o s t e r s the i n t e r p r e t a t i o n of s c o r e s as i f t h e y were comparable when t h e y , i n f a c t , a r e n o t . Thus the r e s u l t s o f t h i s phase of the s t u d y p r o v i d e f o r t h i s c o r r e c t usage and i n t e r p r e t a t i o n of the IQ s c o r e s c a l e s . E q u a t i n g The magnitude of the c o n d i t i o n a l root-mean-square e r r o r s of e q u a t i n g a s s o c i a t e d w i t h b o t h l i n e a r and e q u i p e r c e n t i l e e q u a t i n g methods was i n t e r -p r e t e d i n C h a p t e r IV as _:an i n d i c a t i o n of the n o n - e q u a t a b i l i t y of the t e s t p a i r s i n t h i s s t u d y . I n l i g h t of t h i s f i n d i n g , the c r i t e r i a e s t a b l i s h e d f o r the e q u i v a l e n c e of the t e s t s l e a d i n g t o the i d e n t i f i c a t i o n of n o m i n a l l y p a r a l l e l t e s t p a i r s are r e a s s e s s e d . F o l l o w i n g t h a t , the i m p l i c a t i o n s of the r e s u l t s f o r t e s t i n g p r a c t i c e are examined. The E q u a t a b i l i t y o f N o m i n a l l y P a r a l l e l Test P a i r s I n C h a p t e r s I and I I , the j u s t i f i c a t i o n f o r the e q u a t i n g phase of t h i s s t u d y was e s t a b l i s h e d u s i n g the c o n c e p t s of f u n c t i o n a l , p s y c h o l o g i c a l , and s t a t i s t i c a l e q u i v a l e n c e . The f u n c t i o n a l , or p r a c t i c a l , e q u i v a l e n c e of f o u r of the i n t e l l i g e n c e t e s t s used ( e x c l u d i n g the MHVS) g e n e r a t e d the r e s e a r c h q u e s t i o n r e g a r d i n g the f e a s i b i l i t y of an e q u a t i n g s t u d y . Func-t i o n a l e q u i v a l e n c e a l o n e , however, i s based on the s i m p l e f a c e v a l i d i t y 158 of t e s t s h a v i n g a common name and c l a i m , and was deemed an i n a d e q u a t e j u s t i -f i c a t i o n f o r the c o n s i d e r a t i o n of p a r a l l e l i s m . T h e r e f o r e , p s y c h o l o g i c a l and s t a t i s t i c a l c r i t e r i a were added. The d e t e r m i n a t i o n of p s y c h o l o g i c a l e q u i v a l e n c e of t e s t p a i r s was based on an a n a l y s i s of the s i m i l a r i t y of the p s y c h o l o g i c a l f u n c t i o n measured by each t e s t . Thus t e s t s l a b e l l e d as v e r b a l measures of i n t e l l i g e n c e and h a v i n g o b v i o u s v e r b a l c o n t e n t ( e . g . , WISC-R V e r b a l and PPVT) were c o n s i d e r e d p s y c h o l o g i c a l l y p a r a l l e l . These d e s i g n a t i o n s were f u r t h e r s u p p o r t e d by the r e s u l t s of p r e v i o u s e m p i r i c a l s t u d i e s showing h i g h c o r r e l a t i o n s and/or common f a c t o r l o a d i n g s . The n o t i o n of c o n t e n t s i m i l a r i t y was, however, d e f i n e d i n a broad sense r a t h e r t h a n i n terms of the b a l a n c e of i t e m s measur-i n g s i m i l a r s k i l l c a t e g o r i e s or domains a c r o s s t e s t s as i n the Anchor Test Study ( J a e g e r , 1973). Thus a g l o b a l n o t i o n of v e r b a l measurement may be i n a d e q u a t e t o account f o r d i f f e r e n c e s i n the u n i d i m e n s i o n a l i t y of the v e r b a l t a s k r e q u i r e d f o r the PPVT and the m u l t i d i m e n s i o n a l i t y of the v e r b a l t a s k s r e q u i r e d f o r the f i v e WISC-R V e r b a l s u b t e s t s . A l t h o u g h L o r d and N o v i c k (1968) p r o v i d e d no g u i d e l i n e s f o r t h e degree of t e s t s i m i l a r i t y r e q u i r e d f o r n o m i n a l p a r a l l e l i s m , Marks and L i n d s a y (1972) s t r e s s e d the n o t i o n of s l i g h t d i f f e r e n c e s o n l y among t e s t s c o n s i d e r e d as n o m i n a l l y p a r a l l e l . The l a c k of s p e c i f i c i t y r e g a r d i n g the s i z e of c o r r e l a t i o n s d e l i m i t i n g n o m i n a l p a r a l l e l i s m was s i m i l a r l y n o t e d . A g a i n , a l t h o u g h L o r d and N o v i c k (1968) p r o v i d e d no s t a t i s t i c a l c r i t e r i o n of s i m i l a r i t y , Marks and L i n d s a y (1972) r e f e r r e d t o h i g h c o r r e l a t i o n s . As d i s c u s s e d i n C h a p t e r I , the minimum d i s a t t e n u a t e d c o r r e l a t i o n c o e f f i c i e n t of .70 adopted i n the p r e s e n t s t u d y was based on known c o r r e l a t i o n s among f u n c t i o n a l l y e q u i v a l e n t i n d i -v i d u a l l y a d m i n i s t e r e d i n t e l l i g e n c e t e s t s ( W e c h s l e r , 1974). In C h a p t e r IV i t was n o t e d t h a t the root-mean-square e r r o r s were of a s i m i l a r magnitude a c r o s s a l l t e s t p a i r s and e q u a t i n g p r o c e d u r e s . F o r the range of d i s a t t e n u a t e d c o r r e l a t i o n s r e p o r t e d i n t h i s s t u d y (.68-.92) t h e r e were no a p p r e c i a b l e d i f f e r e n c e s i n t h e s i z e of t h e e r r o r s a s s o c i a t e d w i t h d i f f e r e n c e s i n c o r r e l a t i o n . T h e r e f o r e , h i g h c o r r e l a t i o n was c o n c l u d e d to be a n e c e s s a r y a l t h o u g h not s u f f i c i e n t r e q u i r e m e n t f o r e q u a t i n g . The root-mean-square e r r o r s r e p o r t e d i n the Anchor Te s t Study f o r t e s t s h a v i n g s i m i l a r d i s a t t e n u a t e d c o r r e l a t i o n s t o some of t h o s e r e p o r t e d i n the p r e s e n t s t u d y ( i . e . , > .89) were g e n e r a l l y much l e s s t h a n one raw s c o r e p o i n t ( L i n n , 1975). T h e r e f o r e i t was a d d i t i o n a l l y c o n c l u d e d t h a t c o n t e n t s i m i l a r i t y based on i t e m and domain c o r r e s p o n d e n c e i s r e q u i r e d . I n summary, the r e s u l t s of the p r e s e n t s t u d y suggest the f o l l o w i n g c o n s i d e r a t i o n s f o r the d e t e r m i n a t i o n of n o m i n a l l y p a r a l l e l t e s t p a i r s f o r e q u a t i n g p u r p o s e s . D e s p i t e L o r d ' s (1964) e a r l y d e f i n i t i o n of n o m i n a l p a r a l l e l i s m based on i n t e r c h a n g e a b l e use i n common p r a c t i c e , f u n c t i o n a l e q u i v a l e n c e i s not a s u f f i c i e n t s t a n d a r d where e q u a t i n g i s the g o a l . L o r d and N o v i c k (1968) s t r e s s e d the n o t i o n of p s y c h o l o g i c a l e q u i v a l e n c e i n terms of commonality of the p s y c h o l o g i c a l t r a i t measured. I n the p r e s e n t s t u d y t h i s was adopted as the f i r s t , o r s c r e e n i n g , c r i t e r i o n f o r the i d e n t i f i c a -t i o n of n o m i n a l l y p a r a l l e l t e s t s . As d i s c u s s e d e a r l i e r , t o t h i s must be added the n o t i o n of c o n t e n t p a r a l l e l i s m as used i n the Anchor Te s t Study. T h i s r e q u i r e s a c o r r e s p o n d e n c e of i t e m s between t e s t s i n terms of s p e c i f i c s k i l l a r e a s or domains t e s t e d w i t h i n the more g l o b a l d e f i n i t i o n of the p s y c h o l o g i c a l t r a i t . F i n a l l y , an i n d e x of s t a t i s t i c a l s i m i l a r i t y , namely the c o r r e l a t i o n c o e f f i c i e n t , must be a p p l i e d t o c o n f i r m e m p i r i c a l l y the r e l a t i o n s h i p s e s t a b l i s h e d on the b a s i s of j u d g m e n t a l a n a l y s i s . The d e t e r -m i n a t i o n of the s i z e of t h i s i n d e x i s i n f l u e n c e d by the s i z e of the sample on w h i c h the c o n v e r s i o n s a r e t o be e s t a b l i s h e d . Marks and L i n d s a y (1972) 160 c l a i m e d t h a t , f o r t e s t s d e f i n e d as n o m i n a l l y p a r a l l e l i n the s t r i c t e r sense d i s c u s s e d i n t h i s s e c t i o n , c o r r e l a t i o n s of .80 or even lower are a c c e p t a b l e p r o v i d e d the sample s i z e i s at l e a s t 500. C o n v e r s e l y , s m a l l e r samples r e q u i r e h i g h e r c o r r e l a t i o n s . The^Use and I n t e r p r e t a t i o n of I n t e l l i g e n c e T e s t s From a p r a c t i c a l p o i n t of v i e w , t h e r e s u l t s of the s t u d y e m p h a t i c a l l y c o n f i r m the n o n - e q u i v a l e n c e , t h a t i s , the n o n - i n t e r c h a n g e a b i l i t y of the f i v e i n d i v i d u a l l y - a d m i n i s t e r e d i n t e l l i g e n c e t e s t s examined. As d i s c u s s e d i n C hapter IV, the s i z e of the e r r o r s d e s c r i b i n g the d i s c r e p a n c y between c o n v e r t e d and o b t a i n e d s c o r e s i n d i c a t e d the inadequacy of u s i n g a c o n v e r s i o n based on the a s s u m p t i o n of t e s t e q u i v a l e n c e . T h i s f i n d i n g r e - e m p h a s i z e s the need f o r c a r e f u l t e s t use and i n t e r p r e t a t i o n and s t r e s s e s the r e s p o n s -i b i l i t y p l a c e d on the p r o f e s s i o n a l s c h o o l p s y c h o l o g i s t and p s y c h o m e t r i c i a n t o ensure the p r o p e r u n d e r s t a n d i n g of t e s t a p p l i c a t i o n . L i m i t a t i o n s of the Study The l i m i t a t i o n s of the s t u d y d e r i v e from i s s u e s r e l a t e d t o sample s i z e . These a r e d i s c u s s e d s e p a r a t e l y i n r e l a t i o n t o t h e e f f e c t on norming and on e q u a t i n g . Norming W i t h r e s p e c t t o norming, the i s s u e of s i z e r e l a t e s t o the p r o b l e m of r esponse r a t e . The i s s u e of non-response i s always t r o u b l e s o m e , and p a r t i c u l a r l y so i n a s i t u a t i o n such as the p r e s e n t one where t h e r e i s a heavy r e l i a n c e on the a s s i s t a n c e of v o l u n t e e r s . I n the p r e s e n t : s t u d y , : t h e t a r g e t sample s i z e was d e t e r m i n e d and a s t r a t i f i e d random sample of c h i l d r e n was drawn c o r r e s p o n d i n g t o t h i s t a r g e t s i z e . The a c t u a l number of c h i l d r e n t e s t e d was 63.0% of the t a r g e t number. These c h i l d r e n came from 63.9% of the s c h o o l s and 92.2%> of the s c h o o l d i s t r i c t s o r i g i n a l l y drawn. 161 T h i s r a i s e s t he q u e s t i o n of b i a s i n the p o t e n t i a l d i f f e r e n t i a l i n c l u s i o n and e x c l u s i o n of p e r s o n s i n the sample.. I n the p r e s e n t s t u d y , however, th e i s s u e of b i a s i s e q u i v o c a l . The non-response group i n c l u d e d not o n l y r e f u s a l s t o p a r t i c i p a t e ( a t t h e d i s t r i c t o r s c h o o l l e v e l ) , but a l s o t h o s e f o r whom t e s t i n g arrangements c o u l d not be made or were not f o l l o w e d t h r o u g h . Thus the non - r e s p o n d e r s were not homogeneous w i t h r e s p e c t t o re a s o n s f o r e x c l u s i o n . A d d i t i o n a l l y , as shown i n Chapter IV, c o m p a r i s o n of sample and p o p u l a t i o n p e r c e n t a g e s f o r the s t r a t i f i c a t i o n v a r i a b l e s c o n f i r m e d the o v e r a l l r e p r e s e n t a t i v e n e s s of the sample. T h e r e f o r e , i t i s u n l i k e l y t h a t the low res p o n s e r a t e e f f e c t e d a s y s t e m a t i c b i a s . Equat i n g The l i m i t a t i o n f o r the e q u a t i n g phase o f the s t u d y was r e l a t e d t o the g e n e r a l s i z e o f the sample a p a r t from q u e s t i o n s of i t s d i s p e r s i o n . Marks and L i n d s a y (1972) s t r e s s e d the need f o r a l a r g e sample («* 500) i n o r d e r t o reduce e q u a t i n g e r r o r . I n the p r e s e n t s t u d y , however, sample s i z e would not be e x p e c t e d t o compensate f o r the e r r o r a t t r i b u t a b l e t o the n o n - e q u i v a l e n c e o f t e s t c o n t e n t . T h e r e f o r e , the more i m p o r t a n t c o n s i d e r a -t i o n remains the degree of t e s t p a r a l l e l i s m . D i r e c t i o n s f o r F u r t h e r R e s e a r c h The most o b v i o u s need f o r f u r t h e r r e s e a r c h i n d i c a t e d by the norming phase of the s t u d y i n v o l v e s an e x t e n s i o n of the norms t a b l e s t o o t h e r a g e s — p a r t i c u l a r l y t h r o u g h o u t the WISC-R range of 6 y e a r s 0 months t o 16 y e a r s 11 months. R e s u l t s o f the p r e s e n t s t u d y suggest t h a t r e n o r m i n g would c o n -s i s t e n t l y r e s u l t i n a l o w e r i n g o f IQs. W h i l e t h i s c o u l d be p o s t u l a t e d f o r a l l age g r o u p s , i t i s c u r r e n t l y i m p o s s i b l e t o p r o v i d e B.C. s t a n d a r d i z e d s c o r e s f o r o t h e r t h a n the s p e c i f i c age groups i n c l u d e d i n t h e p r e s e n t s t u d y . A second need i s f o r achievement c o r r e l a t e s t o e s t a b l i s h t h e ' . c r i t e r i o n 162 v a l i d i t y o f the B.C. norms. A t h i r d o r i e n t a t i o n f o r f u r t h e r r e s e a r c h r e g a r d -i n g i n t e l l i g e n c e t e s t s c o r e s c o n c e r n s the c o n s i s t e n t l y h i g h e r performance r e p o r t e d f o r C a n adian c h i l d r e n on s t a n d a r d i z e d t e s t s . S i n c e the r e a s o n s f o r t h i s have not been f u l l y examined, f u r t h e r s t u d i e s may be c o n s i d e r e d . The e q u a t i n g r e s u l t s i n d i c a t e the need f o r r e s e a r c h t o c o n f i r m the uses t o w h i c h i n t e l l i g e n c e t e s t s a re a p p l i e d . The d i f f e r e n t i a l v a l i d a t i o n of t e s t s would h e l p t o a v o i d the problem of o v e r l a p p i n g usage. W i t h r e g a r d to t e s t e q u a t i n g , i t i s u n p r o d u c t i v e t o ' a d v o c a t e f u r t h e r e q u a t i n g e f f o r t s between t e s t s u n l e s s t h e r e i s a h i g h degree of c o n t e n t s i m i l a r i t y . W i t h the t e s t s now a v a i l a b l e f o r the i n d i v i d u a l assessment of c h i l d r e n ' s i n t e l l i -gence, t e s t e q u a t i n g i s judged t o be i n a p p r o p r i a t e . T h e r e f o r e , the more p r o d u c t i v e o r i e n t a t i o n i s toward s p e c i f i c and i n d i v i d u a l t e s t v a l i d a t i o n . Thus the c o n c l u d i n g recommendations f o r t h i s s t u d y are seen t o c o r r e s p o n d t o t h o s e d e r i v e d from a d i f f e r e n t p e r s p e c t i v e : the j u d i c i a l a n a l y s i s of t e s t b i a s d i s c u s s e d i n C h a p t e r I (p. 1 ) . 