UBC Theses and Dissertations

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UBC Theses and Dissertations

Cognitive and noncognitive correlates of statistics achievement Selkirk, Sheena Ann 1982

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COGNIT IVE AND NONCOGNITIVE CORRELATES OF S T A T I S T I C S ACHIEVEMENT by SHEENA ANN SELKIRK O . T . D i p . , M c G i l l U n i v e r s i t y , 1965 B . A . ( H o n . ) , U n i v e r s i t y o f S a s k a t c h e w a n , 1969 A THES IS SUBMITTED IN PARTIAL FULF ILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES D e p a r t m e n t o f E d u c a t i o n a l P s y c h o l o g y and S p e c i a l E d u c a t i o n We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERS ITY OF BR IT ISH COLUMBIA S e p t e m b e r 1982 © Sheena Ann S e l k i r k , 1982 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 t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t he U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 s t u d y . I f u r t h e r a g r e e 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 c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r 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 no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f E d u c a t i o n a l P s y c h o l o g y and S p e c i a l E d u c a t i o n The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 D a t e : S e p t e m b e r , 1982 i i A b s t r a c t T h i s t h e s i s i s a r e p o r t o f an a t t e m p t t o a c c o u n t f o r t h e o b s e r v e d v a r i a n c e i n a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s , w i t h i n a p o p u l a t i o n o f g r a d u a t e s t u d e n t s i n E d u c a t i o n . M e a s u r e s o f t w e l v e i n d e p e n d e n t v a r i a b l e s , s e l e c t e d on t h e b a s i s o f t h e l i t e r a t u r e i n t h e a r e a , were c o l l e c t e d - f r o m v o l u n t e e r s u b j e c t s d u r i n g a c l a s s s e s s i o n o f e a c h o f f o u r c l a s s e s a t t h e U n i v e r s i t i e s o f A l b e r t a , B r i t i s h C o l u m b i a and V i c t o r i a . The v a r i a b l e s i n c l u d e d m e a s u r e s o f v e r b a l c o m p r e h e n s i o n , l o g i c a l r e a s o n i n g , s p a t i a l v i s u a l i z a t i o n , number f a c i l i t y , and c o n c e p t l e a r n i n g . M e a s u r e s o f a t t i t u d e t o w a r d s t a t i s t i c s , o f a t t i t u d e t o w a r d r e s e a r c h and o f a c a d e m i c s e l f - c o n c e p t were c o l l e c t e d , a s were m e a s u r e s o f a c h i e v e m e n t m o t i v a t i o n , o f s p e c i f i c m o t i v a t i o n and o f p e r c e i v e d u t i l i t y . The t w e l f t h i n d e p e n d e n t v a r i a b l e was e x p e r i e n c e , a s m e a s u r e d by t h e number o f m a t h e m a t i c s o r s t a t i s t i c s c o u r s e s p r e v i o u s l y c o m p l e t e d . The measu re o f t h e d e p e n d e n t v a r i a b l e , s t a t i s t i c s a c h i e v e m e n t , was t h e s c o r e o b t a i n e d on a o n e - h o u r common e x a m i n a t i o n . The o r i g i n a l i n t e n t was t o i n v e s t i g a t e t h e d e t e r m i n a n t s o f s t a t i s t i c s a c h i e v e m e n t t h r o u g h t h e a p p l i c a t i o n o f B e n t l e r ' s " c a u s a l m o d e l i n g w i t h l a t e n t v a r i a b l e s " (LVM) a p p r o a c h . U n f o r s e e n d e l a y s i n a d m i n i s t e r i n g t h e m e a s u r e s o f t h e i n d e p e n d e n t v a r i a b l e s a t t h e U n i v e r s i t y o f A l b e r t a r e s u l t e d i n s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s be tween t h e B r i t i s h C o l u m b i a and A l b e r t a p o o l s o f d a t a . C o n s e q u e n t l y , t h e r e s e a r c h q u e s t i o n s were r e d e v e l o p e d so a s t o e x c l u d e c o n s i d e r a t i o n o f t h e LVM a p p r o a c h and any e x p l o r a t i o n o f p o t e n t i a l l a t e n t v a r i a b l e s f r o m t h e a n a l y s i s p l a n . The me thod o f a n a l y s i s was l i m i t e d , t h e n , t o t h e e x a m i n a t i o n o f z e r o - o r d e r c o r r e l a t i o n s and t o t h e c o m p u t a t i o n o f e x p l o r a t o r y f o r w a r d r e g r e s s i o n s . The B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s were a n a l y z e d s e p a r a t e l y . B e c a u s e o f t h e e x p l o r a t o r y n a t u r e o f t h e a n a l y s i s , t h e 0 . 1 0 l e v e l was a d o p t e d a s t h e c r i t e r i o n o f s t a t i s t i c a l s i g n i f i c a n c e . C o r r e l a t i o n a l a n a l y s i s o f t h e B r i t i s h C o l u m b i a s amp l e r e v e a l e d t h a t e x p e r i e n c e , v e r b a l r e a s o n i n g , s p a t i a l v i s u a l i z a t i o n a n d c o n c e p t l e a r n i n g s i g n i f i c a n t l y c o r r e l a t e d w i t h a c h i e v e m e n t . Two c l u s t e r s o f i n t e r c o r r e l a t i o n s ( c o g n i t i v e -e x p e r i e n t i a l and a t t i t u d i n a l - m o t i v a t i o n a l ) were i d e n t i f i e d . O n l y t h e f i r s t c l u s t e r was r e l a t e d t o s t a t i s t i c s a c h i e v e m e n t . A p p l i c a t i o n o f s t e p w i s e r e g r e s s i o n r e v e a l e d t h a t o n l y p a s t e x p e r i e n c e a c c o u n t e d f o r a s t a t i s t i c a l l y s i g n i f i c a n t p r o p o r t i o n o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . The s e t o f 12 v a r i a b l e s t a k e n t o g e t h e r a c c o u n t e d f o r 5 5 . 5 % o f t h e v a r i a n c e . S i m i l a r a n a l y s i s o f t h e A l b e r t a d a t a r e v e a l e d t h a t s p a t i a l v i s u a l i z a t i o n , number f a c i l i t y , c o n c e p t l e a r n i n g , a t t i t u d e t o w a r d s t a t i s t i c s and a t t i t u d e t o w a r d r e s e a r c h s i g n i f i c a n t l y c o r r e l a t e d w i t h s t a t i s t i c s a c h i e v e m e n t . C o g n i t i v e - a t t i t u d i n a l and a t t i t u d i n a l - m o t i v a t i o n a l c l u s t e r s o f i n d e p e n d e n t v a r i a b l e s were i d e n t i f i e d i n t h e c o r r e l a t i o n m a t r i x . B o t h c l u s t e r s a p p e a r e d t o be r e l a t e d t o s t a t i s t i c s a c h i e v e m e n t . The r e s u l t s o f a s t e p w i s e r e g r e s s i o n r e v e a l e d t h a t 5 4 . 9 % o f t h e v a r i a n c e i n a c h i e v e m e n t was a c c o u n t e d f o r by t h e s e t o f 12 i n d e p e n d e n t v a r i a b l e s . T h r e e v a r i a b l e s ( c o n c e p t l e a r n i n g , a t t i t u d e t o w a r d s t a t i s t i c s a n d s p a t i a l v i s u a l i z a t i o n ) c o n t r i b u t e d s i g n i f i c a n t l y i v t o t he e x p l a i n e d v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . When the two s a m p l e s were s u b j e c t e d t o e x p l o r a t o r y r e g r e s s i o n a n a l y s e s , t h e o r d e r o f e n t r y o f t h e i n d e p e n d e n t v a r i a b l e s was n o t s i m i l a r i n t h e two s a m p l e s . The r e s u l t s were d i s c u s s e d i n t e r m s of t h e f i n d i n g s r e p o r t e d i n t h e l i t e r a t u r e a n d o f t h e p o s s i b l e e f f e c t s o f t h e d i f f e r e n t a d m i n i s t r a t i o n t i m e s o f t h e t e s t s . The t h e s i s i s t e r m i n a t e d by a p r e s e n t a t i o n o f some s u g g e s t i o n s f o r f u t u r e r e s e a r c h . V T a b l e o f C o n t e n t s L i s t o f T a b l e s . . . . . i x L i s t o f F i g u r e s x i A c k n o w l e d g e m e n t x i i I. I n t r o d u c t i o n t o t h e P r o b l e m 1 B a c k g r o u n d 1 S t a t i s t i c s A c h i e v e m e n t 3 S t a t e m e n t o f t h e P r o b l e m 7 A P l a u s i b l e M o d e l 8 R e s e a r c h Q u e s t i o n s 10 O r g a n i z a t i o n o f t h e T h e s i s 10 I I . Rev i ew o f L i t e r a t u r e 12 P r e d i c t i o n o f S t a t i s t i c s A c h i e v e m e n t 13 M o t i v a t i o n a l V a r i a b l e s 20 P a t h A n a l y s i s and C a u s a l M o d e l i n g w i t h L a t e n t V a r i a b l e s 21 T h r e e E x p l o r a t o r y M o d e l s 25 I I I . M e t h o d 31 I n s t r u m e n t s 31 M e a s u r e s o f t h e I n d e p e n d e n t V a r i a b l e s . . . . 3 1 V e r b a l C o m p r e h e n s i o n 32 L o g i c a l R e a s o n i n g 33 Number F a c i l i t y 34 S p a t i a l V i s u a l i z a t i o n 35 C o n c e p t L e a r n i n g . . . 3 5 A t t i t u d e Towa rd S t a t i s t i c s 37 A t t i t u d e T o w a r d R e s e a r c h 40 v i A c a d e m i c S e l f - C o n c e p t 42 A c h i e v e m e n t M o t i v a t i o n - 43 P e r c e i v e d U t i l i t y 44 S p e c i f i c M o t i v a t i o n 45 E x p e r i e n c e 45 The M e a s u r e o f t h e D e p e n d e n t V a r i a b l e 46 S u b j e c t s 47 T a r g e t P o p u l a t i o n 47 A c c e s s i b l e P o p u l a t i o n .47 Sample 47 D a t a C o l l e c t i o n a n d P r e p a r a t i o n 47 D a t a C o l l e c t i o n 47 D a t a P r e p a r a t i o n 49 S c o r i n g P r o c e d u r e s 50 P r e l i m i n a r y A n a l y s i s 51 I t em A n a l y s i s 51 E q u i v a l e n c e o f t h e B r i t i s h C o l u m b i a and A l b e r t a S amp l e s 52 I V . P r e l i m i n a r y R e s u l t s a n d F i n a l A n a l y t i c P r o c e d u r e s 53 R e s u l t s o f t h e P r e l i m i n a r y A n a l y s i s 53 D e s c r i p t i o n o f t h e Sample 53 I n t e g r i t y o f t h e D a t a P o o l 55 I t em A n a l y s i s 56 The B r i t i s h C o l u m b i a Sample 56 The A l b e r t a Sample 60 E q u i v a l e n c e o f t h e S a m p l e s 63 v i i R e c a s t i n g o f t he R e s e a r c h Q u e s t i o n s 66 M e t h o d o l o g y o f t h e F i n a l A n a l y s i s 68 C o r r e l a t i o n a l A n a l y s e s 68 The B r i t i s h C o l u m b i a Samp le 68 The A l b e r t a Sample 69 V . R e s u l t s o f t h e F i n a l A n a l y s i s .71 C o r r e l a t i o n a l A n a l y s e s 71 T h e B r i t i s h C o l u m b i a Samp le 71 I n t e r c o r r e l a t i o n s 71 P a r s i m o n i o u s F o r w a r d R e g r e s s i o n 75 The A l b e r t a Sample 76 I n t e r c o r r e l a t i o n s 76 P a r s i m o n i o u s F o r w a r d R e g r e s s i o n 80 E x p l o r a t o r y F o r w a r d R e g r e s s i o n 82 V I . Summary and C o n c l u s i o n s 85 Summary o f t h e I n v e s t i g a t i o n 85 D i s c u s s i o n o f t h e R e s u l t s 90 R e s e a r c h Q u e s t i o n One 92 R e s e a r c h Q u e s t i o n Two 94 R e s e a r c h Q u e s t i o n T h r e e 96 L i m i t a t i o n s o f t h e S t u d y 98 C o n c l u s i o n s and I m p l i c a t i o n s 100 N o t e s 103 L i t e r a t u r e C i t e d 104 A p p e n d i x A . I n i t i a l Form o f t h e C o n c e p t L e a r n i n g T a s k 108 T a s k I n s t r u c t i o n s 108 v i i i C o n c e p t D e s c r i p t i o n . 109 T e s t Q u e s t i o n s 111 A p p e n d i x B. N o n - C o p y r i g h t T e s t M a t e r i a l s 112 I n t r o d u c t o r y S t a t e m e n t . . . 1 1 2 L e t t e r o f C o n s e n t 113 C o n c e p t L e a r n i n g T a s k 114 A t t i t u d e M e a s u r e 116 A c a d e m i c S e l f - C o n c e p t . . . 1 1 9 A c h i e v e m e n t M o t i v a t i o n 120 S p e c i f i c M o t i v a t i o n 121 P e r c e i v e d U t i l i t y . . 121 P a s t E x p e r i e n c e 121 A p p e n d i x C . I n i t i a l Fo rm o f A t t i t u d e S c a l e s 122 T a s k I n s t r u c t i o n s - 1 22 S t a t e m e n t s A b o u t S t a t i s t i c s 122 S t a t e m e n t s o f P o s i t i v e P o l a r i t y 122 S t a t e m e n t s o f N e g a t i v e P o l a r i t y 123 S t a t e m e n t s A b o u t R e s e a r c h 124 S t a t e m e n t s o f P o s i t i v e P o l a r i t y . . 1 2 4 S t a t e m e n t s o f N e g a t i v e P o l a r i t y 125 A p p e n d i x D. A d m i n i s t r a t i o n I n s t r u c t i o n s 127 i x L i s t o f T a b l e s T a b l e 1. L a t e n t and M a n i f e s t V a r i a b l e s I n v e s t i g a t e d and t h e i r S u b s t a n t i v e D e f i n i t i o n s 9 T a b l e 2. C o r r e l a t i o n s o f C o g n i t i v e and N o n c o g n i t i v e V a r i a b l e s w i t h S t a t i s t i c s A c h i e v e m e n t 19 T a b l e 3. M e a s u r e s o f t h e M a n i f e s t V a r i a b l e s and t h e U n d e r l y i n g L a t e n t V a r i a b l e 32 T a b l e 4 . I t em and S c a l e S t a t i s t i c s F o r The A t t i t u d e S c a l e s 39 T a b l e 5. O b t a i n e d Sample S i z e s .. 55 T a b l e 6. S c a l e S t a t i s t i c s ( B r i t i s h C o l u m b i a Samp le ) 56 T a b l e 7. S c a l e S t a t i s t i c s ( A l b e r t a Samp le ) 61 T a b l e 8. I n t e r - c o r r e l a t i o n s among t h e V a r i a b l e s ( B r i t i s h C o l u m b i a Samp le ) 72 T a b l e 9 . P a r t i a l C o r r e l a t i o n s and F - R a t i o s f o r t h e N o n - C o n t r i b u t o r y V a r i a b l e s ( B r i t i s h C o l u m b i a Samp le ) 75 T a b l e 10 . I n t e r - c o r r e l a t i o n s among t h e V a r i a b l e s ( A l b e r t a Samp le ) 77 T a b l e 1 1 . P a r t i a l C o r r e l a t i o n s a n d F - R a t i o s f o r t h e N o n - C o n t r i b u t o r y V a r i a b l e s ( A l b e r t a Samp le ) 80 X T a b l e 12. P a r t i a l C o r r e l a t i o n s and F - R a t i o s f o r 9 N o n - C o n t r i b u t o r y I n d e p e n d e n t V a r i a b l e s ( A l b e r t a S amp l e ) 82 T a b l e 1 3 . O r d e r o f E n t r y , R-Squa re C h a n g e , and B e t a W e i g h t s f o r E x p l o r a t o r y F o r w a r d R e g r e s s i o n s 83 x i L i s t o f F i g u r e s F i g u r e 1. P a t h - A n a l y t i c M o d e l o f A d u l t V o c a b u l a r y S c o r e 23 F i g u r e 2. LVM M o d e l o f A d u l t V o c a b u l a r y S c o r e 24 F i g u r e 3. E x p l o r a t o r y M o d e l " A " o f S t a t i s t i c s A c h i e v e m e n t 28 F i g u r e 4 . E x p l o r a t o r y M o d e l " B " o f S t a t i s t i c s A c h i e v e m e n t 29 F i g u r e 5. E x p l o r a t o r y M o d e l " C " o f S t a t i s t i c s A c h i e v e m e n t 30 F i g u r e 6 . M o d e l o f A c h i e v e m e n t ( ( L e s s E x p e r i e n c e d S t u d e n t ) 101 F i g u r e 7. M o d e l o f A c h i e v e m e n t (More E x p e r i e n c e d S t u d e n t ) 101 x i i A c k n o w l e d g e m e n t I w o u l d f i r s t l i k e t o e x p r e s s my g r a t i t u d e t o my s u p e r v i s o r , D r . T . R o g e r s , who has d e a l t w i t h many p r o b l e m s w i t h t o l e r a n c e and u n d e r s t a n d i n g . The o t h e r members o f my c o m m i t t e e , D r . H. R a t z l a f f and D r . J . S h e r r i l l , b o r e w i t h me p a t i e n t l y ; I am g r a t e f u l t o them b o t h . I wou ld l i k e t o t hank D r . D. B a t e s o n , D r . D. L a y t o n , and D r . R. Randhawa f o r a l l o w i n g me t o u t i l i z e t h e i r c l a s s e s . D r . E. Skakun and D r . T . M c G u i r e o f t h e U n i v e r s i t y o f A l b e r t a d e s e r v e s p e c i a l t h a n k s f o r t h e i r h e r o i c e f f o r t s t o h e l p me l o c a t e m i s s i n g t e s t m a t e r i a l s . F i n a l l y , I w o u l d l i k e t o e x p r e s s my g r a t i t u d e t o t h e s u b j e c t s , who c o m p l e t e d t h e r a t h e r t e d i o u s f o r m s so i n d u s t r i o u s l y and e x p r e s s e d s u c h i n t e r e s t i n t h e s t u d y . 