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UBC Theses and Dissertations

The subjective difficulty of spatial ability tests Schroeder, Klaus Gerhard 1981

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THE SUBJECTIVE DIFFICULTY OF SPATIAL ABILITY TESTS by KLAUS GERHARD SCHROEDER B.Math., U n i v e r s i t y of W a t e r l o o , 1974 B.A., U n i v e r s i t y of W a t e r l o o , 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES Department of P s y c h o l o g y We accept t h i s t h e s i s as co 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 September, 1981 (c) K l a u s Gerhard S c h r o e d e r , 1981 MASTER OF ARTS in In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Psychology The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date October 16, 1981 DF-fi (7/791 A b s t r a c t T e s t s of S p a t i a l O r i e n t a t i o n (Card R o t a t i o n s , Cube Comparisons) and V i s u a l i z a t i o n (Form Board, Paper F o l d i n g , S u r f a c e Development) were a d m i n i s t e r e d t o 537 (266 men, 268 women) u n i v e r s i t y s t u d e n t s . P a r t i c i p a n t s r a t e d the p e r c e i v e d d i f f i c u l t y of each of the t e s t s on a 9 p o i n t s c a l e r a n g i n g from 1 = ve r y easy t o 9 = v e r y d i f f i c u l t . They were asked t o i n d i c a t e which of s i x problem s o l v i n g s t r a t e g i e s they used t o s o l v e t he items on any p a r t i c u l a r t e s t . The s t r a t e g y s t a t ements were d e s i g n e d t o t a p p a r t or whole problem s o l v i n g s t r a t e g i e s . P a r t s t r a t e g i e s i n v o l v e d c o n c e n t r a t i n g on s a l i e n t a s p e c t s of a s t i m u l u s w h i l e whole s t r a t e g i e s i n v o l v e d c o n c e n t r a t i n g on an e n t i r e s t i m u l u s . S i n c e men s c o r e d h i g h e r than women on a l l f i v e t e s t s a n a l y s e s were performed s e p a r a t e l y f o r t he s e x e s . For both men and women the f i r s t p r i n c i p a l component ac c o u n t e d f o r more than 50% of the v a r i a n c e . Thus, p r e v i o u s f i n d i n g s of two s p a t i a l f a c t o r s f o r men and one s p a t i a l f a c t o r f o r women were not s u p p o r t e d . Problem s o l v i n g s t r a t e g y d i d not r e l a t e t o performance on the s p a t i a l t e s t s nor t o d i f f i c u l t y r a t i n g s . There were no c o n s i s t e n t sex d i f f e r e n c e s i n s t r a t e g y except t h a t women i n d i c a t e d t h a t they guessed more on a l l t e s t s . The l i m i t a t i o n s of i n t r o s p e c t i v e r e p o r t s were d i s c u s s e d . For both men and women the p e r c e i v e d d i f f i c u l t y of a p a r t i c u l a r t e s t c o r r e l a t e d more h i g h l y w i t h the t o t a l s c o r e on t h a t t e s t than w i t h the t o t a l s c o r e on any ot h e r t e s t . On the b a s i s of t h i s f i n d i n g i t was c o n c l u d e d t h a t the d i f f i c u l t y index i s a v a l u a b l e one worthy of f u r t h e r s t u d y . The f i n d i n g t h a t men and women d i d not d i f f e r on mean d i f f i c u l t y r a t i n g on t h r e e of the t e s t s , even though they d i f f e r e d s i g n i f i c a n t l y i n performance on a l l t e s t s , was i n t e r p r e t e d t o mean t h a t each person s u b j e c t i v e l y rank o r d e r s the t e s t s i n terms of d i f f i c u l t y . I t was h y p o t h e s i z e d t h a t the p e r c e i v e d d i f f i c u l t y of a t e s t i s , t h e r e f o r e , a f u n c t i o n of the ot h e r t e s t s i n c l u d e d f o r st u d y . There was moderate support f o r the h y p o t h e s i s t h a t , as the d i f f e r e n c e i n r a t e d d i f f i c u l t y f o r p a i r s of t e s t s i n c r e a s e s , the c o r r e l a t i o n between the two d e c r e a s e s . T h i s was the case f o r s i x of 10 comparisons f o r men and t h r e e of 10 comparisons f o r women. I t was suggested t h a t t h i s h y p o t h e s i s would r e c e i v e s t r o n g e r s u p p o r t i f t e s t s of more d i s t i n c t a b i l i t i e s were i n c l u d e d i n the same s t u d y . Table of C o n t e n t s A b s t r a c t i i T a b l e of C o n t e n t s . i v L i s t of T a b l e s v Ac knowledgement s v i i H i s t o r i c a l P e r s p e c t i v e on S p a t i a l A b i l i t y R e s e a r c h . . . . 1 Purpose of the Study 5 Review of the L i t e r a t u r e 7 The d i s t i n c t i o n between s p a t i a l s u b f a c t o r s 8 Sex d i f f e r e n c e s and a b i l i t y l e v e l . . . . 12 P a r t v e r s u s whole problem s o l v i n g s t r a t e g i e s 14 Test d i f f i c u l t y and the c o r r e l a t i o n between t e s t s . . . . . 18 Hypotheses . 2 3 Method 27 Q u e s t i o n n a i r e s 27 Procedure 28 P a r t i c i p a n t s 29 R e s u l t s 2 9 D i s c u s s i o n 43 R e f e r e n c e s 53 T a b l e s 58 Appendix A 89 Appendix B 92 Appendix C 95 Appendix D 102 V L i s t of T a b l e s 1 Means and Sta n d a r d D e v i a t i o n s f o r S p a t i a l Test Scores and D i f f i c u l t y R a t i n g s 59 2 C o r r e l a t i o n s between D i f f i c u l t y R a t i n g s and S p a t i a l T e s t Scores 62 3 Sex by Test Repeated Measures A n a l y s i s of V a r i a n c e on D i f f i c u l t y R a t i n g s . . . . . . . . . . . . 65 4 Frequency of Answers t o Problem S o l v i n g Statements 66 5 C o r r e l a t i o n between Test Scores f o r People who use the 'Same' and ' D i f f e r e n t ' Problem S o l v i n g S t r a t e g i e s ...67 6 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Card R o t a t i o n s T e s t . . . . . . . 70 7 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Cube Comparisons Test 71 8 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Paper F o l d i n g Test 72 9 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the S u r f a c e Development Test 73 10 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Form Board T e s t . . . . ' 74 11 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Form Board T e s t 75-12 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the' Paper F o l d i n g Test 76 13 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the S u r f a c e Development Test 77 v i 14 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Card R o t a t i o n s Test 78 15 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Cube Comparisons Test 79 16 C o r r e l a t i o n s between S p a t i a l T est Scores .80 17 U n r o t a t e d and R o t a t e d Component P a t t e r n M a t r i c e s ,. . .• .83 18 C o r r e l a t i o n between Test Scores f o r People w i t h High and Low D i f f e r e n c e s i n D i f f i c u l t y R a t i n g s ....86 v i i A c k n o w l e d g e m e n t s I w i s h t o t h a n k my c o m m i t t e e m e m b e r s : t h e l a t e D r . E d r o S i g n o r i f o r c h a i r i n g t h e c o m m i t t e e a n d f o r f r e e l y i m p a r t i n g h i s m e t h o d o l o g i c a l k n o w l e d g e D r . S u s a n B u t t f o r h e r a s s i s t a n c e i n p r e p a r a t i o n o f t h e f i n a l d r a f t a s w e l l a s f o r h e r e n c o u r a g e m e n t , a n d D r . J o h n Y u i l l e f o r h i s a d v i c e c o n c e r n i n g t h e p r o b l e m s o l v i n g a s p e c t s o f t h e t h e s i s . I a l s o t h a n k D r . R a l p h H a k s t i a n f o r p r o v i d i n g s t a t i s t i c a l g u i d a n c e , a n d M a r s h a S c h r o e d e r f o r t h e d r a w i n g s a s w e l l a s f o r i n s p i r a t i o n a n d e m o t i o n a l s u p p o r t t h r o u g h o u t t h e p r o j e c t . 1 H i s t o r i c a l P e r s p e c t i v e on S p a t i a l A b i l i t y R esearch In summarizing the r e s u l t s of f a c t o r a n a l y t i c s t u d i e s of i n t e l l e c t u a l a b i l i t i e s W o l f l e (1940) p o i n t e d out t h a t a space f a c t o r was the second most f r e q u e n t l y i n d e n t i f i e d f a c t o r i n the l i t e r a t u r e . A l t h o u g h t h e r e was r e l a t i v e l y l i t t l e o v e r l a p i n the t e s t s used i n many of the i n v e s t i g a t i o n s of s p a t i a l a b i l i t y t o t h i s t i m e , v a r i o u s r e s e a r c h e r s p r o v i d e d n e a r l y i d e n t i c a l d e f i n i t i o n s of the a b i l i t y they presumed to.be measuring. McFarlane (1925) , f o r i n s t a n c e , found a group f a c t o r d i s t i n c t from g e n e r a l i n t e l l i g e n c e which measured an a b i l i t y i n which "uniqueness l i e s i n the f a c t t h a t those persons p o s s e s s i n g i t i n a h i g h degree a n a l y s e and judge b e t t e r about c o n c r e t e s p a t i a l r e l a t i o n s " (p. 5 4 ) . . Koussy (1935) found e v i d e n c e of a f a c t o r which he saw as the " a b i l i t y t o o b t a i n and the f a c i l i t y t o u t i l i z e v i s u a l s p a t i a l imagery" (p. 84) and Thurstone (1938) c h a r a c t e r i z e d , h i s f i r s t p r i m a r y mental a b i l i t y as " f a c i l i t y i n s p a t i a l and v i s u a l imagery" (p. 80). W h i l e B r i t i s h r e s e a r c h e r s , f o r the most p a r t , i n v e s t i g a t e d the n a t u r e of t h i s one g e n e r a l s p a t i a l f a c t o r f o r some time t o come (S m i t h , 1964), numerous American i n v e s t i g a t o r s became i n t e r e s t e d i n s u b f a c t o r s of the i d e n t i f i e d s p a t i a l a b i l i t y . N o t a b l e a r e the f i n d i n g s of G u i l f o r d and Lacey (1947) from the U.S. Army A i r F o r c e s A v i a t i o n P s y c h o l o g y Research Program which m o s t l y used armed s e r v i c e s p e r s o n n e l . T h e i r r e s e a r c h l e d them t o 2 d i v i d e s p a t i a l a b i l i t y i n t o a s p a t i a l v i s u a l i z a t i o n and a s p a t i a l o r i e n t a t i o n f a c t o r . S p a t i a l v i s u a l i z a t i o n was seen as the " a b i l i t y t o imagine the r o t a t i o n of d e p i c t e d o b j e c t s , the f o l d i n g and u n f o l d i n g of f l a t p a t t e r n s , the r e l a t i v e changes of p o s i t i o n of o b j e c t s i n space, the motion .. of machinery. T h i s v i s u a l i z a t i o n f a c t o r i s s t r o n g e s t i n t e s t s t h a t p r e s e n t a s t i m u l u s p i c t o r i a l l y and i n which some m a n i p u l a t i o n or t r a n s f o r m a t i o n t o another v i s u a l arrangement i s i n v o l v e d " (McGee, 1979, p. 8 9 1 ) . S p a t i a l o r i e n t a t i o n was d e f i n e d as the " a b i l i t y t o determine r e l a t i o n s h i p s between d i f f e r e n t s p a t i a l l y a r r a n g e d s t i m u l i and responses and the comprehension of the arrangement of elements w i t h i n a v i s u a l s t i m u l u s p a t t e r n " (McGee, 1979, p. 891). I t . i s not c l e a r , however, on the b a s i s of an a n a l y s i s of the f a c t o r p a t t e r n s l i s t e d by F r e n c h (1951), how d i s t i n c t t h e s e two f a c t o r s might be. Many of the t e s t s p u r p o r t e d t o l o a d on one f a c t o r a l s o l o a d q u i t e h i g h l y on the o t h e r , and t e s t s l a t e r d eveloped t o measure th e s e f a c t o r s more p a r s i m o n i o u s l y ( G u i l f o r d & Zimmerman, 1953) were o f t e n found t o c o r r e l a t e s u b s t a n t i a l l y w i t h one an o t h e r (e.g. r = .67; B o r i c h & Bauman, 1972). As noted by McGee (1979), G u i l f o r d and Lacey (1947) were by no means the o n l y r e s e a r c h e r s t o s p l i t the s p a t i a l f a c t o r . T h u r s t o n e ' s (1950) work, f o r example, had a g r e a t impact on f u t u r e i n v e s t i g a t i o n s of s p a t i a l a b i l i t y s u b f a c t o r s . Thurstone (1950) found t h r e e s e p a r a t e s p a t i a l 3 f a c t o r s , two of which (SI and S3) are s i m i l a r t o the G u i l f o r d and Lacey (1947) s p a t i a l o r i e n t a t i o n f a c t o r , and one (S2) which resembles the s p a t i a l v i s u a l i z a t i o n f a c t o r . C i t i n g Thurstone (1950), B a r r a t t (1955) n o t e s : "The f i r s t space f a c t o r (S1) r e p r e s e n t s the a b i l i t y t o r e c o g n i z e the i d e n t i t y of an o b j e c t when i t i s seen from d i f f e r e n t a n g l e s ; . . . t h e second space f a c t o r (S2) r e p r e s e n t s the a b i l i t y t o imagine the movement or i n t e r n a l d i s p l a c e m e n t among the p a r t s of a c o n f i g u r a t i o n t h a t one i s t h i n k i n g a b o u t ; . . . t h e t h i r d space f a c t o r (S3) r e p r e s e n t s the a b i l i t y t o t h i n k about those s p a t i a l r e l a t i o n s i n which the body o r i e n t a t i o n of the o b s e r v e r i s an e s s e n t i a l p a r t of the problem" (p. 279). In a review of s p a t i a l l i t e r a t u r e , however, M i c h a e l , G u i l f o r d , F r u c h t e r , and Zimmerman (1957) c o n c l u d e d t h a t S1 and S3 c o u l d be combined i n t o one s p a t i a l r e l a t i o n s and o r i e n t a t i o n f a c t o r due t o the f i n d i n g t h a t t e s t s of one of these f a c t o r s o f t e n l o a d e d on the o t h e r . F o l l o w i n g Thurstone (1950), F r e n c h (1951) a l s o i d e n t i f i e d t h r e e s p a t i a l f a c t o r s a f t e r i n t e g r a t i n g the r e s u l t s of over s i x t y f a c t o r a n a l y s e s , many of which were performed by of under the d i r e c t i o n of Thurstone and G u i l f o r d . Space (S) was seen as the a b i l i t y t o p e r c e i v e s p a t i a l p a t t e r n s a c c u r a t e l y and t o compare them w i t h each o t h e r ; S p a t i a l O r i e n t a t i o n (SO) as the a b i l i t y t o remain unconfused by the v a r y i n g o r i e n t a t i o n s i n which a p a t t e r n may be p r e s e n t e d ; and V i s u a l i z a t i o n ( V i ) as the a b i l i t y t o comprehend i m a g i n a r y movements i n 3 - d i m e n s i o n a l space or the a b i l i t y t o m a n i p u l a t e o b j e c t s i n i m a g i n a t i o n . The 4 d i s t i n c t i o n between S and SO i s somewhat u n c l e a r , however, and i t seems t h a t both f a c t o r s might be i n c l u d e d i n the G u i l f o r d and Lacey (1947) d e f i n i t i o n of s p a t i a l o r i e n t a t i o n . The main d i s t i n c t i o n between the two seems merely t o be t h a t f o r S t e s t s one has t o compare two s t i m u l i w h i l e f o r SO t e s t s one works w i t h the same s t i m u l u s . F u r t h e r , i n the a n a l y s e s l i s t e d by French (1951) t h e r e i s a c o n s i d e r a b l e degree of o v e r l a p as t o the t e s t s w i t h h i g h l o a d i n g s on these two f a c t o r s . Given these f i n d i n g s and the f a c t t h a t M i c h a e l et a l . (1957) viewed t h e i r S p a t i a l R e l a t i o n s and O r i e n t a t i o n f a c t o r as a c o m b i n a t i o n of the F r e n c h (1951) S and SO f a c t o r s , i t i s u n d e r s t a n d a b l e t h a t t e s t s of o n l y two s p a t i a l f a c t o r s appeared i n the 1963 v e r s i o n of the K i t of R e f e r e n c e T e s t s f o r C o g n i t i v e F a c t o r s ( F r e n c h , Ekstrom, & P r i c e , 1963). T h i s t r e n d c o n t i n u e d w i t h the 1976 v e r s i o n of the K i t of F a c t o r - R e f e r e n c e d C o g n i t i v e T e s t s (Ekstrom, F r e n c h , & Harman, 1976) when t e s t s f o r two s p a t i a l f a c t o r s , S p a t i a l O r i e n t a t i o n (S) and V i s u a l i z a t i o n (Vz) were i n c l u d e d . Thus i t seems t h a t r e s e a r c h e r s have converged i n t h e i r b e l i e f t h a t the e a r l i e r i d e n t i f i e d g e n e r a l s p a t i a l f a c t o r (e.g. Koussy, 1935; M c F a r l a n e , 1925; T h u r s t o n e , 1938) can be d i v i d e d i n t o two s u b f a c t o r s (McGee, 1979). 