163 REFERENCE NOTES 1. B.C. R e s e a r c h , P e r s o n a l e x p e r i e n c e r e g a r d i n g s a m p l i n g p r o c e d u r e s f o r the B.C. L e a r n i n g Assessment Program. November, 1980. 2. Rees, D. P e r s o n a l communication r e g a r d i n g 1978-1979 s c h o o l enrolment i n B r i t i s h C o l u m b i a , November, 1978. 3. 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Can u s e f u l g e n e r a l - p u r p o s e e q u i v a l e n c y t a b l e s be p r e p a r e d f o r d i f f e r e n t c o l l e g e a d m i s s i o n s t e s t s ? I n A- A n a s t a s i ( E d . ) , T e s t i n g problems i n p e r s p e c t i v e . W ashington, D.C.: Am e r i c a n C o u n c i l on E d u c a t i o n , 1966. A n g o f f , W. H. S c a l e s , norms, and e q u i v a l e n t s c o r e s . I n R. L. T h o r n d i k e ( E d . ) , E d u c a t i o n a l measurement (2nd e d . ) . Washington, D.C.: American C o u n c i l on E d u c a t i o n , 1971. Ar m s t r o n g , R. J . , & J e n s e n , J . A. Can s c o r e s o b t a i n e d from the S l o s s o n I n t e l l i g e n c e Test be used w i t h as much c o n f i d e n c e as s c o r e s o b t a i n e d from the S t a n f o r d - B i n e t I n t e l l i g e n c e S c a l e ? E a s t A u r o r a , N.Y.: S l o s s o n E d u c a t i o n a l P u b l i c a t i o n s , 1970. 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H. , B l a h a , J . , W a l l b r o w n , J . D. , & E n g i n , A. W. The h i e r -a r c h i c a l f a c t o r s t r u c t u r e of the W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n — R e v i s e d . J o u r n a l of P s y c h o l o g y , 1975, 89, 223-235. W e c h s l e r , D. Manual f o r the W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n . N.Y.: P s y c h o l o g i c a l C o r p o r a t i o n , 1949. W e c h s l e r , D. Manual f o r the W e c h s l e r I n t e l l i g e n c e S c a l e f o r C h i l d r e n —  R e v i s e d . N.Y.: P s y c h o l o g i c a l C o r p o r a t i o n , 1974. Wesman, A. C. C o m p a r a b i l i t y v s . e q u i v a l e n c e o f t e s t s c o r e s . T e s t S e r v i c e B u l l e t i n , The P s y c h o l o g i c a l C o r p o r a t i o n , 1958, No. 53. W h i t w o r t h , R. H. Review of WISC-R. I n 0. K. Buros ( E d . ) , The e i g h t h m e n t a l  measurements yearbook ( V o l . 1 ) . H i g h l a n d P a r k , N.J.: Gryphon P r e s s , 1978. W i e d l , K. H., & C a r l s o n , J . S. The f a c t o r i a l s t r u c t u r e of t h e Raven C o l o u r e d P r o g r e s s i v e M a t r i c e s t e s t . E d u c a t i o n a l and P s y c h o l o g i c a l Measurement, 1976, 36, 409-413. Winer, B. J . S t a t i s t i c a l p r i n c i p l e s i n e x p e r i m e n t a l d e s i g n (2nd e d . ) . N.Y.: M c G r a w - H i l l , 1971. W r i g h t , E. N., T h o r n d i k e , R. L., & Hagen, E. Canadian L o r g e - T h o r n d i k e I n t e l l i g e n c e T e s t s . T e c h n i c a l Supplement. T o r o n t o : Thomas N e l s o n , 1972. APPENDIX A LETTERS AND CONSENT FORMS THE UNIVERSITY OF BRITISH COLUMBIA 2075 WESBROOK MALL VANCOUVER, B.C., CANADA V6T1W5 Education Clinic F A C U L T Y OF EDUCATION This is a request for your endorsement of a province-wide research project involving the use of intelligence tests in schools in British Columbia. The project is being undertaken as a doctoral dissertation in the division of Educational Psychology at the University of British Columbia, and has received the approval of the Behavioral Sciences Screening Committee for Research.and Other Studies Involving Human Subjects at the University. Financial support has been provided through a grant from the Educational Research Institute of B.C. The following i s a brief abstract describing the purposes and procedures involved. This research project addresses three questions concerning the use of individual intelligence tests ;in schools in British Columbia. 1. Can test r e s u l t s be -interpreted fairly for Canadian children using published norms established in the United States and B r i t a i n ? The applicability of the existing norms for five individually-administered tests (the Wechsler Intelligence Scale for Children-Revised (WISC-R), the , Slosson Intelligence Test, the Peabody Picture Vocabulary Test, the Standard Progressive Matrices, and the M i l l H i l l Vocabulary Scale) w i l l be assessed in response to this question. ' 2 . Is it f e a s i b l e to make comparisons between IQ scores which .were' obtained. from d i f f e r e n t tests of i n t e l l i g e n c e ? Comparisons of this nature are frequently made based on the assumption of direct score correspondence between intelligence tests. Using the WISC-R as an anchor, the f e a s i b i l i t y of constructing tables of comparable values among the five tests w i l l be examined. 3. Can the M i l l H i l l Vocabulary Scale be used in conjunction with the Standard Progressive Matrices to provide verbal and nonverbal estimates of i n t e l l e c t u a l ability s i m i l a r to that dichotomy provided by WISC-R Verbal and Performance scores? Raven constructed these tests for use in combination and standardized them join t l y in Britain. In North America the Standard Progressive Matrices i s commonly used in isolation as a measure of intelligence. The M i l l H i l l Vocabulary Scale w i l l be introduced in this study to explore i t s v a l i d i t y as a verbal measure of intelligence and to examine i t s combined use with the Standard Progressive Matrices as a measure of general intelligence. The tests w i l l be administered to a random, proportionately representative sample of 540 children, aged 7, 9, and 11 years, from public and independent 176 The following l i s t of schools were randomly selected from School D i s t r i c t No. . Would you please v e r i f y the p r i n c i p a l s ' names so that, given your permission, we may contact them d i r e c t l y . Thank you. I consent to the above -schools being contacted to request t h e i r p a r t i c i p a t i o n i n t h i s research p r o j e c t . In doing so, I give my support to the study with the understanding that each school i s subsequently free to make i t s own d e c i s i o n regarding p a r t i c i p a t i o n . signature On behalf of School D i s t r i c t No. , I decline involvement i n t h i s research p r o j e c t . signature THE UNIVERSITY OF BRITISH COLUMBIA 2075 WESBROOK MALL VANCOUVER, B.C., CANADA V6T 1W5 Education C l i n i c F A C U L T Y OF EDUCATION Your superintendent has given us permission to contact you to request your support and p a r t i c i p a t i o n i n a research project i n v o l v i n g the use of i n t e l l i g e n c e t e s t s i n schools i n B r i t i s h Columbia. The project i s being undertaken as a doctoral d i s s e r t a t i o n i n the d i v i s i o n of Educational Psychology at the U n i v e r s i t y of B r i t i s h Columbia, and has received the approval of the Behavioral Sciences Screening Committee for Research and Other Studies Involving Human Subjects at the U n i v e r s i t y . F i n a n c i a l support has been provided through a grant from the Educational Research I n s t i t u t e of B.C. The following i s a b r i e f abstract describing the purposes and procedures involved.. This research project addresses three questions concerning the use of i n d i v i d u a l i n t e l l i g e n c e t e s t s i n schools i n B r i t i s h Columbia. 1. Can test results be interpreted f a i r l y for Canadian children using •published norms established in the United States and Britain? The a p p l i c a b i l i t y of the e x i s t i n g norms f or f i v e i n d i v i d u a l l y - a d m i n i s t e r e d t e s t s (the Wechsler I n t e l l i g e n c e Scale for Children-Revised (WISC-R), the Slosson I n t e l l i g e n c e Test, the Peabody P i c t u r e Vocabulary Test, the Standard Progressive Matrices, and the K i l l H i l l Vocabulary Scale) w i l l be assessed i n response to t h i s question. 2 . Is i t feasible to make comparisons between IQ scores which were obtained from different tests of intelligence? Comparisons of t h i s nature are frequently made based on the assumption of d i r e c t score correspondence between i n t e l l i g e n c e t e s t s . Using the WISC-R as an anchor, the f e a s i b i l i t y of constructing tables of comparable values among the f i v e t e s t s w i l l be examined. 3. Can the Mill B i l l Vocabulary Scale be used in conjunction with the Standard Progressive Matrices to. provide verbal and nonverbal estimates of intellectual a b i l i t y similar to that dichotomy provided by WISC-R Verbal and Performance scores? Raven constructed these t e s t s f or use i n combination and standardized them j o i n t l y i n B r i t a i n . In North America the Standard Progressive Matrices i s commonly used i n i s o l a t i o n as a measure of i n t e l l i g e n c e . The M i l l H i l l Vocabulary Scale w i l l be introduced i n t h i s study to explore i t s v a l i d i t y as a verbal measure of i n t e l l i g e n c e and to examine i t s combined use with the Standard Progressive Matrices as a measure of general i n t e l l i g e n c e . The tests w i l l be administered to a random, proportionately representative School Code No. I consent to participate in the research project as described concerning the use of intelligence tests in B.C. The person who is a qualified WISC-R test administrator for this school i s : Name: Address: Telephone: signature. I do not consent to participation in this research. signature THE UNIVERSITY OF BRITISH COLUMBIA 2075 \VESBROOK MALL 180 VANCOUVER, B.C., CANADA V6T 1W5 Education Clinic FACULTY OF EDUCATION This i s a request for your participation in a research project involving the use of intelligence tests in public and independent schools in Bri t i s h Columbia. To ensure the applicability of the results to children attending other than public schools, we have included .independent school children in our sample in the same proportion as they exist in the province. We ask that you read the enclosed materials describing the study and sincerely hope that you w i l l agree to be included in this research. The project is being undertaken .as a doctoral dissertation in the division of Educational Psychology at the University of British Columbia, and has received the approval of the Behavioral Sciences Screening Committee for Research and Other Studies Involving Human Subjects at the University. Financial support has been provided through a grant from the Educational Research Institute of B.C. The following :is a brief abstract describing the purposes and procedures involved. This research project addresses three questions concerning the use of individual intelligence tests i n schools in .British Columbia. I. Can test results be interpreted fairly for Canadian children using published norms established in the United States and Britain? The applicability of the existing norms for five individually-administered tests (the Wechsler Intelligence Scale for Children-Revised (WISC-R), the Slosson Intelligence Test, the Peabody Picture Vocabulary Test, the Standard Progressive Matrices, and the M i l l H i l l Vocabulary Scale) w i l l be-assessed in response to this question. "2. Is it feasible to make comparisons between IQ scores which were obtained from different tests of intelligence? Comparisons of this nature are frequently made based on the assumption of direct score correspondence between intelligence tests. Using the "WISC-R as an anchor, the f e a s i b i l i t y of constructing tables of comparable values among the five tests w i l l be examined. 