1 C h a p t e r I.  I n t r o d u c t i o n t o t h e P r o b l e m B a c k g r o u n d In t h e e d u c a t i o n a l p s y c h o l o g y l i t e r a t u r e , much a t t e n t i o n has been p a i d t o t h e p a t t e r n s and c o r r e l a t e s o f a c a d e m i c s u c c e s s among c o l l e g e s t u d e n t s . The r e s e a r c h has f o c u s e d b o t h on g e n e r a l a c a d e m i c s u c c e s s and on a c h i e v e m e n t i n p a r t i c u l a r a c a d e m i c s u b j e c t s ( e . g . , m a t h e m a t i c s , s t a t i s t i c s ) . An e x a m p l e o f t h e f o r m e r g r o u p o f s t u d i e s i s t h a t o f Hackman and T a b e r ( 1 9 7 9 ) . T h e y e x a m i n e d d a t a f r o m u n d e r g r a d u a t e s t u d e n t s , e a c h o f whom had been n o m i n a t e d as "mos t s u c c e s s f u l " o r " l e a s t s u c c e s s f u l " a l o n g a c a d e m i c , p e r s o n a l , i n t e r p e r s o n a l and i n s t i t u t i o n a l d i m e n s i o n s . M u l t i v a r i a t e a n a l y s i s r e v e a l e d t w e l v e p r o f i l e s o f s t u d e n t v a r i a b l e s , s e v e n b e i n g c h a r a c t e r i s t i c o f " s u c c e s s f u l " s t u d e n t s , f i v e o f " u n s u c c e s s f u l " s t u d e n t s . Hackman and T a b e r d e f i n e d a c a d e m i c s u c c e s s r a t h e r g l o b a l l y . T h a t i s , " s u c c e s s f u l " and " u n s u c c e s s f u l " s t u d e n t s were s e l e c t e d by f a c u l t y and p e e r n o m i n a t i o n . More common l y , a s i n g l e v a r i a b l e s u c h a s g r a d e - p o i n t a v e r a g e has been s e l e c t e d t o o p e r a t i o n a l i z e " a c a d e m i c a c h i e v e m e n t " . E x a m p l e s o f i n v e s t i g a t i o n s o f t h i s s o r t i n c l u d e a s t u d y o f t h e r e l a t i o n s h i p o f a c a d e m i c a c h i e v e m e n t and e x p e c t a n c y b e l i e f s ( H e n s o n , 1 9 7 6 ) , a d e t e r m i n a t i o n o f t h e p r e d i c t i v e power o f t h e A m e r i c a n C o l l e g e T e s t i n a commun i t y c o l l e g e s e t t i n g ( M a t h i s , 1 9 7 2 ) , and a me ta-2 a n a l y s i s o f o v e r 100 s t u d i e s o f t h e r e l a t i o n s h i p o f a c a d e m i c a c h i e v e m e n t t o s o c i o - e c o n o m i c s t a t u s ( W h i t e , 1 9 7 9 ) . Among t h e i n v e s t i g a t i o n s o f t h e c o r r e l a t e s o f a c h i e v e m e n t i n a s p e c i f i c s u b j e c t a r e a , a s u b s t a n t i a l number a r e r e p o r t s o f i n v e s t i g a t i o n s o f t h e r e l a t i o n s h i p o f a c h i e v e m e n t i n c o l l e g e m a t h e m a t i c s t o m e a s u r e s o f v a r i o u s i n d e p e n d e n t v a r i a b l e s , b o t h c o g n i t i v e and n o n c o g n i t i v e . D a v i s and R i s s e r ( 1 9 6 5 ) , f o r e x a m p l e , f o u n d t h a t p r e v i o u s m a t h e m a t i c s g r a d e s , s e c o n d a r y s c h o o l g r a d e - p o i n t a v e r a g e , and s c o r e s on a p l a c e m e n t t e s t i n m a t h e m a t i c s were p r e d i c t i v e o f c o l l e g e a l g e b r a g r a d e s . A s e c o n d e x a m p l e i s an i n v e s t i g a t i o n by T r o u t m a n ( 1 9 7 8 ) . He r e p o r t e d t h a t h i g h s c h o o l m a t h e m a t i c s g r a d e s , a measu re o f i n t e l l i g e n c e , c o l l e g e b o a r d s c o r e s and h i g h s c h o o l c l a s s r a n k s p r e d i c t e d g r a d e s i n f i n i t e m a t h e m a t i c s c o u r s e s i n a c o l l e g e f r e s h m a n p o p u l a t i o n . Among t h e n o n c o g n i t i v e v a r i a b l e s , a n x i e t y t o w a r d s m a t h e m a t i c s a p p e a r s t o have been s t u d i e d e x t e n s i v e l y . S e p i e and K e e l i n g ( 1 9 7 8 ) , f o r i n s t a n c e , i n v e s t i g a t e d t h e d i f f e r e n t i a l p r e d i c t i v e power o f g e n e r a l v e r s u s s p e c i f i c a n x i e t y on m a t h e m a t i c s a c h i e v e m e n t . They f o u n d t h a t , f o r t h e c o l l e g e s t u d e n t p o p u l a t i o n f r o m w h i c h t h e i r s amp l e was s e l e c t e d , s p e c i f i c m a t h e m a t i c s a n x i e t y was a b e t t e r p r e d i c t o r o f a c h i e v e m e n t t h a n g e n e r a l a n x i e t y . A u s t i n - M a r t i n (1980) f o u n d t h a t , among f e m a l e c o l l e g e f r e s h m e n , m a t h e m a t i c s a n x i e t y was r e l a t e d t o m a t h e m a t i c s a c h i e v e m e n t , a t t i t u d e s t o w a r d s m a t h e m a t i c s , number o f m a t h e m a t i c s c o u r s e s t a k e n , and p a r e n t s ' o c c u p a t i o n s . 3 S e v e r a l i n v e s t i g a t i o n s have been c o n d u c t e d i n w h i c h t h e g e n d e r d i f f e r e n c e i n m a t h e m a t i c s a c h i e v e m e n t has been e x p l o r e d . R e c e n t l y , R o b i t a i l l e (1981) e x a m i n e d g e n d e r d i f f e r e n c e s on m e a s u r e s o f f i v e d o m a i n s o f m a t h e m a t i c s (numbers and o p e r a t i o n s , g e o m e t r y , m e a s u r e m e n t , a l g e b r a i c t o p i c s , and c o m p u t e r l i t e r a c y ) i n a l a r g e s amp l e o f B r i t i s h C o l u m b i a s c h o o l c h i l d r e n . He f o u n d t h a t , a l t h o u g h some s t a t i s t i c a l l y s i g n i f i c a n t g e n d e r d i f f e r e n c e s a p p e a r e d a t t h e G r a d e 4 l e v e l , by G r a d e 12 s i g n i f i c a n t g e n d e r d i f f e r e n c e s were o b t a i n e d on a l l f i v e m e a s u r e s . In s p i t e o f s u c h r e s u l t s a s t h o s e f o u n d by R o b i t a i l l e , o t h e r s have s u g g e s t e d t h a t s o c i o - c u l t u r a l d i f f e r e n c e s r a t h e r t h a n g e n d e r p e r se a r e i m p o r t a n t d e t e r m i n a n t s o f m a t h e m a t i c s a c h i e v e m e n t (Fennema and S h e r m a n , 1 9 7 7 ) . T h i s s u g g e s t i o n i s s u p p o r t e d by r e s u l t s r e p o r t e d e a r l i e r by Fox ( 1 9 7 6 ) , who s t u d i e d g e n d e r - r e l a t e d f a c t o r s a f f e c t i n g m a t h e m a t i c s p e r f o r m a n c e . She f o u n d t h a t t h e p e r c e p t i o n o f u s e f u l n e s s o f m a t h e m a t i c s and t h e d e g r e e o f s u p p o r t f r o m s i g n i f i c a n t o t h e r s c o r r e l a t e d s t r o n g l y w i t h m a t h e m a t i c s a c h i e v e m e n t . T h e s e v a r i a b l e s w e r e , i n t u r n , r e l a t e d t o p e r c e p t i o n s o f m a t h e m a t i c s as a ma l e d o m a i n . S t a t i s t i c s A c h i e v e m e n t D e s p i t e t h e l a r g e numbers o f c o l l e g e s t u d e n t s who e n t e r e l e m e n t a r y s t a t i s t i c s c o u r s e s i n t h e b e h a v i o r a l s c i e n c e s and t h e o f t e n - h e a r d l a m e n t t h a t " s t a t i s t i c s i s no t f o r m e " , few s t u d i e s r e p o r t e d i n t h e l i t e r a t u r e a d d r e s s d i r e c t l y t h e a r e a o f c o r r e l a t e s o f c o u r s e a c h i e v e m e n t i n s t a t i s t i c s . Of t h e s t u d i e s i n t h i s a r e a , two a r e r e p o r t s o f i n v e s t i g a t i o n s o f t h e 4 r e l a t i o n s h i p o f a s i n g l e i n d e p e n d e n t v a r i a b l e t o s t a t i s t i c s a c h i e v e m e n t , w h i l e t h e r e m a i n i n g f i v e a r e r e p o r t s o f e x a m i n a t i o n s o f t h e c o n t r i b u t i o n s o f s e v e r a l i n d e p e n d e n t v a r i a b l e s . M i c h a e l and M i c h a e l (1969) e x a m i n e d a b i l i t y i n b a s i c a r i t h m e t i c and a l g e b r a i c o p e r a t i o n s a n d f o u n d t h a t t h i s v a r i a b l e a c c o u n t e d f o r s l i g h t l y more t h a n 30% of t h e v a r i a n c e i n p e r f o r m a n c e i n a b a s i c s t a t i s t i c s c l a s s . R o b e r t s and B i l d e r b a c k (1980) e x a m i n e d t h e n o n c o g n i t i v e v a r i a b l e " a t t i t u d e t o w a r d s t a t i s t i c s " . U s i n g t h e i r own s c a l e o f 34 5 - p o i n t L i k e r t i t e m s , t h e y o b s e r v e d c o r r e l a t i o n s o f 0 . 3 3 , 0 . 4 8 and 0 .54 be tween s c a l e s c o r e s a n d t o t a l p o i n t s e a r n e d i n a s t a t i s t i c s c o u r s e f o r t h r e e s u c c e s s i v e c l a s s e s o f s t u d e n t s . T h e s e t h r e e c o r r e l a t i o n s c o r r e s p o n d t o 1 1 % , 2 3 % , and 29% o f t h e v a r i a n c e i n c o u r s e a c h i e v e m e n t , r e s p e c t i v e l y . The p o t e n t i a l c o n t r i b u t i o n s o f e a c h o f s e v e r a l c o g n i t i v e v a r i a b l e s were e x a m i n e d i n two o f t h e m u l t i p l e - v a r i a b l e i n v e s t i g a t i o n s . G i a m b r a (1972) f o u n d t h a t , w i t h t h e e x c e p t i o n o f a c o u r s e i n c a l c u l u s , p r e v i o u s m a t h e m a t i c a l c o u r s e w o r k and a c h i e v e m e n t i n an i n t r o d u c t o r y s t a t i s t i c s c o u r s e were n o t r e l a t e d . H o w e v e r , o v e r a l l g r a d e - p o i n t a v e r a g e was p o s i t i v e l y r e l a t e d t o c o u r s e a c h i e v e m e n t . H u b e r t y and S m i t h (1975) a t t e m p t e d t o d i s c r i m i n a t e among t h e s t u d e n t s who o b t a i n e d one o f f o u r g r a d e l e v e l s i n a b a s i c s t a t i s t i c s c o u r s e , by e x a m i n i n g e i g h t p o t e n t i a l c o g n i t i v e d i s c r i m i n a t o r s commonly f o u n d i n t h e s t u d e n t r e c o r d . Of t h e e i g h t , t h e G r a d u a t e R e c o r d E x a m i n a t i o n V e r b a l and M a t h e m a t i c s t e s t s p r o v e d t o d i s c r i m i n a t e b e s t , bu t 5 even t h e y d i d no t a l l o w " s a t i s f a c t o r y " c l a s s i f i c a t i o n . In a d d i t i o n , a c c u r a c y o f c l a s s i f i c a t i o n v a r i e d w i d e l y f o r t he v a r i o u s g r a d e - s c o r e l e v e l s . B o t h c o g n i t i v e a n d n o n c o g n i t i v e c o r r e l a t e s a n d p r e d i c t o r s o f s t a t i s t i c s a c h i e v e m e n t were c o n s i d e r e d i n t h e r e m a i n i n g t h r e e m u l t i p l e - v a r i a b l e s t u d i e s . H a r t l e y and H a r t l e y (1976) e n t e r e d 23 i n d e p e n d e n t v a r i a b l e s i n a b l o c k s t e p w i s e r e g r e s s i o n p r o c e d u r e . C o g n i t i v e v a r i a b l e s i n c l u d e d m e a s u r e s o f a b s t r a c t r e a s o n i n g , v e r b a l r e a s o n i n g , r e a d i n g c o m p r e h e n s i o n and r e a d i n g s p e e d . S e l f - r a t i n g s o f a r i t h m e t i c a p t i t u d e , a l g e b r a , s p e e d , l o g i c , c o m p r e h e n s i o n , r e t e n t i o n , v o c a b u l a r y , e s s a y - w r i t i n g a b i l i t y , t e c h n i c a l w r i t i n g a b i l i t y and s k i l l a t o r a l p r e s e n t a t i o n were a l s o i n c l u d e d , as were t h e s u b j e c t i v e p r o b a b i l i t i e s o f a t t a i n i n g e a c h o f t h e f o u r p o s s i b l e c o u r s e g r a d e s , and s c o r e s on e a c h o f f i v e s c a l e s a s s e s s i n g a t t i t u d e s t o w a r d s p s y c h o l o g y . The c o g n i t i v e m e a s u r e s a c c o u n t e d f o r 5 1 . 3 % o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t , t h e s e l f - r a t i n g s f o r 1 0 . 5 % , t h e p r e d i c t i o n s o f c o u r s e g r a d e f o r 5 . 9 % , and t h e a t t i t u d e s c a l e s f o r 1 8 . 5 % . F e i n b e r g and H a l p e r i n (1978) r e p o r t e d t h a t a t t i t u d e s t o w a r d s q u a n t i t a t i v e c o n c e p t s , s t a t e a n x i e t y m e a s u r e d d u r i n g a s t a t i s t i c s c l a s s , e x p e c t e d c o u r s e g r a d e , b a s i c m a t h e m a t i c s a c h i e v e m e n t , p e r c e p t i o n s o f m a t h e m a t i c a l a b i l i t y , g e n d e r o f s u b j e c t , number o f p r e v i o u s m a t h e m a t i c s c o u r s e s , a n d s u c c e s s i n p r e v i o u s m a t h e m a t i c s c o u r s e s were s i g n i f i c a n t l y c o r r e l a t e d w i t h a c h i e v e m e n t i n a s t a t i s t i c s c o u r s e . H o w e v e r , none o f t h e c o r r e l a t i o n s e x c e e d e d 0 . 4 0 (be tween c o u r s e a c h i e v e m e n t and b a s i c 6 m a t h e m a t i c s s k i l l s ) , and t h e m a j o r i t y r a n g e d be tween 0 .32 and 0 . 