5 Purpose of the Study A l t h o u g h t h e r e seems t o be f a i r l y w i d e s p r e a d support f o r the view t h a t S and Vz a r e d i s t i n c t f a c t o r s , t h e r e has, n e v e r t h e l e s s , been c o n s i d e r a b l e d i f f i c u l t y i n c l a r i f y i n g the d i s t i n c t i o n s between the two. I t i s p r i m a r i l y t h i s i s s u e t o which the p r e s e n t study i s a d d r e s s e d . As Smith (1964) p o i n t e d o u t , even though the d i f f e r e n c e s between the two have r e c e i v e d d e t a i l e d a n a l y s i s i n terms of such c o n c e p t s as item c o m p l e x i t y , t a s k d i f f i c u l t y (e.g. M i c h a e l et a l . , 1957), and problem s o l v i n g s t r a t e g y (e.g. B a r r a t t , 1953), none of the d i f f e r e n c e s e x p l a i n s the d i s t i n c t i o n s between a l l d i f f e r e n t p a i r s of t e s t s . Thus, f o r example, ev.en though most Vz t e s t s are assumed t o be more d i f f i c u l t and c o m p r i s e d of more complex items than most S t e s t s , c o u nterexamples abound. G e n e r a l l y , t h e r e i s w i d e s p r e a d concensus t h a t Vz t e s t s a r e more d i f f i c u l t ( e.g. Ekstrom et a l . , 1976; W e r d e l i n & S t j e r n b e r g , 1969). I t has not been shown, however, t h a t t h i s phenomenon al o n e a c c o u n t s f o r the two d i s t i n c t f a c t o r s . T h i s i s p r o b a b l y due t o the i n h e r e n t d i f f i c u l t y of o b t a i n i n g a d i f f i c u l t y index f o r a speeded t e s t . F u r t h e r , not a l l t e s t s a r e l i k e l y t o be of the same r e l a t i v e d i f f i c u l t y f o r a l l p e r s o n s and i n o r d e r t o show t h a t the c o r r e l a t i o n s between t e s t s are a f f e c t e d by the d i f f i c u l t y of the t e s t s i n v o l v e d one must compare c o r r e l a t i o n s f o r v a r i o u s groups of p e o p l e . T h i s has not y e t been r e s e a r c h e d and w i l l be 6 one of the concerns of the p r e s e n t s t u d y . Another r e c u r r i n g f i n d i n g has been t h a t a n a l y s i s of s p a t i a l t e s t s c o r e s from men i n d i c a t e s more than one s p a t i a l f a c t o r w h i l e a n a l y s i s of s p a t i a l t e s t s c o r e s from women r e s u l t s i n o n l y one g e n e r a l s p a t i a l f a c t o r ( B a r r a t t , 1955; M i c h a e l , Zimmerman, & G u i l f o r d , 1950; Very, 1976). Men tend t o s c o r e h i g h e r on v a r i o u s t y p e s of s p a t i a l t e s t s ( B a r r a t t , 1955; Maccoby & J a c k l i n , 1974). One p o s s i b l e e x p l a n a t i o n f o r g r e a t e r d i f f e r e n t i a t i o n of a b i l i t i e s i n men i s a f f o r d e d by r e s e a r c h which i n d i c a t e s g r e a t e r d i f f e r e n t i a t i o n of a b i l i t i e s i n groups which e x c e l i n these a b i l i t i e s (see A n a s t a s i (1970) f o r a r e v i e w ) . I t i s not c l e a r , however, how the d i f f i c u l t y of a t e s t r e l a t e s t o a b i l i t y l e v e l . Thus, i t i s p o s s i b l e t h a t the r e p o r t e d sex- d i f f e r e n c e s i n s t r u c t u r e are... i n e x t r i c a b l y t i e d t o d i f f i c u l t y . T h i s w i l l a l s o be i n v e s t i g a t e d . One o t h e r area r e l a t i n g t o the d i s t i n c t i o n between S and Vz which has r e c e i v e d much a t t e n t i o n i s p a r t v e r s u s whole problem s o l v i n g s t r a t e g y . I t i s g e n e r a l l y b e l i e v e d t h a t Vz t e s t s r e q u i r e a person t o keep an e n t i r e s t i m u l u s i n mind (whole) w h i l e performance on S t e s t s i s enhanced by p a y i n g a t t e n t i o n t o the d e t a i l s ( p a r t ) of the s t i m u l u s f i g u r e s ( B a r r a t t , 1953, 1955; Ekstrom e t a l . , 1957; M i c h a e l et a l . , 1950). The q u e s t i o n of whether the problem s o l v i n g s t r a t e g y a f f e c t s the c o r r e l a t i o n s between t e s t s w i l l be i n v e s t i g a t e d by comparing p e o p l e who use the same s t r a t e g i e s t o tho s e who use d i f f e r e n t s t r a t e g i e s on 7 the v a r i o u s t e s t s used i n t h i s s t u d y . The main focus of t h i s s t u d y , t h e n , l i e s not o n l y i n a t t e m p t i n g t o . c o n f i r m p r e v i o u s f i n d i n g s r e l a t e d to sex d i f f e r e n c e s and the p a r t v e r s u s whole approach, but a l s o i n i n v e s t i g a t i n g hypotheses f o r d i s t i n c t groups of p e o p l e . An index of d i f f i c u l t y f o r speeded t e s t s w i l l be proposed and i t s p s y c h o m e t r i c p r o p e r t i e s i n v e s t i g a t e d . For the purposes of t h i s study,, the d e f i n i t i o n s of S p a t i a l O r i e n t a t i o n (S) and V i s u a l i z a t i o n (Vz) are those p r o v i d e d by Ekstrom et a l . (1976): S i s the ' a b i l i t y t o " p e r c e i v e s p a t i a l p a t t e r n s or t o m a i n t a i n o r i e n t a t i o n , w i t h r e s p e c t t o o b j e c t s i n space" (p. 149) and Vz i s the a b i l i t y t o "manipulate or t r a n s f o r m the image of s p a t i a l p a t t e r n s i n t o o t h e r arrangements" (p. 173). The Card R o t a t i o n s T e s t (S1) and the Cube Comparisons Test (S2) were used as measures of S and the Form Board Test ( V z 1 ) , the Paper F o l d i n g Test ( V z 2 ) , and the S u r f a c e Development Test (Vz3) were used as measures of Vz (see Appendix A f o r a d e s c r i p t i o n of these t e s t s ) . Review of the L i t e r a t u r e T h i s s e c t i o n i s d i v i d e d i n t o f o u r main p a r t s . The f i r s t d e a l s w i t h f i n d i n g s r e l a t e d t o the p s y c h o m e t r i c d i s t i n c t i v e n e s s of S ( S p a t i a l O r i e n t a t i o n ) and Vz ( V i s u a l i z a t i o n ) . The second, c o n c e r n s sex d i f f e r e n c e s and a b i l i t y l e v e l . The t h i r d s e c t i o n d e a l s w i t h p a r t v e r s u s whole problem s o l v i n g s t r a t e g i e s , w h i l e the f o u r t h d e a l s 8 w i t h the e f f e c t s of t e s t d i f f i c u l t y on the c o r r e l a t i o n s between t e s t s . The D i s t i n c t i o n between S p a t i a l S u b f a c t o r s As s t a t e d p r e v i o u s l y , S t e s t s sometimes l o a d s i g n i f i c a n t l y on Vz f a c t o r s and v i c a v e r s a . F u r t h e r , a f a c t o r i s sometimes c a l l e d s p a t i a l v i s u a l i z a t i o n even though no V z - t y p e t e s t s are found t o l o a d on i t . Examples of t h i s can be found q u i t e r e a d i l y i n F r e n c h (1951). A case i n p o i n t i s an a n a l y s i s ( r e f e r r e d t o as AFA) i n which the v i s u a l i z a t i o n f a c t o r was l o a d e d by M e c h a n i c a l P r i n c i p l e s a l o n g w i t h mathematics and r e a d i n g t e s t s . In a nother a n a l y s i s (AFE) both a s p a t i a l r e l a t i o n s and a v i s u a l i z a t i o n f a c t o r were i d e n t i f i e d . W h i l e the. v i s u a l i z a t i o n f a c t o r was l o a d e d by Vz-type t e s t s (as here d e f i n e d ) and the s p a t i a l r e l a t i o n s f a c t o r was n o t , no S-type t e s t s were i n c l u d e d i n the b a t t e r y used. The second h i g h e s t l o a d i n g on the s p a t i a l r e l a t i o n s f a c t o r was f o r a t e s t i n which the s u b j e c t was r e q u i r e d t o a d j u s t s t i c k - a n d - r u d d e r c o n t r o l s i n response t o a p a t t e r n of t h r e e l i g h t s . I t i s d i f f i c u l t t o . s e e how t h i s would be t i e d t o performance on the Cards T e s t ( S 1 ) , say, where the s u b j e c t merely i n d i c a t e s whether one p i c t u r e d c a r d i s a r e f l e c t i o n of a n o ther p i c t u r e d c a r d . Other a n a l y s e s shed more l i g h t on the d i s t i n c t i o n between S and Vz. In an a n a l y s i s of a subset of T h u r s t o n e ' s (1938) d a t a F r u c h t e r (1948) found two f a c t o r s Q which resemble S and Vz a l t h o u g h t h e r e was some f a c t o r i a l c o m p l e x i t y . The t e s t s used were Cubes ( S 2 ) , F l a g s (a t e s t q u i t e s i m i l a r t o the Cards Test - S 1 ) , Form Board ( V z l ) , and Paper F o l d i n g ( V z 2 ) . A l t h o u g h a l l t e s t s l o a d e d over .60 on the f a c t o r they were h y p o t h e s i z e d t o measure, Form Board l o a d e d .50 on the S f a c t o r . Thus, w h i l e the d i s t i n c t i o n between S and Vz may not be p e r f e c t l y c l e a r , i t does seem t h a t , i n t h i s sample at l e a s t , an argument f o r two a b i l i t i e s c o u l d be made. The r e s u l t s of M i c h a e l et a l . (1950), w i t h a sample of 500 male s t u d e n t s , p r o v i d e an even c l e a r e r d i s t i n c t i o n between S and Vz. The S t e s t s were Cubes ( S 2 ) , F l a g s , and the Guil.ford-Zimmerman S p a t i a l O r i e n t a t i o n Test (G-Z SO) and the Vz t e s t s were Form Board ( V z 1 ) , Paper F o l d i n g (Vz2) and the Guilford-Zimmerman S p a t i a l V i s u a l i z a t i o n Test (G-Z SV). The r e s u l t s were q u i t e u n e q u i v o c a l i n t h a t two of the S and two of the Vz t e s t s l o a d e d h i g h l y on t h e i r r e s p e c t i v e f a c t o r s and not over .25 on the o t h e r f a c t o r . The G-Z t e s t s were more complex and even though both l o a d e d more h i g h l y on the h y p o t h e s i z e d f a c t o r s than o t h e r t e s t s of those f a c t o r s , t hey a l s o l o a d e d over .40 on the f a c t o r s they were not meant t o t a p . Even so, t h i s s t u d y , perhaps more than any o t h e r ever r e p o r t e d , shows S and Vz t o be d i s t i n c t s p a t i a l f a c t o r s . To be noted i s t h a t n e i t h e r of the G-Z t e s t s were i n c l u d e d i n the 1976 e d i t i o n of the K i t of F a c t o r R e f e r e n c e d C o g n i t i v e T e s t s , a l t h o u g h G-Z SO d i d appear as an S t e s t i n the 1963 K i t . 10 Other . s t u d i e s have not always f a c t o r i a l l y d i f f e r e n t i a t e d t e s t s p u r p o r t e d t o d e f i n e or l o a d s e p a r a t e f a c t o r s . F l e i s h m a n and Dusek (1971), f o r i n s t a n c e , a d m i n i s t e r e d 21 t e s t s from the 1963 K i t t o 90 army e n l i s t e d men and found t h a t a l l s p a t i a l t e s t s used (Cubes - S1, Paper F o l d i n g - Vz2, S u r f a c e Development - Vz3) l o a d e d on the same f a c t o r . . I t i s p o s s i b l e t h a t t h i s f i n d i n g i s due t o the f a c t t h a t o n l y one S t e s t was chosen f o r i n c l u s i o n i n the s t u d y . U s i n g a g r e a t e r v a r i e t y of s p a t i a l t e s t s w i t h a sample of 177 e l e v e n t h and t w e l f t h grade male s t u d e n t s , F r e n c h (1965) a l s o found S and Vz t e s t s t o l o a d on the same f a c t o r . The s i x s p a t i a l t e s t s i n c l u d e d i n h i s b a t t e r y were the t h r e e Vz t e s t s from the 1963 K i t as w e l l as Cards ( S 1 ) , G-Z SO, and a c o n c e a l e d f i g u r e s t e s t . The l a t t e r t e s t has a t t i mes been found t o l o a d w i t h o t h e r S-type t e s t s ( F r e n c h , 1951). Very (1967) employed a number of s p a t i a l t e s t s i n a study of m a t h e m a t i c a l a b i l i t y i n v o l v i n g 193 male and 162 female c o l l e g e s t u d e n t s . The t e s t s used were m o s t l y of the S v a r i e t y (e.g. Cards - S1, Cubes - S2, G-Z SO) but a l s o i n c l u d e d V e r y ' s t e s t of s p a t i a l r e l a t i o n s h i p s . T h i s l a t t e r t e s t i n c l u d e d items r e q u i r i n g the s u b j e c t t o d e t e r m i n e , f o r example, what would happen t o the a r e a of a r e c t a n g l e i f the l e n g t h of each s i d e were d o u b l e d . As c o n c e r n s the s p a t i a l f a c t o r s , the f i n d i n g s were q u i t e sex s p e c i f i c . For women, a l l of the s p a t i a l t e s t s , a l o n g w i t h 11 a number of o t h e r t e s t s , combined to l o a d on what was i n t e r p r e t e d as a s p a t i a l f a c t o r . . : • For .men t h r e e s p a t i a l f a c t o r s were i d e n t i f i e d , two of which seem t o be r e l a t i v e l y pure s p a t i a l f a c t o r s . The f i r s t f a c t o r was d e f i n e d by Cards ( S i ) , Cubes ( S 2 ) , and the s p a t i a l r e l a t i o n s t e s t w h i l e the second f a c t o r had i t s h i g h e s t l o a d i n g f o r G-Z SO but was a l s o l o a d e d by Cards, s p a t i a l r e l a t i o n s , and a t e s t i n v o l v i n g the a b i l i t y t o determine the r u l e which r e l a t e s two groups of l e t t e r s . Thus, a l t h o u g h t h i s study does not p r o v i d e a v e r y s t r i n g e n t t e s t of the h y p o t h e s i s t h a t S and Vz a r e d i s t i n c t , due m a i n l y to a l a c k of t r a d i t i o n a l Vz t e s t s , i t i s i n t e r e s t i n g n o n e t h e l e s s . I f one c o n s i d e r s the n o t a b l e l o a d i n g of G-Z SO on a Vz f a c t o r mentioned p r e v i o u s l y ( M i c h a e l et a l . , 1950) a l o n g w i t h the f i n d i n g t h a t the same t e s t s p l i t away from the S t e s t s f o r the men, but not the women, i t l e a d s one t o c o n s i d e r the p o s s i b i l i t y t h a t Vz and S a r e more d i s t i n c t f o r men than women. B a r r a t t ' s (1955) study p r o v i d e s some c l a r i f i c a t i o n of t h i s m a tter because i t i n c l u d e d t e s t s of both Vz and S and because f a c t o r a n a l y s e s were performed f o r the sexes s e p a r a t e l y (103 women, 96 men). A l t h o u g h t h e r e were t e n s p a t i a l t e s t s and e i g h t p e r s o n a l i t y measures, d i s c u s s i o n w i l l be l i m i t e d t o t e s t s w hich can be c o n s i d e r e d S or Vz or b o t h . The S t e s t s were Cards ( S 1 ) , G-Z SO, F l a g s , and Thu r s t o n e ' s F i g u r e s t e s t , a t e s t which o f t e n l o a d e d w i t h Cards and F l a g s i n the a n a l y s e s p r e s e n t e d by Fr e n c h 1 2 (1951). The Vz t e s t s were the M innesota Paper Form Board ( s i m i l a r t o the Form Board - V z 1 ) , G-Z SV, and the S p a t i a l R e l a t i o n s s u b t e s t of the D i f f e r e n t i a l A p t i t u d e T e s t . T h i s l a t t e r t e s t i s q u i t e s i m i l a r t o the S u r f a c e Development Test (Vz3) i n t h a t b oth i n v o l v e the f o l d i n g of. a 2 - d i m e n s i o n a l s t i m u l u s i n t o a 3 - d i m e n s i o n a l o b j e c t . The r e s u l t s of the a n a l y s e s were q u i t e c l e a r . For men, F l a g s , F i g u r e s , and Cards ( S i ) , a l l S t e s t s , d e f i n e d one f a c t o r w h i l e a l l o t h e r t e s t s , i n c l u d i n g G-Z SO, l o a d e d on another f a c t o r . The o n l y t e s t w i t h any n o t a b l e c o m p l e x i t y was the G-Z SV Test but i t s l o a d i n g on what c o u l d be c a l l e d the S f a c t o r was much lower (.43) than i t s l o a d i n g on what c o u l d be seen as the Vz f a c t o r (.67). For women, on the o t h e r hand, a l l t e s t s mentioned above.loaded on one f a c t o r . T h i s l e d B a r r a t t (1955) t o c o n c l u d e t h a t the "space t e s t s i n the female m a t r i x , d i d not show as c l e a r a d i f f e r e n t i a t i o n . . . . a s d i d the male a n a l y s i s " (p. 286). Sex D i f f e r e n c e s and A b i l i t y L e v e l The f i n d i n g s c i t e d above l e a d one t o ask whether S and Vz a r e s e p a r a t e a b i l i t i e s f o r men o n l y . I t s h o u l d be remembered, f o r example, t h a t much of the work reviewed by F rench (1951), i n c l u d i n g the work of G u i l f o r d and Lacey (1947), i n v o l v e d o n l y male s u b j e c t s . F u r t h e r , the study which r e p o r t e d the c l e a r e s t d i s t i n c t i o n between S and Vz ( M i c h a e l e t a l . , 1950) employed a male sample. A l s o , i t 1 3 i s not c l e a r whether F r u c h t e r ' s (1948) r e s u l t s c o u l d be due t o the sample employed s i n c e Thurstone (1938), whose da t a base F r u c h t e r a n a l y z e d , d i d not d e s c r i b e h i s sample i n terms of sex and p o o l e d the sexes i n d e t e r m i n i n g c o r r e l a t i o n s between t e s t s . I t may be c o n j e c t u r e d , however, when one c o n s i d e r s the time p e r i o d , t h a t men were o v e r r e p r e s e n t e d i n T h u r s t o n e ' s sample. I f i t i s indeed the case t h a t S and Vz are d i s t i n c t f o r men o n l y and t h a t they c o l l a p s e i n t o one g e n e r a l s p a t i a l f a c t o r f o r women, the g u e s t i o n a r i s e s as t o why t h i s s h o u l d be the c a s e . P o s s i b l y b e a r i n g on t h i s i s s u e i s the f i n d i n g t h a t a sex d i f f e r e n c e i n s p a t i a l a b i l i t y has been one of the most c o n s i s t e n t r e s u l t s i n i n d i v i d u a l d i f f e r e n c e s r e s e a r c h ( G a r a i & S c h e i n f e l d , 1968; H a r r i s , 1978; Maccoby & J a c k l i n , 1974). R e s u l t s such as those r e p o r t e d by B a r r a t t (1955) showing t h a t men 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 than women on e i g h t of t e n s p a t i a l t e s t s a r e not a t y p i c a l i n t h i s regard.. A l t h o u g h t h i s sex d i f f e r e n c e i s g e n e r a l l y b e l i e v e d t o o b t a i n on b o t h S and Vz t e s t s (McGee, 1979) the l i t e r a t u r e r e l a t e d t o t h i s i d e a has never been s y s t e m a t i c a l l y r e v i e w e d . In n o t i n g W e r d e l i n ' s (1961) f i n d i n g s , Sherman (1967) wrote t h a t "sex d i f f e r e n c e s do not o c c u r on t e s t s i n which v i s u a l o r g a n i z a t i o n i s e a s i l y comprehended and which a r e t o be m a n i p u l a t e d as g i v e n , but on those i n which the o r g a n i z a t i o n and r e o r g a n i z a t i o n a s p e c t s are e x a g g e r a t e d " (p. 293). T h i s s u g g e s t s , t h e n , t h a t the sex d i f f e r e n c e i s 14 l i m i t e d . t o t e s t s of Vz. Even i f t h i s i s the c a s e , i t s t i l l does not e x p l a i n why men e x h i b i t two s p a t i a l f a c t o r s and women o n l y one. Perhaps r e l a t e d t o t h i s i s the e v i d e n c e r e v i e w e d by A n a s t a s i (1970) i n d i c a t i n g g r e a t e r d i f f e r e n t i a t i o n of a b i l i t i e s i n groups which e x c e l i n the s e . a b i l i t i e s . Examples i n c l u d e more v e r b a l f a c t o r s f o r g i r l s than boys and lower i n t e r c o r r e l a t i o n s among p r i m a r y mental a b i l i t i e s f o r h i g h e r s c o r i n g groups. Thus,, i t i s p o s s i b l e t h a t the sex d i f f e r e n c e i n s p a t i a l a b i l i t y i s r e l a t e d t o why S and Vz a re more d i s t i n c t f o r men than women. P a r t V e r s u s Whole Problem S o l v i n g S t r a t e g i e s In r e l a t i o n t o the g r e a t e r d i f f e r e n t i a t i o n of a b i l i t i e s f o r h i g h s c o r i n g groups i t might w e l l be asked i f groups who e x h i b i t a r e l a t i v e l y g e n e r a l f a c t o r , as opposed t o more numerous s p e c i f i c f a c t o r s , a l s o tend t o b r i n g a more l i m i t