3. Can the Mill H i l l Vocabulary Scale be used -in conjunction with the Standard Progressive Matrices to provide verbal and nonverbal estimates of intellectual ability similar to that dichotomy provided by WISC-R Verbal and 'Performance scores? Raven constructed these tests for use in combination and standardized them jointly in Britain. In North America the Standard Progressive Matrices i s commonly used in isolation as z measure of intelligence. The M i l l H i l l Vocabulary Scale w i l l be introduced in this study to explore i t s v a l i d i t y as a verbal measure of intelligence' and to examine i t s combined use with the Standard Progressive Matrices as a measure of general intelligence. The tests w i l l be administered to a random, proportionately representative code no. 183 Parent Consent Form I consent to 's p a r t i c i p a t i o n i n the 'testing research study at School. I am aware that t h i s w i l l involve two t e s t i n g sessions of approximately one hour each, and that the t e s t s w i l l be returned anonymously to the U n i v e r s i t y of B r i t i s h Columbia for scoring. I understand that c o n f i d e n t i a l i t y of t e s t r e s u l t s w i l l be maintained and that no i n d i v i d u a l scores w i l l be released. I also understand that p a r t i c i p a t i o n i n t h i s p r o j e c t i s voluntary and may be terminated at any time. One of the problems i n doing research of t h i s scope i s to ensure that the c h i l d r e n chosen are t r u l y representative of a l l the c h i l d r e n i n the province. To help us judge t h i s , we have already grouped the c h i l d r e n according to d i s t r i c t , s i z e of school, age, and sex. One further piece of information which we would .like to compare to Census Canada data i s the l e v e l of education of the head of household (that i s , the major wage-earner i n the f a m i l y ) . Would you please put an "X" i n front of the category below which best describes .the completed l e v e l of education of the head of your household. I Grade 8 and below II Grades 9 - 10 I I I Grades 1 1 - 1 3 IV Post-secondary, non-university V Post-secondary, i n c l u d i n g u n i v e r s i t y I am u n w i l l i n g to have involved i n the t e s t i n g research study. signature signature 184 Request for Subject P a r t i c i p a t i o n (to be read to each subject i n d i v i d u a l l y p r i o r to t e s t i n g ) , as you may know by now, you have been selected to take part i n a research project to see how c h i l d r e n i n B r i t i s h Columbia answer questions on some t e s t s . You were chosen p a r t l y because we need c h i l d r e n your age, and p a r t l y because we need c h i l d r e n from t h i s part of B.C. Altogether there are more than 500 c h i l d r e n from a l l over the province doing the same tes t s that you w i l l do. When we f i n i s h I w i l l send these papers with your work to UBC. Your name won't be on them so nobody w i l l know i t was y o u — we only want to see how c h i l d r e n answer the questions, okay? I want you to remember that these te s t s have nothing to do with your schoolwork and w i l l not count for your grades on your report card. Most c h i l d r e n enjoy doing the te s t s and I'm sure you w i l l too. Before we s t a r t , I want you to know that you don't have to do t h i s , but that your help i s important for a l o t of c h i l d r e n i n B.C. I would appreciate i t i f you would .agree to work on these tes t s with me. Okay? THE UNIVERSITY OF BRITISH COLUMBIA 2075 WESBROOK MALL 185 VANCOUVER, B.C., CANADA V6T 1W5 F A C U L T Y OF EDUCATION We are contacting you to request your assistance in a research project involvii the use of individual intelligence tests i n schools in British Columbia. The projec is being undertaken as a doctoral dissertation in the division of Educational Psychology at the University of British Columbia and has received financial support through a grant from the Educational Research Institute of B.C. Enclosed i s a brief abstract describing the purposes of the study. As you know, the process of establishing norms requires a large number of test administra-tions. The design of this study requires that a l l tests be given to a random, representative sample of 540 children, aged 7, 9, and 11 years. These children are being selected from 195 public and independent schools (no more than three children per school) i n 52 school d i s t r i c t s throughout the province of British Columbia. Our procedure has been to randomly select a s t r a t i f i e d sample of schools and then to gain the endorsement of the d i s t r i c t superintendents.arid the support of the school principals. Where possible, we have asked the principals to identify for us the qualified WISC-R tester for his or her school. The principal(s) of the following school(s) have referred your name: We w i l l be contacting you by telephone shortly to ask for your participation in this project. Before doing so however, we wanted you to have a chance to acquaii yourself with the procedures. We are now i n the process of selecting the children for testing and seeking parental consent. Following this, we ask that a l l five tests be administered to each of these children. It i s anticipated that this w i l l require approximately 2h hours' time per child. The tests should be administered in two sessions to be scheduled at your convenience sometime before the end of the school year. Detailed directions and test protocols -will be supplied. To reduce your time, a l l scoring w i l l be done at UBC. We are very aware that this i s a busy time for you and that testing demands are considerable. We hope that you w i l l appreciate, however, the desirability of having local norms for these tests, including a "Canadianized" version of the WISC-I Since we are operating on a limited budget, and since the scope of the project i s large, we must rely on the help and support of many of you to make i t a success. We do assure you a copy of the results of the study for your future use. 187 Individually-Administered I n t e l l i g e n c e Tests: Determination of Norm Relevance and Inter-Test Comparability i n B r i t i s h Columbia This study has two research o r i e n t a t i o n s . The f i r s t i s substantive and addresses three questions concerning the use of i n d i v i d u a l i n t e l l i g e n c e t e s t s i n schools i n B r i t i s h Columbia. The second o r i e n t a t i o n i s method-o l o g i c a l and concerns the a p p l i c a t i o n of equivalent score conversion techniques to i n t e l l i g e n c e test scores. The following four questions summarize the purposes of the study. .1. Car, test results be interpreted fairly for Canadian children using published norms established in the United States and Britain? The a p p l i c a b i l i t y of the e x i s t i n g norms f o r f i v e i n d i v i d u a l l y - a d m i n i s t e r e d te s t s (the Wechsler I n t e l l i g e n c e Scale for Children-Revised (WISC-R), the Slosson I n t e l l i g e n c e Test, the Peabody P i c t u r e Vocabulary Test, the Standard Progressive Matrices, and the M i l l H i l l Vocabulary Scale) w i l l be assessed i n response to t h i s question. 2. Is it feasible to make comparisons between IQ scores which were obtained from different tests of intelligence? Comparisons of t h i s nature are frequently made based on the assumption of d i r e c t score correspondence between i n t e l l i g e n c e t e s t s . Using the TtflSC-R as an anchor, the f e a s i b i l i t y of constructing tables of comparable values among the f i v e t e s t s w i l l be examined. 3. Can the Mill Bill Vocabulary Scale be used in conjunction with the Standard Progressive Matrices to provide verbal and nonverbal estimates of intellectual ability similar to that dichotomy provided by WISC-R Verbal and Performance scores? Raven constructed these t e s t s for use i n combination and standardized them j o i n t l y i n B r i t a i n . In North America the Standard Progressive Matrices i s commonly used i n i s o l a t i o n as a measure of i n t e l l i g e n c e . The M i l l H i l l Vocabulary Scale w i l l be introduced i n t h i s study to explore i t s v a l i d i t y as a verbal measure of i n t e l l i g e n c e and to examine i t s combined use with the Standard Progressive Matrices as a measure of general i n t e l l i g e n c e . 4. What are the meaningfulness and relative efficiency of the linear and equipercentile score equating techniques when applied to intelligence tests? These techniques have previously been compared for reading achievement t e s t s which have a high degree of content s i m i l a r i t y . The a p p l i c a t i o n of these techniques to i n t e l l i g e n c e t e s t s w i l l be explored. 188 APPENDIX B WISC-R CANADIAN SUBSTITUTION ITEMS 189 Canadian S u b s t i t u t i o n Items f o r the WISC-R O r i g i n a l Item No. S u b s t i t u t i o n Acceptable Answers Info. 16. Bulb 17. 1776 19. Border 21. Chile 24. T a l l 27. LA/NY Comp. 17. Senators Who invented the telephone? . B e l l , or Graham B e l l From which country d i d most of the f i r s t s e t t l e r s i n Canada come? Name three oceans that border Canada. In what continent i s Sweden? How " t a l l i s the average Canadian man ? How f a r i s i t from "Toronto to Vancouver? Substitute: Members of Parliament for Senators and Congressmen England, B r i t a i n , Scotland, or France Accept A r c t i c and e i t h e r A t l a n t i c or P a c i f i c , £r both Europe 5'7" - 5 M l " , or 170-180 centimetres 1700-2700 mil e s , or :2700-4300 kilometres Same scoring c r i t e r i a as i n Manual. APPENDIX C PROJECT HANDBOOK Tester's Handbook for the B.C. I n t e l l i g e n c e Testing Research Project Contents: L i m i t a t i o n s on Children to be Included i n the Sample Subjects' Code Numbers and I d e n t i f i c a t i o n of A l t e r n a t i v e s Parent Consent Forms Sample of Parent Consent Forms C h i l d Consent Forms Scheduling Test Sessions and Order of Test Administrations Testing D i r e c t i o n s Scoring D i r e c t i o n s WISC-R Canadianization Summary of D i r e c t i o n s L i m i t a t i o n s on Children to be Included i n the Sample 192 .1 Below i s a segment of the l e t t e r sent to p r i n c i p a l s to guide them i n the preparation of school l i s t s from which the c h i l d r e n were randomly selected f o r t e s t i n g . To guarantee that c h i l d r e n for whom t e s t i n g i s inappropriate do not appear i n the sample, we have asked that the following c h i l d r e n be excluded: "a) p h y s i c a l l y , emotionally, or mentally handicapped c h i l d r e n Please exclude a l l c h i l d r e n e n r o l l e d i n classes f o r the p h y s i c a l l y handicapped, emotionally disturbed, or tr a i n a b l e mentally retarded. These c h i l d r e n usually require s p e c i a l t e s t i n g procedures beyond the nature of t h i s study and to include them would be u n f a i r to t h e i r p a r t i c u l a r needs. b) Native Indian c h i l d r e n Previous studies have indi c a t e d that standardized i n t e l l i g e n c e t e s t s may contain 'items which are c u l t u r a l l y biased against Native Indian c h i l d r e n . Current trends i n t e s t i n g emphasize the need for separate norms f o r these c h i l d r e n . Dr. Oldridge i s hoping to e s t a b l i s h these Native Indian norms for B.C. i n the near future. In the meantime, to avoid m i s a p p l i c a t i o n of the r e s u l t s of the present study, we have decided to exclude Native Indian c h i l d r e n . c) c h i l d r e n who are not fl u e n t i n the use and comprehension of the Engl i s h language Since most of the test s are v e r b a l , i t i s e s s e n t i a l that the c h i l d r e n being tested speak and understand E n g l i s h . Please exclude c h i l d r e n i n ESL cla s s e s , or c h i l d r e n for whom you know verbal t e s t s would be u n f a i r . If there are cases where you have a question about degree of p r o f i c i e n c y , include the names on the l i s t . I f any of these c h i l d r e n are selected i n our sample, we w i l l include an .'English p r o f i c i e n c y measure i n t h e i r t e s t i n g package." . I f you have been assigned to tes t a c h i l d whom you f e e l should not be included on the basis of these r e s t r i c t i o n s , please l e t us know and an al t e r n a t e w i l l be chosen. I t i s important however, that no changes or su b s t i t u t i o n s be made for other reasons. The unbiasedness and representativeness of the sample are dependent of the observance of the random s e l e c t i o n procedures. Subjects' Code Numbers and I d e n t i f i c a t i o n of Alternates 193 ? So you know how i t was done: A l l 7, 9, and 11 year olds i n each school were l i s t e d excluding the three categories of c h i l d r e n described on the previous page. We further l i m i t e d p o t e n t i a l subjects to those who would be within three months of t h e i r h a l f year at the time of t e s t i n g : eg. 7-year-olds would be between 7 y r s . 