3 5 . The a t t e m p t t o p r e d i c t c o u r s e g r a d e u s i n g s t e p w i s e r e g r e s s i o n was so u n s u c c e s s f u l as t o no t be r e p o r t e d i n d e t a i l by t h e a u t h o r s . F i n a l l y , E l m o r e and V a s u (1980) i n v e s t i g a t e d t h e c o r r e l a t i o n o f a t t i t u d e s t o w a r d s m a t h e m a t i c s - r e l a t e d c o u r s e w o r k , number o f p r e v i o u s m a t h e m a t i c s c o u r s e s , g e n d e r o f s t u d e n t , s p a t i a l / v i s u a l i z a t i o n a b i l i t y and sex r o l e o r i e n t a t i o n p a t t e r n (on t h e M a s c u l i n i t y - F e m i n i n i t y s c a l e f r o m t h e MMPI and on s e v e r a l A t t i t u d e s Towa rds F e m i n i s t s s c a l e s ) w i t h a c h i e v e m e n t i n an i n t r o d u c t o r y s t a t i s t i c s c o u r s e . The i n d e p e n d e n t v a r i a b l e s , t a k e n t o g e t h e r , a c c o u n t e d f o r 4 6 . 4 % o f t h e v a r i a n c e i n c o u r s e m a r k . G e n d e r o f s t u d e n t c o n t r i b u t e d m i n i m a l l y ; s p a t i a l v i s u a l i z a t i o n a c c o u n t e d f o r t h e l a r g e s t p r o p o r t i o n ( 1 9 . 5 % ) o f v a r i a n c e . . A t t i t u d e s t o w a r d m a t h e m a t i c s - r e l a t e d c o u r s e w o r k , p r e v i o u s m a t h e m a t i c s c o u r s e w o r k , and sex r o l e o r i e n t a t i o n o f s t u d e n t (on t h e MMPI and on t h e A t t i t u d e T o w a r d s F e m i n i s t s s c a l e ) a c c o u n t e d f o r 1 8 . 1 % , 4 . 7 % , 8 .2% and 1 7 . 1 % , r e s p e c t i v e l y , o f t h e v a r i a n c e i n c o u r s e m a r k s . The r e p o r t e d r e l a t i o n s h i p be tween a c h i e v e m e n t and s p a t i a l / v i s u a l i z a t i o n a b i l i t y i s somewhat o b s c u r e d by a r e c e n t f i n d i n g r e p o r t e d by Sherman ( 1 9 8 0 ) . He f o u n d t h a t by l a t e h i g h s c h o o l , m a l e s p e r f o r m e d s i g n i f i c a n t l y b e t t e r t h a n f e m a l e s i n m a t h e m a t i c s d e s p i t e no s i g n i f i c a n t d i f f e r e n c e s on m e a s u r e s o f s p a t i a l / v i s u a l i z a t i o n . T h i s f i n d i n g may have been i n f l u e n c e d by t h e i n t e r a c t i o n o f a t t i t u d e s t o w a r d s sex r o l e b e h a v i o r s , w h i c h had been r e p o r t e d e a r l i e r (by Fox ( 1976 ) ) t o i n f l u e n c e 7 a c h i e v e m e n t i n m a t h e m a t i c s . S t a t e m e n t o f t h e P r o b l e m As r e v e a l e d by t h e r e s u l t s s u m m a r i z e d a b o v e , i t a p p e a r s t h a t r e s e a r c h i n t o t h e c o r r e l a t e s o f s t a t i s t i c s a c h i e v e m e n t a n d , i n p a r t i c u l a r , o f p e r f o r m a n c e i n i n t r o d u c t o r y s t a t i s t i c s c o u r s e s i n t h e s o c i a l s c i e n c e s , i s i n an e a r l y s t a g e o f d e v e l o p m e n t . T h a t i s , t h e p u b l i s h e d r e s u l t s c a n n o t e a s i l y be o r g a n i z e d i n t o a c o h e r e n t w h o l e . In a d d i t i o n , t h e i n v e s t i g a t i o n s r e p o r t e d i n t h e l i t e r a t u r e s e l d o m a t t e m p t t o r e p l i c a t e p r e v i o u s f i n d i n g s . F u r t h e r , no i n v e s t i g a t i o n o f t h e p r e d i c t i v e power o f m o t i v a t i o n a l v a r i a b l e s , w i t h r e g a r d t o a c h i e v e m e n t i n s t a t i s t i c s , ha s been r e p o r t e d i n t h e l i t e r a t u r e . H a k s t i a n and G a l e ( 1 9 7 9 ) , among o t h e r i n v e s t i g a t o r s , have shown t h a t m o t i v a t i o n a l v a r i a b l e s may a c c o u n t f o r a s much as 20% o f t h e v a r i a n c e i n o v e r a l l a c a d e m i c a c h i e v e m e n t , o v e r and above t h e c o n t r i b u t i o n o f c o g n i t i v e v a r i a b l e s . I t may be t h a t s t u d y o f m o t i v a t i o n a l v a r i a b l e s a s c o r r e l a t e s o r p r e d i c t o r s o f a c h i e v e m e n t i n s t a t i s t i c s w o u l d be a f r u i t f u l a r e a o f i n v e s t i g a t i o n . T h u s , t h e q u e s t i o n i n v e s t i g a t e d i n t h e p r e s e n t t h e s i s was : what a r e t h e r e l a t i v e c o n t r i b u t i o n s o f s e l e c t e d c o g n i t i v e , a t t i t u d i n a l , e x p e r e n t i a l and m o t i v a t i o n a l v a r i a b l e s t o t h e v a r i a n c e i n a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s c l a s s e s i n e d u c a t i o n ? 8 A P l a u s i b l e M o d e l A s o l u t i o n t o t h e p r o b l e m was s o u g h t i n t h e use o f t h e " c a u s a l m o d e l i n g w i t h l a t e n t v a r i a b l e s " a p p r o a c h s u g g e s t e d by B e n t l e r ( 1 9 8 0 ) . T h i s p r o c e d u r e i s u s e d t o e x p l a i n t h e o b s e r v e d r e l a t i o n s h i p s among a s e t o f m e a s u r e d o r m a n i f e s t v a r i a b l e s i n t e r m s o f a mode l i n c o r p o r a t i n g a s m a l l e r number o f u n d e r l y i n g c o n s t r u c t s o r l a t e n t v a r i a b l e s . The c e n t r a l p r o b l e m o f t h e p r o c e d u r e i s t o e s t i m a t e t h e " g o o d n e s s o f f i t " o f a p r o p o s e d mode l t o s amp le d a t a . I f t h e " f i t " i s n o t a c c e p t a b l e , t h e n t h e mode l i s r e j e c t e d . T w e l v e m a n i f e s t v a r i a b l e s were c o n s i d e r e d as i n d e p e n d e n t v a r i a b l e s . The t w e l v e , t o g e t h e r w i t h t h e s i n g l e d e p e n d e n t v a r i a b l e , a r e l i s t e d i n T a b l e 1 w h i c h a l s o c o n t a i n s a s h o r t s u b s t a n t i v e d e f i n i t i o n o f e a c h v a r i a b l e . I t was s u g g e s t e d t h a t e l e v e n o f t h e t w e l v e i n d e p e n d e n t v a r i a b l e s were m a n i f e s t a t i o n s o f one o f t h r e e l a t e n t v a r i a b l e s - c o g n i t i v e , a f f e c t i v e , o r m o t i v a t i o n a l . The t w e l f t h i n d e p e n d e n t v a r i a b l e , p a s t e x p e r i e n c e , was t h o u g h t t o be i n d e p e n d e n t o f t h e t h r e e p r o p o s e d u n d e r l y i n g c o n s t r u c t s . S p e c i f i c a t i o n o f a s i n g l e mode l was a more d i f f i c u l t t a s k . In p a r t i c u l a r , t he p l a c e m e n t o f t h e a r r o w s l i n k i n g t h e l a t e n t v a r i a b l e s , p a s t e x p e r i e n c e and s t a t i s t i c s a c h i e v e m e n t was n o t a c l e a r p r o c e s s . The s p e c i f i c a t i o n o f p a t h c o e f f i c i e n t s p r o v e d e q u a l l y d i f f i c u l t . T h e s e d i f f i c u l t i e s were due t o t h e e a r l y s t a t e o f t h e o r y - b u i l d i n g w i t h i n t h e a r e a . T h e r e f o r e , t h r e e a l t e r n a t i v e m o d e l s , d e s c r i b e d i n C h a p t e r I I , were s p e c i f i e d a n d e v a l u a t e d i n t e r m s o f t h e i r e x p l a n a t o r y power w i t h r e g a r d t o 9 T a b l e 1 L a t e n t and M a n i f e s t V a r i a b l e s I n v e s t i g a t e d and T h e i r B r i e f S u b s t a n t i v e D e f i n i t i o n s L a t e n t V a r i a b l e M a n i f e s t V a r i a b l e D e f i n i t i o n o f M a n i f e s t V a r i a b l e C o g n i t i v e V e r b a l C o m p r e h e n s i o n Number F a c i l i t y L o g i c a l R e a s o n i n g S p a t i a l V i s u a l i z a t i o n C o n c e p t L e a r n i n g a b i l i t y t o u n d e r s t a n d t h e E n g l i s h l a n g u a g e a b i l i t y t o p e r f o r m b a s i c a r i t h m e t i c o p e r a t i o n s w i t h s p e e d a n d a c c u r a c y a b i l i t y t o r e a s o n f r o m p r e m i s e t o c o n c l u s i o n a b i l i t y t o t r a n s f o r m an image of a s p a t i a l p a t t e r n a b i l i t y t o a b s t r a c t a c o n c e p t f r o m e x p l a n a t i o n and e x a m p l e s A t t i t u d i n a l A t t i t u d e Towa rd S t a t i s t i c s A t t i t u d e Towa rd R e s e a r c h A c a d e m i c S e l f - C o n c e p t o r i e n t a t i o n t o w a r d s t u d y i n g and p e r f o r m i n g i n t r o d u c t o r y s t a t i s t i c s o r i e n t a t i o n t o w a r d s t u d y i n g and a p p l y i n g p r i n c i p l e s o f r e s e a r c h d e s i g n and e v a l u a t i n g r e s e a r c h p e r c e p t i o n o f own c o g n i t i v e a b i l i t i e s Mot i v a t i o n a l A c h i e v e m e n t M o t i v a t i o n P e r c e i v e d U t i l i t y S p e c i f i c M o t i v a t i o n t e n d e n c y t o u n d e r t a k e s u c c e s s -o r i e n t e d a c t i v i t i e s p e r c e p t i o n o f s t r e n g t h and n a t u r e o f u s e f u l n e s s o f s t a t i s t i c s c o u r s e p e r c e p t i o n o f s t r e n g t h a n d n a t u r e o f r e a s o n f o r s t u d y i n g s t a t i s t i c s E x p e r i e n c e t o t a l i t y o f p r e v i o u s e x p e r i e n c e w i t h m a t h e m a t i c s , s t a t i s t i c s and r e s e a r c h S t a t i s t i c s A c h i e v e m e n t o v e r a l l know l edge o f i n t r o d u c t o r y d e s c r i p t i v e and i n f e r e n t i a l s t a t i s t i c s s t a t i s t i c s a c h i e v e m e n t . L i k e t h e s t u d i e s o f H a r t l e y a n d H a r t l e y ( 1 9 7 6 ) , F e i n b e r g and H a l p e r i n (1978) and E l m o r e and V a s u ( 1 9 8 0 ) , t h e p r e s e n t i n v e s t i g a t i o n was e x p l o r a t o r y i n n a t u r e . 10 R e s e a r c h Q u e s t i o n s B e c a u s e o f t h e e x p l o r a t o r y n a t u r e o f t h e s t u d y , a s i n g l e mode l was n o t e x a m i n e d . I n s t e a d , t h r e e m o d e l s were a s s e s s e d . Two s p e c i f i c r e s e a r c h q u e s t i o n s were a d d r e s s e d . The f i r s t q u e s t i o n was : Does any one o f t h e t h r e e m o d e l s i n v e s t i g a t e d a c c e p t a b l y r e p r o d u c e t h e o b s e r v e d m a t r i x o f c o r r e l a t i o n s among t h e v a r i a b l e s ? I t was p r o p o s e d t h a t , i f t h e a n a l y s i s o f t h e d a t a r e v e a l e d t h a t none o f t h e t h r e e m o d e l s was t e n a b l e , t h e f o l l o w i n g q u e s t i o n w o u l d be a d d r e s s e d : How much o f t h e v a r i a n c e i n a c h i e v e m e n t i n e l e m e n t a r y s t a t i s t i c s c a n be a c c o u n t e d f o r by e a c h o f t h e t h r e e l a t e n t v a r i a b l e s ( c o g n i t i v e , a t t i t u d i n a l and m o t i v a t i o n a l ) and by t h e m a n i f e s t v a r i a b l e , p a s t e x p e r i e n c e i n m a t h e m a t i c s and s t a t i s t i c s ? O r g a n i z a t i o n o f t h e T h e s i s The r e m a i n d e r o f t h i s t h e s i s i s o r g a n i z e d i n f i v e c h a p t e r s . A r e v i e w o f r e l e v a n t l i t e r a t u r e , a d i s c u s s i o n o f p a t h a n a l y s i s and c a u s a l m o d e l i n g , and a d e l i n e a t i o n o f t h e m o d e l s t o be i n v e s t i g a t e d a r e p r e s e n t e d i n C h a p t e r I I . C h a p t e r I I I c o n s i s t s o f d e s c r i p t i o n s o f t h e m e a s u r e s o f t h e i n d e p e n d e n t and d e p e n d e n t v a r i a b l e s , s a m p l i n g p l a n , d a t a c o l l e c t i o n p r o c e d u r e s and p r e p a r a t i o n o f d a t a f o r a n a l y s i s , and t h e p r e l i m i n a r y a n a l y s i s 11 p l a n . I n c l u d e d i n C h a p t e r IV a r e t h e r e s u l t s o f t h e p r e l i m i n a r y a n a l y s i s . As d i s c u s s e d t h e r e , t h e r e s e a r c h q u e s t i o n s were r e c a s t i n l i g h t o f t h e s e r e s u l t s , and a c o r r e s p o n d i n g c h a n g e i n t h e a n a l y s i s was made. T h e s e c h a n g e s a r e a l s o d e s c r i b e d i n C h a p t e r IV . The r e s u l t s o f t h e s e r e v i s e d a n a l y s e s a r e r e p o r t e d i n C h a p t e r V . C h a p t e r VI i s a r e p o r t o f t h e summary and c o n c l u s i o n s drawn f rom t h e f i n a l r e s u l t s . C h a p t e r I I .  Rev i ew o f L i t e r a t u r e T h i s c h a p t e r i s o r g a n i z e d i n t o t h r e e s e c t i o n s . F i r s t , t h e l i t e r a t u r e r e l a t e d t o t h e p r e d i c t i o n o f a c h i e v e m e n t i n s t a t i s t i c s i s r e v i e w e d . The p o s s i b l e r e l a t i o n s h i p o f m o t i v a t i o n a l v a r i a b l e s t o s t a t i s t i c s a c h i e v e m e n t i s a l s o d i s c u s s e d i n t h i s s e c t i o n . The s e c o n d p a r t c o n t a i n s a d e s c r i p t i o n o f p a t h a n a l y s i s and t h e " c a u s a l m o d e l i n g w i t h l a t e n t v a r i a b l e s " a p p r o a c h ( B e n t l e r , 1 9 8 0 ) . In t h e f i n a l s e c t i o n , t h e t h r e e e x p l o r a t o r y m o d e l s a r e p r e s e n t e d . The many r e p o r t s i n t h e l i t e r a t u r e o f i n v e s t i g a t i o n s o f t h e c o r r e l a t e s and d e t e r m i n a n t s o f g e n e r a l a c a d e m i c a c h i e v e m e n t r e f l e c t t h e h i g h l e v e l o f i n t e r e s t i n t h i s a r e a . B e c a u s e much i s no t o f d i r e c t r e l e v a n c e t o t h e p r e s e n t s t u d y o f t h e p r e d i c t i o n o f s t a t i s t i c s a c h i e v e m e n t , no l i t e r a t u r e i s r e v i e w e d i n t h i s r e p o r t , b e y o n d m e n t i o n o f t h e e x a m p l e s g i v e n i n C h a p t e r I. R a t h e r , t h e r e a d e r i s r e f e r r e d t o two r e c e n t r e v i e w s p r e p a r e d by H a r p e r (1978) a n d S i n g h ( 1 9 7 6 ) . The s i t u a t i o n w i t h r e g a r d t o t h e c o r r e l a t e s a n d d e t e r m i n a n t s o f a c h i e v e m e n t i n m a t h e m a t i c s i s r a t h e r s i m i l a r . T h a t i s , t h e l i t e r a t u r e c o n t a i n s a l a r g e number o f r e p o r t s o f i n v e s t i g a t i o n s o f a p l e t h o r a o f v a r i a b l e s , and has been r e v i e w e d c o m p r e h e n s i v e l y by B e g l e (1979) and by Fennema and Behr ( 1 9 8 0 ) . In a d d i t i o n , much o f t h e l i t e r a t u r e a p p e a r s n o t t o be d i r e c t l y r e l e v a n t t o t h e p r e s e n t s t u d y . In c o n s e q u e n c e , t h e l i t e r a t u r e 13 o f m a t h e m a t i c s a c h i e v e m e n t i s no t d i s c u s s e d , e x c e p t f o r t h e e x a m p l e s m e n t i o n e d i n C h a p t e r I. The r e v i e w o f l i t e r a t u r e i n t h i s t h e s i s i s c o n f i n e d t o r e p o r t s o f i m m e d i a t e r e l e v a n c e t o t h e p r e d i c t i o n o f a c h i e v e m e n t i n s t a t i s t i c s . P r e d i c t i o n o f S t a t i s t i c s A c h i e v e m e n t Seven s t u d i e s o f t h e c o r r e l a t e s and d e t e r m i n a n t s o f a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s were i d e n t i f i e d i n t h e l i t e r a t u r e . Of t h e s e v e n , two were r e p o r t s o f t h e r e l a t i o n s h i p o f a c h i e v e m e n t t o one v a r i a b l e . Two s t u d i e s i n v e s t i g a t e d t h e c o n t r i b u t i o n o f s e v e r a l c o g n i t i v e v a r i a b l e s t o t h e e x p l a i n e d v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . The r e m a i n i n g t h r e e were i n v e s t i g a t i o n s o f b o t h c o g n i t i v e and a f f e c t i v e c o r r e l a t e s a s p r e d i c t o r s o f s t a t i s t i c s a c h i e v e m e n t . M i c h a e l a n d M i c h a e l (1969) a d m i n i s t e r e d a t e s t o f b a s i c m a t h e m a t i c s s k i l l s d u r i n g t h e f i r s t s e s s i o n o f an e l e m e n t a r y c o u r s e i n s t a t i s t i c s t o g r a d u a t e s t u d e n t s i n t h r e e p s y c h o l o g y c l a s s e s ( n=58 ,85 and 41 r e s p e c t i v e l y ) . The t e s t i n c l u d e d 35 a r i t h m e t i c i t e m s a n d 15 a l g e b r a i c i t e m s . The c r i t e r i o n v a r i a b l e was m e a s u r e d u s i n g an u n t i m e d , o p e n - b o o k , m u l t i p l e - c h o i c e e x a m i n a t i o n . In t h e e x a m i n a t i o n , a heav y e m p h a s i s was p l a c e d on s t a t i s t i c a l r e a s o n i n g and c o n c e p t u n d e r s t a n d i n g ; l i t t l e c o m p u t a t i o n was r e q u i r e d . The a u t h o r s c o n c l u d e d t h a t t h e o b t a i n e d c o r r e l a t i o n s ( 0 . 