e d number of problem s o l v i n g s t r a t e g i e s t o bear on the g u e s t i o n s asked of them. In o t h e r words, i s i t p o s s i b l e t h a t p e o p l e who a r e not p a r t i c u l a r l y adept at s o l v i n g s p a t i a l items use the same s t r a t e g i e s f o r a l l t e s t s , w h i l e those who a r e more c a p a b l e attempt d i f f e r e n t s t r a t e g i e s f o r d i f f e r e n t t e s t s ? F u r t h e r , does the type of problem s o l v i n g s t r a t e g y used i n f l u e n c e the c o r r e l a t i o n s between p a i r s of t e s t s ? Most of the i n f o r m a t i o n r e l a t e d t o t h e s e q u e s t i o n s comes from i n v e s t i g a t i o n s r e l y i n g on i n t r o s p e c t i v e r e p o r t s 1 5 as w e l l as numerous h y p o t h e t i c a l s t a t e m e n t s . French (1965) showed t h a t the l o a d i n g of a t e s t on a f a c t o r can be s u b s t a n t i a l l y d i f f e r e n t f o r people who r e p o r t employing d i f f e r e n t problem s o l v i n g s t r a t e g i e s . To b e g i n , F r e n c h d i v i d e d h i s sample of 177 i n t o two groups based on the f o l l o w i n g c r i t e r i a : " G e o m e t r i c a l terms used i n s o l v i n g Cubes items;...Few v i s u a l i z a t i o n i n d i c a t i o n s made i n s o l v i n g Cubes items;...When asked r e p o r t s m e n t a l l y r o t a t i n g the cube on two s e p a r a t e axes" (p. 2 4 ) . S u b j e c t s who were marked p l u s on two or more of these were deemed t o have s o l v e d the Cubes (S2) items i n an a n a l y t i c manner and were compared t o a l l o t h e r s u b j e c t s . The most i n t e r e s t i n g f i n d i n g s were t h a t the l o a d i n g of Cubes on the S p a c e - V i s u a l i z a t i o n f a c t o r dropped from .52 f o r the n o n - a n a l y z e r s t o .07 f o r the a n a l y z e r s and t h a t , f o r the a n a l y z e r s , Cubes l o a d e d on an i n d u c t i o n f a c t o r . A l s o , the c o r r e l a t i o n s between v a r i o u s a b i l i t i e s were found t o d i f f e r f o r p e o p l e who used a system t o s o l v e problems ( a n a l y z e r s ) and those who d i d n o t . " S u b j e c t s who attempt t o s o l v e s p a t i a l or o t h e r problems by o r d i n a r y common sense, perhaps by s i m p l e i n s p e c t i o n u n t i l a s o l u t i o n seems t o o f f e r i t s e l f , succeed p r e t t y much a c c o r d i n g t o t h e i r g e n e r a l i n t e l l i g e n c e as measured by v e r b a l and m a t h e m a t i c a l t e s t s . For those s u b j e c t s , t h e r e f o r e , the c o r r e l a t i o n between • S p a c e - V i s u a l i z a t i o n and the v e r b a l or mathematics f a c t o r s i s h i g h . On the o t h e r hand, the s u b j e c t s who use a system f o r s o l v i n g problems have succeeded i n d e v e l o p i n g some 1 6 s p e c i a l i z a t i o n of t h e i r a b i l i t i e s , and ••• so the c o r r e l a t i o n s drop down" (Fr e n c h , 1965; p. 2 2 ) . A l t h o u g h t h i s study i n c l u d e d both S- and V z - t y p e t e s t s o n l y one s p a t i a l f a c t o r was found. Thus, i t was not p o s s i b l e t o determine whether the h i g h e s t l o a d i n g f o r the Cubes Test would move from an S f a c t o r t o a Vz f a c t o r , depending on the problem s o l v i n g s t r a t e g y used. M i c h a e l et a l . (1950) have h y p o t h e s i z e d t h a t t h i s might indeed be the c a s e . I t was t h e i r b e l i e f t h a t p e o p l e who m e n t a l l y p i c k up. and r o t a t e a cube use a. v i s u a l i z a t i o n p r o c e s s , whereas people who attempt t o i n t e r r e l a t e the p o s i t i o n s of the s i d e s or who p i c t u r e themselves as w a l k i n g around the cubes, use a s p a t i a l o r i e n t a t i o n s t r a t e g y . S i m i l a r l y , they b e l i e v e d t h a t the F l a g s t e s t ( u s u a l l y thought of as an S t e s t ) s h o u l d l o a d on t h e Vz f a c t o r i f the f l a g i s m e n t a l l y p i c k e d up and t u r n e d , and t h a t i t s h o u l d l o a d on the S f a c t o r i f i t i s s o l v e d w i t h o n l y the edges of the f l a g i n mind. In summation, i f a s p a t i a l i t e m i s s o l v e d by k e e p i n g the e n t i r e s t i m u l u s i n mind (the 'whole' problem s o l v i n g s t r a t e g y ) the. t e s t s h o u l d l o a d on a Vz f a c t o r . I f an item i s s o l v e d by c o n c e n t r a t i n g o n l y on v a r i o u s s a l i e n t a s p e c t s of the s t i m u l u s ( e . g . an edge, p o i n t , or s i d e ) , perhaps one a f t e r the o t h e r (the ' p a r t ' problem s o l v i n g s t r a t e g y ) , the t e s t s h o u l d l o a d on an S f a c t o r . U n f o r t u n a t e l y , M i c h a e l e t a l . (1950) d i d not t e s t t h i s h y p o t h e s i s . In r e l a t i o n t o the p a r t v e r s u s whole s t r a t e g y , 17 B a r r a t t (1953) found t h a t p e o p l e who used a p a r t s t r a t e g y (e.g. r o t a t i n g o n l y p a r t of a f i g u r e ) s c o r e d h i g h e r than people who r o t a t e d the whole f i g u r e . A l s o , people who attempted t o r e l a t e the f i g u r e s t o something f a m i l i a r (e.g. a l e t t e r of the a l p h a b e t , a c o n c r e t e o b j e c t ) s c o r e d lower than people who employed a p a r t s t r a t e g y . F u r t h e r , f o u r t y p e s of problem s o l v i n g s t r a t e g i e s f o r the Space s u b t e s t of the D i f f e r e n t i a l A p t i t u d e Test were d e l i n e a t e d . Some people f o l d e d the s t i m u l u s and noted r e l a t i o n s h i p s of p a r t s ; some u n f o l d e d the response f i g u r e and compared t h i s u n f o l d i n g t o the p a t t e r n ; o t h e r s l o o k e d merely f o r cues such as a n g l e i n t e r s e c t i o n s ; and some peopl e c o u l d not s o l v e the problems and r e l i e d on g u e s s i n g . B a r r a t t d i d not r e p o r t which problem • s o l v i n g s t r a t e g y l e d t o the h i g h e s t s c o r e s . A l s o , c o r r e l a t i o n s between the v a r i o u s t e s t s used were not r e p o r t e d s e p a r a t e l y f o r groups who used d i f f e r e n t s t r a t e g i e s . Thus, i t i s not known i f d i f f e r e n t s t r a t e g i e s might r e s u l t i n a d i f f e r e n t f a c t o r s t r u c t u r e . In summary, i t seems t h a t d i f f e r e n t s t r a t e g i e s a r e employed by d i f f e r e n t people i n s o l v i n g the same i t e m s . For the most p a r t , i t i s not known which s t r a t e g i e s r e s u l t i n the h i g h e s t s c o r e s . A l s o , we do not know i f the c o r r e l a t i o n between two t e s t s i s h i g h e r when the same s t r a t e g y i s used f o r both than when a d i f f e r e n t s t r a t e g y i s used f o r each. 1 8 Test D i f f i c u l t y and the C o r r e l a t i o n between T e s t s A l t h o u g h many i n v e s t i g a t o r s concerned w i t h s p a t i a l a b i l i t y have suggested t h a t S t e s t s a r e g e n e r a l l y l e s s d i f f i c u l t than •Vz t e s t s (Ekstrom et a l . , 1976; F r e n c h , 1951; M i c h a e l et a l . , 1957), few e m p i r i c a l s t u d i e s r e l a t e d t o t h i s p o i n t have been attempted. T h i s i s p r o b a b l y ; a r e s u l t of the d i f f i c u l t y of o b t a i n i n g a d i f f i c u l t y index f o r speeded t e s t s . Thus, b e f o r e d i s c u s s i n g f i n d i n g s r e l a t e d t o s p a t i a l a b i l i t y , t e s t s of which a r e , f o r the most p a r t , speeded, s t u d i e s i n v o l v i n g more o b j e c t i v e d i f f i c u l t y i n d i c e s w i l l be r e v i e w e d . That t e s t and item d i f f i c u l t y , a t l e a s t i n the a b s o l u t e sense, i s indeed a p o t e n t v a r i a b l e as c o n c e r n s f a c t o r s t r u c t u r e and the c o r r e l a t i o n s between t e s t s of v a r y i n g d i f f i c u l t y has been amply documented. For example, G u i l f o r d (1941) f a c t o r a n a l y z e d the t e n s u b s c a l e s of the Seashore t e s t of p i t c h d i s c r i m i n a t i o n . S u b s c a l e s c o r e s were o b t a i n e d f o r the 300 c o l l e g e s t u d e n t s by t a b u l a t i n g which of the ten items at each of ten f r e q u e n c y d i f f e r e n c e s they d e t e c t e d c o r r e c t l y . Frequency d i f f e r e n c e s ranged from .5 t o 30 c y c l e s per second and s u b j e c t s e i t h e r passed or f a i l e d each s u b t e s t based on G u i l f o r d ' s attempt t o o b t a i n a non-skewed d i s t r i b u t i o n f o r each of the s u b t e s t s . F a c t o r a n a l y s i s based on t e t r a c h o r i c c o r r e l a t i o n s r e v e a l e d t h r e e f a c t o r s ; F a c t o r I had l o a d i n g s which were i n v e r s e l y p r o p o r t i o n a l t o the d i f f i c u l t y of the items i n v o l v e d i n the s u b t e s t s ; F a c t o r 19 I I had s i g n i f i c a n t l o a d i n g s f o r the more d i f f i c u l t s u b t e s t s and F a c t o r I I I had l o a d i n g s f o r the m o d e r a t e l y d i f f i c u l t s u b t e s t s . G u i l f o r d (1941) summed up h i s study by n o t i n g t h a t "we may a c c e p t the h y p o t h e s i s t h a t . . . ( t h e f a c t o r s ) . . . r e p r e s e n t t h r e e d i s t i n c t human a b i l i t i e s i n v o l v e d i n the comparison and judgment of tones as t o p i t c h " (p. 7 4 ) . Ferguson (1941) o b t a i n e d a r e s u l t q u i t e s i m i l a r t o G u i l f o r d ' s when he s p l i t a 100 word v o c a b u l a r y t e s t i n t o s i x s u b t e s t s of v a r y i n g d i f f i c u l t y . T h i s l e d Ferguson t o suggest t h a t " f a c t o r s deduced from t e s t b a t t e r i e s which are homogeneous w i t h r e s p e c t t o d i f f i c u l t y , a l t h o u g h heterogeneous w i t h r e s p e c t t o c o n t e n t , would l e n d themselves more r e a d i l y t o p s y c h o l o g i c a l l y m e a n i n g f u l i n t e r p r e t a t i o n than f a c t o r s deduced from t e s t b a t t e r i e s which are heterogeneous w i t h r e s p e c t t o both d i f f i c u l t y and c o n t e n t " (p. 329). Thus, the i m p l i c a t i o n i s t h a t d i f f e r e n t f a c t o r s a r i s i n g out of s i m i l a r c o n t e n t a r e due to d i f f e r e n t i a l d i f f i c u l t y . A s tudy performed by Sargent (1940) i n which s u b j e c t s were asked t o s o l v e easy, d i f f i c u l t , and m o d e r a t e l y d i f f i c u l t anagrams a l s o r e l a t e s t o the above f i n d i n g s . In c o r r e l a t i n g mean s o l u t i o n t i m e s f o r the d i f f e r e n t groups of anagrams, i t was found t h a t c o r r e l a t i o n s f o r t e s t s one l e v e l removed i n d i f f i c u l t y ( i . e . easy-moderate, m o d e r a t e - d i f f i c u l t ) were s u b s t a n t i a l l y h i g h e r than c o r r e l a t i o n s between t e s t s two l e v e l s ' removed i n 20 d i f f i c u l t y ( i . e . e a s y - d i f f i c u l t ) . Thus, as the d i f f e r e n c e i n d i f f i c u l t y between the t e s t s i n c r e a s e d the c o r r e l a t i o n between the two d e c r e a s e d . Given t h a t d i f f i c u l t y can have an e f f e c t on c o r r e l a t i o n s , i t i s s t i l l not a t a l l c l e a r t h a t d i f f i c u l t y , per se, causes the c o r r e l a t i o n s . Some r e s e a r c h e r s have p o s t u l a t e d t h a t as one type of item (e.g. an anagram) i s made more d i f f i c u l t , i t s s o l u t i o n r e q u i r e s a d i f f e r e n t type of problem s o l v i n g s t r a t e g y or a b i l i t y . Sargent (1940), f o r i n s t a n c e , had t r a i n e d s u b j e c t s v e r b a l i z e t h e i r t h o u g h t s w h i l e s o l v i n g the anagrams and found t h a t w h i l e t h e - e a s i e r anagrams were s o l v e d as a whole, the more d i f f i c u l t ones were s o l v e d by a p a r t method which i n v o l v e d b r e a k i n g the anagrams i n t o s y l l a b l e s or f a m i l i a r c o m b i n a t i o n s . Along s i m i l a r l i n e s , G u i l f o r d (1941) h y p o t h e s i z e d t h a t the t h r e e f a c t o r s d i s c o v e r e d w i t h the p i t c h d i s c r i m i n a t i o n t e s t r e f l e c t e d a u d i t o r y , a t t e n t i o n a l , and v e r b a l components a l t h o u g h he had no way of knowing which component was r e p r e s e n t e d by w h i c h . f a c t o r . In the area of s p a t i a l a b i l i t y Zimmerman (1954) h y p o t h e s i z e d t h a t "merely by v a r y i n g item d i f f i c u l t y and c o m p l e x i t y a s i n g l e k i n d of t e s t c o u l d be made t o emphasize each of f o u r f a c t o r s i n s u c c e s s i o n from P e r c e p t u a l Speed through Space and V i s u a l i z a t i o n t o Reasoning" (p. 398). W e r d e l i n and S t j e r n b e r g (1969) a t t e m p t e d t o t e s t t h i s 21 h y p o t h e s i s by a d m i n i s t e r i n g S and Vz t e s t s as w e l l as p e r c e p t u a l speed, n u m e r i c a l , and r e a s o n i n g t e s t s t o a sample of e i g h t h grade boys and g i r l s . A l t h o u g h s e p a r a t e S and Vz f a c t o r s were not found f o r t h i s sample, a r e s u l t not i n c o n s i s t e n t w i t h o t h e r f i n d i n g s employing r e l a t i v e l y young samples (e.g. F r e n c h , 1951), the r e s u l t s i n d i c a t e d , f o r some s p a t i a l t e s t s , a " c l e a r tendency f o r i n c r e a s e d c o r r e l a t i o n s w i t h the P ( p e r c e p t u a l speed) and N ( n u m e r i c a l ) f a c t o r s and somewhat lower c o r r e l a t i o n s w i t h the S (space) f a c t o r the more the t e s t i s p r a c t i c e d " (p. 190). Thus, a l t h o u g h t h i s f i n d i n g does not d i r e c t l y a d d r e s s the d i s t i n c t i o n between S and Vz, i t " d o e s show t h a t as a t e s t becomes e a s i e r ( i . e . i s p r a c t i c e d ) i t may measure a d i f f e r e n t a b i l i t y . W e r d e l i n and S t j e r n b e r g (1969) a l s o p o i n t e d o u t , however, t h a t the method by which the items are s o l v e d may change w i t h i n c r e a s e d p r a c t i c e . Thus, f o r the t e s t which showed the most pronounced p r a c t i c e e f f e c t , a t e s t q u i t e s i m i l a r t o Cards ( S 1 ) , they noted t h a t "the problem...might a f t e r the p r a c t i c e p e r i o d a t l e a s t p a r t of the time be s o l v e d w i t h o u t the s u b j e c t s h a v i n g t o t u r n the v a r i o u s f i g u r e s around i n t h e i r minds" (p. 191). The f i n d i n g s r e l a t e d t o s p a t i a l a b i l i t y , i n c o n t r a s t t o the s t u d i e s by G u i l f o r d (1941) and Ferguson (1941), do not i n v o l v e an o p e r a t i o n a l d e f i n i t i o n of d i f f i c u l t y . For i n s t a n c e , Zimmerman (1954) assumes t h a t k e e p i n g t r a c k of t h r e e t u r n s of a p l a n e i s more d i f f i c u l t than keeping 22 t r a c k of merely one t u r n . W e r d e l i n and S t j e r n b e r g (1969) assume t h a t as a t e s t i s p r a c t i c e d i t becomes e a s i e r . While t h i s k i n d of l o g i c i s h a r d l y d e b a t a b l e , c o n s i d e r a t i o n of d i f f i c u l t y i n t h i s manner does not a l l o w one t o a s s e s s i t s e f f e c t s e m p i r i c a l l y . For example, most people would agree t h a t . a t e s t i n v o l v i n g t h r e e t u r n s i s more d i f f i c u l t than one i n v o l v i n g one t u r n when the same s t i m u l i a r e used i n both (as i s the case w i t h Zimmerman, 1954). There would p r o b a b l y n o t , however, be the same degree of agreement i f p e o p l e were asked t o compare the d i f f i c u l t y of a t e s t i n v o l v i n g t h r e e t u r n s of one s t i m u l u s t o the d i f f i c u l t y of a t e s t i n v o l v i n g the f o l d i n g and u n f o l d i n g of a p i e c e of paper. Thus, what i s needed i s a measurement of d i f f i c u l t y . To t h i s end, i t i s proposed t h a t the d i f f i c u l t y a person has i n c o m p l e t i n g a t e s t can be a s s e s s e d by a s k i n g how d i f f i c u l t he or she found the t e s t . W h i l e t h i s i s a r e l a t i v e l y s u b j e c t i v e i n d e x , and not n e c e s s a r i l y r e l a t e d t o d i f f i c u l t y i n d i c e s based on p a s s / f a i l c o n s i d e r a t i o n s (see N u n n a l l y , 1978), i t i s b e l i e v e d t o be a v a l u a b l e one. T h i s i s e s p e c i a l l y so because i t a l l o w s f o r c a r e f u l c o n s i d e r a t i o n of i n d i v i d u a l d i f f e r e n c e s . Not o n l y can one determine how d i f f i c u l t a p e r s o n found a t e s t , but how d i f f i c u l t a person found one t e s t r e l a t i v e t o o t h e r s . F u r t h e r , i t would be p o s s i b l e , e m p i r i c a l l y , r a t h e r than a n e c d o t a l l y , t o i n v e s t i g a t e the r e l a t i o n s h i p between d i f f i c u l t y and the t o p i c s r e v i e w e d above ( i . e . sex 23 d i f f e r e n c e s , problem s o l v i n g s t r a t e g i e s , s t r u c t u r e of s p a t i a l a b i l i t y ) . For i n s t a n c e , one c o u l d r e a d i l y determine whether p e o p l e who use c e r t a i n problem s o l v i n g s t r a t e g i e s f i n d a t e s t more or l e s s d i f f i c u l t than p e o p l e who do not use the s e s t r a t e g i e s . A l s o , the e f f e c t t h a t t e s t d i f f i c u l t y has on the c o r r e