3 mos. and 7 yrs. 9 mos. This was done i n an attempt to simulate standardization procedures f o r the WISC-R, where a l l c h i l d r e n were tested within s i x weeks of t h e i r midyear (see p.17 i n the WISC-R Manual). One subject and one alt e r n a t e were randomly selected at each age l e v e l i n each school. They are coded as i n the following example: 9901 - 17 - A 9901 - 34 - B where 9901 i s the school code number 17,' 34 are simply order numbers on the school l i s t s A i s the first-drawn subject B i s the alt e r n a t e subject The parents of a l l "A" c h i l d r e n were contacted f i r s t and these c h i l d r e n w i l l appear i n the f i n a l sample i f consent was given. "B" c h i l d r e n should be used only i f an alt e r n a t e i s required. The p r i n c i p a l of each school has forms ready to contact "B" parents a f t h i s i s necessary. This step can therefore be taken immediately and doesn't require a contact with UBC. If there are any queries or complications, however, please c a l l us c o l l e c t at any time. .194 Parent Consent Forms (sample on next page) 3 Please get from the p r i n c i p a l the signed consent form for each c h i l d before any t e s t i n g i s done. The code number i n the upper r i g h t hand corner i s our only means of i d e n t i f i c a t i o n of the subject and therefore must appear on each t e s t •protocol (enter as name). We also need to know the l e v e l of education of the head of household. Please t r a n s c r i b e t h i s information (the Roman numeral) on the front of the WISC-R pr o t o c o l . 195 code no. P a r e n t Consent Form I consent to 's p a r t i c i p a t i o n i n the t e s t i n g r e s e a r c h s t u d y a t S c h o o l . I am aware t h a t t h i s w i l l i n v o l v e two t e s t i n g s e s s i o n s of a p p r o x i m a t e l y one hour each, and t h a t the t e s t s w i l l be r e t u r n e d anonymously t o the U n i v e r s i t y of B r i t i s h Columbia f o r s c o r i n g . I u n d e r s t a n d t h a t c o n f i d e n t i a l i t y o f t e s t r e s u l t s w i l l be m a i n t a i n e d and t h a t no i n d i v i d u a l s c o r e s w i l l be r e l e a s e d . I a l s o u n d e r s t a n d t h a t p a r t i c i p a t i o n i n t h i s p r o j e c t i s v o l u n t a r y and may be t e r m i n a t e d a t any t i m e . s i g n a t u r e One of the problems i n d o i n g r e s e a r c h of t h i s scope i s t o ensure t h a t the c h i l d r e n chosen a r e t r u l y r e p r e s e n t a t i v e of a l l t h e c h i l d r e n i n the p r o v i n c e . To h e l p us judge t h i s , we have a l r e a d y grouped the c h i l d r e n a c c o r d i n g t o d i s t r i c t , s i z e of s c h o o l , age, and sex. One f u r t h e r p i e c e of i n f o r m a t i o n w h i c h we would l i k e t o compare t o Census Canada d a t a i s t h e l e v e l of educa-t i o n of the head of h o u s e h o l d ( t h a t i s , the major wage-earner i n the f a m i l y ) . Would you p l e a s e put an "X" i n f r o n t of the c a t e g o r y below w h i c h b e s t d e s c r i b e s the c ompleted l e v e l of e d u c a t i o n of the head of your h o u s e h o l d . I Grade 8 and below I I Grades 9-10 I I I Grades 11-13 IV P o s t - s e c o n d a r y , n o n - u n i v e r s i t y V P o s t - s e c o n d a r y , i n c l u d i n g u n i v e r s i t y I am u n w i l l i n g t o have i n v o l v e d i n the t e s t i n g r e s e a r c h s t u d y . s i g n a t u r e C h i l d Consent Forms (Request for Subject P a r t i c i p a t i o n ) 196 ,5 Stapled to the front of each c h i l d ' s t e s t package i s the consent form to be read p r i o r to t e s t i n g . I t i s recognized that a large part of a school psychologist's or psychometrician's p r o f e s s i o n a l s k i l l involves s o l i c i t i n g and maintaining the cooperation of c h i l d r e n during t e s t i n g . Since t h i s . s k i l l i s involved i n the administration of i n d i v i d u a l i n t e l l i g e n c e t e s t s , i t w i l l be necessary i n many cases to encourage subjects' p a r t i c i p a t i o n . On the other hand, however, i t i s contrary to the purposes of the study and the v a l i d i t y of t e s t r e s u l t s , to coerce any c h i l d who i s s e r i o u s l y opposed to p a r t i c i p a t i o n . Please use your judgement concerning unwillingness on the part of the c h i l d . I f i t i s necessary to s e l e c t an a l t e r n a t i v e , please arrange to have the "B" c h i l d tested following procedures ou t l i n e d on page 2 of t h i s handbook. The p r i n c i p a l has been i n s t r u c t e d regarding these procedures and has the parent l e t t e r s and consent forms on hand. Scheduling Test Sessions and Order of Test Administration 197 6 Please schedule two testing sessions for each child on different days (i.e. not morning and afternoon of the same day). During Session I, administer the WTSC-R. At Session II, administer the other three tests. Please note that the Standard Progressive Matrices and the M i l l L H i l l Vocabulary Scale are con-sidered as one test and are given in the order: SPM followed by MHVS. The order of administration i s important and we ask that you do not alter i t . In each case the WISC-R i s given f i r s t . The other tests have been counter-balanced for order and randomly assigned to children. This procedure w i l l control for any possible sequence effects that could occur. It i s therefore important that the order be maintained. Testing Directions Follow the manual procedures as usual for the WISC-R, the Slosson, the Peabody Picture Vocabulary Test, and the Raven's Standard Progressive Matrices. The directions for the M i l l H i l l Vocabulary Scale accompany the test record forms in the test package. Scoring Directions A l l tests w i l l be scored at UBC: this procedure w i l l both save you time and guarantee the anonymity of results. Please, therefore, ensure that you record responses f u l l y to allow a second party to score accurately.. 198 WISC-R Canadian!zation 7 The s u b s t i t u t i o n items f o r the WISC-R have been enclosed w i t h i n each p r o t o c o l . They include a l t e r n a t e wordings and responses for s i x Information items and one Comprehension item. The items i n the pro t o c o l have been c i r c l e d i n red to remind you to make the s u b s t i t u t i o n s . Please read only the new wordings i n each case. You are welcome to keep these l i s t s f o r your own use. The s u b s t i t u t i o n s were recommended by Dr. P h i l i p Vernon of the U n i v e r s i t y of Calgary i n the B u l l e t i n of the Canadian Psychological A s s o c i a t i o n . These wordings were found to y i e l d item pass percentages for a Canadian sample which are c l o s e r to the o r i g i n a l norm sample than .are pass percentages using the o r i g i n a l wording. The norms which we w i l l provide you as a r e s u l t of t h i s study w i l l be ap p l i c a b l e only to these wordings. Summary of Di r e c t i o n s 8 1. get parent consent forms from the p r i n c i p a l 2. schedule 2 t e s t i n g sessions per c h i l d Session ill 3. record code number, sex, and birthdate of the c h i l d on each p r o t o c o l 4. record the l e v e l of education of the head of household from the green Parent Consent Form to the top of the WISC-R p r o t o c o l 5. read the Request for Subject P a r t i c i p a t i o n (pale yellow form) 6. administer the WISC-R with the Canadian s u b s t i t u t i o n s (goldenrod form) Session #11 7. check that code number, etc. (as i n #1. above) are on each te s t p r o t o c o l 8. administer t e s t s i n s p e c i f i e d order Please r e t a i n the Parent Consent Forms at the -school u n t i l a l l t e s t i n g i s completed APPENDIX D MHVS SCORING GUIDES 201 M i l l H i l l Vocabulary Scoring Guides Set A l.CAP 1 p o i n t — C o v e r ( l i d ) f o r a b o t t l e . . . . L i k e a cork (Q) l i k e a l i d . . . . Wear i t (Q) a baseball cap....To put a cap on, put a top on....Cover the top....A small quantity of explosive i n a wrapper....Anything l i k e a c a p — t o p of a mushroom....Hat....A thing you wear (put) on your head....What you shoot i n a gun.... Something you wear to keep the sun out of your eyes 0 points—Boy's cap 2.LOAF 1 point—Spend time idly....Do nothing....Bread that i s shaped and baked as one piece.... Food shaped l i k e a loaf of bread.... Food (Q) you eat it....Dough....You bake i t . . . . L o a f of bread....It has a crust....Meatloaf 0 points—White....Meat....It's round.... I t ' s long.... Something you eat....Piece of bread.... Bread 3.FROCK 1 point—Gown... .Dress Loose outer garment Clothes You wear i t . . . . I t keeps you warm 0 p o i n t s — 3b.DRESS 1 p o i n t — ( G i r l s ) Wear it....Blouse and s k i r t combined i n one....An outer garment worn by women, g i r l s and babies.... Clothes.... Formal clothes.... Clothing.... To put clothes on....Decorate....Trim.... Adorn.... Gown.... Frock.... Like t h i s ( i n d i c a t i n g a dress worn) 0 p o i n t s — S k i r t 4.DAMP 1 p o i n t — A b i t wet....Sort of wet and sort of dry....Grass i s damp with dew on i t . . . . S l i g h t l y wet....Moist....Moisture....Not dry.... When i t rains....Put the washing our (Q) i t ' s damp 0 points—Dry....Grass i s damp.... Floor i s damp (Q) you mustn't s i t on it....Wet 202 5.NEAR 1 point—Close....Not f a r . . . . J u s t beside....Touching....By....Next.... Almost....Together....Near somebody (Q) you're t a l k i n g to them.... Nearly at i t 0 points—Nearly....There 6.UNHAPPY 1 point—Sad.... Sorrowful....Unlucky....When something's wrong....Dis-appointed. ... If someone h i t s you....When you don't l i k e nobody....When you cry.... Sulky....Not happy 0 points—When you fight....When you've done something....When you're unhappy....Angry....Mad 7.DISTURB 1 point—Bug, bother, hastle, annoy....Destroy the peace, quiet, or rest of....Break i n upon with noise or other d i s t r a c t i o n . . . . P u t out of order....Make uneasy....Interrupt....Inconvenience....Wake you up....Make a noise....Disturb people (Q) don't leave them alone.... Disturb the cat (Q) i t scratches.... I f you're doing work and some-body talks to you 0 points—Noise....By angry....Make fun of you....Asleep 8.BATTLE 1 p o i n t — A f i g h t between opposing armed forces....Fighting or war.... Fight....Contest....Struggle....Contend....Soldiers have a b a t t l e . . . . A war.... Shooting....When you charge....A duel....You k i l l each other 0 points—Argument....Army....You win.... 9.RECEIVE 1 point—Someone gives you something, you get it....Take something (offered or sent or given)....Take into one's hands or possession.... Take, accept, admit or get something....Acquire, obtain, get some-thing .... Receive a l e t t e r (Q) you get one....It comes to you....Meet someone....Welcome....Brought....Receive a par c e l (Q) undo i t . . . . Receive something off someone 0 points—Send....Take away.... Give.... Receive a l e t t e r (Q) put i t i n the pot.... Receive anything 203 10.VIEW 1 p o i n t — A n act of seeing.... Sight.... The power of seeing.... Something seen. ...A scene.... .A way of looking at or considering a matter.... Opinion....See....Watch....Vision....Photo....See France from Dover (Q) good view....From a window.... See something from a distance 0 p o i n t s — N i c e place.... Show.... Go to view somebody i f they've been i l l . . . . G e t a view of the lake.... 11.CONTINUE 1 point—Keep up, keep on, keep doing....When you see part of the show th i s week and again next week....When you do one part and i t continues, you do another part....Go on....Go on with (something) a f t e r stopping ....Begin again....Resume....Last....Endure....Do i t again.... F i n i s h l a t e r on....Follow on.... Continue the same work.... Something that stopped and started.... Stop and then continue on 0 points—Again....Start....Ended....Keep stopping.... Go on to some-thing else....When you're doing something....The show w i l l continue next week 12.STARTLE 1 p o i n t — F r i g h t e n suddenly.... Surprise....A sudden shock of surprise or f r i g h t . . . . Scare, frighten....Alarm.... Shock.... Stun....Make some-one jump....Shaken....Afraid suddenly....Someone comes i n suddenly (Q) you're s t a r t l e d . . . . 