4 5 , 0 . 5 3 and 0 . 5 7 ) were s u f f i c i e n t l y h i g h t o a l l o w u s e o f t h e m a t h e m a t i c s s k i l l s t e s t a s a p r e d i c t o r o f a c h i e v e m e n t i n s t a t i s t i c s . R o b e r t s a n d B i l d e r b a c k (1980) r e p o r t e d t h e d e v e l o p m e n t and 14 p a r t i a l v a l i d a t i o n o f a measu re o f a t t i t u d e s t o w a r d s s t a t i s t i c s . The f i n a l s c a l e c o n s i s t e d o f 34 i t e m s " c o u c h e d i n s t a t i s t i c a l j a r g o n " , e a c h o f w h i c h was e n d o r s e d u s i n g a f i v e - p o i n t L i k e r t s c a l e . The s c a l e was a d m i n i s t e r e d t o t h r e e c l a s s e s o f g r a d u a t e s t u d e n t s e n r o l l e d i n an i n t r o d u c t o r y s t a t i s t i c s c o u r s e ( n = 9 2 , 8 l , 6 5 r e s p e c t i v e l y ) . They d i d n o t s t a t e e i t h e r a t w h i c h p o i n t i n t h e c o u r s e t h e s c a l e was a d m i n i s t e r e d o r whe the r e a c h c l a s s was g i v e n t h e measu re a t t h e same r e l a t i v e p o i n t i n t h e c o u r s e . The a u t h o r s c o n c l u d e d t h a t t h e o b t a i n e d c o r r e l a t i o n s ( 0 . 3 3 , 0 . 4 5 and 0 .54 f o r e a c h o f t h e t h r e e c l a s s e s ) were h i g h e n o u g h t o j u s t i f y p r e d i c t i v e use o f t h e s c a l e . T h i s c o n c l u s i o n i s m i n i m a l l y j u s t i f i e d , s i n c e t h e m e a s u r e o n l y a c c o u n t e d f o r 11% t o 29% o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . R o b e r t s and B i l d e r b a c k (1980) a l s o c o n c l u d e d t h a t use o f t h e s c a l e t o d i a g n o s e t h e l e v e l o f s t a t i s t i c s a n x i e t y i n t h e i n d i v i d u a l s t u d e n t was j u s t i f i e d by t h e h i g h i n t e r n a l . c o n s i s t e n c y c o e f f i c i e n t s ( g r e a t e r t h a n 0 . 9 0 ) . W h i l e t h e h i g h i n t e r n a l c o n s i s t e n c y v a l u e d o e s n o t i n i t s e l f p r o v i d e e v i d e n c e f o r h i g h v a l i d i t y , i t d o e s s e t a h i g h t h e o r e t i c a l maximum o f 0 . 9 5 on any e m p i r i c a l v a l i d i t y c o e f f i c i e n t . G i a m b r a (1972) c o l l e c t e d i n f o r m a t i o n a b o u t t h e t y p e and number o f p r e v i o u s m a t h e m a t i c s c o u r s e s t a k e n a n d o v e r a l l g r a d e -p o i n t a v e r a g e f r o m c l a s s e s o f s o p h o m o r e s e n r o l l e d i n an i n t r o d u c t o r y b e h a v i o r a l s c i e n c e s t a t i s t i c s c o u r s e ( n = l 6 6 ) . He f o u n d t h a t , o f t h e m a t h e m a t i c s c o u r s e s t a k e n ( c a l c u l u s , f i n i t e m a t h e m a t i c s , a d v a n c e d a l g e b r a , e l e m e n t a r y a l g e b r a ) , o n l y c a l c u l u s was r e l a t e d t o s t a t i s t i c s a c h i e v e m e n t . In a d d i t i o n , a 15 s t r o n g p o s i t i v e r e l a t i o n s h i p was o b t a i n e d be tween o v e r a l l g r a d e -p o i n t a v e r a g e a n d s t a t i s t i c s a c h i e v e m e n t . G i a m b r a c o n c l u d e d t h a t o v e r a l l g r a d e - p o i n t a v e r a g e was a p o s s i b l e p r e d i c t o r o f s t a t i s t i c s a c h i e v e m e n t . He d i d n o t r e p o r t any c o r r e l a t i o n s , p r e s e n t i n g h i s r e s u l t s o n l y i n t e r m s o f f r e q u e n c y d i s t r i b u t i o n s , e v a l u a t e d by means o f c h i - s q u a r e s t a t i s t i c s . H a r t l e y and H a r t l e y (1976) c o l l e c t e d d a t a f r om e a c h o f 57 u n d e r g r a d u a t e s t u d e n t s e n r o l l e d i n a p s y c h o l o g i c a l s t a t i s t i c s and r e s e a r c h d e s i g n c o u r s e . The 23 i n d e p e n d e n t v a r i a b l e s i n c l u d e d f o u r m e a s u r e s o f c o g n i t i v e v a r i a b l e s ( V e r b a l R e a s o n i n g and A b s t r a c t R e a s o n i n g f r o m t h e D i f f e r e n t i a l A p t i t u d e T e s t ; R e a d i n g C o m p r e h e n s i o n and R e a d i n g S p e e d f r o m t h e D a v i s R e a d i n g T e s t ) . M e a s u r e s o f 10 a s p e c t s o f a c a d e m i c s e l f - c o n c e p t , f i v e m e a s u r e s o f a t t i t u d e t o w a r d s p s y c h o l o g y , and t h e s u b j e c t i v e p r o b a b i l i t y o f a t t a i n i n g e a c h o f f o u r p o s s i b l e c o u r s e g r a d e s s e r v e d a s t h e o t h e r 19 i n d e p e n d e n t v a r i a b l e s . The d e p e n d e n t v a r i a b l e was o v e r a l l s t a t i s t i c s a c h i e v e m e n t , a s m e a s u r e d by t o t a l p o i n t s a c c u m u l a t e d d u r i n g t h e c o u r s e . R e s u l t s f r o m two r e g r e s s i o n p r o c e d u r e s were r e p o r t e d . The f i r s t p r o c e d u r e was a f r e e s t e p w i s e m u l t i p l e r e g r e s s i o n . The e n t i r e s e t o f 23 i n d e p e n d e n t v a r i a b l e s was e n t e r e d . T o g e t h e r , t h e 23 v a r i a b l e s a c c o u n t e d f o r 8 6 . 3 % o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . More t h a n o n e - h a l f o f t h i s v a r i a n c e (49%) was a c c o u n t e d f o r by V e r b a l R e a s o n i n g a l o n e . Ten o t h e r v a r i a b l e s a c c o u n t e d f o r a f u r t h e r 32% o f t h e e x p l a i n e d v a r i a n c e . In o r d e r o f e n t r y , t h e y w e r e : a t t i t u d e t o w a r d s p s y c h o l o g y - s o c i a l w e l f a r e ; s u b j e c t i v e p r o b a b i l i t y o f a t t a i n i n g 1 6 an " A " ; r a t i n g o f s k i l l a t o r a l p r e s e n t a t i o n s ; a t t i t u d e t o w a r d s p s y c h o l o g y - s o c i a l r e s p o n s i b i l i t y ; a t t i t u d e t o w a r d p s y c h o l o g y -p r e f e r e n c e f o r l a b o r a t o r y e x p e r i m e n t s ; e s s a y - w r i t i n g s k i l l s ; m e n t a l s p e e d ; a b i l i t y t o r e t a i n m a t e r i a l r e a d ; s u b j e c t i v e p r o b a b i l i t y o f a t t a i n i n g a " B " ; a n d , s u b j e c t i v e p r o b a b i l i t y o f a t t a i n i n g a " C " . The s e c o n d r e g r e s s i o n p r o c e d u r e was an a p r i o r i a p p r o a c h i n w h i c h a l l t h e i n d e p e n d e n t v a r i a b l e s were e n t e r e d i n b l o c k s . The b l o c k s o f v a r i a b l e s , i n o r d e r o f e n t r y , were c o g n i t i v e , a t t i t u d i n a l , s e l f - r a t i n g and p r e d i c t i o n s o f c o u r s e g r a d e . The f o u r b l o c k s a c c o u n t e d f o r 51 .3%, 1 8 . 5 % , 1 0 . 5 % and 5.9% of t h e v a r i a n c e r e s p e c t i v e l y . The a u t h o r s c o n c l u d e d t h a t t h e p r e d i c t i v e p r o c e s s had been s u c c e s s f u l , d e s p i t e t h e r i s k o f i n f l a t i o n i n t h e m u l t i p l e R due t o a low s u b j e c t t o v a r i a b l e r a t i o ( 5 7 : 2 3 ) . They a l s o recommended t h a t t h e r e g r e s s i o n e q u a t i o n be u s e d t o d e t e c t s t u d e n t s w i t h p o t e n t i a l p r o b l e m s a t t h e b e g i n n i n g o f a c o u r s e . F e i n b e r g a n d H a l p e r i n (1978) a d m i n i s t e r e d m e a s u r e s o f 16 c o g n i t i v e and a f f e c t i v e v a r i a b l e s d u r i n g t h e f i r s t c l a s s s e s s i o n t o 278 u n d e r g r a d u a t e a n d 71 g r a d u a t e s t u d e n t s e n r o l l e d i n an i n t r o d u c t o r y s t a t i s t i c s c o u r s e . E i g h t o f t h e 16 z e r o - o r d e r c o r r e l a t i o n s be tween a c h i e v e m e n t a n d e a c h i n d e p e n d e n t v a r i a b l e were s t a t i s t i c a l l y s i g n i f i c a n t : s t a t e a n x i e t y ( r = - 0 . 2 2 ) ; m a t h e m a t i c s - s k i l l s ( r = + 0 . 4 0 ) ; a t t i t u d e t o w a r d s q u a n t i t a t i v e c o n c e p t s ( r = + 0 . 3 5 ) ; e x p e c t e d c o u r s e g r a d e ( r = + 0 . 3 3 ) ; r a t i n g o f s u c c e s s i n m a t h e m a t i c s c o u r s e s ( r = + 0 . 3 4 ) ; number o f m a t h e m a t i c s c o u r s e s ( r = + 0 . 3 l ) ; p e r c e p t i o n s o f m a t h e m a t i c s a b i l i t y r e l a t i v e 1 7 t o t h e c l a s s ( r = + 0 . 3 3 ) ; and p e r c e p t i o n s o f m a t h e m a t i c s a b i l i t y r e l a t i v e t o o t h e r s t u d e n t s i n ma jo r a r e a ( r = + 0 . 2 5 ) . The a n a l y s i s o f t h e r e s u l t i n g c o r r e l a t i o n m a t r i x r e v e a l e d , f i r s t , t h a t an a t t e m p t t o p r e d i c t a c h i e v e m e n t i n s t a t i s t i c s f r o m t h e 16 i n d e p e n d e n t v a r i a b l e s was n o t s u c c e s s f u l . The a u t h o r s a t t r i b u t e d t h i s r e s u l t t o t h e h i g h d e g r e e o f c o m m o n a l i t y among t h e i n d e p e n d e n t v a r i a b l e s . Of t h e t h i r t y - s i x p o s s i b l e i n t e r -c o r r e l a t i o n s among t h e e i g h t s t a t i s t i c a l l y s i g n i f i c a n t i n d e p e n d e n t v a r i a b l e s and s t a t i s t i c s a c h i e v e m e n t , o n l y t h r e e were n o n - s i g n i f i c a n t ( p > 0 . 0 5 ) . H o w e v e r , none o f t h e o b t a i n e d c o r r e l a t i o n s be tween s t a t i s t i c s a c h i e v e m e n t a n d any o f t he i n d e p e n d e n t v a r i a b l e s w e r e , by t h e m s e l v e s , v e r y h i g h . The v a l u e s r a n g e d be tween - 0 . 2 2 a n d 0 . 4 0 , a c c o u n t i n g f o r be tween 4 . 8 % and 16% o f t he o b s e r v e d v a r i a n c e i n a c h i e v e m e n t . An i n d e p e n d e n t j udgement a b o u t t h e d e g r e e o f c o m m o n a l i t y and the " s u c c e s s " o f t h e r e g r e s s i o n c a n n o t be made, s i n c e F e i n b e r g and H a l p e r i n r e p o r t e d n e i t h e r . E l m o r e and V a s u (1980) a d m i n i s t e r e d 29 m e a s u r e s o f one o f f o u r t y p e s o f v a r i a b l e s ( a t t i t u d e s t o w a r d s m a t h e m a t i c s ; a t t i t u d e s t o w a r d s f e m i n i s m a n d s e x - r o l e s ; s p a t i a l v i s u a l i z a t i o n a b i l i t y ; and d e m o g r a p h i c o r b i o g r a p h i c ) t o 188 g r a d u a t e s t u d e n t s f r o m 11 d i s c i p l i n e s who were e n r o l l e d i n an i n t r o d u c t o r y c o u r s e i n i n f e r e n t i a l s t a t i s t i c s . Of t h e 29 v a r i a b l e s , 15 were s i g n i f i c a n t l y c o r r e l a t e d w i t h o v e r a l l c o u r s e m a r k . Two were s c a l e s m e a s u r i n g a t t i t u d e s t o w a r d s f e m i n i s m ( i . e . , "human r e p r o d u c t i o n " , r = + 0 . 2 5 , and " c h i l d c a r e " , r = - 0 . 3 l ) . T h r e e were t e s t s o f s p a t i a l v i s u a l i z a t i o n ( P a p e r F o l d i n g , r = + 0 . 4 5 , S u r f a c e 18 D e v e l o p m e n t , r = + 0 . 3 5 , and Cube C o m p a r i s o n s , r = + 0 . 2 4 ) . The r e m a i n i n g e i g h t t e s t s were m e a s u r e s o f a t t i t u d e s t o w a r d s m a t h e m a t i c s ( t h e r a n g e o f c o r r e l a t i o n s b e i n g +0 .23 t o + 0 . 3 1 ) . Two o f t h e b i o g r a p h i c o r d e m o g r a p h i c . v a r i a b l e s were s t a t i s t i c a l l y s i g n i f i c a n t l y c o r r e l a t e d w i t h a c h i e v e m e n t ( g e n d e r o f s t u d e n t , r = + 0 . 2 6 ; a n d p r e v i o u s s t a t i s t i c s c o u r s e s t a k e n , r = + 0 . 2 2 ) . A s t e p w i s e m u l t i p l e r e g r e s s i o n r e v e a l e d t h a t 4 6 . 4 % o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t was a c c o u n t e d f o r by t h e f u l l s e t o f 29 v a r i a b l e s . R e d u c i n g t h e m o d e l by e l i m i n a t i n g one s u b s e t o f v a r i a b l e s a t a t i m e r e v e a l e d t h a t t h r e e s u b s e t s ( s p a t i a l v i s u a l i z a t i o n , a t t i t u d e s t o w a r d s f e m i n i s t s and s e x - r o l e m e a s u r e s ) c o n t r i b u t e d s i g n i f i c a n t l y t o t h e v a r i a n c e e x p l a i n e d ( r e d u c t i o n s i n R - s q u a r e = 0 . 0 5 1 , 0 . 0 3 2 and 0 . 