l a t i o n between t e s t s i s open t o i n v e s t i g a t i o n on the b a s i s of s u b j e c t i v e t e s t d i f f i c u l t y i n d i c e s f o r speeded t e s t s . Hypotheses H y p o t h e s i s 1 The d i f f i c u l t y r a t i n g a s s i g n e d t o a t e s t w i l l c o r r e l a t e more n e g a t i v e l y w i t h the t o t a l s c o r e on t h a t t e s t than w i t h the t o t a l s c o r e on any oth e r t e s t . R a t i o n a l e : T h i s i s a t e s t of the adequacy of the d i f f i c u l t y r a t i n g s c a l e . I f t h i s i s not g e n e r a l l y the case then i t would be d i f f i c u l t t o j u s t i f y i n t e r p e r s o n comparisons based on the d i f f i c u l t y i n d i c e s . F u r t h e r , groups c r e a t e d on t h e b a s i s of the d i f f i c u l t y i n d i c e s c o u l d n o t , m e a n i n g f u l l y , be compared on any performance or a b i l i t y v a r i a b l e . H y p o t h e s i s 2 Men w i l l s c o r e s i g n i f i c a n t l y h i g h e r on Vz, but not on S t e s t s , than women. R a t i o n a l e : T h i s i s a t e s t of W e r d e l i n ' s (1961) h y p o t h e s i s . F u r t h e r , i t i s an attempt t o support the 24 o f t e n c i t e d sex d i f f e r e n c e i n s p a t i a l a b i l i t y . H y p o t h e s i s 3 Men w i l l r a t e Vz t e s t s , but not S t e s t s , as s i g n i f i c a n t l y l e s s d i f f i c u l t than w i l l women. R a t i o n a l e : I f r a t e d d i f f i c u l t y c o r r e l a t e s w i t h a b i l i t y or performance l e v e l , the d i f f i c u l t y f i n d i n g s s h o u l d p a r a l l e l those of a b i l i t y ( H y p o t h e s i s 2 ) . H y p o t h e s i s 4 People u s i n g a p a r t approach on one t e s t and a whole approach on another .test w i l l e x h i b i t a, lower c o r r e l a t i o n between these t e s t s than p e o p l e u s i n g the same approach on both t e s t s . R a t i o n a l e : T h i s i s an i n d i r e c t t e s t of the f i n d i n g t h a t p e o p l e who use d i f f e r e n t approaches f o r d i f f e r e n t t a s k s have "succeeded i n d e v e l o p i n g some s p e c i a l i z a t i o n of t h e i r a b i l i t i e s " ( F r e n c h , 1965; p. 2 2 ) . A l s o , the h y p o t h e s i s t h a t any p a r t i c u l a r t e s t can change from b e i n g an S t e s t t o b e i n g a Vz t e s t depending on the s t r a t e g y employed ( M i c h a e l et a l . , 1950) can be t e s t e d i n t h i s way. H y p o t h e s i s 5 The sexes w i l l d i f f e r i n the s t r a t e g i e s they employ t o s o l v e the items on v a r i o u s t e s t s . R a t i o n a l e : T h i s h y p o t h e s i s r e l a t e s t o the statement made by W e r d e l i n and S t j e r n b e r g (1969) t h a t the way i n which items a re s o l v e d may change w i t h p r a c t i c e . I f the ' w i t h p r a c t i c e ' a s p e c t of t h i s p o s t u l a t e i s taken to imply t h a t the items become e a s i e r and i f women do, i n f a c t , 25 f i n d c e r t a i n t e s t s more d i f f i c u l t than men t h i s h y p o t h e s i s would i n d i r e c t l y t e s t the assumption put f o r t h by W e r d e l i n and S t j e r n b e r g . H y p o t h e s i s 6 For S t e s t s , people u s i n g a p a r t approach w i l l s c o r e s i g n i f i c a n t l y h i g h e r than p e o p l e u s i n g a whole approach. For Vz t e s t s the r e v e r s e w i l l be the c a s e . R a t i o n a l e : The S t e s t s do not r e q u i r e a r e s t r u c t u r i n g of the s t i m u l u s . I t would be more e f f i c i e n t , as found by B a r r a t t (1953), t o compare the s a l i e n t a s p e c t s of the f i g u r e s r a t h e r than the f i g u r e s as a whole. The Vz t e s t s , on the o t h e r hand, do r e q u i r e a r e s t r u c t u r i n g of the s t i m u l u s i n o r d e r to compare i t t o the f i g u r e ( s ) from which the answer must be chosen. Thus, i t would p r o b a b l y be more e f f i c i e n t to keep the e n t i r e r e s t r u c t u r e d s t i m u l u s i n mind when s e a r c h i n g f o r an answer than t o make the many comparisons n e c e s s a r y f o r c o r r e c t s o l u t i o n . H y p o t h e s i s 7 For S t e s t s , people u s i n g a p a r t approach w i l l f i n d the t e s t s l e s s d i f f i c u l t than p e o p l e u s i n g a whole approach. For Vz t e s t s the r e v e r s e w i l l be the c a s e . R a t i o n a l e : I f r a t e d d i f f i c u l t y c o r r e l a t e s w i t h a b i l i t y , the d i f f i c u l t y f i n d i n g s s h o u l d p a r a l l e l t hose of a b i l i t y ( H y p o t h e s i s 6 ) . 26 H y p o t h e s i s 3 S t e s t s w i l l be r a t e d as l e s s d i f f i c u l t than Vz t e s t s . R a t i o n a l e : T h i s h y p o t h e s i s t e s t s s t a tements made t o t h i s e f f e c t by Zimmerman (1954) and by Ekstrom et a l . (1976) i n the Manual of the K i t of F a c t o r - R e f e r e n c e d C o g n i t i v e T e s t s . I t i s not c l e a r t h a t t h i s h y p o t h e s i s has ever been t e s t e d e i t h e r w i t h o b j e c t i v e or s u b j e c t i v e (as used here) d i f f i c u l t y r a t i n g s . H y p o t h e s i s 9 P r i n c i p a l component a n a l y s i s of the f i v e s p a t i a l t e s t s c o r e s w i l l y i e l d a f i r s t p r i n c i p a l component of s m a l l e r v a r i a n c e f o r men than f o r women. R a t i o n a l e : T h i s i s an at t e m p t e d c o n f i r m a t i o n of Very (1967) and B a r r a t t (1955) t h a t S and Vz are more d i s t i n c t f o r men than women. H y p o t h e s i s 10 For p a i r s of t e s t s , ' as t h e d i f f e r e n c e i n r a t e d d i f f i c u l t y i n c r e a s e s the c o r r e l a t i o n between the two w i l l d e c r e a s e . R a t i o n a l e : The ev i d e n c e d i s c u s s e d p r e v i o u s l y i n d i c a t e s t h a t the c o r r e l a t i o n s between t e s t s d e c r e a s e as the d i f f e r e n c e i n o b j e c t i v e d i f f i c u l t y i n c r e a s e s (Ferguson, 1941; G u i l f o r d , 1941; Sar g e n t , 1940). T h i s h y p o t h e s i s t e s t s t h e s e f i n d i n g s a t a more i n d i v i d u a l l e v e l i n t h a t i t t a k e s i n t o account how d i f f i c u l t each t e s t was f o r each i n d i v i d u a l r a t h e r than a t a group l e v e l . 27 Method Q u e s t i o n n a i r e s The Card R o t a t i o n s Test ( S i ) and the Cube Comparisons Test (S2) were used as measures of S p a t i a l O r i e n t a t i o n ( S ) , and the Form Board Test ( V z l ) , the Paper F o l d i n g Test ( V z 2 ) , and the S u r f a c e Development Test (Vz3) were used as measures of V i s u a l i z a t i o n ( V z ) . These t e s t s were taken from the 1976 v e r s i o n of the K i t of F a c t o r - R e f e r e n c e d C o g n i t i v e T e s t s (Ekstrom e t a l . , 1976). P a r t one of each t e s t was used. T e s t s Vz3 and V z l were completed t h i r d and f i f t h , r e s p e c t i v e l y . The o r d e r of the o t h e r t h r e e t e s t s (S1, S2, and Vz2) was randomized. For the d i f f i c u l t y r a t i n g a 9 p o i n t s c a l e l a b e l l e d a t t h r e e p o i n t s (1 = v e r y easy, 5 = m o d e r a t e l y e a s y / d i f f i c u l t , 9 = v e r y d i f f i c u l t ) was used (see Appendix B ) . There was one r a t i n g s c a l e f o r each t e s t and the t e s t t o be r a t e d on each s c a l e was made s a l i e n t by p r e c e d i n g the s c a l e w i t h s t i m u l u s items from the a p p r o p r i a t e t e s t . Problem s o l v i n g s t r a t e g y was a s s e s s e d w i t h s i x items f o r each t e s t (see Appendix C ) . To each statement p a r t i c i p a n t s were t o answer e i t h e r 'TRUE' or 'FALSE'. Statements f o r each t e s t were a g a i n preceded by sample items from t h a t t e s t (see Appendix D f o r an e x p l a n a t i o n of t h e . s t a t e m e n t s u s e d ) . 28 Procedure A f t e r a b r i e f i n t r o d u c t i o n t o the purposes of the stu d y , p a r t i c i p a n t s were asked t o complete a t i t l e page by i n d i c a t i n g age, sex, year of u n i v e r s i t y , u n i v e r s i t y f a c u l t y and major. They were a l s o asked t o p r o v i d e t h e i r student i d e n t i f i c a t i o n numbers on t h i s page i f they wanted anonymous feedback. A f t e r p a r t i c i p a n t s i n d i c a t e d t h a t they had completed the t i t l e page they were asked i f t h e r e were any q u e s t i o n s . A f t e r a n swering t h e s e , the f o l l o w i n g p rocedure was employed f o r each of the t e s t s . P a r t i c i p a n t s were asked t o t u r n the page and read the i n s t r u c t i o n s t o the next t e s t (see Ekstrom et a l . , 1976 f o r the i n s t r u c t i o n s ) . A f t e r 1.5 minutes they were asked t o i n d i c a t e i f they had not f i n i s h e d the i n s t r u c t i o n s by r a i s i n g t h e i r hands. I f a m a j o r i t y of people had f i n i s h e d , an a d d i t i o n a l 15 seconds were a l l o w e d . O t h e r w i s e , an a d d i t i o n a l 30 seconds were g i v e n . At the end of t h i s t i m e , p a r t i c i p a n t s were t o l d t o ' s t a r t now'. At the end of the time a l l o w e d f o r c o m p l e t i o n of each t e s t (see Appendix A ) , p a r t i c i p a n t s were t o l d t o ' s t o p ' . A f t e r the l a s t t e s t ( V z l ) p a r t i c i p a n t s were asked t o r a t e the d i f f i c u l t y of each t e s t (see Appendix B) and t o i n d i c a t e how they s o l v e d the items on each of the t e s t s (see Appendix C ) . T h i s p a r t of the study was not t i m e d . Upon c o m p l e t i o n p a r t i c i p a n t s were asked t o t a k e t h e i r b o o k l e t s t o the f r o n t of the room. 29 At a l a t e r date feedback was p r o v i d e d i n d i c a t i n g an i n d i v i d u a l ' s performance as w e l l as means f o r each of the t e s t s . P a r t i e i p a n t s P a r t i c i p a n t s were r e c r u i t e d i n i n t r o d u c t o r y p s y c h o l o g y c l a s s e s d u r i n g the f a l l term of the 1980/81 academic y e a r . A l t h o u g h 572 peopl e r e t u r n e d b o o k l e t s , 35 of t h e s e were dropped from a l l a n a l y s e s because one or more of the t e s t s were not completed. People were d e l e t e d due t o the p o s s i b i l i t y t h a t they worked on a t e s t a t an i n a p p r o p r i a t e time ( i . e . when they s h o u l d have been c o m p l e t i n g another t e s t ) . Thus, a l l a n a l y s e s a r e based on a maximum of 537 p e o p l e . The mean age of the 537 p a r t i c i p a n t s (266 men, 268 women, 3 sex not s p e c i f i e d ) was 18.78 (minimum 17, maximum 4 0 ) . Of the 484 people who r e p o r t e d a f a c u l t y , 51.7% were r e g i s t e r e d i n A r t s , 21.9% i n S c i e n c e , 12.2% i n E n g i n e e r i n g , and 14.2% i n v a r i o u s o t h e r f a c u l t i e s . Of the 492 p e o p l e who r e p o r t e d year of r e g i s t r a t i o n , 73.2% were i n f i r s t , 23.8% i n second, 2.6% i n t h i r d , and 0.4% i n f o u r t h y e a r . R e s u l t s 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 d i f f i c u l t y r a t i n g s and a l l t e s t s c o r e s ( c o r r e c t e d f o r g u e s s i n g ) a re p r e s e n t e d by sex and f o r the t o t a l group i n T a b l e 1. Due t o the l a r g e number of pe o p l e i n v o l v e d i n most 30 a n a l y s e s t o be d i s c u s s e d below, t r e n d s ( i . e . .05 < p_ < .10) were t r e a t e d as n o n s i g n i f i c a n t . F u r t h e r , when post hoc comparisons were performed S c h e f f e ' s method (Hays, 1973), w i t h the s i g n i f i c a n c e l e v e l s et a t .05, was used e x c l u s i v e l y . Moreover, a l l 2x2 C h i - s q u a r e v a l u e s r e p o r t e d are based on Ya t e s ' c o r r e c t i o n r e g a r d l e s s of exp e c t e d c e l l f r e q u e n c y (Ferguson, 1976). In c o n s i d e r a t i o n of the w i d e l y c i t e d sex d i f f e r e n c e s i n s p a t i a l a b i l i t y a l l a n a l y s e s were performed f o r the sexes s e p a r a t e l y as w e l l as f o r the t o t a l group. In the case of a n a l y s i s of v a r i a n c e (ANOVA) sex i s always a f a c t o r . H y p o t h e s i s 1 . The: d i f f i c u l t y r a t i n g a s s i g n e d t o a t e s t . w i l l c o r r e l a t e more n e g a t i v e l y w i t h the t o t a l s c o r e on t h a t t e s t than w i t h the t o t a l s c o r e on any o t h e r t e s t . The c o r r e l a t i o n s r e l a t e d t o t h i s h y p o t h e s i s a r e p r e s e n t e d i n Table 2. For women, men, and the t o t a l group, the c o r r e l a t i o n s were as p r e d i c t e d . For men the c o r r e l a t i o n s between d i f f i c u l t y r a t i n g and t e s t s c o r e ranged from -.24 (Cubes) t o -.59 ( S u r f a c e Development) w h i l e f o r women they ranged from -.16 (Form Board) t o -.64 ( S u r f a c e Development). Thus, a l t h o u g h t h e r e a r e s u b s t a n t i a l d i f f e r e n c e s i n the magnitude of the c o r r e l a t i o n s , p e r c e i v e d d i f f i c u l t y does appear t o be r e l a t e d t o performance. F u r t h e r , the p e r c e i v e d d i f f i c u l t y of any p a r t i c u l a r t e s t i s more 31 r e l a t e d t o performance on t h a t t e s t than t o performance on any o t h e r t e s t . H y p o t h e s i s 2 Men w i l l s c o r e s i g n i f i c a n t l y h i g h e r on Vz, but not on S t e s t s , than women. In o r d e r t o s t r i n g e n t l y t e s t t h i s h y p o t h e s i s a H o t e l l i n g ' s T 2 a n a l y s i s was performed w i t h the f i v e s p a t i a l t e s t s c o r e s s e r v i n g as the dependent v a r i a b l e s . Men and women were found t o d i f f e r s i g n i f i c a n t l y (F (5,528) = 26.42, £ < .01) and pos t hoc m u l t i p l e comparisons r e v e a l e d t h a t men 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 than women on a l l t e s t s (see Table 1 f o r means and st a n d a r d d e v i a t i o n s ) . I t seems, t h e r e f o r e , t h a t the sex d i f f e r e n c e i n s p a t i a l a b i l i t y i s not l i m i t e d o n l y t o t e s t s of Vz, but m a n i f e s t s i t s e l f on S t e s t s as w e l l . H y p o t h e s i s 3 Men w i l l r a t e Vz t e s t s , but not S t e s t s , as s i g n i f i c a n t l y l e s s d i f f i c u l t than w i l l women. For t h i s a n a l y s i s the f i v e d i f f i c u l t y r a t i n g s were t r e a t e d as r e p e a t e d measures and a Sex x Test D i f f i c u l t y r e p e a t e d measures ANOVA was performed (see T a b l e 3 ) . T h i s r e v e a l e d s i g n i f i c a n t e f f e c t s f o r Sex (F (1,529) = 62.07, 2 < .001), Test D i f f i c u l t y (F (4,2116) = 327.17, p_ < .001), and a Sex x Test D i f f i c u l t y i n t e r a c t i o n (F (4,2116) = 24.50, p_ < .01). Post hoc comparisons i n d i c a t e d t h a t women r a t e d both the Cubes and S u r f a c e 32 Development t e s t s as more d i f f i c u l t than d i d men. There were no s i g n i f i c a n t d i f f e r e n c e s on the o t h e r t e s t s (see Tab l e 1 f o r means and s t a n d a r d d e v i a t i o n s ) . C o n s i d e r i n g t h a t t h e r e were sex d i f f e r e n c e s on o n l y two of the t e s t s (one S and one Vz) support f o r t h i s h y p o t h e s i s does not seem adequate. The sex d i f f e r e n c e s i n a b i l i t y ( i . e . s i g n i f i c a n t d i f f e r e n c e s on a l l t e s t s ) do not p a r a l l e l the f i n d i n g s c o n c e r n i n g d i f f i c u l t y . W i t h i n sex comparisons based on t h i s a n a l y s i s w i l l be d i s c u s s e d under H y p o t h e s i s 8. H y p o t h e s i s 4 . People u s i n g a p a r t approach on one t e s t and a- whole approach on another t e s t w i l l e x h i b i t a lower c o r r e l a t i o n between th e s e t e s t s than people u s i n g the same approach on both t e s t s . The number of people who answered ' t r u e ' t o the v a r i o u s s t a tements r e g a r d i n g problem s o l v i n g s t r a t e g y are g i v e n i n Table 4. Of i n t e r e s t t o t h i s h y p o t h e s i s a re the f i r s t f o u r s t a tements f o r each t e s t . For any p a r t i c u l a r t e s t , p e o p l e who answered ' t r u e ' t o one or more of the p a r t s t r a t e g i e s (as i n d i c a t e d i n Appendix D) and answered ' f a l s e ' t o a l l of the whole s t r a t e g i e s a re d e f i n e d as the ' p a r t ' subgroup. The 'whole' subgroup c o n s i s t s of peop l e who answered ' t r u e ' t o one or more of the whole s t r a t e g i e s and ' f a l s e ' t o a l l of the p a r t s t r a t e g i e s . A t h i r d subgroup, t o be c o n s i d e r e d l a t e r , c o n s i s t s of people who answered ' t r u e ' t o a t l e a s t 33 one p a r t s t r a t e g y as w e l l as a t l e a s t one whole s t r a t e g y . T h i s group i s r e f e r r e d t o as t h e ' p a r t / w h o l e ' subgroup. Thus, f o r the Paper F o l d i n g T e s t , f o r i n s t a n c e , a person who answered ' t r u e ' t o s t r a t e g i e s one and two and ' f a l s e ' t o t h r e e and f o u r would f a l l i n t o the p a r t / w h o l e subgroup; a person who answered ' t r u e ' t o s t r a t e g y one and ' f a l s e ' t o the r e s t would be i n the whole subgroup; a person who answered ' t r u e ' t o s t r a t e g y two and ' f a l s e ' t o the r e s t would be i n the p a r t subgroup; and peop l e who answered ' f a l s e ' t o a l l f o u r s t r a t e g i e s would not be c o n s i d e r e d i n any a n a l y s i s i n v o l v i n g problem s o l v i n g s t r a t e g y . For p a i r s of t e s t s , t h e n , p e o p l e who f e l l i n t o the same subgroup on both t e s t s ( i . e . i n t o the p a r t subgroup on both t e s t s or i n t o the whole subgroup on both t e s t s ) were deemed t o have used the 'same' problem s o l v i n g approach t o both t e s t s . Those who f e l l i n t o d i f f e r e n t subgroups f o r the two t e s t s ( i . e . the p a r t subgroup f o r one t e s t and the whole subgroup f o r the o t h e r ) were deemed t o have employed ' d i f f e r e n t ' problem s o l v i n g approaches t o the two t e s t s . The number of peop l e who f e l l i n t o the 'same' and ' d i f f e r e n t ' groups f o r each p a i r of t e s t s as w e l l as the c o r r e l a t i o n s between the t e s t s f o r the two groups are g i v e n i n Table 5. For the t o t a l sample, as w e l l as f o r the sexes s e p a r a t e l y , the c o r r e l a t i o n s between the 'same' and ' d i f f e r e n t ' groups were compared by f i r s t u s i n g F i s h e r ' s £ t o 2 t r a n s f o r m a t i o n (Hays, 1973). Of the 30 co m p a r i s o n s , 34 13 n e g a t i v e and 17 p o s i t i v e z_ v a l u e s were o b t a i n e d . None of these s u r p a s s e d the c r i t i c a l v a l u e f o r a o n e - t a i l e d t e s t ( 1 . 