0 points—Something ,startled you.... Something happens quickly 13. PERFUME 1 p o i n t — A smell (Q) comes i n a b o t t l e and you spray i t on your neck .... Cologne....A l i q u i d having the sweet smell of flowers....A sweet smell....Put a sweet-smelling l i q u i d on....Fragrance....Scent.... Stuff i n a b o t t l e (Q) i t smells nice, good....What you put i n your bath....Ladies wear i t when they go out 0 points—Something you put on....Perfume i s what you use....Make up .... Powder.... Shampoo.... Sweet.... Ladies wear i t (Q).... Smell (Q).... Odor 14. MALARIA 1 p o i n t — A disease characterized by p e r i o d i c c h i l l s followed by fever and sweating.... I l l n e s s . . . . Sickness....Makes you i l l 0 points—When a man f e e l s sick....You come out i n spots....You get a cold 204 15.MINGLE 1 point—Mix....Associate....Blend....Fuse....Combine....Merge i n t o . . . . Get i n a crowd....Jumble....Mingle i n a bunch of ch i l d r e n . . . . Joined together.... Get amongst....Join....Wander i n a crowd 0 p o i n t s — C o l l e c t together.... 16.FASCINATED 1 po i n t — D e l i g h t e d . . . . A t t r a c t e d very strongly....Enchanted by charming qualities....Amazed....Interesting....Something makes you look a l o t ....Pleased....When someone looks nice....See a thing and can't b e l i e v e i t . . . . 0 points—Astonished....Frightened....Amused....A feeling....Something pleasing.... Like the look of....Fancy 17.BRAG 1 p o i n t — S a y you're the greatest.... Say you can do something better than the other person....Boast....Talk about oneself.... Think you're good....To be proud....Big t a l k . . . . T e l l i n g a story (Q) make a l o t up .... Show off 0 p o i n t s — T a l k too much.... Gloat....Talking about one thing a l l the time....You brag because you won the game 18.PROSPER 1 p o i n t — B e successful....Have good fortune....Flourish....Get more ....Get wealthy.... Better off....Have money (Q) prosper by s e l l i n g again....Make money....Have good luck 0 points—Do good....Live....Do a thing well....Do i t right....When you're given something 19. ANONYMOUS 1 p o i n t — B y or from a person whose name i s not known or not given.... Having no name....Nameless....Unknown....Don't know who did i t . . . . A person who wrote something and didn't put h i s name at the bottom 0 p o i n t s — P e n name....False....Letter....Won't t e l l 20. VERIFY 1 p o i n t — P r o v e (something) to be true....Confirm....Test correctness 205 of....Check f o r accuracy.... Get proof.... Confirm.... Find out.... Id e n t i f y . . . . Correct or make sure....That a statement i s made and correct 0 points—Compare....View c l o s e l y . . . . C l a r i f y . . . . G i v e evidence.... Swear ....Witness a thing....Agree 21. RUSE 1 point—Trick....Stratagem....Artifice....Dodge....Wile 0 p o i n t s — 22. FORMIDABLE 1 p o i n t — H a r d to overcome....Hard to deal with....To be dreaded.... Appalling....Fearful 0 points—Something you can't do 23.IMMERSE 1 point — P l u n g e into a l i q u i d . . . . Baptize.by dipping under water.... Involve deeply....Absorb....Submerge 0 p o i n t s — 24. DOCILE 1 p o i n t — E a s i l y managed.... Obedient.... E a s i l y taught....Willing to learn 0 p o i n t s — 25. VIRILE 1 point—Manly....Masculine.... F u l l of manly strength or masculine vigor....Vigorous....Forceful 0 p o i n t s — 26.SULTRY 1 p o i n t — H o t , close, and moist.... F u l l of passion....Fiery 0 p o i n t s — 206 27.STANCE 1 point—Manner of standing, posture....A standing p l a c e . . . . P o s i t i o n 1 p o i n t s — 28.EFFACE 1 point—Rub out....Blot out....Do away with....Destroy....Wipe out 0 p o i n t s — 29.SENSUAL 1 point—Having to do with the bo d i l y senses rather than wit- the mind or soul.... Caring too much for the pleasures of the senses....Lustful .... Lewd 0 p o i n t s — S e n s i t i v e 207 M i l l H i l l Vocabulary Scoring Guides Set B 1.TOMATO 1 point—Fruit....Vegetable....A j u i c y f r u i t used as a v e g e t a b l e — most tomatoes are red when r i p e . . . . Round and red....You eat i t . . . . Red b a l l with a s t a l k on 0 p o i n t s — 2.REST 1 point—Sleep....Ease a f t e r work or effort....Freedom from anything that t i r e s , troubles, disturbs or pains....Quiet....Be s t i l l , sleep ....Stop moving.... Li e , r e c l i n e , s i t , lean, etc. for rest or ease.... Be at ease.... Relax.... Become inactive....What i s l e f t . . . . S t o p working ....When you're t i r e d . . . . Rest on a chair....Nap 0 p o i n t s — T i r e d . . . . R e s t l e s s 3.PATCH 1 p o i n t — A piece put on to mend a hole or tear....A piece of c l o t h , etc. put over a wound or sore....Like a bandaid....Fix something that has a hole i n i t . . . . A p rotective pad over an injured eye....A piece of ground—a garden patch....To put patches on....Mend....Darn....Patch your trousers when they are ripped....Cover a hole 0 points—Tear....Bare.... Space....Hole....Patch of sky....Patch your clothes (Q)....Get a patch from Scouts ( i e badge).... Something you put on your pants (Q) 4.AFRAID 1 p o i n t — N o t brave.... Feeling f e a r . . . . Frightened.... F i l l e d with fear or apprehension.... F e a r f u l . . . . Scared....You cry....You run away.... Araid of a l i o n 0 points—You're afraid....You're sad 5.CRUEL 1 poin t — F o n d of causing pain to others and de l i g h t i n g i n t h e i r suf-f e r i n g . .. .Not caring about pain and s u f f e r i n g of others.... Causing pain and suffering....Mean....Evil.... Showing a c r u e l nature....Un-208 kind....Bad....Hurt....Be nasty....Bully....Take things from someone ....Cruel to a dog (Q) h i t i t Hor r i b l e Awful....Beat somebody up....You k i l l an animal 0 p o i n t s — S t r i c t S e l f i s h Unhappy Don't be c r u e l (Q) don't do it....mad 6.BLAZE 1 p o i n t — A br i g h t flame or f i r e . . . . A n intense l i g h t , glare....A v i o l e n t outburst.... Burn with a bright flame....Be on fire....Mark (a tree, t r a i l , etc.) by chipping o ff a piece of bark.... F i r e . . . . Light (Q) i t blazes....When you get i n a rage 0 p o i n t s — B l a z e away.... Blade of grass.... Burn (Q) 7.ACHE 1 p o i n t — B e i n continued pain....Be eager, wish very much....A-dull, steady pain....Hurt....Long....Yearn....Throb....Hurt....Stiff.... Not very well....In your tummy (Q) nasty....Headeache, toothache.... Ailment.... Sore....Pain....Soreness 0 p o i n t s — 8.SQUABBLE 1 p o i n t — A petty, noisy quarrel.... Fight....Argue.... Squabble with a boy (Q) take i t away from him.... Squabble over something (Q) shout ....Squabble over a skipping rope (Q) both want i t 0 points—Talking....With people....Making a noise 8b.QUARREL 1 p o i n t — A n angry dispute or disagreement Find f a u l t Feud Fight.... Same as squabble 0 p o i n t s — G e t angry, mad 9.RAGE 1 point—Mad (Q) r e a l l y mad....Tantrum....Temper....Violent anger.... F i t of v i o l e n t anger....Violence....An idea, etc. that i s popular f o r a short time....Great enthusiasm.... Storm.... Be wild....Be angry.... Lose one's temper.... Get i n a rage (Q) s t a r t a f i g h t 0 points—Terror....Noise....Rage up....really scared....in a bad mood ....cross 209 10.SHRIVEL 1 p o i n t — D r y up....Wither.... Shrink and wrinkle....Waste away, become useless....Make helpless or useless....Make l e s s . . . . C u r l up.... Crinkle up....Go small.... S h r i v e l up by the heat.... S h r i v e l up (Q) go dead.... S h r i v e l up l i k e a c r i s p . . . . Loss of f l e s h . . . . S h r i v e l on the f i r e (Q) be burnt up....Raisins are s h r i v e l l e d (Prunes) 0 p o i n t s — B u r n up. .. ,'Warp. .. .Piece of paper i s screwed up....Get s o f t ....Turn brown....Go rotten....When you're cold or c h i l l y ( i e shiver) 11.CONNECT 1 p o i n t — H i t c h (go, put) together.... J o i n (one thing to another).... Link (two things together).... Fasten t o g e t h e r . . . . U n i t e . — J o i n or l i n k together i n an e l e c t r i c a l circuit....Connect on the telephone (Q) put you through.... Catch a train....With something....Together....Attach ....Connect things together....Hip bone connects to the leg bone.... Wire up something, wire your speaker into tape deck 0 p o i n t s — T a l k on the phone.... Send a message.... Connect wireless with another s t a t i o n . . . . Connect two wires (Q)....Plug i t i n 12.PROVIDE 1 point—Supply.... Furnish.... Supply (or arrange) means of support.... Take care for the future....Get ready....Prepare....Deliver goods.... Save....Care for....Help.... Buy.... Provide a meal (Q) get i t ready.... Do something provided you don't do something else....Give people what they need—food and s t u f f . . . . G i v e (Q) 0 p o i n t s — L e t . . . . C a r e f u l . . . . T o receive....Plenty....Share....Provide food 13.STUBBORN 1 p o i n t — N o t wanting ( w i l l i n g ) to do i t . . . . F i x e d i n purpose or opinion ....Not giving i n to arguments or requests.... Characterized by obstinacy ....Hard to deal with or manage.... I n f l e x i b l e i n opinion or i n t e n t i o n ....Intractible....Resistant....Refuse....Won't be told....Won't do i t . . . . L i k e a mule (Q)....Won't change h i s mind 0 points—Sulky....Angry....Quarrelsome....Stern....When you're naughty (Q) doing wrong....Bad....Stupid 14.SCHOONER 1 p o i n t — A ship with two or more masts and fore-and-aft s a i l s . . . . Type of boat, ship....Yacht....Fishing boat.... Something that f l o a t s . . . . Something at sea....Goes on water 210 0 points—Steam ship....Barge .Submarine .A v e h i c l e (Q) 15. LIBERTY 1 point—Freedom.... The r i g h t or power to do as one pleases....Live free....Have your own way....Go out and enjoy yourself....Nothing to do....Take a l i b e r t y (Q) do something you're not t o l d to 0 p o i n t s — P e a c e . . . . V i c t o r y . . . . J u s t i c e . . . . Statue (of L i b e r t y ) . . . . Women's ri g h t s (Q) 16. COURTEOUS 1 p o i n t — P o l i t e . . . . Thoughtful of others....Pleasant....Nice....Generous ....Manners....Kind....When someone helps another person 0 points—Good....Proud 17.RESEMBLANCE 1 p o i n t — A s i m i l a r appearance.... Likeness.... Emphasizes looking a l i k e ....Like someone else....Like parents....Copied....Just the same.... Like a twin 0 points—Familiar....When a thing happens again.... 18.THRIVE 1 point—Grow strong....Grow vigorously.... Be successful.... Grow r i c h ....Prosper....Improve....Increase....Grow....Be healthy....When you've been i l l and you get better.... Successful.... Rich.... Carry on....Go on 0 p o i n t s — L i v e a long time....Get through an i l l n e s s . . . . 19.PRECISE 1 point—Exact....Accurate....Definite....Careful....Strict....Scrupulous .... Prim.... Just so....Neat....Precise date (Q) state a c e r t a i n date ....To mean what you say....Talk posh (Q) not l i k e a country boy.... Right on 0 points—True....Same....Just....At once....Right away.... Sure.... Definitely....Abrupt....Tidy....Ladylike....Nice....Cute....Smart.... At t h i s very moment 211 20. ELEVATE 1 p o i n t — L i f t up... .Raise... .Put i n high s p i r i t s . . . .Elate. .. .Turn up-wards ....Make s p i r i t s rise....Go up ( i n e l e v a t o r ) . . . . Gain height.... P u l l up....Carry up....Take up....Hold up 0 points—Up....High....Build up....Move....Go up and down....Keep your s p i r i t s up....Like s t a i r s (Q) 21. DWINDLE 1 point—Make or become smaller and smaller.... Shrink....Diminish... . Lessen....Decline....Wane 0 p o i n t s — 22. LAVISH 1 p o i n t — V e r y free or too free i n giving or spending....Prodigal.... Very abundant....More than enough.... Given or spent too f r e e l y . . . . Extravagant 0 points—Something posh....Luxurious 23. WHIM 1 p o i n t — A sudden fancy or notion.... Freakish of capricious idea or desire.... 