0 8 2 r e s p e c t i v e l y ) . The a u t h o r s c o n c l u d e d t h a t a t t i t u d e s t o w a r d s f e m i n i s t s and s e x -r o l e s , i n a d d i t i o n t o t h e a b i l i t y t o v i s u a l i z e o b j e c t s i n s p a c e , were p r e d i c t o r s o f s t a t i s t i c s a c h i e v e m e n t . They o u t l i n e d p l a n s t o e n l a r g e t h e s c o p e o f t h e m o d e l by t e s t i n g t h e c o n t r i b u t i o n s o f o t h e r c o g n i t i v e v a r i a b l e s . A summary o f t h e z e r o - o r d e r c o r r e l a t i o n s be tween a c h i e v e m e n t i n s t a t i s t i c s and a number o f t h e c o g n i t i v e and n o n c o g n i t i v e v a r i a b l e s i n v e s t i g a t e d i n t h e s e s e v e n s t u d i e s i s p r e s e n t e d i n T a b l e 2. O n l y c o r r e l a t i o n s w h i c h were | 0 . 2 0 | o r g r e a t e r were i n c l u d e d i n T a b l e 2 . The c o r r e l a t i o n s be tween s t a t i s t i c s a c h i e v e m e n t and t h e v a r i o u s p r e d i c t o r s r a n g e d f r o m 0.21 t o 0 . 7 0 i n a b s o l u t e v a l u e . W i t h t h e e x c e p t i o n o f t h e c o r r e l a t i o n be tween v e r b a l r e a s o n i n g and s t a t i s t i c s a c h i e v e m e n t 19 T a b l e 2 C o r r e l a t i o n s o f C o g n i t i v e and N o n c o g n i t i v e V a r i a b l e s w i t h S t a t i s t i c s A c h i e v e m e n t V a r i a b l e C o r r e l a t i o n A u t h o r s B a s i c M a t h e m a t i c s S k i l l s : 0 . 4 5 t o 0 . 57 M&M* 0 . 4 0 F&H V e r b a l R e a s o n i n g : 0 . 7 0 H&H A b s t r a c t R e a s o n i n g : 0 .42 . H&H R e a d i n g C o m p r e h e n s i o n : 0 . 4 7 H&H R e a d i n g S p e e d : 0 .58 H&H S p a t i a l V i s u a l i z a t i o n : Cube C o m p a r i s o n s 0 .24 E&V S u r f a c e D e v e l o p m e n t 0 . 3 5 E&V P a p e r F o l d i n g 0 . 4 5 E&V A t t i t u d e Toward S t a t i s t i c s : 0 . 3 3 t o 0 . 54 R&B A t t i t u d e Toward Q u a n t i t a t i v e C o n c e p t s : 0 . 3 5 F&H A t t i t u d e Towa rds M a t h e m a t i c s : M a t h e m a t i c s As M a l e D o m a i n : 0 .23 E&V U s e f u l n e s s o f M a t h e m a t i c s : 0 .23 E&V M o t h e r ' s A t t i t u d e : 0 . 2 5 E&V F a t h e r ' s A t t i t u d e : 0 . 2 7 E&V A t t i t u d e Toward S u c c e s s i n M a t h e m a t i c s : 0 . 2 7 E&V E f f e c t e n c e M o t i v a t i o n : 0 . 2 9 E&V T e a c h e r ' s A t t i t u d e : 0 . 2 9 E&V S e l f - C o n f i d e n c e : 0.31 E&V S t a t e A n x i e t y : . - 0 . 2 2 F&H A t t i t u d e s Toward P s y c h o l o g y : V a l u e o f P s y c h o l o g y : 0 .32 H&H P r e f e r e n c e f o r L a b o r a t o r y E x p e r i m e n t s -0 .21 H&H A t t i t u d e s Towa rd F e m i n i s t s : Human R e p r o d u c t i o n : - 0 . 2 5 E&V C h i l d C a r e : -0.31 E&V MMPI S c a l e ( F e m i n i n i t y ) : 0 . 2 5 E&V S e l f - R a t i n g s : A r i t h m e t i c : 0 . 2 6 H&H R e l a t i v e t o C l a s s : 0 . 3 3 F&H R e l a t i v e t o M a j o r s : 0 . 2 5 F&H M a t h e m a t i c s C o u r s e w o r k : Number o f C o u r s e s : 0 . 34 F&H S u c c e s s i n C o u r s e s : 0.31 F&H S t a t i s t i c s C o u r s e T a k e n : 0 . 2 2 E&V G e n d e r o f S u b j e c t : 0 . 2 6 E&V E x p e c t e d C o u r s e G r a d e : 0 . 3 3 F&H S u b j e c t i v e P r o b a b i l i t i e s : - 0 . 2 4 t o 0 . 42 H&H * M&M=Michael and M i c h a e l ( 1 9 6 9 ) ; R & B = R o b e r t s a n d B i l d e r b a c k ( 1 9 8 0 ) ; F & H = F e i n b e r g and H a l p e r i n ( 1 9 7 8 ) ; H & H = H a r t l e y and H a r t l e y ( 1 9 7 6 ) ; E&V=Elmore and V a s u ( 1 9 8 0 ) . 20 r e p o r t e d by H a r t l e y and H a r t l e y ( 1 9 7 6 ) , no c o r r e l a t i o n above | 0 . 6 0 | was r e p o r t e d . The c o r r e l a t i o n s be tween a c h i e v e m e n t and c o g n i t i v e v a r i a b l e s w e r e , g e n e r a l l y , s l i g h t l y h i g h e r t h a n were t h o s e be tween a c h i e v e m e n t and n o n c o g n i t i v e v a r i a b l e s . T h i s o v e r a l l r e s u l t i s i n a c c o r d w i t h t h e g e n e r a l c o n s e n s u s i n t h e body o f m a t h e m a t i c s a c h i e v e m e n t l i t e r a t u r e ( e . g . , A i k e n , 1976 ; K u l m , 1 9 8 0 ) . S p e c i f i c a l l y , c o g n i t i v e v a r i a b l e s a c c o u n t e d f o r 6% t o 49% o f t h e o b s e r v e d v a r i a n c e i n m a t h e m a t i c s o r a r i t h m e t i c a c h i e v e m e n t , w i t h a t y p i c a l v a l u e o f a p p r o x i m a t e l y 16%. A t y p i c a l v a l u e f o r t h e n o n c o g n i t i v e v a r i a b l e s w o u l d be a b o u t 9% o f t h e o b s e r v e d v a r i a n c e , w i t h t he r a n g e i n v a r i a n c e a c c o u n t e d f o r b e i n g a p p r o x i m a t e l y 4% t o 2 9 % . M o t i v a t i o n a l V a r i a b l e s W i t h t h e e x c e p t i o n o f E l m o r e and V a s u ( 1 9 8 0 ) , who i n v e s t i g a t e d a measu re o f a t t i t u d e c a l l e d " e f f e c t a n c e m o t i v a t i o n " , none o f t h e s t u d i e s r e v i e w e d c o n s i d e r e d t h e c o n t r i b u t i o n o f m o t i v a t i o n a l v a r i a b l e s t o t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . M o t i v a t i o n , may, i n f a c t , a c c o u n t f o r a s much a s 20% o f t h e v a r i a n c e i n o v e r a l l a c a d e m i c a c h i e v e m e n t ( H a k s t i a n and G a l e , 1 9 7 9 ) , and an unknown p e r c e n t a g e o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . Of t h e m o t i v a t i o n a l c o n s t r u c t s d i s c u s s e d i n t h e l i t e r a t u r e , p e r h a p s t h e most f r e q u e n t l y i n v e s t i g a t e d has been t h e r e l a t i o n s h i p o f a c h i e v e m e n t m o t i v e t o a c a d e m i c a c h i e v e m e n t ( A t k i n s o n , 1 9 7 8 ) . A c h i e v e m e n t m o t i v e has been d e f i n e d a s " a p a t t e r n o f 21 p l a n n i n g o f a c t i o n s and o f f e e l i n g s c o n n e c t e d w i t h s t r i v i n g t o a c h i e v e some i n t e r n a l i z e d s t a n d a r d o f e x c e l l e n c e . . . t h e a t t i t u d e i s t o w a r d a c h i e v e m e n t i t s e l f " ( V i d l e r , 1977 , p . 2 6 1 ) . F u r t h e r , i t h a s been s t a t e d t h a t a m e a s u r e d d i f f e r e n c e i n a b i l i t y o b t a i n e d u n d e r a c h i e v e m e n t - o r i e n t e d c o n d i t i o n s may be g i v e n a m o t i v a t i o n a l i n t e r p r e t a t i o n w i t h no l e s s j u s t i f i c a t i o n t h a n an a b i l i t y - o r i e n t e d i n t e r p r e t a t i o n ( A t k i n s o n , 1 9 7 8 ) . F rom t h i s p e r s p e c t i v e , m o t i v a t i o n can be h y p o t h e s i z e d t o a c c o u n t f o r a m e a s u r a b l e p r o p o r t i o n o f t h e v a r i a n c e i n a c a d e m i c a c h i e v e m e n t . A t k i n s o n ' s o p i n i o n i s t h a t be tween 20% and 25% o f t h e v a r i a n c e i n a c h i e v e m e n t i s a t t r i b u t a b l e t o t h e d i r e c t and i n d i r e c t e f f e c t s o f m o t i v a t i o n a l v a r i a b l e s . T h i s t h e o r e t i c a l s t a n c e i s i n a c c o r d w i t h t h e e m p i r i c a l f i n d i n g o f H a k s t i a n a n d G a l e ( 1 9 7 9 ) . H o w e v e r , t h e m a g n i t u d e o f t h e c o n t r i b u t i o n o f m o t i v a t i o n t o t h e v a r i a n c e i n a c a d e m i c a c h i e v e m e n t i s h i g h l y c o n t r o v e r s i a l . F o r e x a m p l e , V i d l e r (1977) r e p o r t e d t h a t t h e g e n e r a l f i n d i n g o f r e s e a r c h i n w h i c h t h e r e l a t i o n s h i p be tween a c h i e v e m e n t m o t i v e and a c a d e m i c a c h i e v e m e n t h a s been s t u d i e d i s t h a t no s t r o n g r e l a t i o n s h i p e x i s t s . F u r t h e r , t h e r e s u l t s o f a t t e m p t s t o i n c r e a s e a c h i e v e m e n t m o t i v a t i o n by means o f t r a i n i n g p r o g r a m s b e a r no r e l a t i o n s h i p t o o b s e r v e d i n c r e a s e s i n a c a d e m i c p e r f o r m a n c e ( V i d l e r , 1 9 7 7 ) . F i n a l l y , E l m o r e and V a s u (1980) r e p o r t e d t h a t a m e a s u r e o f " e f f e c t a n c e m o t i v a t i o n " a c c o u n t e d f o r o n l y 10% o f t h e v a r i a n c e i n t h e i r measu re o f s t a t i s t i c s a c h i e v e m e n t . A l t h o u g h most a t t e n t i o n i n t h e l i t e r a t u r e has been f o c u s e d 22 on a c h i e v e m e n t m o t i v e i t s e l f , two o t h e r a s p e c t s have r e c e i v e d some a t t e n t i o n . They a r e a ) m o t i v e t o s u c c e e d i n a t a s k and b) p e r c e p t i o n o f t h e u s e f u l n e s s o f a t a s k . B o t h may u n d e r l i e s t r i v i n g f o r s u c c e s s . T h i s i n t e r p r e t a t i o n i s drawn f r o m t h e work o f R a y n o r ( 1 9 7 8 ) , who i n v e s t i g a t e d c o n t i n g e n t and n o n c o n t i n g e n t p a t h s t o a g o a l . C o n t i n g e n t p a t h s a r e t h o s e p e r c e i v e d by t h e i n d i v i d u a l a s b e i n g more c o n s i s t e n t w i t h f u t u r e a c h i e v e m e n t t h a n a r e n o n c o n t i n g e n t p a t h s . T h e s e c o n s t r u c t s have been o p e r a t i o n a l i z e d a s t h e i m m e d i a t e s t a t e d r e a s o n s f o r u n d e r t a k i n g a t a s k , and t h e p e r c e i v e d p r e s e n t and f u t u r e u t i l i t y Of t h e t a s k . P a t h A n a l y s i s and C a u s a l M o d e l i n g  w i t h L a t e n t V a r i a b l e s  P a t h a n a l y s i s i s a q u a n t i t a t i v e me thod w h i c h f a c i l i t a t e s t h e t e s t i n g and e x p l i c i t f o r m u l a t i o n o f " c a u s a l " m o d e l s d e r i v e d f r o m t h e o r y . N u m e r i c a l e s t i m a t e s o f t h e s t r e n g t h o f " c a u s a l " e f f e c t s a r e d e r i v e d , w h i c h c a n i n t u r n be u s e d t o t e s t t h e f i t o f t h e f o r m u l a t e d mode l ( W o l f l e , 1 9 8 0 ) . " C a u s a l m o d e l i n g w i t h l a t e n t v a r i a b l e s " (LVM) i s an a p p r o a c h w h i c h a l s o . f a c i l i t a t e s t h e e x p l i c i t f o r m u l a t i o n and t e s t i n g o f m o d e l s d e r i v e d f r o m t h e o r y . The l a t t e r a p p r o a c h i s an e x t e n s i o n o f p a t h a n a l y s i s , w h i c h i n c o r p o r a t e s h y p o t h e t i c a l c o n s t r u c t s c a l l e d " l a t e n t v a r i a b l e s " i n t o t h e m o d e l s w h i c h a r e t h e n t e s t e d ( B e n t l e r , 1 9 8 0 ) . B o t h a n a l y t i c p r o c e d u r e s a l l o w t h e t e s t i n g o f a t h e o r e t i c a l m o d e l u s i n g v a l u e s • o b t a i n e d f r o m s a m p l e d a t a . In t h i s s e c t i o n o f t h e p r e s e n t c h a p t e r , t h e two a p p r o a c h e s a r e 23 d i s c u s s e d w i t h t h e a i d o f a p a i r o f s i m p l e e x a m p l e s . L i k e m u l t i p l e r e g r e s s i o n , p a t h a n a l y s i s a n d t h e LVM a p p r o a c h e s a r e s t a t i s t i c a l t e c h n i q u e s w h i c h a r e u s e d t o a n a l y z e a c o r r e l a t i o n m a t r i x , and w h i c h y i e l d i n f o r m a t i o n a b o u t t h e l i n e a r r e l a t i o n s h i p s among t h e v a r i a b l e s . The u s e r o f b o t h t e c h n i q u e s , l i k e t h e u s e r o f m u l t i p l e r e g r e s s i o n , a s sumes t h a t t h e r e s i d u a l s have e x p e c t e d v a l u e s o f z e r o , have e q u a l v a r i a n c e s , and a r e s t a t i s t i c a l l y i n d e p e n d e n t b o t h o f e a c h o t h e r and o f t h e e x p l a n a t o r y v a r i a b l e s i n t h e s t r u c t u r a l e q u a t i o n s . The ma jo r d i f f e r e n c e be tween m u l t i p l e r e g r e s s i o n t e c h n i q u e s and t h e o t h e r two a p p r o a c h e s i s t h a t , i n t h e l a t t e r , t h e c o m p u t a t i o n a l r e s u l t s a r e t r e a t e d by t h e r e s e a r c h e r a s e x p l i c i t s t a t e m e n t s o f t h e o r e t i c a l r e l a t i o n s h i p s r a t h e r t h a n a s s t a t e m e n t s o f e m p i r i c a l r e l a t i o n s h i p s ( W o l f l e , 1 9 8 0 ) . F i g u r e s 1 and 2 d e p i c t an e x a m p l e o f a p a t h - a n a l y t i c m o d e l and an LVM, r e s p e c t i v e l y . B o t h r e p r e s e n t m o d e l s o f a c h i e v e m e n t c h i l d e d u c a t i o n ^ on v o c a b u l a r y t e s t s i n a d u l t s . The p a t h - a n a l y t i c mode l t r e a t s t h e t h r e e i n d e p e n d e n t v a r i a b l e s , e d u c a t i o n o f c h i l d , IQ o f c h i l d and IQ o f a d u l t , a s i n f l u e n c i n g t h e d e p e n d e n t v a r i a b l e ( a d u l t v o c a b u l a r y s c o r e ) i n a " c a u s a l " way . A d u l t IQ e x e r t s a d i r e c t c h i l d IQ v o c a b u l a r y F i g u r e 1 P a t h - A n a l y t i c M o d e l o f A d u l t V o c a b u l a r y S c o r e 24 i n f l u e n c e ; t h e r e m a i n i n g two v a r i a b l e s e x e r t t h e i r i n f l u e n c e i n d i r e c t l y . The LVM shown i n F i g u r e 2 i n c l u d e s t h e same m e a s u r e d v a r i a b l e s a s d i d t h e p a t h - a n a l y t i c m o d e l . Howeve r , two h y p o t h e t i c a l c o n s t r u c t s , o r l a t e n t v a r i a b l e s have been c h i l d e d u c a t i o n c h i l d i n t e l l i g e n c e a d u l t i n t e l l i g e n c e a d u l t f IQ a d u l t v o c a b u l a r y F i g u r e 2 LVM M o d e l o f A d u l t V o c a b u l a r y S c o r e p o s t u l a t e d . The f o u r m e a s u r e d v a r i a b l e s a r e i n t e r p r e t e d a s b e i n g m a n i f e s t a t i o n s o f t h e two l a t e n t v a r i a b l e s . The l a t e n t v a r i a b l e , C h i l d I n t e l l i g e n c e , " c a u s e s " c h a n g e s i n t h e s c o r e s on m e a s u r e s o f C h i l d IQ and E d u c a t i o n o f C h i l d . The m e a s u r e d v a r i a b l e s , A d u l t IQ and V o c a b u l a r y S c o r e o f A d u l t , a r e m a n i f e s t a t i o n s o f t h e l a t e n t v a r i a b l e A d u l t I n t e l l i g e n c e . The t e r m " c a u s e " i s f r e q u e n t l y e n c o u n t e r e d i n t h e l i t e r a t u r e when p a t h a n a l y s i s i s e x p l a i n e d , d i s c u s s e d o r a p p l i e d . As Cook and C a m p b e l l (1979) have o b s e r v e d , t h e r e e x i s t a p l e t h o r a o f p h i l o s o p h i c a l v i e w s on t h e s u b j e c t o f c a u s a l i t y . In t h i s t h e s i s , t h e word " c a u s e " i s meant o n l y t o be a d e s i g n a t i o n f o r a p l a u s i b l e e x p l a n a t i o n . W o l f l e (1980) e x p l a i n e d t h e ma in a d v a n t a g e o f t h e u s e o f p a t h a n a l y t i c p r o c e d u r e s a s f o l l o w s : 25 P r o b a b l y t h e g r e a t e s t a d v a n t a g e o f p a t h a n a l y s i s i s t h a t i t p r o v i d e s a means by w h i c h t h e n a t u r e o f t h e p r o b l e m a d d r e s s e d by an e m p i r i c a l s t u d y may be h a n d i l y s u m m a r i z e d . I t r e q u i r e s t h e r e s e a r c h e r t o t h i n k a b o u t c a u s e , p a r t i c u l a r l y s y s t e m s o f i n t e r c a u s a l c o n n e c t i o n s . . . a n d p r o v i d e s an e x p l i c i t l i n k be tween a p r i o r i t h e o r e t i c a l n o t i o n s o f c a u s a l c o n n e c t i o n s and q u a n t i t a t i v e e s t i m a t e s o f c a u s a l i m p a c t . ( p . 