6 5 ). Given t h e s e f i n d i n g s , i t may be c o n c l u d e d t h a t the d i s t i n c t i o n between p a r t and whole problem s o l v i n g (as here measured) has l i t t l e t o do w i t h the c o r r e l a t i o n s between t e s t s . H y p o t h e s i s 5 The sexes w i l l d i f f e r i n the s t r a t e g i e s they employ t o s o l v e the items on v a r i o u s t e s t s . To a s s e s s t h i s h y p o t h e s i s 2x2 C h i - s q u a r e (male/female v e r s u s t r u e / f a l s e ) a n a l y s e s were performed f o r each of the 30 s t r a t e g y s t a t e m e n t s (see Table 4 f o r the number of people i n each g r o u p ) . On a l l t e s t s women i n d i c a t e d t h a t they guessed more (p_ < .05 i n a l l c a s e s ) . F u r t h e r , women answered ' t r u e ' t o the f o l l o w i n g s t a t e m e n t s more o f t e n than men: I m e n t a l l y f o l d e d the paper, punched a h o l e , and then m e n t a l l y u n f o l d e d i t and compared i t t o the p o s s i b l e answers (from Paper F o l d i n g ; ^ (1 ) = 4.1.2, 2 < - 0 5 ) ? 1 d i d n ' t use any p a r t i c u l a r s t r a t e g y (from S u r f a c e Development; (1 ) = 23.20, p_ < .001); I noted some d i s t i n c t a s p e c t of the f i g u r e (e.g. bottom p a r t or t o p l e f t c o r n e r ) and s o l v e d the f i g u r e s w i t h t h i s f e a t u r e i n mind (from Cards; (1) = 6.81, p_ < .01); I used a p e n c i l t o draw the l a r g e f i g u r e out of the s m a l l e r ones (from Form Board; (1) = 4.80, 2 < .05) . 35 At a more g l o b a l l e v e l , C h i - s q u a r e t e s t s were performed t o determine i f , on each t e s t , sex was independent of o v e r a l l s t r a t e g y employed ( i . e . p a r t , whole, p a r t / w h o l e ) . The o n l y t e s t t o rea c h s i g n i f i c a n c e h i g h l i g h t e d by the f a c t t h a t a g r e a t e r p e r c e n t a g e of men (36.9 compared t o 25.6% of the women) f e l l i n t o the p a r t subgroup, w h i l e a g r e a t e r p e r c e n t a g e of women (64.9 compared t o 53.6% of the men) f e l l i n t o the p a r t / w h o l e subgroup (see T a b l e s 6 t o 10 f o r the number of men and women i n each group f o r each t e s t ) . G e n e r a l l y , t h e n , t h i s h y p o t h e s i s may be r e j e c t e d . Only t h r e e of the twenty statements which were d e s i g n e d t o r e f l e c t p a r t or whole problem s o l v i n g s t r a t e g y d i s c r i m i n a t e d men from women. A l s o , on o n l y one t e s t d i d the sexes d i f f e r i n o v e r a l l s t r a t e g y employed and t h i s f i n d i n g may w e l l have been i n f l u e n c e d by the s m a l l number of people i n the p a r t subgroup.. H y p o t h e s i s 6 For S t e s t s , p e o p l e u s i n g a p a r t approach w i l l s c o r e s i g n i f i c a n t l y h i g h e r than p e o p l e . u s i n g a whole approach. For Vz t e s t s the r e v e r s e w i l l be the c a s e . For each t e s t a Sex x S t r a t e g y ( p a r t , whole, p a r t / w h o l e ) ANOVA was performed (see T a b l e s 6 t o 10 f o r the source t a b l e s and means). In a l l c a s e s , men 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 than women (see H y p o t h e s i s 2 f o r a more a p p r o p r i a t e s t a t i s t i c a l t e s t of the s e f i n d i n g s ) . Of was f o r the Cards t e s t T h i s was 36 major c o n c e r n f o r t h i s h y p o t h e s i s are the S t r a t e g y and Sex x S t r a t e g y f i n d i n g s . For the Cards Test a s i g n i f i c a n t e f f e c t f o r S t r a t e g y was found (F (2,519) = 4.33, 2 '< .05), a l t h o u g h post hoc comparisons ( S c h e f f e ) i n d i c a t e d no s i g n i f i c a n t d i f f e r e n c e s between any two of the subgroups. On.the o t h e r S t e s t (Cubes) t h e r e was a s i g n i f i c a n t Sex x S t r a t e g y i n t e r a c t i o n (F (2,518) = 4.07, p_ < .05). A l t h o u g h post hoc comparisons r e v e a l e d no w i t h i n sex d i f f e r e n c e s , the male p a r t / w h o l e subgroup s c o r e d h i g h e r than the female whole and p a r t / w h o l e subgroups, and the male p a r t subgroup d i d not s c o r e h i g h e r than any female subgroup. In c o n s i d e r i n g these r e s u l t s i t i s i m p o r t a n t t o note the r e l a t i v e l y few people i n the p a r t subgroups (19- men, 21 women). For the Vz t e s t s , t h e r e was a s i g n i f i c a n t S t r a t e g y e f f e c t f o r Paper F o l d i n g (F (2,521) = 3.53, 2 < -05) and s i g n i f i c a n t Sex x S t r a t e g y (F (2,512) = 5.14, 2 K a n d S t r a t e g y (F (2,512) = 5.52, g .< .01) e f f e c t s f o r S u r f a c e Development. For the Form Board Test the o n l y s i g n i f i c a n t e f f e c t was Sex. Post hoc comparisons f o r the Vz t e s t f i n d i n g s i n d i c a t e d t h a t , f o r Paper F o l d i n g , the p a r t subgroup s c o r e d lower than the p a r t / w h o l e subgroup. To be noted i s t h a t the p a r t subgroup c o n s i s t e d of o n l y 25 p e o p l e . The Sex x S t r a t e g y i n t e r a c t i o n f o r S u r f a c e Development was h i g h l i g h t e d by the f i n d i n g t h a t the male whole subgroup s c o r e d lower than the male p a r t subgroup. There were no 37 o t h e r w i t h i n sex d i f f e r e n c e s , and a l l male subgroups s c o r e d h i g h e r than a l l female subgroups. Given the s i g n i f i c a n t sex d i f f e r e n c e s i n performance (see H y p o t h e s i s 2) the a n a l y s e s of major concern t o t h i s h y p o t h e s i s a r e the S t r a t e g y and Sex x S t r a t e g y post hoc comparisons. The o n l y w i t h i n sex comparison t o a c h i e v e s i g n i f i c a n c e ( S u r f a c e Development) does not support the h y p o t h e s i s s i n c e the male whole subgroup s c o r e d lower than the male p a r t subgroup. F u r t h e r , the o n l y post hoc comparison r e l a t e d t o S t r a t e g y which was s i g n i f i c a n t (Paper F o l d i n g ) d i d not i n d i c a t e t h a t the p a r t and whole subgroups d i f f e r e d . Thus, i t seems t h a t performance i s not t i e d t o problem s o l v i n g s t r a t e g y i n a c o n s i s t e n t manner and the h y p o t h e s i s may be l a r g e l y r e j e c t e d . H y p o t h e s i s 7 For S t e s t s , people u s i n g a p a r t approach w i l l f i n d the t e s t s l e s s d i f f i c u l t than p e o p l e u s i n g a whole approach. For Vz t e s t s the r e v e r s e w i l l be the c a s e . For each t e s t a Sex x S t r a t e g y ( p a r t , whole, p a r t / w h o l e ) ANOVA was performed w i t h d i f f i c u l t y r a t i n g s e r v i n g as the dependent v a r i a b l e (see T a b l e s 11 t o 15 f o r the source t a b l e s and means). Except f o r the Form Board Test women r a t e d a l l t e s t s as more d i f f i c u l t than d i d men. Si n c e sex d i f f e r e n c e s r e l a t e d t o d i f f i c u l t y were d i s c u s s e d p r e v i o u s l y ( H y p o t h e s i s 3) based on a more a p p r o p r i a t e s t a t i s t i c a l p r o c e d u r e , they w i l l not be d i s c u s s e d f u r t h e r h e r e . 38 Two o t h e r e f f e c t s a l s o reached s i g n i f i c a n c e . On the Paper F o l d i n g Test post hoc a n a l y s e s of the S t r a t e g y e f f e c t (F (2,526) = 5.47, p < .01) r e v e a l e d t h a t the p a r t subgroup r a t e d the t e s t as more d i f f i c u l t than each of the o t h e r two groups. A l t h o u g h t h e r e was a s i g n i f i c a n t Sex x S t r a t e g y i n t e r a c t i o n f o r the S u r f a c e Development Test (F (2,512) = 4.69, p_ < .01), p o s t hoc comparisons d i d not r e v e a l any w i t h i n sex d i f f e r e n c e s . A l l male subgroups r a t e d the t e s t as l e s s d i f f i c u l t than a l l female subgroups. S i n c e ' o n l y one f i n d i n g was i n the h y p o t h e s i z e d d i r e c t i o n (the S t r a t e g y e f f e c t f o r Paper F o l d i n g ) t h i s h y p o t h e s i s may be l a r g e l y r e j e c t e d . H y p o t h e s i s 8 S t e s t s w i l l be r a t e d as l e s s d i f f i c u l t than Vz t e s t s . T h i s h y p o t h e s i s was a s s e s s e d by p e r f o r m i n g w i t h i n sex post hoc comparisons on the v a r i o u s mean d i f f i c u l t y r a t i n g s (see H y p o t h e s i s 3 f o r a d i s c u s s i o n of the r e p e a t e d measures d e s i g n employed). For bo t h men and women the Paper F o l d i n g Test and the Cubes Test were the o n l y two t e s t s which d i d not d i f f e r s i g n i f i c a n t l y i n mean d i f f i c u l t y r a t i n g . Women r a t e d the t e s t s , from e a s i e s t t o most d i f f i c u l t , i n the f o l l o w i n g o r d e r : Cards ( S 1 ) , Paper F o l d i n g ( V z 2 ) , Cubes ( S 2 ) , S u r f a c e Development ( V z 3 ) , Form Board ( V z l ) . Except t h a t the o r d e r of S u r f a c e Development and Form Board was r e v e r s e d , men o r d e r e d the t e s t s i n the 39 same way. Support f o r t h i s h y p o t h e s i s i s tenuous. A l t h o u g h two Vz t e s t s were r a t e d most di'f f i c u l t . ( S u r f a c e Development and Form Board) the o t h e r Vz t e s t (Paper F o l d i n g ) d i d not d i f f e r i n r a t e d d i f f i c u l t y from the more d i f f i c u l t S t e s t (Cubes). H y p o t h e s i s 9 P r i n c i p a l component a n a l y s i s of the f i v e s p a t i a l t e s t s c o r e s w i l l y i e l d a f i r s t p r i n c i p a l component of s m a l l e r v a r i a n c e f o r men than f o r women. The c o r r e l a t i o n m a t r i c e s which were f a c t o r e d a r e p r e s e n t e d i n Table 16. To be noted i s t h a t , w i t h few e x c e p t i o n s , the c o r r e l a t i o n s among t e s t s of the same type ( i . e . w i t h i n S and w i t h i n Vz t e s t c o r r e l a t i o n s ) a r e h i g h e r than the c o r r e l a t i o n s between S and Vz t e s t s . • Even though t h i s i s the ca s e , however, the e i g e n v a l u e c o r r e s p o n d i n g t o the second p r i n c i p a l component was never g r e a t e r than u n i t y . The f i r s t p r i n c i p a l component accounted f o r 52.5, 52.1, and 56.8% of the v a r i a n c e f o r men, women, and the t o t a l group, 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 p e r c e n t a g e s f o r the second p r i n c i p a l component were 17.1, 16.3, and 15.1. F u r t h e r , v i s u a l i n s p e c t i o n of the m a t r i c e s p r e s e n t e d i n Ta b l e 16 r e v e a l s few d i f f e r e n c e s i n magnitude i n the c o r r e l a t i o n s f o r men and women. R e g a r d l e s s of the f i n d i n g s p r e s e n t e d above and i g n o r i n g the p o s s i b i l i t y of over f a c t o r i n g when the second component a c c o u n t s f o r so l i t t l e v a r i a n c e (see Harman, 40 1976), two p r i n c i p a l components were e x t r a c t e d and r o t a t e d t o s i m p l e s t r u c t u r e u s i n g a Varimax r o t a t i o n . The o b t a i n e d p a t t e r n m a t r i c e s a r e p r e s e n t e d i n Table 17. I n t e r p r e t a t i o n of these m a t r i c e s would i n d i c a t e t h a t the Vz t e s t s d e f i n e F a c t o r I and t h a t the S t e s t s d e f i n e F a c t o r I I . The a n a l y s e s f o r two f a c t o r s are i n c l u d e d f o r i l l u s t r a t i v e purposes o n l y . T h i s i s a l s o t r u e of the a n a l y s e s f o r the t o t a l group because the t e s t f o r i n e q u a l i t y of the v a r i a n c e / c o v a r i a n c e m a t r i c e s (see M o r r i s o n , 1976) i n d i c a t e d t h a t the da t a f o r men and women s h o u l d n o t , i d e a l l y , have been p o o l e d ( J{ (15) = 32.71, 2 < .01). The l i k e l i h o o d t h a t the t w o - f a c t o r s o l u t i o n s r e p r e s e n t an o v e r f a c t o r i n g of the data i s suggested by the a p p l i c a t i o n of the t h r e e most commonly used' t e s t s f o r the number of f a c t o r s t o r e t a i n (see H a k s t i a n , 1973). The 'Kaiser-Guttman r u l e ' ( e i g e n v a l u e s g r e a t e r than u n i t y ) s u g g e s t s one f a c t o r f o r both men and women. The 'maximum l i k e l i h o o d - r a t i o t e s t ' s u g g e s t s two f a c t o r s f o r men ( % (1 ) = .59, g = .44) and one f a c t o r f o r women ( % (5) =10.08, 2 = -07). F i n a l l y , the 'Scree t e s t ' ( f i n d i n g the break i n the cu r v e of p l o t t e d e i g e n v a l u e s ) i n d i c a t e s one f a c t o r f o r both men and women. Thus, t h r e e of t h r e e t e s t s f o r women and two of t h r e e t e s t s f o r men suggest one s p a t i a l f a c t o r . Due t o the a u t h o r ' s b e l i e f t h a t the da t a have p r o b a b l y been o v e r f a c t o r e d the t w o - f a c t o r f i n d i n g s w i l l not be pursued 41 f u r t h e r . H y p o t h e s i s 10 For p a i r s of t e s t s , as the d i f f e r e n c e i n r a t e d d i f f i c u l t y i n c r e a s e s the c o r r e l a t i o n between the two w i l l d e c r e a s e . For any two g i v e n t e s t s , the a b s o l u t e v a l u e of the d i f f e r e n c e i n r a t e d d i f f i c u l t y was c a l c u l a t e d f o r each p e r s o n . On the b a s i s of the d i s t r i b u t i o n of t h i s v a l u e a median s p l i t procedure was employed t o y i e l d two groups; a group w i t h a 'low' d i f f e r e n c e i n d i f f i c u l t y (the low d i f f e r e n c e g r o u p ) , and a group w i t h a ' h i g h ' d i f f e r e n c e i n d i f f i c u l t y (the h i g h d i f f e r e n c e g r o u p ) . T h i s s t r a t e g y was f o l l o w e d f o r men and women s e p a r a t e l y , and a l s o f o r the group as a whole. The v a l u e s used t o d e f i n e the two groups were the same f o r the male, female, and t o t a l groups w i t h two e x c e p t i o n s (see Table 18 f o r the v a l u e s u s e d ) . F o l l o w i n g the c r e a t i o n of the low and h i g h d i f f e r e n c e groups the c o r r e l a t i o n between the two t e s t s i n v o l v e d was computed f o r each group. For c l a r i f i c a t i o n of the procedure employed, two t e s t s w i l l be chosen (Paper F o l d i n g and S u r f a c e Development). For each person i n the t o t a l group the d i f f i c u l t y r a t i n g of Paper F o l d i n g was s u b t r a c t e d from the d i f f i c u l t y r a t i n g of S u r f a c e Development. The a b s o l u t e v a l u e of t h i s d i f f e r e n c e was taken and a f r e q u e n c y d i s t r i b u t i o n o f , i n t h i s c a s e , 537 v a l u e s was o b t a i n e d . I n s p e c t i o n of t h i s 42 d i s t r i b u t i o n r e v e a l e d t h a t 268 p e o p l e had a b s o l u t e v a l u e s of two or l e s s w h i l e 269 p e o p l e had a b s o l u t e v a l u e s of t h r e e or more. S i n c e i t was d e s i r e d t o c r e a t e . t w o groups of a p p r o x i m a t e l y e q u a l s i z e , those people w i t h v a l u e s of two or l e s s d e f i n e d the low d i f f e r e n c e group, and people w i t h v a l u e s g r e a t e r than two c o m p r ised the h i g h d i f f e r e n c e group. F o l l o w i n g t h i s , the c o r r e l a t i o n between Paper F o l d i n g and S u r f a c e Development was computed f o r both the low and h i g h d i f f e r e n c e groups. T h i s p r o c e d u r e was f o l l o w e d f o r each p a i r , of t e s t s ( i . e . 