0 p o i n t s — 24.SURMOUNT 1 p o i n t — R i s e above....Be above or on top of....Go up and across.... Overcome 0 p o i n t s — 25. BOMBASTIC 1 p o i n t — U s i n g bombast (high-sounding, pompous language) 0 p o i n t s — 26. RECUMBENT 1 p o i n t — L y i n g down....Reclining....Leaning 212 0 p o i n t s — 27.ENVISAGE 1 point—Foresee....Visualize....Form a mental image of 0 p o i n t s — APPENDIX E BRITISH COLUMBIA NORMS TABLES 214 BRITISH COLUMBIA NORMS TABLES fo r Wechsler I n t e l l i g e n c e Scale f o r Children-Revised Peabody P i c t u r e Vocabulary Test Slosson I n t e l l i g e n c e Test Standard Progressive Matrices M i l l H i l l Vocabulary Scale AGES 7*5, 9h, Hh Barbara J . Holmes Un i v e r s i t y o f . B r i t i s h Columbia August, 1980 215 The tables which are presented i n t h i s manual were prepared as a portion of a doc t o r a l d i s s e r t a t i o n study i n the Department of Educational Psychology at the U n i v e r s i t y of B r i t i s h Columbia. F i n a n c i a l support f o r the study was provided through.a grant from the Educational Research I n s t i t u t e of B r i t i s h Columbia and a bursary from the Canadian A s s o c i a t i o n for Educational Psychology. I wish to express my thanks to my committee chairman, Dr. Todd Rogers, who provided the methodological expertise f o r the study and a model of the unrelenting pursuit f o r excellence. I also wish to thank Dr. Buff Oldridge f o r h i s always generous support, advice and grass-roots assistance. A large measure of appreciation goes to the 44 school psychologists and psychometricians across the province whose volunteer t e s t i n g con-t r i b u t i o n s made t h i s study p o s s i b l e . This work i s dedicated to them. And thanks to my graduate student colleagues and friends f o r t h e i r w i l l i n g and multiple contributions i n many stages of the p r o j e c t . A f i n a l word of appreciation goes to 340 c h i l d r e n i n p u b l i c and independent schools throughout B.C. who gave t h e i r time and energies to helping a l l of us through f i v e test administrations. 216 .Table of Contents Page Introduction 1 Standardization Procedures 2 S t r a t i f i c a t i o n of the Sample 2 WISC-R Canadianization 3 Preparation of the Norms Tables 3 Canadian S u b s t i t u t i o n Items f o r the WISC-R 4 S t a t i s t i c a l Properties of the Tests 5 Int e r p r e t a t i o n of the Tables i n Appendix B 5 The Results of Renorming 9 References 10 Appendix A. B r i t i s h Columbia Norms Tables 11 Appendix B. P e r c e n t i l e Ranks f o r . B r i t i s h Columbia '30 i n Terms of American Norms 2 1 7 L i s t of Tables Table Page 1 R e l i a b i l i t y C o e f f i c i e n t s by Age 6 2 Standard Errors of Measurement by Age 7 3 C o r r e l a t i o n C o e f f i c i e n t s by Age 8 A B r i t i s h Columbia Standardization of the WISC-R 12 Scaled Score Equivalents of Raw Scores B B r i t i s h Columbia Standardization of the WISC-R 15 IQ Equivalents of Sums of Scaled Scores C B r i t i s h Columbia Standardization of the PPVT 18 D B r i t i s h Columbia Standardization of the SIT 21 E B r i t i s h Columbia Standardization of the .SPM .24 F B r i t i s h Columbia Standardization of the MHVS .27 G B r i t i s h Columbia Sample-Scored with American 31 Norms Introduction 218 Many of the tests used i n schools i n B r i t i s h Columbia were prepared and standardized i n the United States. The purpose of t h i s p r o j e c t was to produce p r o v i n c i a l l y representative norms f o r four commonly used i n d i v i d u a l t e s t s of i n t e l l i g e n c e : the Wechsler I n t e l l i g e n c e Scale f o r Children-Revised (WISC-R), the Peabody P i c t u r e Vocabulary Test (PPVT), the Slosson I n t e l l i g e n c e Test (SIT), and the Standard Progressive Matrices (SPM). A f i f t h t e s t , the M i l l H i l l Vocabulary Scale (MHVS) was also included. Although the MHVS i s l i t t l e known i n B.C., i t was developed as a complement to the SPM; Raven recommended, the combined use of the two tests " i n place of a s i n g l e test of 'general i n t e l l i g e n c e ' "(1960, p.3). This paper contains, i n condensed form, a d e s c r i p t i o n of the stan-d a r d i z a t i o n procedures and the s t a t i s t i c a l p roperties of the t e s t s . The B.C. norms tables for a l l f i v e t e s t s are included i n Appendix A. I n Appendix B are tables of selected standard deviations with the corres-ponding IQ scores and p e r c e n t i l e ranks for the B.C. sample when scored  using the published (American) norms. Please d i r e c t any request f o r information beyond what i s included i n t h i s manual to: B. Holmes % Education C l i n i c Faculty of Education U.B.C. Vancouver, B.C. V6T 1Z5 1 219 Standardization Procedures Description of the Population The norms i n this manual are applicable to the population of non-Native Indian1, English-speaking children at .three age levels — IH years, 9h years and 11^ years — attending public and independent schools i n Br i t i s h Columbia. The population was further restricted to exclude children enrolled i n classes for the physically handicapped, emotionally disturbed or trainable mentally retarded. Stratification of the Sample A s t r a t i f i e d sampling design was used employing the s t r a t i f i c a t i o n variables described below: Geographic region. The province of B.C. was divided into the six adminis-trative regions determined by the Ministry of Education. Community size. Three community sizes were used: A under 1,000 B 1,001 to 50,000 C over 50,000 Size of school. School size was defined by total student enrollment. Three size categories were used: I under 150 II 151 to 300 III over 300 Age. Age was defined within 3 months of the midyear. Thus the three age groups included represent the following age ranges: Native Indian children were excluded in the hope of better serving their testing needs through the provision of separate norms. A project with this purpose i s currently being planned (see More & Oldridge, 1980). WISC-R norms for Native Indian children representing three bands in south-western B.C. are currently available (Seyfort, Spreen & Lahmer, 1980). 2 7 years 3 months 0 days - 7 years 8 months 30 days 9 years 3 months 0 days - 9 years 8 months 30 days 11 years 3 months 0 days - 11 years 8 months 30 days Sex. Within each age group, the c h i l d r e n were divided equally by sex. A random sample of 340 c h i l d r e n was selected i n a manner to pro-p o r t i o n a t e l y represent the population described according to these v a r i a b l e s . WISC-R Canadianization The WISC-R was administered using the Canadian s u b s t i t u t i o n items l i s t e d on the following page. These items were recommended by Dr. P h i l i p Vernon of the U n i v e r s i t y of Calgary i n the Canadian Psychological  A s s o c i a t i o n B u l l e t i n (1977). Vernon found the rev i s e d wordings to y i e l d item pass percentages f o r a Canadian sample which are closer to the .American standardization sample than are pass percentages using the o r i g i n a l wording. Please note that the Canadian s u b s t i t u t i o n items  must be used f o r the B.C. norms tables to be app l i c a b l e . Preparation of the Norms Tables  IQs The WISC-R scaled scores and IQ scores were prepared following the procedures used by the Psychological Corporation (Wechsler, 1974, pp.21-24).. Both PPVT and SIT IQ scores were prepared i n the manner described i n the PPVT Manual (Dunn, 1965, pp. 28-29). These procedures produce deviation IQs cal c u l a t e d separately f o r each age l e v e l . This represents a change i n metric f o r SIT IQs, since they were o r i g i n a l l y reported i n r a t i o .form (Slosson, 1977). 221 P e r c e n t i l e ranks The p e r c e n t i l e ranks published i n the WISC-R Manual (p. 25) may be applied to the B.C. WISC-R norms. For a l l other t e s t s , the p e r c e n t i l e ranks are included i n the tables. S t a t i s t i c a l Properties of the 'Tests R e l i a b i l i t y c o e f f i c i e n t s , i n t e r c o r r e l a t i o n s and standard errors of measurement for a l l tests are presented i n Tables 1 through 3. Below each table i s information regarding the data included i n the c a l c u l a t i o n s . .Interpretation of the Tables i n Appendix B The tables i n Appendix B were prepared i n response to a request from p r a c t i c i n g school psychologists. These tables are to be used when the t e s t s have been scored using the o r i g i n a l norms provided i n the r e s -pective test manuals. The i n c l u s i o n of p e r c e n t i l e ranks allows :for i n t e r p r e t a t i o n of a score i n terms of i t s rank p o s i t i o n within the B.C. population. Examination of these tables shows co n s i s t e n t l y higher means on a l l tests for the B.C. sample than f o r the respective-standardization groups. The varying IQ - p e r c e n t i l e r e l a t i o n s h i p s across t e s t s are a r e s u l t of v a r i a t i o n s i n the shapes of .the t e s t score d i s t r i b u t i o n s and i n "their standard deviations. 222 Table 1 Re l i a b i l i t y Coefficients by Age Test Age 9h Ilk WISC-R Information Similarities Arithmetic Vocabulary Comprehension Picture Completion Picture Arrangement Block Design Object Assembly Coding Verbal IQ Performance IQ F u l l Scale IQ PPVT SIT SPM MHVS ,69 .68 .72 .59 .66 .61 .75 .85 .63 ,86 .88 .86 .88 .78 .89 . 7 6 ,68 .77 .65 .75 .98 .68 .55 .81 .67 .93 .83 .88 .87 .79 .92 ..83 .86 .80 .70 .82 .71 .67 .42 .77 . 62 .93' .82 .87 ..87 .88 .83 .88 Note: The r e l i a b i l i t y coefficients for a l l tests are split-half correlations corrected by the Spearman-Brown formula. Since this type of r e l i a b i l i t y is not appropriate for use with Coding, there are no r e l i a b i l i t i e s reported for this test. The coefficients of the WISC-R IQ Scales were calculated from the formula for the r e l i a b i l i t y of a composite group of tests (Guilford, 1954, p, 393). 6 223 Table .2 Standard Errors of Measurement by Age. Age Test 73s 9h WISC-R Information 1.63 1.75 1.12 S i m i l a r i t i e s 1.75 1.46 1.30 Arithmetic 1.52 1.72 1.63 Vocabulary 1.86 1.46 1.26 Comprehension 1.68 «43 1.62 Pi c t u r e Completion 1.87 1.74 1.63 Pi c t u r e Arrangement 1.51 2.05 .2.30 Block Design 1.10 1.35 1.47 Object Assembly 1.81 1.72 1.82 Coding Verbal IQ .5.39 4.07 4.08 Performance IQ 4.98 6.23 6.61 F u l l Scale IQ 5.16 5.41 5.63 PPVT 5.20 5.41 5.41 SIT 7.04 6.87 .5.20 SPM 2.40 2.28 .2.70 MHVS 1.98 "2.23 2.18 Note: The standard errors of measurement are i n scaled score u n i t s f o r the WISC-R te s t s ; i n IQ units f o r the WISC-R, PPVT, and SIT IQ scales; and i n raw score units f o r the SPM and MHVS. 7 224 Table 3 Correlation Coefficients by Age WISC-R Verbal IQ Perfor-mance IQ F u l l Scale IQ PPVT IQ SIT IQ SPM PPVT •59 .32 .56 AGE 71s SIT SPM .77 ...26 • .35 .42 .68 .40 .62 .25 .32 MHVS .72 .32 .64 .58 .72 .....24 PPVT .64 .46 .62 AGE 9h SIT SPM .65 .43 .54 • ..53 .67 .52 .62 .40 .42 MHVS .72 ..35 .61 .64 .59 ..31 PPVT .70 .38 .62 AGE llh SIT SPM .82 .45 ..57 .54 .79. .56 .62 .34 .54 MHVS .81 .48 .75 .72 .77 ..44 The correlation coefficients were computed using IQ PPVT and SIT and raw scores for the SPM and MHVS. scores for the WISC--R, .8 The Results of Renorming 225 I n t e l l i g e n c e tests are t r a d i t i o n a l l y scaled i n a manner which assigns the mean score a value of 100 and the standard deviation a value of 15 or 16. Included i n the B.C. standardization procedure was the re-alignment of the IQ test score scales f o r three t e s t s (WISC-R, PPVT, SIT) to mean 100 and standard deviation 15. (The SPM and MHVS were retained as raw score scales with new p e r c e n t i l e ranks for B.C.) The B.C. sample scored higher and with less v a r i a b i l i t y than the American standardization samples using American norms; therefore the B.C. r e s c a l i n g procedure r e s u l t e d i n lowering and spreading out the score scales. The r e s u l t i s that below average students w i l l score lower with.B.C. than American norms, while students who are much above average w i l l score the same or even higher with B.C. norms. 9 226 References Dunn, L.M. Expanded manual for the Peabody P i c t u r e Vocabulary Test. C i r c l e Pines, Minn.: American Guidance Service, 1965. More, A.J. & Oldridge, B. An approach to non-discriminatory assessment of Native Indian c h i l d r e n . B.C. Journal of Special Education, 1980, 4(1)-, 51-59. Raven, J. Guide to the Standard Progressive Matrices. Sets A,B,C,D and E. London, England: H.K. Lewis, 1960. Seyfort, B., Spreen, 0. & Lahmer,. A c r i t i c a l look at the WISC-R with Native Indian c h i l d r e n . A l b e r t a Journal of Educational Research, . 1980, 26(1) , .14-24. Slosson, R.L. Slosson I n t e l l i g e n c e Test (SIT) for Children and Adults. East Aurora, N.Y.: Slosson Educational P u b l i c a t i o n s , Inc., 1977. Vernon, P.E. F i n a l report on modifications of WISC-R for Canadian use. Canadian Psychological A s s o c i a t i o n B u l l e t i n , .1977., 5.(1), 5-7.. Wechsler, D. Manual for the Wechsler I n t e l l i g e n c e Scale f o r Children- Revised. N.Y.: Psychological Corporation, .1974. 