184) H o w e v e r , B e n t l e r (1980) p o i n t e d ou t t h a t m o d e l s b a s e d o n l y on m a n i f e s t v a r i a b l e s (as i s u s u a l w i t h p a t h a n a l y t i c p r o c e d u r e s s u c h a s t h o s e d i s c u s s e d by W o l f l e ) a r e h i g h l y s e n s i t i v e t o s a m p l i n g and measurement e r r o r . He s t a t e d : T h u s , o f p a r t i c u l a r i m p o r t a n c e , I b e l i e v e , i s t h e m o d e l i n g o f a p r o c e s s a t t h e l e v e l o f l a t e n t r a t h e r t h a n m e a s u r e d v a r i a b l e s (MV) , s i n c e t h e M V ' s o n l y r a r e l y c o r r e s p o n d i n a o n e - t o - o n e f a s h i o n w i t h t h e c o n s t r u c t s o f i n t e r e s t t o t h e r e s e a r c h e r . . . c o n c l u s i o n s a b o u t an MV mode l c a n n o t be r e l i e d u p o n , s i n c e v a r i o u s t h e o r e t i c a l e f f e c t s w i l l o f n e c e s s i t y be e s t i m a t e d i n a b i a s e d m a n n e r . They a l s o w i l l no t r e p l i c a t e i n o t h e r s t u d i e s t h a t a r e i d e n t i c a l e x c e p t f o r t h e l e v e l o f p r e c i s i o n o f e r r o r i n t h e v a r i a b l e s . T h u s , t h e ma in v i r t u e s o f LVMs a r e t h e i r a b i l i t y t o s e p a r a t e e r r o r f r o m m e a n i n g f u l e f f e c t s and t h e a s s o c i a t e d p a r a m e t r i c i n v a r i a n c e . . . ( p . 434) L V M ' s may be a p p l i e d t o p r o j e c t s w h i c h a r e e i t h e r e x p l o r a t o r y o r c o n f i r m a t o r y i n n a t u r e . An LVM mode l may be u s e d e i t h e r t o examine o b s e r v e d r e l a t i o n s h i p s i n a s e a r c h f o r p l a u s i b l e e x p l a n a t i o n s o r t o t e s t p r e v i o u s l y f o r m u l a t e d h y p o t h e t i c a l r e l a t i o n s h i p s ( e i t h e r t h e o r y - o r d a t a - b a s e d ) . I t i s i n t h e e x p l o r a t o r y c o n t e x t t h a t t h e LVM a p p r o a c h was a p p l i e d t o t h e a r e a o f c o r r e l a t e s and d e t e r m i n a n t s o f s t a t i s t i c s a c h i e v e m e n t . T h r e e E x p l o r a t o r y M o d e l s I t may be c o n c l u d e d f r o m t h e r e v i e w o f t h e l i t e r a t u r e o f 26 t h e c o r r e l a t e s and d e t e r m i n a n t s o f a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s t h a t t h e a r e a i s i n a r e l a t i v e l y young e p i s t e m o l o g i c a l s t a t e . I t a p p e a r s t o be a t a d e s c r i p t i v e s t a g e , i n w h i c h some i m p o r t a n t c o r r e l a t e s o f a c h i e v e m e n t ( e . g . , a b s t r a c t o r l o g i c a l r e a s o n i n g ) have been i n d i c a t e d , b u t i n w h i c h o t h e r p o t e n t i a l c o r r e l a t e s ( e . g . a c h i e v e m e n t m o t i v a t i o n ) have n o t y e t been i n v e s t i g a t e d . F u r t h e r , t h e s t u d i e s t o d a t e have y i e l d e d l i t t l e i n f o r m a t i o n a b o u t d i r e c t and i n d i r e c t e f f e c t s o f any v a r i a b l e on a c h i e v e m e n t i n s t a t i s t i c s . I t was d e c i d e d t h a t an LVM a p p r o a c h w h i c h i n c l u d e d t h e h y p o t h e t i c a l c o n s t r u c t s o f " c o g n i t i o n " , " a t t i t u d e " , " m o t i v a t i o n " , and " e x p e r i e n c e " c o u l d f u r t h e r t h e s t a t e o f t h e a r e a . I t c o u l d do so i n two ways . F i r s t , an LVM a p p r o a c h c o u l d i n d i c a t e , by t h e e x a m i n a t i o n o f s e v e r a l a l t e r n a t i v e m o d e l s , some o f t h e d i r e c t and i n d i r e c t e f f e c t s o f t h e s e l a t e n t v a r i a b l e s on s t a t i s t i c s a c h i e v e m e n t . E f f e c t s c o u l d be c o m p a r e d a c r o s s t h e s e v e r a l m o d e l s . B e c a u s e o f t h e a d v a n t a g e s o f LVM o v e r p a t h a n a l y s i s m e n t i o n e d a b o v e , t h e e f f e c t s c o u l d be m e a s u r e d i n a r e l a t i v e l y e r r o r - f r e e way. In a d d i t i o n , t h e c o n t r i b u t i o n o f m o t i v a t i o n a l v a r i a b l e s c o u l d be e x a m i n e d , and c o n t r a s t e d w i t h t h a t o f c o g n i t i v e , a t t i t u d i n a l a n d e x p e r i e n t i a l v a r i a b l e s . The m e a s u r e d v a r i a b l e s s e l e c t e d f o r s t u d y were t h o s e w h i c h have been f o u n d t o c o r r e l a t e r e l a t i v e l y h i g h l y w i t h s c o r e s o r g r a d e s i n s t a t i s t i c s , o r w h i c h were h y p o t h e s i z e d t o c o r r e l a t e w i t h s t a t i s t i c s a c h i e v e m e n t b e c a u s e o f o b t a i n e d c o r r e l a t i o n s w i t h g e n e r a l a c a d e m i c a c h i e v e m e n t ( e . g . , m o t i v a t i o n ) . The c o g n i t i v e v a r i a b l e s s e l e c t e d i n c l u d e d a r i t h m e t i c s k i l l s and 27 n u m e r i c c o n c e p t l e a r n i n g ( b a s e d on M i c h a e l and M i c h a e l ' s (1969) f i n d i n g ) . ; v e r b a l r e a s o n i n g and a b s t r a c t r e a s o n i n g ( b o t h b a s e d on f i n d i n g s o f H a r t l e y and H a r t l e y ( 1 9 7 6 ) ) ; and s p a t i a l / v i s u a l i z a t i o n ( b a s e d on E l m o r e and V a s u ' s (1980) f i n d i n g ) . The a t t i t u d i n a l v a r i a b l e s i n c l u d e d a t t i t u d e t o w a r d s s t a t i s t i c s and a t t i t u d e t o w a r d s r e s e a r c h ( b a s e d on f i n d i n g s o f R o b e r t s and B i l d e r b a c k (1980) and o f F e i n b e r g and H a l p e r i n ( 1 9 7 8 ) ) , and a c a d e m i c s e l f - e s t e e m ( b a s e d on f i n d i n g s o f H a r t l e y and H a r t l e y ( 1 9 7 6 ) ) . The m o t i v a t i o n a l v a r i a b l e s s e l e c t e d f o r s t u d y were b a s e d on r e s e a r c h by A t k i n s o n (1978) a n d R a y n o r (1978) and i n c l u d e d a c h i e v e m e n t m o t i v e , p e r c e i v e d u t i l i t y and s p e c i f i c m o t i v a t i o n . The i n c l u s i o n o f an e x p e r i e n t i a l v a r i a b l e was b a s e d on t h e f i n d i n g s o f F e i n b e r g and H a l p e r i n (1978) and E l m o r e and V a s u ( 1 9 8 0 ) . T h r e e m o d e l s were c o n s i d e r e d f o r e x a m i n a t i o n i n t he p r e s e n t s t u d y . They a r e p r e s e n t e d i n F i g u r e s 3, 4 and 5. The names o f t h e 11 v a r i a b l e s w h i c h a r e h y p o t h e s i z e d t o be m a n i f e s t a t i o n s o f t h e t h r e e l a t e n t v a r i a b l e s a r e i n c l u d e d o n l y i n F i g u r e 3. O n l y t h e l a t e n t v a r i a b l e s a r e l i s t e d i n F i g u r e s 4 and 5. I t s h o u l d be n o t e d t h a t t h e m a n i f e s t a t i o n s o f t h o s e v a r i a b l e s a r e i d e n t i c a l t o t h o s e shown i n F i g u r e 3. T h a t i s , " C o g n i t i o n " i s h y p o t h e s i z e d t o m a n i f e s t t h e f i v e c o g n i t i v e m e a s u r e d v a r i a b l e s . The l a t e n t v a r i a b l e s " A t t i t u d e " and " M o t i v a t i o n " a r e s i m i l a r l y h y p o t h e s i z e d t o be m a n i f e s t e d i n t h e t h r e e a t t i t u d i n a l and t h r e e m o t i v a t i o n a l v a r i a b l e s r e s p e c t i v e l y . T h e r e was no g u i d a n c e a v a i l a b l e i n t h e l i t e r a t u r e w i t h r e g a r d t o t h e p l a c e m e n t o f p a t h v e c t o r s , t o t h e w e i g h t s t o be 28 V e r b a l C o m p r e h e n s i o n Number F a c i l i t y L o g i c a l R e a s o n i n g V i s u a l i z a t i o n N u m e r i c C o n c e p t L e a r n i n g A t t i t u d e t o S t a t i s t i c s S e l f - C o n c e p t A t t i t u d e t o R e s e a r c h Need A c h i e v e m e n t P e r c e i v e d U t i l i t y S p e c i f i c M o t i v a t i o n E x p e r i e n c e -- C o g n i t i o n < A t t i t u d e - M o t i v a t i o n F i g u r e 3 E x p l o r a t o r y M o d e l " A " o f S t a t i s t i c s A c h i e v e m e n t A c h i e v e m e n t a s s i g n e d t o any p a r t i c u l a r p a t h , o r t o t h e d i r e c t o r i n d i r e c t e f f e c t s o f any i n d e p e n d e n t v a r i a b l e . Unde r t h e s e c i r c u m s t a n c e s , many d i f f e r e n t m o d e l s c o u l d be h y p o t h e s i z e d and t e s t e d . In t h e p r e s e n t s t u d y , t h e t h r e e m o d e l s s e l e c t e d f o r i n v e s t i g a t i o n were c o n s i d e r e d t o be o r d e r e d i n c o m p l e x i t y . F o r m u l a t i n g and s u b s e q u e n t l y e v a l u a t i n g m o d e l s i n t h i s way has been recommended by B e n t l e r ( 1 9 7 8 ) , who has n o t e d t h a t m u l t i p l e m o d e l f o r m u l a t i o n s c a n make i t p o s s i b l e t o a t t a i n a f u l l e r u n d e r s t a n d i n g o f a phenomenon . When t h e n a t u r e o f t h e t h e d i r e c t a n d i n d i r e c t e f f e c t s i s l i t t l e known, f o r m u l a t i o n and e v a l u a t i o n o f s e v e r a l m o d e l s may f a c i l i t a t e t h e i n c o r p o r a t i o n o f " h u n c h e s a n d g u e s s e s " i n t o a more r i g o r o u s and a c c u r a t e m o d e l , t h e r e b y a d v a n c i n g t h e c o n s t r u c t i o n o f t h e o r y i n t h e a r e a o f i n t e r e s t . The t h r e e m o d e l s s e l e c t e d f o r e x a m i n a t i o n a r e r a t h e r e l e m e n t a r y . M o d e l " A " ( F i g u r e 3) h y p o t h e s i z e s d i r e c t e f f e c t s o n l y , and no i n d i r e c t e f f e c t s o f any v a r i a b l e , on s t a t i s t i c s 29 a c h i e v e m e n t . E x p l o r a t o r y mode l " B " i s somewhat more c o m p l e x . M o d e l " C " i s more c o m p l e x s t i l l . M o d e l " A " i s a somewhat l i t e r a l r e p r e s e n t a t i o n o f t h e c i r c u m s t a n c e s u n d e r w h i c h t h e d a t a were c o l l e c t e d . T h a t i s , i t i s a mode l w h i c h r e f l e c t s t h e f a c t t h a t t h e m e a s u r e s o f t h e 12 i n d e p e n d e n t v a r i a b l e s were c o l l e c t e d d u r i n g t h e same t e s t s e s s i o n . The t h r e e l a t e n t and s i n g l e m a n i f e s t v a r i a b l e c o n t r i b u t e d i r e c t l y t o a c h i e v e m e n t . F u r t h e r , no c o v a r i a n c e be tween any p a i r o f t h e l a t e n t v a r i a b l e s , o r o f a l a t e n t v a r i a b l e w i t h p a s t e x p e r i e n c e , was h y p o t h e s i z e d . C o g n i t i o n ^ M o t i v a t i o n F i g u r e 4 E x p l o r a t o r y M o d e l " B " o f S t a t i s t i c s A c h i e v e m e n t M o d e l s " B " and " C " , on t h e o t h e r h a n d , b o t h p l a c e t h e m a n i f e s t v a r i a b l e E x p e r i e n c e a s d e f i n e d i n t h i s i n v e s t i g a t i o n i n i t s t e m p o r a l p o s i t i o n . T h a t i s , d e s p i t e t h e f a c t t h a t E x p e r i e n c e i s m e a s u r e d d u r i n g t h e same s e s s i o n a s a r e t h e o t h e r 11 m a n i f e s t v a r i a b l e s , i t r e f l e c t s a p a s t e v e n t , w h i c h may have i n f l u e n c e d t h e t h r e e l a t e n t v a r i a b l e s . M o d e l " B " ( F i g u r e 4) h y p o t h e s i z e s t h a t t h e o n l y i n d i r e c t e f f e c t on a c h i e v e m e n t i s t h a t o f E x p e r i e n c e . The e f f e c t on a c h i e v e m e n t i s f e l t t h r o u g h t h e d i r e c t i n f l u e n c e s o f C o g n i t i o n , A t t i t u d e a n d M o t i v a t i o n . No o t h e r i n d i r e c t e f f e c t s a r e A c h i e v e m e n t 30 E x p e r i e n c e >• C o g n i t i o n >. A c h i e v e m e n t t A t t i t u d e . t . M o t i v a t i o n F i g u r e 5 E x p l o r a t o r y M o d e l " C " o f S t a t i s t i c s A c h i e v e m e n t h y p o t h e s i z e d . E a c h o f t h e l a t e n t v a r i a b l e s , C o g n i t i o n , M o t i v a t i o n and A t t i t u d e , a r e h y p o t h e s i z e d t o have a d i r e c t e f f e c t on a c h i e v e m e n t , and n o t t o c o v a r y among t h e m s e l v e s . L i k e M o d e l " B " , mode l " C " ( F i g u r e 5) a l s o h y p o t h e s i z e s t h a t E x p e r i e n c e e x e r t s an i n d i r e c t e f f e c t on A c h i e v e m e n t t h r o u g h i t s e f f e c t on C o g n i t i o n , A t t i t u d e and M o t i v a t i o n . A t t i t u d e i s h y p o t h e s i z e d t o e x e r t an i n f l u e n c e b o t h d i r e c t l y and i n d i r e c t l y , t h r o u g h i t s e f f e c t on C o g n i t i o n . M o t i v a t i o n i s h y p o t h e s i z e d t o a c t d i r e c t l y on A t t i t u d e a l o n e , c o n s e q u e n t l y e x e r t i n g no d i r e c t i n f l u e n c e on A c h i e v e m e n t . The s h i f t i n t h e e f f e c t t y p e o f t h e l a t e n t v a r i a b l e , M o t i v a t i o n , f r o m d i r e c t t o i n d i r e c t , i s an i n c r e a s e i n t h e c o m p l e x i t y o f t h e mode l w h i c h r e f l e c t s t h e s p e c u l a t i o n i n t h e m o t i v a t i o n a l l i t e r a t u r e a b o u t t h e n a t u r e o f t h e i n f l u e n c e o f m o t i v a t i o n ( A t k i n s o n , 1 9 7 8 ) . 