10 p a i r s f o r f i v e t e s t s ) . The c o r r e l a t i o n s f o r the h i g h and low d i f f e r e n c e groups were compared by f i r s t u s i n g F i s h e r ' s r t o Z t r a n s f o r m a t i o n . These c o r r e l a t i o n s , a l o n g w i t h the number of peo p l e e n t e r i n g i n t o t h e i r c o m p u t a t i o n , a r e p r e s e n t e d i n T a b l e 18. For the t o t a l sample f i v e of the 10 comparisons were s i g n i f i c a n t (p_ < .05, o n e - t a i l e d ) i n t h a t t h e ' low d i f f e r e n c e group e x h i b i t e d a h i g h e r c o r r e l a t i o n between the two t e s t s than the h i g h d i f f e r e n c e group. For men, s i x of the 10 comparisons were s i g n i f i c a n t and f o r women t h r e e of the comparisons were s i g n i f i c a n t . To a d d r e s s the p o s s i b i l i t y t h a t these r e s u l t s may, i n some way, be a r t i f a c t u a l due t o a t r u n c a t i o n of range or l e s s e n e d v a r i a b i l i t y , the v a r i a n c e s of the low and h i g h d i f f e r e n c e groups were compared on the t e s t s i n v o l v e d . On those comparisons f o r which a s i g n i f i c a n t " d i f f e r e n c e i n 43 c o r r e l a t i o n s was found, the f o l l o w i n g d i f f e r e n c e s i n v a r i a b i l i t y were noted; on the Paper F o l d i n g / C a r d s comparison the low d i f f i c u l t y group was more v a r i a b l e on Paper F o l d i n g (F (252,284) = 1.34, £ < .01):; on the Paper F o l d i n g / S u r f a c e Development comparison the low d i f f i c u l t y female group was more v a r i a b l e on S u r f a c e Development (F (115,163) = 1.36, £ < .05); . on the S u r f a c e Development/Cubes comparison the low d i f f i c u l t y male group was more v a r i a b l e on Cubes (F (160,104) = 1.36, £ < .05). Thus, t h e r e seems t o be some support f o r the h y p o t h e s i s t h a t p e r c e i v e d d i f f e r e n c e s i n d i f f i c u l t y a r e r e l a t e d t o the c o r r e l a t i o n s between t e s t s . The e f f e c t , however, seems t o be much s t r o n g e r f o r men ( s i x of 10) than f o r women ( t h r e e of 10). D i s c u s s i o n In g e n e r a l , the major purpose of t h i s study was t o c l a r i f y the d i s t i n c t i o n between two s u b f a c t o r s of s p a t i a l a b i l i t y i n terms of problem s o l v i n g s t r a t e g y and p e r c e i v e d d i f f i c u l t y of the t e s t s i n v o l v e d . S e c o n d a r i l y , s p a t i a l t e s t s were the v e h i c l e used t o t e s t some t h e o r e t i c a l n o t i o n s t h a t d i f f e r e n c e s i n p e r c e i v e d d i f f i c u l t y between two t e s t s would a f f e c t the c o r r e l a t i o n between th e s e same t e s t s . I t was found t h a t two s u b f a c t o r s ( i . e . S p a t i a l O r i e n t a t i o n and V i s u a l i z a t i o n ) d i d not m a n i f e s t t hemselves i n t h i s s t u d y . T h i s was the case f o r both men and women: 44 a r e s u l t which runs c o n t r a r y t o the f i n d i n g s of B a r r a t t (1955) and Very (1967) t h a t men would e x h i b i t more than one s p a t i a l f a c t o r w h i l e women would e x h i b i t o n l y one. Re f e r e n c e d p r e v i o u s l y was the id e a t h a t , depending on the problem s o l v i n g s t r a t e g y employed, a t e s t c o u l d move from one f a c t o r t o the o t h e r . S i n c e two f a c t o r s were not found, t h i s h y p o t h e s i s c o u l d not. be t e s t e d . . I t was p o s s i b l e , however, t o t e s t whether or not a group of people who used the same s t r a t e g y on each of two t e s t s would e x h i b i t a h i g h e r c o r r e l a t i o n between t h e s e two t e s t s than a group which used d i f f e r e n t s t r a t e g i e s on the two t e s t s . Of i n t e r e s t i n t h i s r e g a r d was the f i n d i n g t h a t people who use d i f f e r e n t s t r a t e g i e s f o r d i f f e r e n t t a s k s have "succeeded i n d e v e l o p i n g some s p e c i a l i z a t i o n of t h e i r a b i l i t i e s " ( F r e n c h , 1965; p. 2 2 ) . T h i s , a g a i n , was not borne out by the d a t a . Of the 30 comparisons (10 f o r each of men, women, and the t o t a l group) not one was s i g n i f i c a n t . F u r t h e r , the i d e a t h a t use of p a r t problem s o l v i n g s t r a t e g i e s on S t e s t s and whole problem s o l v i n g s t r a t e g i e s on Vz t e s t s would enhance performance ( B a r r a t t , 1953; •Michael e t a l . , 1950) r e c e i v e d no s u p p o r t . Even though the d i s t i n c t i o n between S and Vz i s l o s t f o r the purposes of t h i s s t u d y , the f o r m a t i o n of subgroups on the b a s i s of problem s o l v i n g s t r a t e g y ( i . e . p a r t , whole, p a r t / w h o l e ) was not h e l p f u l i n d e t e r m i n i n g who would s c o r e i n a p r e d i c t e d d i r e c t i o n on any t e s t s . 45 Add t o t h i s the f i n d i n g s which l a r g e l y r e j e c t e d the hypotheses t h a t p e r c e i v e d d i f f i c u l t y would be t i e d t o problem s o l v i n g s t r a t e g y and t h a t the sexes would d i f f e r i n the s t r a t e g i e s employed, one i s l e f t wondering what problem s o l v i n g s t r a t e g y has t o do w i t h any of the v a r i a b l e s mentioned thus f a r . Of p a r t i c u l a r importance i n t h i s r e g a r d i s the f a c t t h a t so many i n v e s t i g a t o r s have documented a r e l a t i o n s h i p between problem s o l v i n g s t r a t e g y and one or more of these v a r i a b l e s . One p o s s i b i l i t y which must be addressed i n an attempt t o e x p l a i n these n o n s i g n i f i c a n t r e s u l t s i s t h a t the p a r t i c i p a n t s d i d not respond s e r i o u s l y t o t h i s a s p e c t of the s t u d y . There a re a number of f i n d i n g s , however, which m i t i g a t e a g a i n s t such a c o n c l u s i o n . For i n s t a n c e , on a l l t e s t s women i n d i c a t e d t h a t they guessed more. When t h i s i s c o n s i d e r e d i n c o n j u n c t i o n w i t h the f i n d i n g t h a t men sc o r e d h i g h e r than women on a l l t e s t s , i t i s not s u r p r i s i n g . A l s o , a l t h o u g h the r e l a t i o n s h i p i s not p e r f e c t , b oth men and women i n d i c a t e d t h a t they guessed more on the t e s t s they p e r c e i v e d t o be more d i f f i c u l t . F u r t h e r , t h e r e was an i n d i c a t i o n t h a t p e o p l e responded 'TRUE' t o 'I d i d n ' t use any p a r t i c u l a r s t r a t e g y ' more o f t e n f o r the more d i f f i c u l t t e s t s . T h i s i s a l s o not s u r p r i s i n g i f one assumes t h a t a person who has d i f f i c u l t y i n s o l v i n g a p a r t i c u l a r i t e m w i l l b r i n g a v a r i e t y of problem s o l v i n g s t r a t e g i e s t o bear on t h a t i t e m . Thus, the e v i d e n c e i s not c o n s i s t e n t w i t h the id e a t h a t 4 6 respondents d i d not take these items s e r i o u s l y . One problem, however, i s t h a t most p a r t i c i p a n t s tended t o answer i n the same d i r e c t i o n on a number of stat e m e n t s d e s i g n e d t o tap p a r t v e r s u s whole problem s o l v i n g s t r a t e g y . On two of these (one from Paper F o l d i n g , one from Cubes) over 80% of the respondents answered 'TRUE' w h i l e on f o u r (one each from Cards and S u r f a c e Development, two from Cubes) over 80% answered 'FALSE'. With the e x c e p t i o n of S u r f a c e Development, th e s e response p a t t e r n s l e d t o v e r y few people b e i n g i n c l u d e d i n the p a r t subgroups ( i . e . never more than 10%) as compared t o the whole- and p a r t / w h o l e subgroups. T h i s , t h e n , r e s u l t e d i n a l o s s of power t o d e t e c t d i f f e r e n c e s among groups (Hays, 1973). One o t h e r major concern w i t h the assessment of problem s o l v i n g s t r a t e g y i s the i n t r o s p e c t i v e n a t u r e of the t a s k . For i n s t a n c e , response t o the s t r a t e g y s t a t e m e n t s may r e q u i r e a person t o v e r b a l i z e some h i g h e r o r d e r c o g n i t i v e p r o c e s s e s and i t has been suggested t h a t p e o p l e have l i t t l e or no i n t r o s p e c t i v e a c c e s s t o these p r o c e s s e s ( N i s b e t t & W i l s o n , 1977). Thus, i t has been proposed t h a t when peopl e a c t u a l l y do attempt t o r e p o r t on c o g n i t i v e p r o c e s s e s they may, i n f a c t , base t h e i r r e p o r t s on the e x t e n t t o which a s t i m u l u s ( i . e . a s t r a t e g y s t atement) i s a p l a u s i b l e e x p l a n a t i o n f o r some b e h a v i o u r ( i . e . s o l v i n g a s p a t i a l i t e m ) . An example of t h i s may be a f f o r d e d by the s t r a t e g y s t a t e m e n t s f o r the Cubes t e s t . 47 A l t h o u g h a s i g n i f i c a n t p o r t i o n of French's (1965) sample agreed t o h a v i n g used e i t h e r g e o m e t r i c a l terms, or r o t a t i n g the cube on s e p a r a t e axes, or b o t h , o n l y 6.8% of the p r e s e n t sample i n d i c a t e d t h a t they 'had an X and Y a x i s i n mind when s o l v i n g the i t e m s ' . On the o t h e r hand, 89.5% i n d i c a t e d agreement w i t h S t r a t e g y 1 ( i . e . comparing s y m b o l s ) . I t has a l s o been suggested t h a t i n t r o s p e c t i v e r e p o r t s a r e , t o some e x t e n t , based on s o c i a l d e s i r a b i l i t y (Di V e s t a , I n g e r s o l l , & Sunshine, 1971). Thus, f o r i n s t a n c e , i f people b e l i e v e t h a t s o l v i n g items i n one f a s h i o n i s more v a l u e d than s o l v i n g them i n some o t h e r f a s h i o n , t h e i r responses might not be i n d i c a t i v e of the s t r a t e g i e s , they a c t u a l l y employed. Thus, the p r o p o s a l s of both N i s b e t t and W i l s o n (1977) and Di V e s t a et a l . (1971) may r e l a t e t o why so many people responded i n the same way on many of the problem s o l v i n g s t a tements i n c l u d e d i n t h i s s t u d y . . S i n c e t h e r e i s no way t o t e s t e i t h e r of the s e a s s e r t i o n s , however, i t must be c o n c l u d e d t h a t the f a i l u r e of problem s o l v i n g s t r a t e g y t o r e l a t e t o o t h e r v a r i a b l e s i n t h i s s tudy cannot be r e a d i l y e x p l a i n e d . T h e r e f o r e , i n what f o l l o w s , problem s o l v i n g s t r a t e g y w i l l not be d i s c u s s e d f u r t h e r . I t i s suggested, however, t h a t i f one wishes t o pursue t h i s m atter i t would be p r e f e r a b l e not t o s u p p l y p a r t i c i p a n t s w i t h problem s o l v i n g s t r a t e g i e s i n o r d e r t o , i f n o t h i n g e l s e , a v o i d the problem of e x p e r i m e n t e r i n d u c e d s o c i a l 48 d e s i r a b i l i t y of response ( B a r r a t t , 1953). As c o n cerns sex d i f f e r e n c e s , the s i m i l a r i t i e s were more s t r i k i n g than the d i f f e r e n c e s . A l t h o u g h men s c o r e d h i g h e r than women on a l l t e s t s (not j u s t Vz as p r e d i c t e d ) , l a r g e d i f f e r e n c e s i n the c o r r e l a t i o n s between t e s t s d i d not . m a n i f e s t t h e m s e l v e s . For i n s t a n c e , the l a r g e s t d i s c r e p a n c y i n the t e s t s c o r e m a t r i c e s was .14. S i m i l a r l y , the l a r g e s t sex d i f f e r e n c e f o r c o r r e l a t i o n s between t e s t d i f f i c u l t y and t e s t s c o r e was .18. A l s o , w i t h . the e x c e p t i o n of one r e v e r s a l on the two most d i f f i c u l t t e s t s , the sexes rank o r d e r e d the t e s t s on the b a s i s of d i f f i c u l t y i n the same way. F i n a l l y , even though men s c o r e d h i g h e r than women on a l l t e s t s , women and men d i d not d i f f e r s i g n i f i c a n t l y on the d i f f i c u l t y r a t i n g of t h r e e of the t e s t s . The l a s t p o i n t , t h e n , l e a d s one t o a d i s c u s s i o n of the d i f f i c u l t y i n d e x . Why, i t may be asked, does d i f f i c u l t y r a t i n g c o r r e l a t e s u b s t a n t i a l l y w i t h t e s t performance ( f o r the t o t a l group as w e l l as f o r the sexes s e p a r a t e l y ) when i t does not n e c e s s a r i l y d i f f e r e n t i a t e the sexes? A l t h o u g h the answer i s by no means o b v i o u s , one e x p l a n a t i o n may be t h a t any one i n d i v i d u a l c o n s i d e r s the d i f f i c u l t y of the t e s t s as a group b e f o r e r a t i n g any one t e s t i n d i v i d u a l l y . T h i s might r e s u l t i n what c o u l d be seen as a rank o r d e r i n g of the t e s t s . I f , f o r i n s t a n c e , a perso n c o n s i d e r s t h a t the t e s t s as a group a r e mo d e r a t e l y e a s y / d i f f i c u l t , each t e s t may be compared t o t h i s 49 d i f f i c u l t y index b e f o r e b e i n g r a t e d . The a c t u a l / s c a l e p o i n t of the d i f f i c u l t y r a t i n g may not be of the utmost importance, but r a t h e r the n u m e r i c a l r a t i n g of one t e s t compared t o a n o t h e r . T h i s , t h e n , l e a d s one t o c o n c l u d e t h a t the d i f f i c u l t y of a t e s t (as measured i n t h i s s t udy) i s a r e l a t i v e matter and w i l l be i n f l u e n c e d by o t h e r t e s t s i n c l u d e d f o r st u d y . Thus, f o r example, the average d i f f i c u l t y r a t i n g of the Cards t e s t s might change from 4.0 i n a study comprised s o l e l y of s p a t i a l t e s t s t o 7.0 i n a study c o m prised of t r i v i a l a r i t h m e t i c and v e r b a l t e s t s . I f t h i s i s the case then i t i s an e m p i r i c a l matter t o determine whether d i f f i c u l t y r a t i n g c o r r e l a t e s w i t h performance when t e s t s of d i f f e r e n t a b i l i t i e s a r e i n c l u d e d i n the same st u d y . A l s o i n r e l a t i o n t o p e r c e i v e d d i f f i c u l t y , the f a c t o r a n a l y t i c r e s u l t s of t h i s s tudy do not su p p o r t the f i n d i n g s of G u i l f o r d (1941) t h a t the f i r s t f a c t o r had l o a d i n g s which were i n v e r s e l y p r o p o r t i o n a l t o d i f f i c u l t y i n d i c e s . A p o s s i b l e e x p l a n a t i o n i s t h a t , i n t h i s s t u d y , c o n t r a r y t o the s t u d i e s of G u i l f o r d (1941) and Ferguson (1941), d i f f e r e n t people p e r c e i v e d d i f f e r e n t t e s t s t o be more or l e s s d i f f i c u l t . For i n s t a n c e , 45% of the men p e r c e i v e d Cubes t o be more d i f f i c u l t than Paper F o l d i n g w h i l e 38% p e r c e i v e d Paper F o l d i n g t o be more d i f f i c u l t than Cubes. The r e s u l t s were s i m i l a r f o r women. Thus, t h e r e seem t o be l a r g e i n d i v i d u a l d i f f e r e n c e s i n how d i f f i c u l t one t e s t i s p e r c e i v e d t o be i n r e l a t i o n t o a n o t h e r . F u r t h e r 50 support f o r t h i s c o n t e n t i o n i s s u p p l i e d by an a n a l y s i s of the c o r r e l a t i o n s between the d i f f i c u l t y r a t i n g s of the v a r i o u s t e s t s . The l a r g e s t c o r r e l a t i o n s i n the s e m a t r i c e s were, f o r men and women, r e s p e c t i v e l y , .30 and .22. Thus, w h i l e i t may be a s i m p l e matter t o say t h a t i t i s more d i f f i c u l t t o d e t e c t f r e q u e n c y d i f f e r e n c e s - of .5 c y c l e s than 30 c y c l e s , i t i s q u i t e another matter to say t h a t S t e s t s , f o r i n s t a n c e , a r e l e s s d i f f i c u l t than Vz t e s t s (Ekstrom e t a l . , 1976; M i c h a e l et a l . , 1950). I t i s p r o b a b l y f o r t h i s reason t h a t the . c o r r e l a t i o n m a t r i c e s -among d i f f i c u l t y r a t i n g s were not s i m i l a r t o the c o r r e l a t i o n m a t r i c e s among t e s t s c o r e s . That d i f f i c u l t y i s , i n d e e d , an imp o r t a n t v a r i a b l e i s a t t e s t e d t o by the f i n d i n g s t h a t the c o r r e l a t i o n between two t e s t s can be a f f e c t e d by how d i s c r e p a n t the d i f f i c u l t y r a t i n g s of these two t e s t s a r e . The f i n d i n g s r e l a t e d t o these c o r r e l a t i o n a l d i f f e r e n c e s o n l y used i n f o r m a t i o n about the d i f f i c u l t y of one t e s t r e l a t i v e t o the o t h e r . That i s , no c o n s i d e r a t i o n was g i v e n t o how d i f f i c u l t the two t e s t s a c t u a l l y were. To be noted, a g a i n , i s t h a t t h i s study i n v o l v e d t e s t s of o n l y one g e n e r a l a b i l i t y . Thus, i t can o n l y be suggested t h a t t h i s same r e s e a r c h s t r a t e g y be a p p l i e d t o s t u d i e s i n v o l v i n g two, and p o s s i b l y more, d i s t i n c t a b i l i t i e s . I t may w e l l be the case t h a t the i n d i v i d u a l d i f f e r e n c e s i n p e r c e i v e d r e l a t i v e d i f f i c u l t y would, i n such a s t u d y , be l e s s e n e d . I t would then be a s i m p l e 51 matter t o compare the c o r r e l a t i o n s among d i f f i c u l t y r a t i n g s t o the t e s t s c o r e c o r r e l a t i o n m a t r i c e s . I t i s h y p o t h e s i z e d t h a t , w i t h t e s t s from d i f f e r e n t domains, these m a t r i c e s would be much more s i m i l a r than the ones i n the p r e s e n t s t u d y . T h i s i s , of c o u r s e , based on the f i n d i n g t h a t as the d i f f e r e n c e i n p e r c e i v e d d i f f i c u l t y of two t e s t s i n c r e a s e s , the c o r r e l a t i o n between the two may d e c r e a s e . I t i s p o s s i b l e t h a t a study of t h i s n a t u r e would e x p l a i n , or c l a r i f y , why a d i f f i c u l t v o c a b u l a r y t e s t Can l o a d on a s p a t i a l f a c t o r ( F r e n c h , 1 9 5 1 ) . Perhaps the s t r u c t u r e of i n t e l l e c t i s i n e x t r i c a b l y t i e d t o the s t r u c t u r e of t e s t d i f f i c u l t y . I t may be c o n c l u d e d t h a t s u b j e c t i v e d i f f i c u l t y r a t i n g s a r e v a l u a b l e i n t h a t they p r o v i d e an o p e r a t i o n a l d e f i n i t i o n f o r the d i f f i c u l t y of speeded t e s t s . T h i s i s e v i d e n c e d by the f i n d i n g t h a t t e s t d i f f i c u l t y c o r r e l a t e s , a t t i m e s s u b s t a n t i a l l y , w i t h t o t a l t e s t s c o r e . I t would be i n t e r e s t i n g t o know i f t h i s f i n d i n g g e n e r a l i z e s t o t e s t s of o t h e r a b i l i t y domains (e.g. r e a s o n i n g , n u m e r i c a l ) and i f i t makes any d i f f e r e n c e whether a l l t e s t s measure the same a b i l i t y . The f i n d i n g s r e l a t e d t o problem s o l v i n g a r e u n f o r t u n a t e ; not because of t h e i r i n s i g n i f i c a n c e , but because the reason f o r t h e i r i n s i g n i f i c a n c e i s not c l e a r . A l t h o u g h i t seems t h a t d i f f i c u l t y i s not r e l a t e d t o how s p a t i a l items a re s o l v e d , i t may be t h a t the measures used i n t h i s study were not s e n s i t i v e enough t o p o i n t out any 52 r e l a t i o n s h i p which may e x i s t . F i n a l l y , the r e l a t i o n s h i p between sex d i f f e r e n c e s i n performance and sex d i f f e r e n c e s i n d i f f i c u l t y a r e e n l i g h t e n i n g . A l t h o u g h men s c o r e d h i g h e r on a l l t e s t s , sex d i f f e r e n c e s i n d i f f i c u l t y r a t i n g s were found on o n l y two of the t e s t s . I t would be i n t e r e s t i n g t o know the p a t t e r n of d i f f i c u l t y r a t i n g s from a study which i n c l u d e d t e s t s of two a b i l i t i e s ; one i n which women e x c e l (e.g. v e r b a l ) and one i n which men e x c e l ( e . g . s p a t i a l ) . The use of s u b j e c t i v e t e s t d i f f i c u l t y r a t i n g s as d i f f i c u l t y i n d i c e s f o r speeded t e s t s i s s t r o n g l y recommended. The r a t i n g s a r e both easy t o o b t a i n and seem to be v a l i d measures. 