10 227 Appendix A Bri t i s h Columbia Norms Tables 11 7 yrs; 3 mos. 0 days through 7 yrs. 8 mos. 30 days Table A B r i t i s h Columbia Standardization of the WISC-R Scaled Score Equivalents of Raw Scores VERBAL PERFORMANCE Scaled Score 1 0-2 0 0 0-5 0-1 2 3 1 i-2 6-7 2 3 4 2 3-4 8 3-4 4 - 3 5 9-H 5 5 5 4 • 12-13 6 6 6 5 6 14-15 7-8 7 8 9 10 11 i2 13 14 15 16 17 18 19 Infor-mation S i m i l -a r i t i e s A r i t h -metic Vocab-ulary 7 8 9 io 11 12 13 14 15 16 17 18-30 6-7 8 9 10 11 12 13 14 15 16 17 18 19-30 8 9 10 11 12 13 14 15-i8 27 28-29 30-31 32-33 34-35 36-64 Compre-hension 16 9 7 17-18 10 8 i9-20 11 9 21 12-i3 10 22 14 11 23-24 15 12 25-26 16 13 17 18 19-20 21-22 23 24-34 Scaled Score 1 2 3 4 5 6 14 15 16 17 i8 19 Picture Com-p l e t i o n P i c t u r e Arrange-ment Block Design Object Assembly 0-4 0-1 0-1 0-3 5-6 2 2 4 7-8 3-4 3 5 9 5 4 6-8 10 6-8 - 9-11 11 9-12 5 12-13 12 13-16 6-9 14 13 17-18 10-11 15-16 14 19-21 12-14 17 15 22-23 .15-18 18-19 16 24-26 19-22 20-21 17 27 23-26 22 i8 28-29 27-31 23 19 30-32 32-36 24 - 33-35 37-42 25-26 20 36-38 43-46 27 21 39-41 47-50 28 22 42 51 29 23-26 43-48 52-62 30-33 Coding 0-20 21 .22 23 24-26 27-28 29-32 33-35 36-40 41-42 43-44 45 46 47 48 49 50 Scaled Score 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ts3 OO 9 yrs. 3 mos. 0 days through 9 y r s i 8 mos. 30 days Table A(continued) B r i t i s h Columbia Standardization of the WISC-R Scaled Score Equivalents of Raw Scores VERBAL PERFORMANCE Picture Picture Scaled Infor- S i m i l - A r i t h - Vocab- Compre- Scaled Com- Arrange— Block Object Scaled Score mation a r i t i e s metic ulary hension Score p l e t i o n ment Design Assembly Coding Score 1 0-4 0-2 0-2 0-14 0-4 i 0-8 0-3 0-7 0-6 0-20 1 2 5 3-4 3-4 15-17 5-6 2 9-10 4-6 8-9 7-8 21-22 2 3 6-7 5-6 5-6 18-20 7-8 3 11 7-10 10-11 9-10 23-24 3 4 8 7 7 21 9-10 4 i2 11-14 12 11-12 25-26 4 5 9 8 8 22 11 5 . 13 15-16 13-14 13-14 27 5 6 10 9 9 23 12 6 14 17-21 15 15-16 28-29 6 7 i i i o 10 24 13 7 15 22-23 16-19 17 30 7 8 - - 11 25-26 14 8 16 24 20-23 18-20 31-32 8 9 12 11 - 27 15 9 17 25-27 24-27 21 33-35 9 10 13 12-13 12 28-29 16-17 10 18 28-30 28-30 22-23 36-38 10 11 14 14 - 30-31 18 11 19 31 31-34 . 24 39-41 11 12 15 15-16 13 32-33 19 12 - 32-33 35-37 25 42-44 12 13 16 17 - 34-35 20 13 20 34-36 38-41 - 45-47 13 14 17-18 18-19 14 36-37 21 14 21 37 42-47 26-27 48-51 14 15 19 20 - 38-40 22 15 22 38-39 48-49 28 52 15 16 20 21-22 15 41-43 23-25 16 - 40-43 50-52 29 53-62 16 17 21 23-24 i6 44 26 17 23 44 53-55 30 63-65 17 18 22 25-26 17 45 27 18 24 45 56-57 31 66-68 18 19 23-30 27-30 i s 46-64 28-34 19 25-26 46-48 58-62 32-33 69-93 19 M ro 11 yrs. 3 mos. 0 days through l l yrs. 8 mos. 30 days table A(continued) B r i t i s h Columbia Standardization of the WISC-R Scaled Score Equivalents of Raw Scores VERBAL PERFORMANCE Picture Picture Scaled Infor- S i m i l - A r i t h - Vocab- Compre- Scaled Com- Arrange- Block Object Score mation a r i t i e s metic ulary hension Score p l e t i o n ment Design Assembly Coding 1 0-6 0-4 0-4 0-16 0-5 1 0-10 0-4 0-13 0-10 0-22 2 7 5 5-6 17-18 6-7 2 11-12 5 14-15 11-12 23-25 3 8 6 7-8 19-20 8-9 3 13 -14 6-7 16-17 13-14 26-28 4 9 ' 7 9 2i-22 10 4 15 8-11 18-20 15-16 29-31 5 10 8 io 23-24 11-13 5 - 12-19 21-23 17-18 32-34 6 11 9-10 11 25-26 14-15 6 16 20-25 24-26 19 35-37 7 12-13 11-12 12 27-28 16 7 17 26-27 27-28 20-21 38-40 8 14 13-14 13 29-30 17 8 18 28 29-32 22-23 41-43 9 15 15 - 31-33 18-19 9 19 29-30 33-35 24 44-46 10 16-17 16-17 i4 34-35 20 10 20 31-32 36-38 25 47-48 11 18 18-19 - 36-37 21 11 2l 33 39-41 26-27 49-51 12 19 20 15 38-39 22-23 12 22 34-36 42-45 28 52-55 13 20 21 - 40-42 24-25 13 - 37 46-48 29 56-58 14 21 22 16 43 26 14 23 38-39 49-54 30 59-63 15 22-23 23 - 44 27 15 - 40 55-57 31 64-65 16 24 24 17 45 - 16 - 41-43 58 32 66-72 17 25 25-26 - 46-47 28 17 24 44-45 59 - 73-75 18 26 27 18 48-49 29 18 25 46-47 60 33 76-78 19 27-30 28-30 — 50-64 30-34 19 26 48 61-62 79-93 Scaled Score ro o T a b l e B B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e W I S C - R I Q E q u i v a l e n t s o f Sums o f S c a l e d S c o r e s Sum o f S c a l e d S c o r e s IQ V E R B A L Sum o f S c a l e d S c o r e s IQ Sum o f S c a l e d S c o r e s I Q 41 88 81 1 4 1 42 89 82 143 4 3 9 0 83 144 44 92 84 145 45 93 85 147 46 94 86 148 47 96 87 149 • 48 97 88 151 9 45 49 98 89 152 10 46 5 0 1 0 0 90 154 11 48 51 101 91 .155 12 49 52 102 13 5 0 53 104 14 52 5 4 105 15 5 3 5 5 107 16 5 4 5 6 - 1 0 8 17 56 57 109 18 57 5 8 111 19 5 8 59 112 20 60 60 1 1 3 21 61 61 115 22 62 62 116 23 64 6 3 117 24 65 64 1 1 9 25 66 65 120 26 68 66 121 27 69 67 1 2 3 28 70 68 1 2 4 29 72 69 125 30 7 3 70 127 31 74 71 1 2 8 32 7 6 72 129 .33 77 7 3 131 34 78 74 132 35 80 75 133 36 81 76 135 37 82 77 136 38 84 78 137 39 85 79 139 4 0 86 80 .140 T a b l e B ( c o n t i n u e d ) B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e W I S C - R IQ E q u i v a l e n t s o f Sums o f S c a l e d S c o r e s PERFORMANCE Sum o f Sum o f S c a l e d S c a l e d . S c o r e s 10 S c o r e s I Q 51 101 52 103 5 3 104 54. 106 15 45 55 108 16 47 56 109 17 4 8 57 111 18 50 58 112 19 52 59 114 20 53 60 115 21 55 61 117 22 56 62 118 23 58 6 3 120 24 59 64- 122 25 61 65 123 26 62 66 125 27 64 67 • 126 28 66 68 128 29 67 69 129 30 69 70 131 31 70 71 132 32 72 72 134 33 73 73 136 34 75 74 137 35 76 75 139 36 78 76 140 37 80 77 142 38 81 78 143 39 83 79 145 40 84 80 146 41 86 81 148 42 87 82 150 4 3 89 83 151 44 90 84 153 45 92 85 154 46 94 86 155 47 95 48 97 49 98 50 100 T a b l e B ( c o n t i n u e d ) B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e W I S C - R 233 I Q E q u i v a l e n t s o f Sums o f S c a l e d S c o r e s Sum o f Sum o f — F U L L S C A L E Sum o f Sum o f S c a l e d S c a l e d S c a l e d S c a l e d S c o r e s IQ S c o r e s IQ S c o r e s IQ S c o r e s I Q 61 68 101 101 141 134 62 69 102 101 142 134 63 69 103 102 1 4 3 135 64 70 1 0 4 1 0 3 144 1 3 6 65 71 105 104 145 137 ' 27 40 66 72 1 0 6 105 146 138 67 73 107 106 147 1 38 28 41 68 74 108 106 148 1 3 9 29 42 69 74 109 107 149 1 4 0 30 42 70 75 1 1 0 108 150 "141 31 43 71 76 111 109 151 142 32 44 72 77 112 1 1 0 152 142 33 45 73 78 113 .110 153 143 34 46 74 7 8 114 111 154 144 35 46 75 79 115 1 1 2 155 145 36 47 76 80 116 113 156 146 37 4 8 77 81 117 114 157 147 38 49 78 82 1 18 115 158 147 39 5 0 79 82 119 1 1 5 159 148 40 50 80 8 3 1 2 0 116 1 6 0 149 41 51 81 84 121 117 161 1 5 0 42 52 82 85 122 1 18 162 151 43 5 3 8 3 86 123 119 163 152 44 54 84 87 124 1 2 0 164 152 45 55 85 88 125 1 2 0 165 153 46 55 86 88 126 121 166 1 5 4 47 56 87 89 127 .122 167 155 48 57 88 9 0 128 123 1 68 156 -49 5 8 89 91 129 124 169 156 5 0 59 90 92 1 3 0 124 1 7 0 157 51 60 91 92 131 125 171 158 52 60 92 93 132 126 172 1 5 9 5 3 61 93 94 1 3 3 127 173 1 6 0 5 4 62 94 95 134 128 55 63 95 96 .135 128 56 64 96 96 136 1 2 9 57 64 97 97 137 1 3 0 58 65 98 98 138 131 59 66 99 99 139 132 60 67 100 1 0 0 1 4 0 133 17 7 yrs. 3 mos. through Table C n „ 7 yrs. 9 mos. B r i t i s h Columbia Standardization of the Peabody Picture Vocabulary Test IQ and Percentile Equivalents of Raw Scores Raw Score IQ % i l e Raw Score IQ % i l e 71 105 62 72 107 67 73 108 71 34 40 74 110 75 35 42 75 112 78 36 44 76 114 82 37 45 77 116 84 38 47 78 117 85 39 49 79 119 -&r-40 51 80 121 91 41 52 81 122 92 42 54 82 124 93 43 56 83 126 94 44 58 84 128 95 45 59 85 130 96 46 61 86 131 97 47 63 87 133 99 48 65 88 135 99.6 49 66 89 136 50 68 90 138 51 70 91 140 52 72 92 142 53 73 93 144 54 75 1 94 145 55 77 2 95 147 56 79 , 4 96 149 57 80 6 97 150 58 82 10 98 152 59 84 14 99 154 60 86 18 100 156 61 88 21 101 158 62 89 29 102 159 63 91 .38 103 160 64 93 -•41 65 94 44 66 96 -hi 67 98 50 68 100 :53 69 102 ;56 70 103 58 18 235 9 yrs. 3 mos. through Table C(continued) 9 y r s < 9 m 0 S -B r i t i s h Columbia Standardization of the Peabody Picture Vocabulary Test IQ and Percentile Equivalents of Raw Scores Raw Score IQ % i l e Raw Score IQ % i l e 81 98 JiO 82 99 50 83 101 51 84 103 56 85 104 • 61 46 40 86 106 66 47 42 87 108 72 48 43 88 109 76 49 45 89 111 79 50 47 90 112 •80 51 48 91 114 83 52 50 92 116 86 53 52 93 117 88 54 53 94 119 89 55 55 95 121 90 56 56 96 122 93 57 58 97 124 96 58 60 98 126 .97 59 62 2 99 127 98 60 63 .2 100 129 98 61 65 2 .101 131 99 62 66 .3 102 132 63 68 4 103 134 64 70 4 104 136 65 71 5 105 137 66 73 . 5 106 139 67 75 6 107 140 68 76 -6 108 142 69 78 7 109 144 70 80 8 110 145 71 81 9 111 147 72 83 9 112 149 73 84 10 113 150 74 86 12 114 152 75 88 16 115 154 76 89 21 116 155 77 91 26 117 157 78 93 .30 118 159 79 94 32 119 160 80 96 35 19 Table C(continued) B r i t i s h Columbia Standardization of the Peabody Picture Vocabulary Test IQ and Percentile Equivalents of Raw Scores 236 11 yrs. 3 mos. through 11 yrs., 9 mos. % i l e Raw Score IQ % l l e Raw Score IQ % i l e 81 85 12 111 129 97 82 87 18 112 130 98 83 88 21 113 132 99 84 90 23 114 133 85 91 24 115 135 86 93 26 116 136 87 94 31 117 138 88 96 38 118 139 89 97 45 119 141 • 90 98 51 120 142 91 100 56 121 144 92 101 60 122 145 93 103 64 123 146 94 104 65 124 148 95 106 66 125 149 96 107 68 126 151 97 109 76 127 152 98 110 74 128 154 99 112 77 129 155 100 • 113 80 130 • 157 101 114 84 131 158 102 116 87 132 160 103 117 88 104 119 •88' 105 120 89 106 122 91 107 123 93 108 125 95 109 126 96 110 128 97 20 Table D B r i t i s h Columbia Standardization of the Slosson Intelligence Test IQ and Percentile Equivalents of Raw Scores 23 7 7 yrs. 3 mos. through 7 yrs. 9 mos. . Raw Score IQ % i l e Raw Score IQ % i l e 111 112 78 112 115 •84 113 118 88 84 40 114 120 91 85 42 115 123 94 86 44 116 126 96 87 47 117 129 97 88 50 118 131 99 89 52 119 134 90 55 120 137 91 58 121 140 92 61 122 142 93 63 123 .145 94 66 124 148 95 69 2 125 150 96 72 3 126 153 97 74 5 127 156 98 77 6 128 159 99 - 80 8 .129 160 100 82 10 101 85 13 102 88 19 103 91 27 104 93 36 105 96 •42 106 99 46 107 102 . 53 108 104 59 109 107 68 110 110 74 21 238 9 yrs. 3 mos. Table D(continued) through 9 yrs.. 9 mos. B r i t i s h Columbia Standarization of the Slosson Intelligence Test IQ and Percentile.; Equivalents of Raw Scores Raw Score IQ % i l e Raw Score IQ % i l e 121 106 64 122 108 70 123 110 74 124 112 78 125 114 82 126 116 87 127 118 90 88 40 128 120 90 89 42. 129 122 91 90 44 130 124 93 91 46 131 126 95 92 48 132 128 96 93 50 133 130 97 94 52 134 132 99 95 54 135 134 96 56 136 136 97 58 137 138 98 60 138 140 99 62 139 142 100 64 140 144 101 66 141 146 102 68 142 148 103 70 143 150 104 72 144 152 105 74 2 145 154 106 76 3 146 156 107 78 4 147 158 108 80 5 148 160 109 82 8 110 84 11 111 86 14 112 88 21 113 90 28 114 92 34 115 94 40 116 96 43 117 98 45 118 100 47 119 102 52 120 104 58 22 239 11 yrs. 3 mos. through Table D(continued) U y r s > 9 m o s > B r i t i s h Columbia Standardization of the Slosson Intelligence Test •IQ and Percentile Equivalents of Raw Scores Raw Score IQ % i l e Raw Score IQ % i l e Raw Score IQ % i l e 111 73 141 118 91 112 74 2 142 119 92 113 76 4 143 120 93 114 77 6 144 122 94 115 79 7 145- 124 96 116 80 9 146 125 96 117 82 12 147 126 97 118 83 14 148 128 97 89 40 119 85 .16 149 129 97 90 42 120 86 19 150 131 98 91 43 121 88 22 151 132 98 92 45 122 89 24 152 134 93 46 123 91 26 153 135 94 48 124 92 28 154 137 95 49 125 94 33 155 .138 96 51 126 95 36 156 140 97 • 52 127 97 40 157 141 98 54 128 98 44 158 143 99 55 129 100 48 159 144 100 56 130 101 50 160 146 101 58 131 103 53 161 147 102 60 132 104 58 162 149 103 61 133 106 62 163 150 104 62 134 107 66 164 152 105 64 135 109 70 165 153 106 65 136 110 74 166 155 107 67 137 112 77 167 156 108 68 138 113 ' 82 168 158 109 70 139 114 86 169 159 110 71 140 116 88 170 161 23 240 7 y r s . 3 m o s . t h r o u g h T a b l e E 7 y r s . ! 9 m o s . B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n , o f t h e S t a n d a r d P r o g r e s s i v e M a t r i c e s P e r c e n t i l e E q u i v a l e n t s o f Raw S c o r e s Raw S c o r e % i l e 11 6 12 7 13 12 14 17 15 21 16 27 17 35 18 4 0 19 46 20 51 21 58 22: 63 23 65 24 68 25 72. 26 76 27 7 8 28 79 29 8 1 30 84 31 87 32 9 0 33 92 34 93 35 9 4 3 6 97 ' 37 97 38 98 39 98 40 99 41 9 9 . 5 24 241 9 y r s . 3 m o s . t h r o u g h T a b l e E ( c o n t i n u e d ) g y r s > q m o s < B r i t i s h C o l u m h i a S t a n d a r d i z a t i o n o f t h e S t a n d a r d P r o g r e s s i v e M a t r i c e s P e r c e n t i l e E q u i v a l e n t s o f Raw S c o r e s Raw S c o r e % i l e 16 1 17 2 18 3 19 • 5 20 9 21 13 22 17 23 20 24 22 .. 25 26 26 2 9 27 3 0 28 32 29 3 6 30 42 31 45 32 49 3 3 5 3 3 4 57 35 62 3 6 67 37 ' 73 38 77 39 82 40 86 4 1 89 42 92 43 94 44 9 4 45 95 46 96 47 98 25 242 11 y r s . 3 m o s . „ , , -, r , / • • J N t h r o u g h T a b l e E ( c o n t x n u e d ) n y r s > 9 \ q s B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e S t a n d a r d . P r o g r e s s i v e M a t r i c e s P e r c e n t i l e ; E q u i v a l e n t s o f Raw S c o r e s Raw S c o r e . % i l e 20 1 21 1 22 1 23 2 24 2 25 2 26 3 27 5 28 7 29 9 3 0 11 31 15 32, 18 33 20 34 27 3 5 35 36 4 0 37 46 38 5 3 39 58 40 62 41 67 42 74 4 3 82 44 84 45. 87 46 90 4 7 92 48 95 49 98 26 243 7 y r s . 3 mos T a b l e F t h r o u g h 7 y r s . 9 mos B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e M i l l H i l l V o c a b u l a r y S c a l e , S e t A p l u s S e t B P e r c e n t i l e E q u i v a l e n t s o f R a w S c o r e s T o t a l Raw-S c o r e % i l e 6 7 1 8 4 9 8 10 1 1 11 15 12 22. 13 27 14 34 15 4 4 16 54 17 63 18 7 3 19 82 20 87 21 92 22 96 23 97 24 99 25 9 9 . 3 26 9 9 . 6 27 Table F(continued) Bri t i s h Columbia Standardization of the M i l l H i l l Vocabulary Scale, Set A plus Set B Percentile Equivalents of Raw Scores Total Raw Score % i l e 6 7 8 9 2 10 2 11. 