31 C h a p t e r I I I .  M e t h o d The p r o c e d u r e s f o l l o w e d t o e x p l o r e the- r e s e a r c h q u e s t i o n s w h i c h were p r e s e n t e d i n C h a p t e r II a r e d e s c r i b e d i n t h i s c h a p t e r . The i n s t r u m e n t s u s e d t o measu re t h e 12 i n d e p e n d e n t v a r i a b l e s a n d t h e d e p e n d e n t v a r i a b l e a r e d e s c r i b e d f i r s t . In t h e s e c o n d s e c t i o n , t h e p r o c e d u r e f o l l o w e d t o o b t a i n t h e s a m p l e s o f s u b j e c t s i s p r e s e n t e d . T h i r d , t h e p r o c e d u r e s o f d a t a c o l l e c t i o n and p r e p a r a t i o n a r e d e s c r i b e d i n d e t a i l . The f i n a l s e c t i o n o f t h e c h a p t e r i s t h e d e s c r i p t i o n o f t h e p r e l i m i n a r y a n a l y s i s p r o c e d u r e s . I n s t r u m e n t s M e a s u r e s o f t h e I n d e p e n d e n t V a r i a b l e s Of t h e m e a s u r e s o f t h e t w e l v e i n d e p e n d e n t v a r i a b l e s , t h r e e were d e v e l o p e d and p i l o t - t e s t e d f o r t h i s s t u d y , w h i l e t he r e m a i n i n g n i n e were s e l e c t e d f r o m t h e l i t e r a t u r e . The 12 v a r i a b l e s , t o g e t h e r w i t h t h e name o f t h e t e s t u s e d t o measu re e a c h , a r e l i s t e d i n T a b l e 3. The t h r e e i n d e p e n d e n t v a r i a b l e s f o r w h i c h m e a s u r e s were d e v e l o p e d and p i l o t - t e s t e d a r e ma rked by a s t e r i s k s . In t h e f o l l o w i n g d e s c r i p t i o n , t h e m a n i f e s t v a r i a b l e s a r e p r e s e n t e d i n t h e o r d e r i n w h i c h t h e y a r e l i s t e d i n T a b l e 3. The d e s c r i p t i o n o f t h e p r o c e d u r e u s e d t o d e v e l o p and p i l o t - t e s t t h e 32 T a b l e 3 M e a s u r e s o f t h e M a n i f e s t V a r i a b l e s and the U n d e r l y i n g L a t e n t V a r i a b l e L a t e n t V a r i a b l e M a n i f e s t V a r i a b l e M e a s u r e C o g n i t i v e V e r b a l C o m p r e h e n s i o n A d v a n c e d V o c a b u l a r y T e s t L o g i c a l R e a s o n i n g D i a g r a m m i n g R e l a t i o n s Number F a c i l i t y M u l t i p l i c a t i o n and S u b t r a c t i o n S p a t i a l V i s u a l i z a t i o n Pape r F o l d i n g C o n c e p t L e a r n i n g * C o n c e p t L e a r n i n g A t t i t u d i n a l A t t i t u d e Toward A t t i t u d e Towa rd S t a t i s t i c s * S t a t i s t i c s A t t i t u d e Toward A t t i t u d e Toward R e s e a r c h R e s e a r c h * A c a d e m i c S e l f - C o n c e p t • S e l f - C o n c e p t M o t i v a t i o n a l A c h i e v e m e n t M o t i v a t i o n - * * P e r c e i v e d U t i l i t y _ * * S p e c i f i c M o t i v a t i o n - * * — * * * E x p e r i e n c e _ * * * D e v e l o p e d a n d p i l o t - t e s t e d f o r t h i s s t u d y . * * T h i s m e a s u r e was no t g i v e n a t i t l e . * * * T h i s m a n i f e s t v a r i a b l e .was n o t a s s i g n e d t o a l a t e n t v a r i a b l e . t h r e e "new" i n s t r u m e n t s i s i n c l u d e d u n d e r t h e r e s p e c t i v e v a r i a b l e name. V e r b a l C o m p r e h e n s i o n . V e r b a l c o m p r e h e n s i o n was m e a s u r e d u s i n g t h e A d v a n c e d V o c a b u l a r y T e s t d e v e l o p e d by E k s t r o m , F r e n c h and Harman ( 1 9 7 6 ) . The t e s t c o n s i s t s o f two p a r t s o f s i m i l a r d i f f i c u l t y g r a d i e n t s . No e v i d e n c e f o r t h e p a r a l l e l n a t u r e o f t h e p a r t s i s p r e s e n t e d . E a c h p a r t c o n t a i n s 18 i t e m s a n d r e q u i r e s f o u r m i n u t e s o f t e s t i n g t i m e . E a c h i t e m i s made up o f a s t i m u l u s word f o l l o w e d by f i v e c h o i c e s , f r o m w h i c h s u b j e c t s c h o o s e t h e most synonymous a l t e r n a t e . The s c o r e i s t h e number o f c o r r e c t c h o i c e s on b o t h p a r t s . F o r a s a m p l e o f 181 c o l l e g e 33 s t u d e n t s , E k s t r o m e t a I . (1976) r e p o r t e d an o b s e r v e d mean o f 1 3 . 8 , a s t a n d a r d d e v i a t i o n o f 5.2 and an i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t o f 0 . 7 9 . W i t h r e g a r d t o t h e h y p o t h e s i z e d r e l a t i o n s h i p be tween t h i s t e s t and m e a s u r e s o f s t a t i s t i c s a c h i e v e m e n t , no s t u d y w h i c h c o l l e c t e d d a t a on t h i s measu re was i d e n t i f i e d i n t h e l i t e r a t u r e . H o w e v e r , H a r t l e y and H a r t l e y (1976) o b s e r v e d t h a t t h e V e r b a l C o m p r e h e n s i o n s u b t e s t o f t h e D i f f e r e n t i a l A p t i t u d e T e s t c o r r e l a t e d 0 .70 w i t h t h e i r m e a s u r e o f s t a t i s t i c s a c h i e v e m e n t . T h e t e s t i s s i m i l a r i n t y p e o f t a s k t o t h e A d v a n c e d V o c a b u l a r y T e s t . The D i f f e r e n t i a l A p t i t u d e s u b t e s t was no t s e l e c t e d f o r u se i n t h e p r e s e n t s t u d y b e c a u s e o f c o n s t r a i n t s on a v a i l a b l e t e s t i n g t i m e . S p e c i f i c a l l y , t h e number o f m e a s u r e s w h i c h were t o be a d m i n i s t e r e d i m p o s e d a s e v e r e l i m i t on t h e t i m e t h a t any s i n g l e measu re c o u l d t a k e . L o g i c a l R e a s o n i n g . The m e a s u r e o f t h i s a b i l i t y was a D i a g r a m m i n g R e l a t i o n s h i p s T e s t ( E k s t r o m e t a l . , 1 9 7 6 ) , w h i c h c o n s i s t s o f two s i m i l a r p a r t s o f 15 i t e m s e a c h . F o r e a c h i t e m , s u b j e c t s a r e a s k e d t o s e l e c t one o f f i v e Venn d i a g r a m s w h i c h t h e y f e e l b e s t i l l u s t r a t e s t h e l o g i c a l r e l a t i o n s h i p s among a s e t o f t h r e e o b j e c t s . E a c h p a r t o f t h e t e s t t a k e s f o u r m i n u t e s o f t e s t i n g t i m e . The s c o r e i s t h e t o t a l number o f c o r r e c t i t e m r e s p o n s e s . When E k s t r o m e t a l . (1976) a d m i n i s t e r e d t h i s t e s t t o " o v e r 5 0 0 " n a v a l r e c r u i t s , t h e y o b t a i n e d a mean s c o r e o f 1 2 . 1 , a s t a n d a r d d e v i a t i o n o f 5.2 a n d a n i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t o f 0 . 7 9 . No p r e v i o u s i n v e s t i g a t i o n a p p e a r s t o have u s e d t h i s measu re 34 i n an a t t e m p t t o a c c o u n t f o r t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . Howeve r , H a r t l e y a n d H a r t l e y (1976) f o u n d t h a t a s i m i l a r m e a s u r e , t h e A b s t r a c t R e a s o n i n g s u b t e s t f r o m t h e D i f f e r e n t i a l A p t i t u d e T e s t , c o r r e l a t e d 0 .42 w i t h s t a t i s t i c s a c h i e v e m e n t . A g a i n , t h i s p a r t i c u l a r s u b t e s t was t o o l o n g t o be a d m i n i s t e r e d d u r i n g t h i s i n v e s t i g a t i o n . D i a g r a m m i n g R e l a t i o n s h i p s a p p e a r s t o be a t e s t t a p p i n g s i m i l a r s k i l l s ( E k s t r o m e t a l . , 1 9 7 6 ) . Number F a c i l i t y . The measu re c h o s e n f o r t h i s a b i l i t y was a t e s t o f S u b t r a c t i o n and M u l t i p l i c a t i o n ( E k s t r o m e t a l . , 1 9 7 6 ) , w h i c h c o n s i s t s o f two p a r t s o f s i m i l a r d i f f i c u l t y , e a c h p a r t t a k i n g two m i n u t e s o f t e s t i n g t i m e . E a c h h a l f i s made up o f 60 i t e m s . In e a c h p a r t , a row o f 10 t w o - d i g i t s u b t r a c t i o n s i s a l t e r n a t e d w i t h a row o f 10 m u l t i p l i c a t i o n s o f a t w o - d i g i t number by a o n e - d i g i t number . The t e s t has a s i n g l e s c o r e , t h e t o t a l number o f c o r r e c t r e s p o n s e s . E k s t r o m and h e r c o l l e a g u e s a d m i n i s t e r e d t h e f i r s t h a l f o f t h i s t e s t t o " o v e r 5 0 0 " n a v a l r e c r u i t s . A n a l y s i s o f t h e r e s u l t i n g d a t a y i e l d e d a mean s c o r e o f 19.3, a s t a n d a r d d e v i a t i o n o f 9.1 a n d an i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t o f 0 . 8 6 . T h i s m e a s u r e has n o t been u s e d i n any i d e n t i f i e d a t t e m p t t o e x p l a i n t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . T h e r e a r e , h o w e v e r , two r e p o r t e d r e s u l t s o f some r e l e v a n c e . M i c h a e l and M i c h a e l (1969) r e p o r t e d t h a t a m e a s u r e o f a r i t h m e t i c a b i l i t y c o m b i n e d w i t h one o f a l g e b r a i c s k i l l s a c c o u n t e d f o r 2 2 . 1 % o f t h e o b s e r v e d v a r i a n c e i n c o u r s e ma rks i n s t a t i s t i c s . F e i n b e r g a n d H a l p e r i n (1977) o b s e r v e d a c o r r e l a t i o n o f 0 . 40 ( a c c o u n t i n g f o r 35 16% o f t h e v a r i a n c e ) be tween b a s i c m a t h e m a t i c s s k i l l s and s t a t i s t i c s a c h i e v e m e n t . S p a t i a l V i s u a l i z a t i o n . T h i s a b i l i t y was m e a s u r e d by a t e s t o f P a p e r F o l d i n g ( E k s t r o m e t a l . , 1 9 7 6 ) , w h i c h c o n s i s t s , o n c e a g a i n , o f two p a r t s o f s i m i l a r l e n g t h and d i f f i c u l t y . E a c h h a l f c o n t a i n s 10 i t e m s and t a k e s t h r e e m i n u t e s o f t e s t i n g t i m e . E a c h i t e m d e p i c t s , , i n two o r t h r e e d r a w i n g s , s u c c e s s i v e f o l d s made i n a s q u a r e s h e e t o f p a p e r . The f i n a l d r a w i n g s h o w s , i n a d d i t i o n t o a l l t h e f o l d s , one h o l e p u n c h e d t h r o u g h a l l l a y e r s o f t h e f o l d e d p a p e r . The s u b j e c t ' s t a s k i s t o s e l e c t t h e c o r r e c t one o f f i v e d i a g r a m s t h a t d e p i c t s how t h e p a p e r m i g h t l o o k when f u l l y r e o p e n e d . A n a l y s i s o f t e s t r e s u l t s c o l l e c t e d f rom 46 c o l l e g e s t u d e n t s y i e l d e d a mean o f 1 3 . 8 , a s t a n d a r d d e v i a t i o n o f 4 . 5 and an i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t o f 0 . 8 4 ( E k s t r o m e t a l . , 1 9 7 6 ) . D e s p i t e t h e f i n d i n g o f a r e l a t i o n s h i p be tween s p a t i a l v i s u a l i z a t i o n a b i l i t y and m a t h e m a t i c s a c h i e v e m e n t ( e . g . , S h e r m a n , 1 9 8 0 ) , t h i s a b i l i t y h a s a t t r a c t e d l i t t l e a t t e n t i o n a s a p o s s i b l e c o r r e l a t e o f a c h i e v e m e n t i n s t a t i s t i c s . The s i n g l e s t u d y o f d i r e c t r e l e v a n c e was r e p o r t e d by E l m o r e and V a s u ( 1 9 8 0 ) , who o b t a i n e d a c o r r e l a t i o n o f 0 .45 be tween t h i s measu re and a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s . They r e p o r t e d t h a t o b t a i n e d c o r r e l a t i o n s be tween a c h i e v e m e n t a n d o t h e r m e a s u r e s o f s p a t i a l v i s u a l i z a t i o n were no t a s h i g h ( i . e . , 0 . 24 and 0 . 3 5 ) . C o n c e p t L e a r n i n g . The measu re o f t h i s v a r i a b l e was d e v e l o p e d f o r t h i s s t u d y . 36 The i n i t i a l f o r m o f t h i s t a s k ( A p p e n d i x A) was composed o f a o n e - h a l f p age d e s c r i p t i o n o f t h e c o n c e p t o f " s u m m a t i o n " , p l u s n i n e c o m p u t a t i o n a l i t e m s w h i c h t e s t e d u n d e r s t a n d i n g o f t h e c o n c e p t . U n f a m i l i a r n o t a t i o n was s u b s t i t u t e d f o r t h e u s u a l c a p i t a l s i g m a . Summat ion o v e r one and two s u b s c r i p t s was d e s c r i b e d i n t h e t e s t . The c o n c e p t o f " s u m m a t i o n " was s e l e c t e d as t h e r e q u i r e d t a s k f o r two r e a s o n s . F i r s t , i t i s an a l g e b r a i c c o n c e p t w h i c h i s u n f a m i l i a r t o most b e g i n n i n g s t a t i s t i c s s t u d e n t s i n E d u c a t i o n . S e c o n d , t h e l e a r n i n g o f s u c h a c o n c e p t ( s h o u l d any l e a r n i n g o c c u r ) i s no t a w a s t e d e f f o r t . I t i s f u n d a m e n t a l t o t h e u n d e r s t a n d i n g o f i n t r o d u c t o r y s t a t i s t i c s . When t h e i n i t i a l f o r m ( A p p e n d i x A) was a d m i n i s t e r e d t o 23 t h i r d - and f o u r t h - y e a r E d u c a t i o n s t u d e n t s ( n = 1 5 , 8 ) , t h e mean number o f i t e m s a t t e m p t e d was 4 . 6 5 , and t h e mean number c o r r e c t was 1 . 4 8 . A l t h o u g h 19 . o f t h e 23 s u b j e c t s had c o r r e c t l y r e s p o n d e d t o t h e f i r s t i t e m , t h e r e was no c l e a r p a t t e r n o f r e s p o n s e t o any o f t h e r e m a i n i n g e i g h t i t e m s . F u r t h e r , v e r y few s u b j e c t s r e s p o n d e d c o r r e c t l y t o any o t h e r i t e m . C o n s e q u e n t l y , t h e c o n c e p t d e s c r i p t i o n was s i m p l i f i e d , t h e i t e m s r e v i s e d a c c o r d i n g l y , and t h e number o f i t e m s i n c r e a s e d t o 13 ( s e e A p p e n d i x B ) . The c o n c e p t o f summat ion was r e t a i n e d s i n c e , a s m e n t i o n e d a b o v e , i t i s e s s e n t i a l f o r s t u d e n t s t o m a s t e r b u t i s unknown t o most e n t e r i n g s t u d e n t s . The d e s c r i p t i o n o f t h e c o n c e p t was l i m i t e d , h o w e v e r , t o summat ion o v e r one s u b s c r i p t i n o r d e r t o make t h e t a s k l e s s d i f f i c u l t . The i n s t r u c t i o n s f o r t h e t a s k d i d no t m e n t i o n any 37 s t r a t e g i e s o r o t h e r c o g n i t i v e a i d s f o r t h e c o m p l e t i o n o f t he t a s k , b e y o n d a g e n e r a l s t a t e m e n t t h a t " y o u c a n r e f e r t o t h e d e s c r i p t i o n o f t h e c o n c e p t w h i l e a n s w e r i n g t h e q u e s t i o n s , and y o u c a n do t h e q u e s t i o n s i n any o r d e r you w i s h " . S u b j e c t s e n t e r e d t h e i r a n s w e r s t o t h e i t e m s i n t h e s p a c e s p r o v i d e d . The t i m e - l i m i t was 12 m i n u t e s . The s c o r e was t h e number o f c o r r e c t i t e m r e s p o n s e s . B e c a u s e t h i s measu re was d e v e l o p e d f o r t h i s s t u d y , no d a t a t o s u p p o r t c l a i m s o f e m p i r i c a l v a l i d i t y e x i s t e d . H o w e v e r , some s u p p o r t , i n t e r m s o f c o n s t r u c t v a l i d i t y , c a n be m a r s h a l l e d f r o m t h e l i t e r a t u r e . M i c h a e l and M i c h a e l ( 1 9 6 9 ) , f o r e x a m p l e , r e p o r t e d a c o r r e l a t i o n o f 0 . 