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London: U n i v e r s i t y of London P r e s s , 1 9 6 4 . T h u r s t o n e , L.L. P r i m a r y M e n t a l A b i l i t i e s . C h i c a g o : U n i v e r s i t y of Chicago P r e s s , 1 9 3 8 . T h u r s t o n e , L.L. Some p r i m a r y a b i l i t i e s i n v i s u a l t h i n k i n g . U n i v e r s i t y of Chicago P s y c h o m e t r i c L a b o r a t o r y R e p o r t , 1 9 5 0 , No. 5 9 . V e r y , P.S. D i f f e r e n t i a l f a c t o r s t r u c t u r e s i n ma t h e m a t i c a l a b i l i t y . , G e n e t i c P s y c h o l o g y Monographs, 1 9 6 7 , 7 5 , . 1 6 9 - 2 0 7 . W e r d e l i n , I . G e o m e t r i c a l A b i l i t y and the Space F a c t o r s i n Boys and G i r l s . Lund, Sweden: U n i v e r s i t y of Lund P r e s s , 1 9 6 1 . W e r d e l i n , I . , & S t j e r n b e r g , G. On the n a t u r e of the p e r c e p t u a l speed f a c t o r . Scandanavian J o u r n a l of P s y c h o l o g y , 1 9 6 9 , J _ 0 , 1 8 5 - 1 9 2 . W o l f l e , D. F a c t o r a n a l y s i s t o 1 9 4 0 . P s y c h o m e t r i c Monographs (No. 3 ) • Chi c a g o : U n i v e r s i t y of Chicago P r e s s , 1 9 4 0 . Zimmerman, W.S. Hypotheses c o n c e r n i n g the n a t u r e of s p a t i a l f a c t o r s . 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, 1 9 5 4 , 1 4 , 3 9 6 - 4 0 0 . 58 Tables T a b l e 1 Means and Standard D e v i a t i o n s f o r S p a t i a l T est Scores and D i f f i c u l t y R a t i n g s T o t a l Group Test Score D i f f i c u l t y R a t i n g Form Board Mean 54.59 6.49 Stan d a r d D e v i a t i o n 19.56 1.71 Number of People 537 537 Paper F o l d i n g Mean 6 . 1 9 4.50 Stan d a r d D e v i a t i o n 2.46 1.81 Number of People 537 537 S u r f a c e Development Mean •17.12 6.42 Stan d a r d D e v i a t i o n 8.45 2.18 Number of People 537 537 Card R o t a t i o n s Mean 50.89 3.38 Stan d a r d D e v i a t i o n 16.79 1 .86 Number of People 537 536 Cube Comparisons Mean 7 . 8 1 4.79 Stan d a r d D e v i a t i o n 5.10 1 .75 Number of People 537 534 T a b l e 1 c o n t i n u e d Men Test Score D i f f i c u l t y R a t i n g Form Board Mean 60.46 6.52 Standard D e v i a t i o n 19.37 1 . 68 Number of People 266 266 Paper F o l d i n g Mean 6.88 4.26 St a n d a r d D e v i a t i o n 2.24 1.81 Number of People 266 266 S u r f a c e Development Mean 20.71 5.49 Stan d a r d D e v i a t i o n 7.67 2.17 Number of People 266 266 Card R o t a t i o n s Mean 55.50 3.17 Stan d a r d D e v i a t i o n 15.48 1.84 Number of People 266 265 Cube Comparisons Mean 9.33 4.42 Stan d a r d D e v i a t i o n 5.13 1 .70 Number of People 266 264 Table 1 c o n t i n u e d Women Test Score P i f f i c u l t y R a t i n g Form Board Mean St a n d a r d D e v i a t i o n Number of People 48.60 17.88 268 6.44 1 .75 268 Paper F o l d i n g Mean St a n d a r d D e v i a t i o n Number of People 5.50 2.48 268 4.74 1 .79 268 S u r f a c e Development Mean St a n d a r d D e v i a t i o n Number of People 13.56 7.68 268 7.37 1 .75 268 Card R o t a t i o n s Mean St a n d a r d D e v i a t i o n Number of People 46. 1 9 16.73 268 3.60 1 .86 268 Cube Comparisons Mean St a n d a r d D e v i a t i o n Number of People 6.26 4.59 268 5. 1 5 1 .74 268 62 Ta b l e 2 C o r r e l a t i o n s between D i f f i c u l t y R a t i n g s and S p a t i a l T est S c o r e s 1 Number 2 T o t a l Group D i f f i c u l t y R a t i n g Vz 1 Vz2 Vz3 SI S2 Vz1 -.23 - .22 -.37 -.09 -.07 Vz2 .05 -.52 -.40 -.11. -.08 Vz3 . 1 5 -.28 -.68 -.11 -.09 S1 . 1 0 -.12 -.30 -.45 -.19 S2 . 1 3 -.08 -.30 -.15 -.28 537 537 537 536 534 T a b l e 2 c o n t i n u e d Men 6 3 D i f f i c u l t y Rat i n q Vz1 Vz2 Vz3 S1 S2 Vz 1 -.34 -.23 - .28 -.12 - .03 Vz2 -.01 -.53 - .35 -.09 .07 Test Score Vz3 . 1 5 -.24 - .59 -.10 .07 S1 . 05 -.13 - . 1 7 -.40 -.13 S2 . 1 2 .00 - .20 -.16 -.24 Number 266 266 266 265 264 T a b l e 2 c o n t i n u e d Women D i f f i c u l t y R a t i n g 64 Number V z l Vz2 Vz3 S1 S2 Vz 1 -.16 -.16 -.29 .02 .01 Vz2 .09 -.49 -.31 . -.07 -.11 Vz3 . 1 6 •-.27 . -.64 -.03 -.06 'SI . 12 -.06 -.25 -.49 -.16 S2 . 14 -.09 -.18 -.09 -.22 268 268 268 268 268 Vz1 = Form Board Vz2 = Paper F o l d i n g Vz3 = S u r f a c e Development 51 = Card R o t a t i o n s 52 = Cube Comparisons The c o r r e l a t i o n s i n each column are a l l based on the same number of p e o p l e . Table 3 Sex by Test Repeated Measures A n a l y s i s of V a r i a n c e on D i f f i c u l t y R a t i n g s Source df Sex (S) 1 E r r o r between 519 Test (T) 4 S x T 4 E r r o r w i t h i n 2116 MS 305.02 4.91 938.32 70.27 2.87 62.07*** 327.17*** 24.50*** Means and Number of People Men Women Form Board 6.54 6.44 Paper F o l d i n g 4.28 4.74 S u r f a c e Development 5.50 7.37 Card R o t a t i o n s 3.19 3.60 Cube Comparisons 4.41 5.15 Number of Peop l e 263 268 * * * 2 < .001 T a b l e 4 Frequency of Answers t o Problem S o l v i n g Statements T o t a l Group Men Women True F a l s e True F a l s e True Fal's* Form Board S t r a t e g y 1 300 229 1 38 122 161 1 05 S t r a t e g y 2 346 1 84 177 84 1 68 98 S t r a t e g y 3 226 301 99 161 1 27 1 38 S t r a t e g y 4 276 249 1 27 1 32 1 47 1 1 6 S t r a t e g y 5 1 04 425 38 223 64 201 S t r a t e g y 6 51 479 28 233 21 2 45 Paper F o l d i n g S t r a t e g y 1 434 1 03 206 60 227 41 S t r a t e g y 2 1 1 6 418 57 208 56 210 S t r a t e g y 3 1 23 411 65 201 56 209 S t r a t e g y 4 1 56 374 86 1 74 70 1 97 S t r a t e g y 5 87 443 27 234 59 - 207 S t r a t e g y 6 34 495 1 8 244 1 5 249 S u r f a c e Development S t r a t e g y 1 1 55 381 77 189 77 1 90 S t r a t e g y 2 339 1 97 1 69 97 1 67 1 00 S t r a t e g y 3 68 464 29 235 37 228 S t r a t e g y 4 307 224 1 55 1 1 0 1 49 1 1 4 S t r a t e g y 5 1 35 401 42 223 92 1 76 S t r a t e g y 6 46 490 1 4 251 32 236 Card R o t a t i o n s S t r a t e g y 1. 70 462 40 224 30 235 S t r a t e g y 2 364 1 69 1 66 99 195 70 S t r a t e g y 3 237 296 1 1 3 152 1 22 1 43 S t r a t e g y 4 344 184 171 94 1 70 90 S t r a t e g y 5 49 484 1 1 254 37 228 S t r a t e g y 6 1 7 517 7 258 10 256 Cube Comparisons S t r a t e g y 1 478 56 233 30 242 26 S t r a t e g y 2 205 326 107 1 55 96 1 70 S t r a t e g y 3 36 496 24 238 1 2 255 S t r a t e g y 4 28 504 •1 3 249 1 5 252 S t r a t e g y 5 91 441 25 237 65 202 S t r a t e g y 6 35 496 1 4 248 21 245 Table 5 Correlation between Test Scores for People who use the 'Same' and 'Different' Problem Solving Strategies Total Group Tests 1 Same Strategy Di f ferent Strategy z-valui n 3 r" n r_ Vz1/Vz2 115 .46 4 5 .63 -1 . 34 V Z 1 / V Z 3 86 .39 60 .56 -1 .29 V Z 1 / S 1 73 .42 * 49 .26 .96 VZ1/S2 121 .38 43 .42 -.26 Vz2/Vz3 133 .57 82 .68 -1 .22 Vz2/S1 123 .42 44 .30 .76 Vz2/S2 227 .38 43 .30 .58 V z 3 / S 1 81 .50 62 .48 .15 Vz3/S2 1 34 .42 78 .38 .30 S1/S2 1 18 .43 59 .58 -1 .23 Table 5 c o n t i n u e d Men T e s t s Same S t r a t e q y D i f f e r e n t S t r a t e g y z - v a l u i n r_ n Vz1/Vz2 63 .52 21 : .72 -1.22 Vz1/Vz3 43 .35 29 .30 .19 V z l / S I 41 .41 23 .28 .51 VZ1/S2 57 .29 18 .37 -.29 Vz2/Vz3 70 .52 39 .62 - . 7 6 Vz2/S1 70 .47- 24 .32 .70 Vz2/S2 1 00 .26 22 .30 -.19 Vz3/S1 50 .43 29 .36 • '34 Vz3/S2 61 .37 35 .34 .16 S1/S2 66 .46 27 .55 -.51 69 Table 5 c o n t i n u e d Women T e s t s Same S t r a t e g y D i f f e r e n t S t r a t e g y z-valu< n r n r_ Vz1/Vz2 52 .35 24 .40 - . 1 9 Vz1/Vz3 43 .38 31 .51 .66 Vz1/S1 32 .32 26 .08 .90 VZ1/S2 64 .37 25 .46 -.43 Vz2/Vz3 63 .56 43 .29 1 .62 Vz2/S1 53 .30 20 • 21 .36 Vz2/S2 1 27 .43 20 .06 1 .58 Vz3/S1 31 .44 33 .40 . 1 9 Vz3/S2 73 • 41 , 43 .22 1 .07 S1/S2 52 .30 32 .49 -.95 = Form Board = Paper F o l d i n g = S u r f a c e Development = Card R o t a t i o n s = Cube Comparisons z - v a l u e f o r the comparison of the c o r r e l a t i o n s f o r the same and d i f f e r e n t s t r a t e g y groups. The number of p e o p l e . Vz1 Vz2 Vz3 S1 S2 4 The c o r r e l a t i o n between the two t e s t s i n v o l v e d . T a b l e 6 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Card R o t a t i o n s Test Source df MS F Sex (Se) 1 1,1832 . 42 47.37*** S t r a t e g y ( S t ) 2 1082.26 4.33 Se x St 2 188.30 .75 E r r o r 519 249.77 Means and Number of People Men Women Whole 52.47 (97) 43.96 (67) P a r t 58.60 (25) 43.92 (25) Part/Whole 57.27 (141) 47.99 (170) * * *** p_ < .05 e < . 0 1 p < . 0 0 1 T a b l e 7 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Cube Comparisons Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 518 MS 1 .179.08 24.06 94.92 23.32 50.57*** 1 .03 4.07* Means and Number of Peo p l e Men Women Whole 8. 68 (151 ) 6.56 (170) P a r t 8.89 (19) 5.86 (21 ) Part/Whole 10.57 (88) 5.80 (75) * 2 <• - 0 5 ** 2 < - 0 1 *** 2 < -ocn T a b l e 8 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Paper F o l d i n g Test Source df Sex . (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 521 MS 252.52 1 9.39 3.58 5.49 45.92*** 3.53* .65 Means and Number of People Men Women Whole 6.90 (164) 5.54 (177) P a r t 5.32 (14) 4.89 (11) Part/Whole 7.17 (85) 5.59 (76) * £ < .05 ** p < .01 *** 2 < -00 1 Table 9 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the S u r f a c e Development Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 512 MS 6553.63 308.56 287. 12 55.91 117.22*** 5.52** 5.14** Means and Number of People Men Women Whole 1 8.54 (95) 1 3.60 (84) P a r t 24.48 (49) 1 3.52 (49) Part/Whole 21 .28 (117) 1 4 . 1 1 (124) * p < .05 ** p < .01 *** p < .001 74 . T a b l e 10 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r T o t a l Score on the Form Board Test Source MS F Sex (Se) 1 18241.85 52.20*** S t r a t e g y ( S t ) 2 91.21 .26 Se x St 2 86.54 .25 E r r o r 513 349.44 Means and Number of People Men Women Whole 60.81 (85) 47.31 (74) P a r t 57.78 (18) 48.04 (26) Part/Whole 60.66 ( 151 ) 49.26 (165) * 2 K ' ° 5 ** 2 < - 0 1 *** 2 < -001 75 Table 11 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Form Board Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 513 MS .50 .94 .06 2.91 F .1 7 .32 .02 Means and Number of People Men Women Whole 6.52 (85) 6.50 (74) P a r t 6.33 (18) 6.27 (26) Part/Whole 6.56 ( 151 ) 6.48 (165) * 2 < ' ° 5 ** p < .01 *** 2 < - C 0 1 T a b l e 12 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Paper F o l d i n g Test Source df Sex (Se) i S t r a t e g y ( S t ) 2 Se x St 2 E r r o r . 5 2 V MS 3 4 . 8 2 1 7 . 1 9 4 . 7 3 3 . 1 4 1 1 . 0 8 * * * 5 . 4 7 * * 1 . 5 0 Means and Number of People Men Women Whole 4 . 1 2 ( 1 6 4 ) 4 . 6 6 ( 1 7 7 ) P a r t 5 . 8 6 ( 1 4 ) • 5 . 1 8 ( 1 1 ) Part/Whole 4 . 2 2 ( 8 5 ) 4 . 8 7 ( 7 6 ) 2 < . 0 5 2 < .01 *** 2 < - 0 0 1 ** T a b l e 13 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the S u r f a c e Development Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 512 MS • 458. 13 1 .93 17.91 3.82 120.02*** .51 4.69** Means and Number of People Men Women Whole 5.78 (95) 7.13 (84) P a r t 4.80 (49) 7.65 (49) Part/Whole 5.44 (117) 7.31 (124) * 2 < - 0 5 ** 2 < * 0 1 *** 2 < -001 78 Table 14 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Card R o t a t i o n s Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 518 MS 20. 30 .85 .97 3.36 F 6.05* .25 .28 Means and Number of People Men Women Whole 3.24 (97) 3.55 (67) P a r t 3.08 (25) 3.84 (25) Part/Whole 3.11 (140) 3.49 (170) * p_ < .05 ** 2 < - 0 1 *** 2 < -00 1 Table 15 Sex by S t r a t e g y A n a l y s i s of V a r i a n c e f o r D i f f i c u l t y R a t i n g of the Cube Comparisons Test Source df Sex (Se) 1 S t r a t e g y ( S t ) 2 Se x St 2 E r r o r 516 MS 78. 05 2.20 8.17 2.88 2 7 . 1 4 * * * .77 2.84 Means and Number of People Men Women Whole 4.44 ( 1 49) 4.94 (170) P a r t 4.42 (19) 5.29 (21 ) Part/Whole 4.25 (88) 5.53 (75) * £ < .05 ** 2 < .01 *.** £ < .001 T a b l e 16 C o r r e l a t i o n s between S p a t i a l T est S c o r e s 1 T o t a l Group (n = 537) Vz 1 Vz2 Vz3 S1 S2 Vz 1 1 .00 .52 .52 .39 .36 Vz2 1 .00 .59 .41 .36 Vz3 • 1 .00 .48 .47 S1 1 .00 .48 S2 1.00 T a b l e 16 c o n t i n u e d Men (n = 266) Vz 1 Vz2 Vz3 SI S2 Vz1 1 .00 Vz2 .51 1 .00 Vz3 .39 .53 1 .00 S1 .35 .36 .40 1 .00 S2 .33 .26 .44 .48 1 .00 82 Table 16 c o n t i n u e d Women (n = 268) VZ1 Vz2 Vz3 S1 S2 V z l 1.00 .44 . 53 .31 .26 Vz2 .1 -00 . 55 . 36, .34 Vz3 1 .00 .43 .36 S1 1.00 .38 S2 1 .00 Vz 1 = Form Board Vz2 = Paper F o l d i n g Vz3 = S u r f a c e Development 51 = Card R o t a t i o n s 52 = Cube Comparisons 83 T a b l e 17 U n r o t a t e d and R o t a t e d Component P a t t e r n M a t r i c e s T o t a l Group (n = 537) U n r o t a t e d R o t a t e d T e s t s 1 F a c t o r I F a c t o r I I F a c t o r I F a c t o r I I Vz1 .74 -.38 .81 .19 Vz2 .77 -.38 .83 .20 Vz3 . .82 . -.12 . .71 .44 51 .72 .42 .29 .78 52 .70 .53 .19 .86 E i g e n v a l u e s and Percentage of V a r i a n c e 1. 2.84 56.8% 2. .75 15.1% 3. .52 10.4% 4. .49 9.9% 5. .39 7.9% 84 Table 17 c o n t i n u e d Men (n = 266) U n r o t a t e d R o t a t e d T e s t s F a c t o r I F a c t o r 11 F a c t o r I F a c t o r I I V z l .71 -.36 .77 .19 Vz2 .74 -.48 .88 .13 Vz3 .77 -.07 .63 • .46 51 .71 .41 .26 .78 52 .68 .56 .14 .87 E i g e n v a l u e s and P e r c e n t a g e of V a r i a n c e 1. 2.63 52.5% 2. .85 17.1% 3. .61 12.2% 4. .53 10.5% 5. .39 7.7% 85 Table 17 c o n t i n u e d Women (n = 268) T e s t s F a c t o r I F a c t o r I I F a c t o r I F a c t o r I I Vz1 .71 -.46 .85 .06 Vz2 .76 -.20 .73 .30 Vz3 .82 -.20 .77 .34 51 .68 .40 .29 .73 52 .62 .60 .13 .86 E i g e n v a l u e s and P e r c e n t a g e of V a r i a n c e 1. 2.60 52.1% 2. .82 16.3% 3. .62 12.4% 4. .54 10.9% 5. .42 8.4% 1 Vz1 = Form Board Vz2 = Paper F o l d i n g Vz3 = S u r f a c e Development 51 = Card R o t a t i o n s 52 = Cube Comparisons 86 T a b l e 18 C o r r e l a t i o n between Test Scores f o r People w i t h High and Low D i f f e r e n c e s i n D i f f i c u l t y Rat i n g s T o t a l Group T e s t s 1 V a l u e 2 Low D i f f e r e n c e High D i f f e r e n c e z - v a l u e r 5 n r V Z 1 / V Z 2 2 290 .58 247 .48 1 .55 V Z 1 / V Z 3 1 236 .58 301 • 48 1 .60 VZ1/S1 3 299 .49 237 .39 1 .4.5 VZ1/S2 2 31.1 .37 224 .42 - .67 Vz2/Vz3 2 268 .68 269 . 53 2 .82** Vz2/S1 1 252 .53 284 .35 2 . 61 ** Vz2/S2 1 269 • .51 266 .22 3 .89*** Vz3/S1 3 284 .66 252 .41 4 . 00*** Vz3/S2 2 287 .54 248 •41 1 .97* S1/S2 1 233 .48 301 .50 - .30 Table 18 continued Men Tests Value Low Difference Hiqh Difference z-value n r_ n r_ V Z 1 / V Z 2 2 1 39 .57 1 27 . 50 .78 V Z 1 / V Z 3 1 114 .48 1 52 .31 1 .60 Vz1/S1 3 141 .49 . 1 24 .32 1 .72* V Z 1 / S 2 2 144. .38 1 20 .38 -.03 Vz2/Vz3 2 1 52 .62 114 . 44 1 .99* Vz2/S1 1 . 1 26 .51 1 39 .26 2.37** Vz2/S2 1. 1 22 .54 1 42 .03 4.56*** Vz3/S1 2 1 25 .58 1 40 . 35 2.36** Vz3/S2 2 1 60 .55 1 04 .31 2.32* S1/S2 1 124 .51. 139 .47 .39 T a b l e 18 c o n t i n u e d Women T e s t s Value Low D i f f e r e n c e High D i f f e r e n c e z - v a l u e n_ r n r_ V Z 1 / V Z 2 2 •1 50 .52 118 .' .36 1.56 V Z ' 1 /V Z 3 1 . 121' .60 147 .50 1.11 Vzl/S1 2 117 .43 151 .30 1.14 V Z 1 / S 2 2 1 66 .25 102 . 32 -.65 Vz2/Vz3 2 115 .67 1 53 .50 2.16* Vz2/S1 1 1 24 .53 144 .27 2.53** Vz2/S2 1 1 46 .41 122 .29 1.10 Vz3/S1, 3 1 1 5 .64 .. 153 . 44 2.21* Vz3/S2 2 .1 24 .41 1 44 .35 .58 S1/S2 1 1 08 .31 1 60 . 44 -1.19 1 Vz1 = Form Board Vz2 = Paper F o l d i n g Vz3 = S u r f a c e Development 51 = Card R o t a t i o n s 52 = Cube Comparisons T h i s v a l u e was used t o d e f i n e the low and h i g h d i f f e r e n c e groups. For any p a i r of t e s t s , i f the a b s o l u t e v a l u e of the d i f f e r e n c e i n d i f f i c u l t y r a t i n g of the two t e s t s was l e s s than or e q u a l t o t h i s v a l u e a person would be i n the low d i f f e r e n c e group. z - v a l u e f o r the comparison of the c o r r e l a t i o n s f o r the low and h i g h d i f f e r e n c e groups. * 2 < «05, one t a i l e d ** p < .01, one t a i l e d *** 2 < -001, one t a i l e d The number of p e o p l e . The c o r r e l a t i o n between the two t e s t s i n v o l v e d . 