2' 12 3 13 3 14. 4 15 5 16 7 17 8 18 1.4 19 19 20 24 21 32 22 38 23 44 24 52 25 60 26 66 27 73 28 78 29 82 30 87 31 92 32 96 33 97 34 99 244 9 yrs. 3 mos through 9 yrs. 9 mos 28 T a b l e F ( c o n t i n u e d ) B r i t i s h C o l u m b i a S t a n d a r d i z a t i o n o f t h e M i l l H i l l V o c a b u l a r y S c a l e , S e t A p l u s S e t B P e r c e n t i l e E q u i v a l e n t s o f Raw S c o r e s T o t a l Raw S c o r e % i l e 13 : 2 - 14- 2 15 3 16 4-17 4 18 5 19 7 20 9 21 "11 22 14 23 18 24 21 25 24 26 30 27 37 28 42 29 47 30 52. 31 62 32 71 33 77 34 8 3 35 89 36 93 37 94 38 96 39 98 40 99 41 9 9 . 5 245 11 y r s . 3 mos t h r o u g h 11 y r s . 9 mos Appendix B P e r c e n t i l e Ranks for B r i t i s h Columbia i n Terms of American Norms B r i t i s h Columbia Sample Scored with American Norms Relation of IQs to Standard Deviations and Percentile Ranks AGE lh Number of SDs from the Mean WISC-R PPVT IQ SIT IQ Number of SDs from the Mean Verbal IQ Perfor-mance IQ F u l l Scale IQ IQ Score % i l e c I Q Score % i l e IQ Score % i l e IQ Score % i l e IQ Score /Sile +3 149 148 99 144 149 151 +3 +2.5 142 141 ;98 138 99 142 99.9 145 99.9 +2.5 +2 135 99 135 96 132 98 134 95 139 97 +2 +1.5 128 96 128 90 126 92 127 90 133 94 +1.5 +1 121 85 122 82 120 81 119 74 .127 84 +1 + .5 114 75 115 68 114 70 112 65 121 72 + .5 0 107 50 109 , 50 108 50 104 50 115 50 0 - .5 100 33 103 •27 102 34 96 .33 109 34 -.5 -1 93 20 96 16 96 14 89 12 103 15 -1 -1.5 86 6 90 4 90 6 81 2 97 5 -1.5 -2 79 2 83 1 84 .1 74 91 2 -2 -2.5 72 77 78 66 85 1 -2.5 -3 65 70 72 .59 79 -3 31 Table G(continued) B r i t i s h Columbia Sample Scored with American Norms Relation of IQs to Standard Deviations and Percentile Ranks AGE 9h Number of SDs from :the Mean WISC -R PPVT IQ SIT IQ Number of SDs from the Mean Verbal IQ Perfor- j mance IQ F u l l Scale IQ IQ Score % i l e IQ Score % i l e IQ Score % i l e IQ Score % i l e IQ Score % i l e +3 142 148 146 154 151 +3 +2.5 136 99 141 139 99 147 144 +2.5 +2 130 97 135 98 133 96 140 98 138 97 +2 +1.5 124 92 128 94 126 90 133 '94 131 90 +1.5 +1 118 82 122 85 120 83 126 83 125 85 +1 + .5 112 69 115 67 113 67 119 66 118 68 + .5 0 106 50 109 50 107 50 112 50 112 50 •+ .5 100 '32 103 32 101 30 105 27 106 "35 + .5 +1 94 15 96 18 94 14 98 11 99 15 +1 +1.5 88 . 7 90 6 88 3 91 7 93 3 +1.5 +2 82 1 83 3 81 . 1 84 4 86 1 +2 +2.5 76 77 75 77 3 80 +2.5 +3 70 70 68 70 .1. 73 +3 32 Table G(continued) B r i t i s h Columbia Sample Scored with American Norms Relation of IQs to Standard Deviations and Percentile Ranks AGE Ilk WISC -R Number of Perfor- . F u l l Number of SDs from Verbal mance Scale PPVT SIT SDs from the Mean IQ IQ IQ IQ IQ the Mean IQ IQ IQ IQ IQ Score % i l e Score % i l e Score % i l e Score % i l e Score % i l e +3 141 150 143 154 156 +3 +2.5 134 143 137 147 149 99 +2.5 +2 128 99.6 136 99 130 98 139 98 141 98 +2 +1.5 121 96 129 94 123 94 132 91 134 95 +1.5 +1 115 •87 122 87 .117 84 124 81 126 89 +1 + .5 108 69 115 72 110 66 117 .67 119 72 + .5 0 102 50 108 50 104 50 109 50 111 50 0 - .5 96 32 101 29 98 24 101 24 103 34 - .5 -1 89 14 94 17 .91 12 94 9 96 19 -1 -1.5 83 6 87 6 85 •6 86 4 88 7 -1.5 -2 76 4 80 1 78 .2 79 3 81 2 -2 -2.5 70 1 73 72 1 71 2 73 1 -2.5 -3 63 66 65 64 1 66 -3 33 APPENDIX F ANOVA AND COCHRAN 251 Table FI Summary of Analysis of Variance for WISC-R Subtest and Scaled Score Means by Age Source df SS MS Scaled Scores: Information Between Within 2 337 2 . 0 6 3 0 4 2 . 6 8 1 . 0 3 9 . 0 3 0 . 1 1 S i m i l a r i t i e s Between Within 2 3 3 7 1 . 0 2 3 0 6 3 . 9 5 0 . 5 1 9 . 0 9 0 . 0 6 Arithmetic Between Within 2 3 3 7 0 . 6 0 2 8 8 5 . 3 6 0 . 3 0 8 . 5 6 0 . 0 4 Vocabulary Between Within 2 337 0 . 6 9 2 8 8 9 . 8 1 0 . 3 5 8 . 5 8 0 . 0 4 Comprehension Between Within 2 3 3 7 0 . 9 0 2 9 8 5 . 0 5 0 . 4 5 8 . 8 6 0 . 0 5 P i c t u r e Completion Between Within 2 337 1 2 . 2 0 2 9 8 0 . 3 1 6 . 1 0 8 . 8 4 0 . 6 9 P i c t u r e Arrangement Between Within 2 3 3 7 0 . 1 6 3 0 8 7 . 7 6 0 . 0 8 9 . 1 6 0 . 0 1 Block Design Between Within 2 3 3 7 2 . 7 8 3 0 4 1 . 0 0 1 .39 9 . 0 2 0 . 1 5 Object Assembly Between Within 2 337 0 . 6 0 2 9 8 1 . 3 6 0 . 3 0 8 . 8 5 0 . 0 3 Coding Between 2 337 1 . 3 2 3 0 9 4 . 2 3 0 . 6 6 9 . 1 8 0 . 0 7 252 . 7 5 F 2 , - " X - 3 9 Table FI continued Source df SS MS Sums of Scaled  Scores: Verbal Between Within 2 3 3 7 1 7 . 7 3 4 2 4 4 0 . 9 2 8 . 8 7 1 2 5 . 9 4 0 . 0 7 Performance Between Within 2 337 3 6 . 0 5 3 1 4 3 2 . 3 7 1 8 . 0 3 9 3 . 2 7 0 . 1 9 F u l l Scale Between Within 2 337 8 0 . 3 9 1 1 2 9 6 5 . 3 8 4 0 . 2 0 3 3 5 . 2 1 0 . 1 2 Table F2 C Values for Cochran's Test f o r Homogeneity of Variance C=(maximum variance/sum of variances) Scaled Scores: Information 0.35 S i m i l a r i t i e s 0.35 Arithmetic 0.35 Vocabulary 0.34 Comprehension 0.35 Picture Completion 0.36 Pi c t u r e Arrangement 0.34 Block Design 0.35 Object Assembly 0.34 Coding 0.34 Sums of Scaled Scores: Verbal 0.35 Performance 0.36 F u l l Scale 0.36 Note: A l l C non-significant. APPENDIX G GRAPHIC EQUIPERCENTILE EQUATING PROCEDURE PPVT IQ TO WISC-R VERBAL IQ, AGE7% 255 Table GI D i s t r i b u t i o n of PPVT IQ Scores and WISC-R Verbal IQ Scores, Age lh Cumulative Percentage WISC-R Cumulative Percentage PPVT Frequency Frequency Below VIQ Frequency Frequency Belo\ 137 1 114 99.1 129 3 114 97.4 135 1 113 98.3 125 1 111 96.5 133 2 112 96.5 124 2 110 94.7 130 1 110 95.6 123 2 108 93.0 128 2 109 93.9 121 2 106 91.2 124 2 107 92.1 120 2 104 89.5 121 3 105 89.5 119 2 102 87.7 119 5 102 85.1 117 2 100 86.0 117 1 97 84.2 116 1 98 85.1 115 1 96 83.3 115 1 97 84.2 114 4 95 79.8 113 4 96 80.7 112 4 91 76.3 112 6 92 75.4 110 4 87 72.8 109 2 86 73.7 108 5 83 68.4 108 7 84 67.5 107 4 78 64.9 107 2 77 65.8 105 7 74 58.8 105 3 75 63.2 103 3 67 56.1 104 3 72 60.5 101 1 64 55.3 103 7 67 54.4 100 6 63 50.0 101 4 62 50.9 98 1 57 49.1 100 6 58 45.6 96 4 56 45.6 99 5 52 41.2 94 4 52 42.1 96 5 47 36.8 93 3 48 39.5 94 3 42 34.2 91 4 45 36.0 93 5 39 29.8 89 16 41 21.9 92 4 34 26.3 87 3 25 19.3 90 3 30 23.7 86 4 22 15.8 89 2 27 21.9 84 3 18 13.2 88 2 25 20.2 82 7 15 7.0 86 2 23 18.4 80 2 8 5.3 85 1 21 17.5 79 3 6 2.6 84 2 20 15.8 77 1 3 1.8 81 4 18 12.3 75 1 2 .9 80 3 14 9.6 70 1 1 78 1 11 8.8 77 4 10 5.3 76 2 6 3.5 74 3 4 .9 70 1 1 256 80 90 100 110 120 WISC-R VERBAL PPVT IQ 130 !Q 140 Figure GI. Relative cumulative frequencies for PPVT IQs and WISC-R Verbal IQs, age 7%. 257 Table G2 Equipercentile Points for PPVT IQ and WISC-R Verbal IQ from Graphic Procedure P e r c e n t i l e PPVT WISC-R Per c e n t i l e PPVT WISC-R Rank IQ VIQ Rank IQ VIQ 0.5 73.5 71.5 93.0 125.2 123.0 0.7 74.3 72.4 95.0 128.0 124.7 1.0 75.3 73.3 97.0 131.5 128.3 1.4 76.2 74.0 98.0 134.3 131.8 1.8 76.8 74.7 98.4 135.5 132.2 2.0 77.3 74.9 98.8 137.0 133.7 3.0 78.5 75.6 99.0 138.2 134.8 4.0 79.6 76.3 5.0 80.4 76.8 8.0 82.5 78.5 12.0 84.5 81.3 17.0 87.0 85.0 20.0 87.3 87.5 24.0 87.8 90.2 30.0 89.8 93.5 34.0 92.0 95.3 40.0 94.3 98.0 46.0 96.5 100.5 50.0 98.5 102.0 54.0 100.5 103.3 60.0 103.5 105.3 66.0 106.7 107.0 70.0 108.8 108.5 74.0 111.0 110.0 78.0 113.3 111.8 82.0 115.7 114.0 85.0 117.8 115.8 88.0 120.3 117.7 90.0 122.0 119.3 258 80 90 100 110 120 130 PPVT IQ Figure G2. Hand-graphed equ i p e r c e n t i l e conversion l i n e (PPVT IQ to WISC-R Verbal IQ, age Ih.)• APPENDIX H NORMALIZED LINEAR EQUATING RESULTS 2 6 0 Table Hi Equivalent Scores Normalized PPVT IQs to Normalized WISC-R Verbal IQs (Age 7h) r X Y = ' 6 8 ' r X X = ' 8 6 ' r Y Y = ' 8 8 Normalized Linear Equating PPVT IQs Y* S y > 60 59.982 3.299 67 66.982 2.816 70 69.982 2.614 74 73.982 2.353 77 76.982 2.164 81 80.982 1.926 84 83.982 1.761 86 85.982 1.659 88 87.982 1.565 92 91.982 1.409 95 94.982 1.325 97 96.982 1.289 98 97.982 1.278 99 98.982 1.271 100 99.982 1.268 101 100.982 1.270 102 101.982 1.276 103 102.982 1.287 104 103.982 1.303 106 105.982 1.346 108 107.982 1.404 110 109.982 1.476 112 111.982 1.559 114 113.982 1.652 115 114.982 1.702 117 116.982 1.807 120 119.982 1.976 122 121.982 2.094 124 123.982 2.217 126 125.982 2.344 129 128.982 2.538 133 132.982 2.806 140 139.982 3.290 Y.= 100.000 'RMS ;=13.454 261 Table H2 Equivalent Scores Normalized PPVT IQs to Normalized WISC-R Verbal IQs (Age 9h) r X Y = ' 7 2 ' r X X = - 9 3 ' r Y Y = « 8 7 Normalized Linear Equating PPVT IQs Y* s W J. ^ o Y* 60 60.318 3.039 68 68.286 2.528 72 72.270 2.281 74 74.262 2.161 75 75.258 2.103 76 76.254 2.044 77 77.250 1.987 79 79.242 1.874 80 80.238 1.820 81 81.234 1.766 83 83.226 1.663 85 85.218 1.565 88 88.206 1.433 90 90.198 1.355 92 92.190 1.289 93 93.186 1.260 94 94.182 1.235 96 96.174 1.195 98 98.166 1.171 100 100.158 1.163 102 102.150 1.172 104 104.142 1.199 106 106.134 1.240 109 109.122 1.328 111 111.114 1.402 112 112.110 1.442 113 113.106 1.485 114 114.102 1.530 116 116.094 1.625 118 118.086 1.726 120 120.078 1.832 122 122.070 1.943 126 126.054 2.175 128 128.046 2.295 130 130.038 2.418 137 137.010 2.860 Y.= 100.000 RMS=12.432 262 Table H3 Equivalent Scores Normalized PPVT IQs to Normalized WISC-R Verbal IQs (Age 11%) rXY ' 7 8 ' rXX •93, r y Y = .87 Normalized Linear Equating PPVT IQs Y* o SY* 60 59.428 3.105 69 68.518 2.519 73 72.558 2.269 75 74.578 2.147 77 76.598 2.028 79 78.618 1.913 83 82.658 1.695 86 85.688 1.546 88 87.708 1.457 89 88.718 1.415 91 90.738 1.340 93 92.758 1.276 96 95.788 1.206 98 97.808 1.179 100 99.828 1.169 102 101.848 1.177 104 103.868 1.202 105 104.878 1.221 106 105.888 1.243 107 106.898 1.269 109 108.918 1.332 110 109.928 1.367 111 110.938 1.406 113 112.958 1.490 115 114.978 1.583 117 116.998 1.683 118 118.008 1.735 119 119.018 1.789 121 121.038 1.900 122 122.048 1.957 124 124.068 2.074 126 126.088 2.194 127 127.098 2.255 130 130.128 2.441 133 133.158 2.632 140 140.228 3.090 Y.= . 100.000 RMS =12.000 263 Table H4 Equivalent Scores Normalized SIT IQs and Normalized WISC-R Verbal IQs (Age llh) r v v = .89, r v v = .93, r w = .88 Normalized Linear Equating SIT IQs Y* S Y * 60 59.625 2.543 67 66.695 2.162 71 70.735 1.951 74 73.765 1.797 77 76.795 1.648 80 79.825 1.505 83 82.855 1.370 84 83.865 1.327 85 84.875 1.286 87 86.895 1.207 88 87.905 1.171 90 89.925 1.103 91 90.935 1.073 93 92.955 1.020 95 94.975 .978 96 95.985 .962 98 98.005 .940 99 99.015 .935 100 100.025 .934 101 101.035 .936 103 103.055 .951 105 105.075 .981 106 106.085 1.001 108 108.105 1.049 109 109.115 1.077 111 111.135 1.141 114 114.165 1.252 116 116.185 1.334 118 118.205 1.421 120 120.225 1.512 123 123.255 1.656 126 126.285 1.805 129 129.315 1.960 133 133.355 2.171 140 140.425 2.552 Y.= 100.000 RMS =9.429 264 Table H5 Equivalent Scores Normalized SIT IQs to Normalized WISC-R F u l l Scale IQs (Age 11%) r X Y = ' 8 9 ' r X X = • 8 7> ~ .88 Normalized Linear Equating SIT IQs s„, o Y* 60 59.601 2.837 67 66.706 2.415 71 70.766 2.180 74 73.811 2.009 77 76.856 1.844 80 79.901 1.685 83 82.946 1.536 84 83.961 1.488 85 84.976 1.443 87 87.006 1.356 88 88.021 1.315 90 90.051 1.241 91 91.066 1.207 93 93.096 1.149 95 95.126 1.103 96 96.141 1.086 98 98.171 1.062 99 99.186 1.056 100 100.201 1.054 101 101.216 1.057 103 103.246 1.074 105 105.276 1.106 106 106.291 1.128 108 108.321 1.181 109 109.336 1.213 111 111.366 1.283 114 114.411 1.405 116 116.441 1.496 118 118.471 1.592 120 120.501 1.693 123 123.546 1.852 126 126.591 2.018 129 129.636 2.189 133 133.696 2.424 140 140.801 2.847 Y.= 100.000 RMS =10.458 265 Table H6 Equivalent Scores Normalized MHVS Raw Scores to Normalized WISC-R Verbal IQs (Age llh) r ^ = .92, r ^ = .93, r y Y = .88 Normalized MHVS Raw Linear Equating Scores Y* s,T. o Y* 13 62.768 2.258 16 70.037 1.891 17 72.460 1.773 18 74.883 1.657 19 77.306 1.544 20 79.729 1.436 21 82.152 1.332 22 84.575 1.234 23 86.998 1.144 24 89.421 1.064 25 91.844 .995 26 94.267 .942 27 96.690 .905 28 99.113 .888 29 101.536 .891 30 103.959 .915 32 108.805 1.015 33 111.228 1.088 34 113.651 1.171 36 118.497 1.364 38 123.343 1.579 40 128.189 1.810 41 130.612 1.929 42 133.035 2.050 45 140.304 2.422 Y.= 28.343 •RMS ,=9.175 P e r m i s s i o n i s h e r e b y g r a n t e d t o Ms. B a r b a r a J . Holmes t o r e p r o d u c e t h e WISC-R s u b s t i t u t i o n i t e m s f r o m t h e a r t i c l e , " F i n a l R e p o r t o n M o d i f i c a t i o n s o f WISC-R f o r C a n a d i a n U s e " ( C a n a d i a n P s y c h o l o g i c a l A s s o c i a t i o n B u l l e t i n , 1 9 7 7 , No. 5, pp. 5 - 7 ) , i n h e r Ed.D. d i s s e r t a t i o n , " I n i d v i d u a l l y - A d m i n i s t e r e d I n t e l l i g e n c e T e s t s : An . A p p l i c a t i o n o f A n c h o r T e s t N o r m i n g a n d E q u a t i n g P r o c e d u r e s i n B r i t i s h C o l u m b i a " , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 981, a n d t o t h e N a t i o n a l L i b r a r y o f C a n a d a t o c o p y them on m i c r o f i l m a n d t o l e n d o r s e l l c o p i e s o f t h e f i l m . P l e a s e n o t e t h a t t h i s m a t e r i a l a p p e a r s i n A p p e n d i x B, p. 188. 

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