89 Appendix A D e s c r i p t i o n of S p a t i a l T e s t s 90 Card R o t a t i o n s Test (S1) "Suggested by Thu r s t o n e ' s C a r d s . Each i t e m g i v e s a drawing of a c a r d c u t i n t o an i r r e g u l a r shape. To i t s r i g h t a r e . . . . ( e i g h t ) . . . . o t h e r drawings of the same c a r d , sometimes merely r o t a t e d and sometimes t u r n e d over t o i t s ot h e r s i d e . The s u b j e c t i n d i c a t e s whether or not the c a r d has been t u r n e d over" (Ekstrom e t a l . , 1976, p. 150). Length: 3 minutes f o r 10 items (80 p o s s i b l e a n s w e r s ) . Cube Comparisons Test (S2) "Suggested by Thurstone's Cubes. Each item p r e s e n t s two drawings of a cube. Assuming no cube can have two f a c e s a l i k e , the s u b j e c t i s t o i n d i c a t e which items p r e s e n t drawings t h a t can be of the same cube and which p r e s e n t drawings t h a t cannot be of the same cube" (Ekstrom et a l . , 1976, p. 150). Leng t h : 3 minutes f o r 21 i t e m s . Form Board Test (Vz1) "Each i t e m p r e s e n t s 5 shaded.drawings of p i e c e s , some or a l l of which can be put t o g e t h e r t o form a f i g u r e p r e s e n t e d i n o u t l i n e form. The t a s k i s t o i n d i c a t e which of the p i e c e s , when f i t t e d t o g e t h e r , would form the o u t l i n e " (Ekstrom e t a l . , 1976, p. 174). Le n g t h : 8 minutes f o r 24 items (120 p o s s i b l e a n s w e r s ) . 91 Paper F o l d i n g Test (Vz2) "Suggested by T h u r s t o n e ' s Punched H o l e s . For each item s u c c e s s i v e - drawings i l l u s t r a t e two or t h r e e f o l d s made i n a square sheet of paper. The f i n a l d rawing of the f o l d e d paper shows where a h o l e i s punched i n i t . The s u b j e c t s e l e c t s one of 5 drawings to show how the punched sheet would appear when f u l l y reopened" (Ekstrom e t a l . , 1976, p. 176). Length: 3 minutes f o r 10 i t e m s . S u r f a c e Development Test (Vz3) "Suggested by T h u r s t o n e ' s t e s t of the same name. In t h i s t e s t , drawings are p r e s e n t e d of s o l i d forms t h a t c o u l d be made w i t h paper or sheet m e t a l . With each drawing t h e r e i s a diagram showing how a p i e c e of paper might be cut and f o l d e d so as t o make the s o l i d form. D o t t e d l i n e s show where the paper i s f o l d e d . One p a r t of the diagram i s marked t o c o r r e s p o n d t o a marked s u r f a c e i n the d r a w i n g . The s u b j e c t i s t o i n d i c a t e which l e t t e r e d edges i n the drawing c o r r e s p o n d t o numbered edges or d o t t e d l i n e s i n the diagram" (Ekstrom e t a l . , 1976, p. 174). L e n g t h : 5 minutes f o r 6 items (30 p o s s i b l e a n s w e r s ) . 92 A p p e n d i x B D i f f i c u l t y R a t i n g Q u e s t i o n n a i r e 93 On the following page use Che scale presented below to Indicate how d i f f i c u l t you found each of the tests you just completed. For instance, i f you found a test to be very easy, c i r c l e _1« If you found i t to be very d i f f i c u l t , c i r c l e 9_. If you found i t to be moderately e a s y / d i f f i c u l t , c i r c l e 5_. C i r c l e the number on the scale which r e f l e c t s how d i f f i c u l t you found the t e s t . 1 2 3 4 5 6 7 8 9 very easy moderately e a s y / d i f f i c u l t very d i f f i c u l t 94 1 very easy 4 5 6 moderately easy/difficult very di f f i c u l t V 4 5 6 moderately easy/difficult 9 very di f f i c u l t 4 5 6 moderately easy/difficult very di f f i c u l t n 4 C i very easy 4 5 6 moderately easy/difficult 9 very dif f i c u l t ODO>_ • • o n o very easy moderately easy/difficult very d i f f i c u l t Appendix C Strategy Q u e s t i o n n a i r e 96 L i s t e d on the following pages are a number of questions r e l a t e d to how you solved the items i n the tests you just completed. At the top of each page a number of the items from each test are reproduced. With these i n mind think, back to when you were working on the test i n question. Then, keep i n mind how you generally solved the items and c i r c l e TRUE for those statements which describe how you solved the problems and FALSE for those statements which do not. NOTE: Do not respond on the basis of how you solved one or two of the items. RESPOND ON THE BASIS OF HOW YOU SOLVED THE ITEMS IN GENERAL. 97 I mentally folded the paper, punched a hole, and then mentally unfolded It and compared It to the possible answers. TRUE FALSE 1 noted where one or two of the holes would be and then t r i e d to f i n d an answer that had these one or two holes i n the same place ( i . e . I didn't a c t u a l l y f o l d and unfold the paper). TRUE F A L S E I t r i e d to determine through how many thicknesses of paper the hole would have to go and then picked one of the answers that had that many holes ( i . e . I didn't a c t u a l l y unfold the paper with the holes). TRUE F A L S E I worked backwards; I looked at the drawing with the hole and then unfolded i t mentally ( i . e . I didn't ac t u a l l y f o l d the paper up to begin with). TRUE FALSE 1 guessed when 1 wasn't sure. TRUE F A L S E 1 didn't use any p a r t i c u l a r strategy. TRUE FALSE 98 I mentally picked up one of the cubes and rotated It to li n e i t up with a ce r t a i n symbol on the other one and then checked whether or not the other symbols were i n the ri g h t place. TRUE FALSE Without mentally picking up the cube, I determined i f any two of the symbols on both cubes bore the same r e l a t i o n to one another. TRUE F A L S E I had an X and Y axis i n mind when solving the items. TRUE FALSE I pictured myself as walking around the cubes. TRUE FALSE I guessed when I wasn't sure. TRUE FALSE I didn't use any p a r t i c u l a r strategy. TRUE FALSE I mentally folded up the figure and mentally placed It on top of the figure already folded up. I mentally folded up the figure and then, without necessarily placing i t on top of the figure already folded up, I t r i e d to match the l e t t e r s and numbers. 1 t r i e d to match the numbers and l e t t e r s up without ever doing any mental f o l d i n g . 1 chose a number I wanted to f i n d a l e t t e r for and then mentally folded only those parts of the figure that had to do with that number. I guessed when I wasn't sure. I didn't use any p a r t i c u l a r strategy. 100 I noted that some of the figures looked l i k e l e t t e r s of the alphabet or f a m i l i a r objects and solved them with t h i s i n mind. TRUE FALSE I noted some d i s t i n c t aspect of the figure (eg. bottom part or top l e f t corner) and solved the figures with t h i s feature i n mind. TRUE F A L S E I mentally rotated a figure and mentally placed i t on top of the other figures to see i f they were the same. TRUE FALSE I mentally rotated one of the figures and then, without necessarily placing one figure on top of the other, compared the two. TRUE F A L S E I guessed when I wasn't sure. TRUE F A L S E I didn't use any p a r t i c u l a r strategy. TRUE FALSE 101 • • • L • I mentally placed one item a f t e r the other into the figure u n t i l i t was f u l l . TRUE FALSE I kept the large figure i n mind and t r i e d to arrange the smaller pieces to f i t i t . TRUE FALSE I used a p e n c i l to draw the large figure out of the smaller ones. TRUE FALSE 1 used t r i a l and erro r . 1 guessed when 1 wasn't sure. TRUE F A L S E TRUE FALSE I didn't use any p a r t i c u l a r strategy. TRUE FALSE 1 0 2 Appendix D R a t i o n a l e f o r i n c l u d i n g Strategy Statements 103 For each t e s t s i x s t r a t e g y statements were i n c l u d e d . Two of the s e (the l a s t two) were the same f o r each t e s t . 'I d i d n ' t use any p a r t i c u l a r s t r a t e g y ' was i n c l u d e d t o ensure t h a t people who f e l t t h a t none of the o t h e r s t r a t e g i e s a p p l i e d t o them would, i n f a c t , have a r e a s o n a b l e c h o i c e . 'I guessed when I wasn't su r e ' was i n c l u d e d on the s t r e n g t h of B a r r a t t ' s (1953) f i n d i n g t h a t i n s o l v i n g the items of the Space s u b t e s t of the D i f f e r e n t i a l A p t i t u d e T e s t , some people c o u l d not s o l v e the items and r e l i e d on g u e s s i n g . The r e m a i n i n g problem s o l v i n g s t a t e m e n t s a r e a l l d i f f e r e n t and are d e s i g n e d t o t a p • e i t h e r p a r t or whole problem s o l v i n g s t r a t e g i e s . I f an answer of 'TRUE' t o a statement i m p l i e d t h a t the whole f i g u r e was kept i n mind, the item was deemed t o be a whole problem s o l v i n g s t r a t e g y . I f an answer of 'TRUE' i m p l i e d t h a t o n l y a c e r t a i n a s p e c t or p a r t of a s t i m u l u s f i g u r e was kept i n mind t o a t t a i n s o l u t i o n of the problem, the it e m was c o n s i d e r e d t o be a p a r t problem s o l v i n g s t r a t e g y . Card R o t a t i o n s Test ( S i ) Answering 'TRUE' t o 'I noted t h a t some of the f i g u r e s l o o k e d l i k e l e t t e r s of the a l p h a b e t or f a m i l i a r o b j e c t s and s o l v e d them w i t h t h i s i n mind' ( S t r a t e g y 1) i s a whole problem s o l v i n g s t r a t e g y . T h i s statement • was i n c l u d e d because of B a r r a t t ' s (1953) f i n d i n g t h a t p e o p l e who, on 1 04 the F i g u r e s t e s t , a ttempted t o r e l a t e the items t o something f a m i l i a r s c o r e d lower than p e o p l e who used a p a r t s t r a t e g y . Answering 'TRUE' t o ' I noted some d i s t i n c t a s p e c t of the f i g u r e (e.g. bottom p a r t or t o p l e f t c o r n e r ) and s o l v e d the f i g u r e s w i t h t h i s f e a t u r e i n m i n d ' ( S t r a t e g y 2) i s a p a r t problem s o l v i n g s t r a t e g y , w h i l e a n s w e r i n g .'TRUE' to ' I m e n t a l l y r o t a t e d a f i g u r e and m e n t a l l y p l a c e d i t on to p of the o t h e r f i g u r e s t o see i f they were the same' ( S t r a t e g y 3) i s a whole problem s o l v i n g s t r a t e g y . Both items were suggested by B a r r a t t ' s (1953) f i n d i n g t h a t p eople who r o t a t e d o n l y p a r t of a f i g u r e s c o r e d h i g h e r than p e o p l e who r o t a t e d the whole f i g u r e . Answering 'TRUE' t o 'I m e n t a l l y . r o t a t e d one of the f i g u r e s and t h e n , w i t h o u t n e c e s s a r i l y p l a c i n g one f i g u r e on t o p of the o t h e r , compared the two' ( S t r a t e g y 4) i s a whole problem s o l v i n g s t r a t e g y . A l t h o u g h the statement was suggested by B a r r a t t (1953), i t was p r i m a r i l y i n c l u d e d i n o r d e r t o determine how p e o p l e s o l v e d the Cards i t e m s , g i v e n t h a t they were u s i n g a whole approach. Cube Comparisons Test (S2) Answering 'TRUE' t o 'I m e n t a l l y p i c k e d up one of the cubes and r o t a t e d i t to l i n e i t up w i t h a c e r t a i n symbol on the o t h e r one and then checked whether not the o t h e r symbols were i n the r i g h t p l a c e ' ( S t r a t e g y 1) i s a whole problem s o l v i n g s t r a t e g y . The r a t i o n a l e f o r i n c l u d i n g 105 t h i s statement i s the same as t h a t f o r i n c l u d i n g S t r a t e g y 4 f o r Cards. Answering 'TRUE' t o 'Without m e n t a l l y p i c k i n g up the cube, I determined i f any two of the symbols on both cubes bore the same r e l a t i o n t o one a n o t h e r ' ( S t r a t e g y 2) i s a p a r t problem s o l v i n g s t r a t e g y . T h i s statement was suggested by S t r a t e g y 2 from Cards i n t h a t o n l y p a r t of the s t i m u l u s i s c o n s i d e r e d . Answering 'TRUE' t o 'I had an X and Y a x i s i n mind when s o l v i n g the items' ( S t r a t e g y 3) i s a whole problem s o l v i n g s t r a t e g y . The statement was suggested by French (1965) who noted t h a t some people r e p o r t e d s o l v i n g the Cubes items by m e n t a l l y r o t a t i n g the cubes on two s e p a r a t e axes. Answering 'TRUE' t o 'I p i c t u r e d myself as w a l k i n g around the cubes' ( S t r a t e g y 4) i s a whole problem s o l v i n g s t r a t e g y . T h i s statement i s based on the i d e a t h a t .people who p i c t u r e themselves as w a l k i n g around the cubes use a s p a t i a l o r i e n t a t i o n s t r a t e g y ( M i c h a e l e t a l . , 1950), w h i l e t h o s e who m e n t a l l y p i c k up and r o t a t e a cube use a v i s u a l i z a t i o n p r o c e s s ( S t r a t e g y 1). Form Board Test ( V z l ) I n s p e c t i o n of the s t i m u l i f o r t h i s t e s t might suggest t h a t , s i n c e every i t e m c o n s i s t s of f i v e d i s t i n c t p i e c e s , a p a r t s t r a t e g y would be the o n l y p o s s i b l e one. However, c o n s i d e r a t i o n must a l s o be g i v e n t o the f i g u r e a t the t o p 106 of each column which was t o be completed, or f i l l e d i n , by some subset of the f i v e d i s t i n c t p i e c e s . Thus, s t a t e m e n t s which i n d i c a t e d t h a t t h i s f i g u r e was kept i n mind as a whole were termed whole problem s o l v i n g s t r a t e g i e s . I f , however, the f i g u r e was not c o n s i d e r e d m e n t a l l y ( i . e . u s i n g the a c t u a l f i g u r e r a t h e r than a mental r e p r e s e n t a t i o n of i t ) i t was assumed t h a t a p a r t s t r a t e g y was used. Due t o the l a c k of p u b l i s h e d r e p o r t s r e l a t i n g t o problem s o l v i n g s t r a t e g y f o r t h i s t e s t , the above r a t i o n a l e f o r i n c l u d i n g the v a r i o u s statements a p p l i e s t o a l l s t a t e m e n t s . Answers of 'TRUE' t o 'I m e n t a l l y p l a c e d one item a f t e r the o t h e r i n t o the f i g u r e u n t i l i t was f u l l ' ( S t r a t e g y 1) or 'I kept the l a r g e f i g u r e i n mind and t r i e d t o a r r a n g e the s m a l l e r p i e c e s t o f i t i t ' ( S t r a t e g y 2 ) were whole problem s o l v i n g s t r a t e g i e s . Answers of 'TRUE' t o 'I used a p e n c i l t o draw the l a r g e f i g u r e out of the s m a l l e r ones' ( S t r a t e g y 3) or 'I used t r i a l and e r r o r ' ( S t r a t e g y 4) were p a r t problem s o l v i n g s t r a t e g i e s . Paper F o l d i n g Test ( V z 2 ) Answers of 'TRUE' t o 'I m e n t a l l y f o l d e d the paper, punched a h o l e , and then m e n t a l l y u n f o l d e d i t and compared i t t o the p o s s i b l e answers' ( S t r a t e g y 1) or 'I worked backwards; I l o o k e d a t the drawing w i t h the h o l e s and then 1 0 7 u n f o l d e d i t m e n t a l l y ( i . e . I d i d n ' t a c t u a l l y f o l d the paper up t o b e g i n w i t h ) ' ( S t r a t e g y 4) were whole. problem s o l v i n g s t r a t e g i e s . Answers of 'TRUE' t o 'I noted where one or two of the h o l e s would be and then t r i e d t o f i n d an answer t h a t had these one or two h o l e s i n the same p l a c e ( i . e . I d i d n ' t a c t u a l l y f o l d and u n f o l d the p a p e r ) ' ( S t r a t e g y 2) or 'I t r i e d t o determine through how many t h i c k n e s s e s of paper the h o l e would have t o go and then p i c k e d one of the answers t h a t had t h a t many h o l e s ( i . e . I d i d n ' t a c t u a l l y u n f o l d the paper w i t h the h o l e s ) ' ( S t r a t e g y 3) were p a r t problem s o l v i n g s t r a t e g i e s . A l l s t a t e m e n t s were suggested by the problem s o l v i n g s t r a t e g i e s l i s t e d by B a r r a t t (1953) f o r the Space s u b t e s t of the D i f f e r e n t i a l A p t i t u d e T e s t . S t r a t e g i e s 2 and 3 were meant t o t a p whether peo p l e were merely l o o k i n g f o r cues ( i . e . p o s i t i o n of h o l e s , number of t h i c k n e s s e s ) ; and S t r a t e g i e s 1 and 4 i n v o l v e d f o l d i n g and/or u n f o l d i n g of f i g u r e s . S u r f a c e Development Test (Vz3) Answers of 'TRUE' t o 'I m e n t a l l y f o l d e d up the f i g u r e and m e n t a l l y p l a c e d i t on t o p of the f i g u r e a l r e a d y f o l d e d up' ( S t r a t e g y 1) or 'I m e n t a l l y f o l d e d up the f i g u r e and t h e n , w i t h o u t n e c e s s a r i l y p l a c i n g i t on t o p of the f i g u r e a l r e a d y f o l d e d up, I t r i e d t o match the l e t t e r s and numbers' ( S t r a t e g y 2) were whole problem s o l v i n g 108 s t r a t e g i e s . Answers of 'TRUE' t o 'I t r i e d t o match the numbers and l e t t e r s up w i t h o u t ever d o i n g any mental f o l d i n g ' ( S t r a t e g y 3) or 'I chose a number I wanted t o f i n d a l e t t e r f o r and then m e n t a l l y f o l d e d o n l y those p a r t s of the f i g u r e t h a t had t o do w i t h t h a t number' ( S t r a t e g y 4) were p a r t problem s o l v i n g s t r a t e g i e s . These statements were i n c l u d e d on the s t r e n g t h of the M i c h a e l e t a l . (1950) h y p o t h e s i s t h a t i f e n t i r e f i g u r e s are kept i n mind ( S t r a t e g i e s 1 and 2) a t e s t would l o a d on a v i s u a l i z a t i o n f a c t o r , whereas i f o n l y s a l i e n t a s p e c t s of the f i g u r e s are c o n s i d e r e d ( S t r a t e g i e s 3 and 4) the t e s t would l o a d a s p a t i a l o r i e n t a t i o n f a c t o r . 

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