4 7 be tween s t a t i s t i c s a c h i e v e m e n t and a m e a s u r e o f l e a r n i n g o f a l g e b r a i c c o n c e p t s . F u r t h e r , F e i n b e r g and H a l p e r i n (1978) f o u n d t h a t a measu re o f b a s i c m a t h e m a t i c a l s k i l l s c o r r e l a t e d 0 . 4 0 w i t h c o u r s e a c h i e v e m e n t i n s t a t i s t i c s . A t t i t u d e Towa rd S t a t i s t i c s . The measu re o f t h i s v a r i a b l e was d e v e l o p e d f o r t h i s s t u d y . An i n i t i a l i t e m p o o l ( A p p e n d i x C) o f 32 i t e m s was f i r s t c o n s t r u c t e d . E a c h i t e m i n q u i r e d a b o u t t h e s u b j e c t ' s d e g r e e o f a g r e e m e n t w i t h a s t a t e m e n t a b o u t some f a c e t o f s t u d y i n g , c a l c u l a t i n g o r t h i n k i n g a b o u t s t a t i s t i c s . The i n i t i a l p o o l o f i t e m s was c o n s t r u c t e d so t h a t i t i n c l u d e d s t a t e m e n t s a b o u t mos t a r e a s o f c o n c e r n t o i n t r o d u c t o r y s t a t i s t i c s / r e s e a r c h d e s i g n s t u d e n t s . The a r e a s were t h o s e i d e n t i f i e d i n t h e l i t e r a t u r e , by f a c u l t y and g r a d u a t e s t u d e n t s , and f r o m p e r s o n a l e x p e r i e n c e . E x t e n t o f a g r e e m e n t was m e a s u r e d on a s e v e n - p o i n t L i k e r t s c a l e , w i t h p o i n t 1 b e i n g " s t r o n g l y 38 d i s a g r e e " and p o i n t 7 b e i n g " s t r o n g l y a g r e e " . A n e u t r a l p o i n t was p r o v i d e d , l a b e l l e d " n e i t h e r a g r e e n o r d i s a g r e e ' . H a l f o f t h e i t e m s were worded p o s i t i v e l y , and h a l f n e g a t i v e l y . The s c o r e w a s . e q u a l t o t h e t o t a l o f t h e n u m e r i c r e s p o n s e s , a f t e r i t e m s o f n e g a t i v e p o l a r i t y had been r e v e r s e d . T h e r e f o r e , i t r e f l e c t e d t h e d e g r e e o f p o s i t i v e a t t i t u d e t o w a r d s s t a t i s t i c s . The 3 2 - i t e m p o o l o f i t e m s m e a s u r i n g a t t i t u d e t o w a r d s t a t i s t i c s was r a n d o m l y c o m b i n e d w i t h t h e 33 i n i t i a l i t e m s m e a s u r i n g A t t i t u d e Toward R e s e a r c h , d e s c r i b e d i n t h e n e x t s e c t i o n . The 65 i t e m s were t h e n a d m i n i s t e r e d t o 120 t h i r d - and f o u r t h - y e a r s t u d e n t s e n r o l l e d i n E d u c a t i o n a l P s y c h o l o g y c o u r s e s . The c o n t e n t o f t h e c o u r s e s f r o m w h i c h s u b j e c t s , were s o l i c i t e d d i d n o t e m p h a s i z e s t a t i s t i c s o r r e s e a r c h d e s i g n . The e x c l u s i o n o f s t a t i s t i c s and r e s e a r c h d e s i g n c o u r s e s was i n t e n d e d t o a l l o w s e l e c t i o n o f s t a t i s t i c a l l y n a i v e s u b j e c t s ( c o r r e s p o n d i n g t o b e g i n n i n g s t u d e n t s i n s t a t i s t i c s ) . I t em a n a l y s i s o f t h e p i l o t - s t u d y d a t a r e v e a l e d t h a t 27 o f t h e 33 i t e m s c o n c e r n i n g a t t i t u d e s t o w a r d s s t a t i s t i c s c o r r e l a t e d 0 .50 o r g r e a t e r w i t h t h e t o t a l s c o r e . The t e n i t e m s i n e a c h o f t h e p o s i t i v e and n e g a t i v e p o l e s w h i c h c o r r e l a t e d 0 . 5 0 o r h i g h e r w i t h t h e t o t a l s c o r e , b u t w h i c h s t i l l , a s a g r o u p , r e f l e c t e d a l l a r e a s o f c o n c e r n i n c l u d e d i n t h e o r i g i n a l i t e m p o o l , were s e l e c t e d f o r i n c l u s i o n f o r t h e f i n a l s c a l e ( A p p e n d i x B ) . D e s c r i p t i v e s t a t i s t i c s f o r t h e g r o u p s o f i t e m s o f n e g a t i v e and p o s i t i v e p o l a r i t y , w h i c h were merged i n t o t h e f i n a l 2 0 - i t e m s c a l e a r e r e p o r t e d i n t h e l e f t - h a n d c o l u m n o f T a b l e 4 . The l e f t - h a n d c o l u m n o f T a b l e 4 a l s o c o n t a i n s a d e s c r i p t i o n o f 39 T a b l e 4 I tem and S c a l e S t a t i s t i c s f o r t h e A t t i t u d e S c a l e s (n=120) S t a t i s t i c s R e s e a r c h I t em s t a t i s t i c s : P o s i t i v e i t e m s : N o . o f I t ems 10 10 Mean 3 .50 3 . 7 9 Mean s . d . 1 . 59 1 . 65 Mean i t e m / t o t a l c o r r . 0.61 0 . 6 3 N e g a t i v e i t e m s : N o . o f I t ems 10 1 0 Mean 4.01 4 .52 Mean s . d . 1 .78 1 .64 Mean i t e m / t o t a l c o r r . 0 .64 0 .62 S c a l e s t a t i s t i c s : N o . o f I t ems 20 20 Mean 7 4 . 0 2 8 4 . 6 9 s . d . 2 2 . 4 2 21 . 75 S t a n , e r r o r 5 .60 5 .50 H o y t ' s ANOVA 0 . 9 3 0 . 9 3 s t a t i s t i c s c a l c u l a t e d f r o m t h e t o t a l s c o r e s o f t h e 120 s u b j e c t s , f o r t h e 20 i t e m s s e l e c t e d f o r t h e f i n a l f o r m . The s t a t i s t i c s i n d i c a t e t h a t i t e m s o f b o t h n e g a t i v e and p o s i t i v e p o l a r i t y d i s p l a y s u f f i c i e n t v a r i a n c e t o a l l o w d i s c r i m i n a t i o n among p e r s o n s . R e s p o n s e s a r e , on t h e a v e r a g e , c l u s t e r e d a b o u t t h e n e u t r a l p o i n t . The d e s c r i p t i v e s t a t i s t i c s p r e s e n t e d f o r t h e 20-i t e m s c a l e i n d i c a t e t h a t i t i s h i g h l y i n t e r n a l l y c o n s i s t e n t . F u r t h e r , t o t a l s c o r e s v a r y enough t o a l l o w p o s s i b l e d i s c r i m i n a t i o n among p e o p l e The mean i s c l o s e t o t h e t h e o r e t i c a l v a l u e o f 70 on a 1 4 0 - p o i n t s c a l e . In t h e f o r m a d m i n i s t e r e d i n t h i s i n v e s t i g a t i o n ( A p p e n d i x B ) , t h e t w e n t y i t e m s were r a n d o m l y c o m b i n e d w i t h t h e t w e n t y i t e m s o f t h e measu re o f A t t i t u d e Towa rd R e s e a r c h , d e s c r i b e d i m m e d i a t e l y b e l o w . 40 T h i s m e a s u r e o f a t t i t u d e t o w a r d s s t a t i s t i c s was no t e m p i r i c a l l y v a l i d a t e d . Howeve r , some e v i d e n c e f o r c o n t e n t v a l i d i t y was g a t h e r e d . F i r s t , t h e i n i t i a l i t e m p o o l was s u b m i t t e d t o a s e r i e s o f f a c u l t y members a n d f e l l o w g r a d u a t e s t u d e n t s f o r r e v i e w o f t h e u n i d i m e n s i o n a l i t y o f e a c h i t e m , and o f t h e c o n t e n t o f t h e p o o l o f i t e m s a s a w h o l e . As a g r o u p , t h e p a n e l i n d i c a t e d t h a t t h e i t e m p o o l was s u f f i c i e n t l y b r o a d and i n c l u d e d u n i v o c a l i t e m s w h i c h a s s e s s e d a t t i t u d e a b o u t e a c h ma jo r a r e a o f c o n c e r n t o i n t r o d u c t o r y s t a t i s t i c s s t u d e n t s . S e c o n d , a c o m p a r i s o n was made w i t h t h e 3 4 - i t e m s c a l e o f R o b e r t s and B i l d e r b a c k ( 1 9 8 0 ) . A c o p y o f t h e measu re was no t r e c e i v e d i n t i m e t o be u s e d i n t h i s i n v e s t i g a t i o n , bu t c o m p a r i s o n o f t h e i t e m s on t h e i r s c a l e w i t h t h o s e i n c l u d e d i n t h e f i n a l f o r m o f t h e s c a l e d e v e l o p e d f o r t h i s s t u d y r e v e a l e d t h a t t h e l a t t e r measu re d i d i n d e e d t a p t h e same a r e a s o f c o n c e r n . W i t h r e g a r d t o b r o a d e r i s s u e s o f c o n s t r u c t v a l i d i t y , o t h e r i n v e s t i g a t i o n s have i n d i c a t e d t h a t m e a s u r e s o f a t t i t u d e a c c o u n t f o r a r e l i a b l e p r o p o r t i o n o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . R o b e r t s and B i l d e r b a c k (1980) o b s e r v e d c o r r e l a t i o n s o f 0 . 3 3 t o 0 .54 be tween t h e i r measu re o f a t t i t u d e t o w a r d s t a t i s t i c s and o b t a i n e d c o u r s e mark i n s t a t i s t i c s . F u r t h e r , E l m o r e and V a s u (1980) r e p o r t e d an o b s e r v e d c o r r e l a t i o n o f 0 .43 be tween m e a s u r e s o f a t t i t u d e t o w a r d s m a t h e m a t i c s and a c h i e v e m e n t i n s t a t i s t i c s . A t t i t u d e Towa rd R e s e a r c h . A m e a s u r e o f t h i s v a r i a b l e was 41 d e v e l o p e d f o r t h i s s t u d y . An i n i t i a l i t e m p o o l ( A p p e n d i x C) o f 34 i t e m s was c o n s t r u c t e d . E a c h i t e m e n q u i r e d a b o u t d e g r e e o f a g r e e m e n t w i t h a s t a t e m e n t a b o u t some f a c e t o f s t u d y i n g , e v a l u a t i n g , o r t h i n k i n g a b o u t r e s e a r c h d e s i g n o r " r e s e a r c h " . The i n i t i a l i t e m p o o l was d e v i s e d so as t o i n c l u d e s t a t e m e n t s a b o u t most a r e a s o f c o n c e r n t o s t u d e n t s o f i n t r o d u c t o r y r e s e a r c h d e s i g n . The a r e a s o f c o n c e r n were t h o s e i d e n t i f i e d i n t h e l i t e r a t u r e , by f a c u l t y members , by f e l l o w g r a d u a t e s t u d e n t s , and f r o m p e r s o n a l e x p e r i e n c e . S o u r c e s o f s t a t e m e n t s and o f a r e a s o f c o n c e r n were u t i l i z e d i n a manner s i m i l a r t o t h a t d e s c r i b e d a b o v e , i n t h e d e s c r i p t i o n o f t h e d e v e l o p m e n t o f t h e A t t i t u d e T o w a r d S t a t i s t i c s - s c a l e . I t em r e s p o n s e was , a g a i n , m e a s u r e d on a s e v e n - p o i n t L i k e r t s c a l e , w i t h p o i n t 1 b e i n g " s t r o n g l y d i s a g r e e " and p o i n t 7 b e i n g " s t r o n g l y a g r e e " . A n e u t r a l p o i n t was p r o v i d e d , l a b e l l e d " n e i t h e r a g r e e n o r d i s a g r e e " . H a l f t h e i t e m s were wo rded p o s i t i v e l y , and h a l f n e g a t i v e l y . The s c o r e was e q u a l t o t h e t o t a l o f t h e n u m e r i c r e s p o n s e s , a f t e r i t e m s o f n e g a t i v e p o l a r i t y had been r e v e r s e d . The s c o r e t h e r e f o r e r e f l e c t e d t h e d e g r e e o f p o s i t i v e a t t i t u d e t o w a r d r e s e a r c h and r e s e a r c h d e s i g n . The 33 i t e m s were r a n d o m l y c o m b i n e d w i t h t h e 32 i t e m s m e a s u r i n g A t t i t u d e T o w a r d S t a t i s t i c s . The r e s u l t i n g 6 5 - i t e m f o r m was a d m i n i s t e r e d t o t h e same s u b j e c t s d e s c r i b e d a b o v e . I t em a n a l y s i s o f t h e p i l o t - s t u d y d a t a r e v e a l e d t h a t 28 i t e m s e n q u i r i n g a b o u t r e s e a r c h o r r e s e a r c h d e s i g n c o r r e l a t e d 0 . 5 0 o r g r e a t e r w i t h t h e t o t a l s c a l e s c o r e . A g a i n , t h e t e n i t e m s i n e a c h o f t h e p o s i t i v e and n e g a t i v e p o l e s w h i c h 42 c o r r e l a t e d 0 .50 o r h i g h e r w i t h t h e t o t a l s c o r e , b u t w h i c h s t i l l , a s a g r o u p , r e f l e c t e d a l l a r e a s o f c o n c e r n i n c l u d e d i n t h e o r i g i n a l i t e m p o o l , were s e l e c t e d f o r i n c l u s i o n i n t h e f i n a l s c a l e ( A p p e n d i x B ) . S t a t i s t i c s f o r t h e g r o u p s o f i t e m s o f n e g a t i v e and p o s i t i v e p o l a r i t y , and t h e f i n a l 2 0 - i t e m s c a l e a r e r e p o r t e d i n t h e r i g h t -hand c o l u m n o f T a b l e 4. The r i g h t - h a n d c o l u m n o f T a b l e 4 a l s o c o n t a i n s s t a t i s t i c s c a l c u l a t e d f r o m t h e t o t a l s c o r e s , f o r t h e 20 i t e m s i n c l u d e d i n t h e f i n a l s c a l e . E x c e p t t h a t t h e mean s c o r e i s somewhat h i g h e r t h a n t h a t o b s e r v e d f o r t h e 2 0 - i t e m A t t i t u d e Towa rd S t a t i s t i c s s c a l e , t h e s t a t i s t i c s c l o s e l y r e s e m b l e e a c h o t h e r . T h i s s c a l e has no e m p i r i c a l v a l i d i t y d a t a a s s o c i a t e d w i t h i t . H o w e v e r , a p a n e l r e v i e w ( u t i l i z i n g t h e comments o f f a c u l t y members and f e l l o w - g r a d u a t e s t u d e n t s ) i n d i c a t e d t h a t t h e s c a l e was v a l i d i n t e rms o f c o n t e n t . S p e c i f i c a l l y , t h e i t e m s t a p p e d t h e m a j o r a r e a s o f c o n c e r n t o i n t r o d u c t o r y s t u d e n t s i n s t a t i s t i c s and r e s e a r c h d e s i g n . No s c a l e s m e a s u r i n g t h i s v a r i a b l e were i d e n t i f i e d i n t h e l i t e r a t u r e . A c a d e m i c S e l f - C o n c e p t • The m e a s u r e o f t h i s v a r i a b l e ( A p p e n d i x B) was t h e sum o f t h e s u b j e c t ' s r e s p o n s e s t o f o u r t e e n i t e m s . The a b i l i t i e s r a t e d were t h o s e i n v e s t i g a t e d by H a r t l e y and H a r t l e y ( 1 9 7 6 ) , w i t h t h e a d d i t i o n o f f i v e w h i c h were a b s t r a c t e d f r o m a l i s t o f r e s e a r c h - r e l a t e d c o m p e t e n c i e s c o m p i l e d by S a n d e r s and Wor then ( 1 9 7 0 ) . The f i v e a d d i t i o n a l a b i l i t i e s were i n c l u d e d b e c a u s e t h e y a p p e a r e d t o be h i g h l y r e l e v a n t t o f e e l i n g s o f c o m p e t e n c e i n s t a t i s t i c s . E a c h i t e m r e q u e s t e d t h e 43 s u b j e c t t o e n d o r s e , on a s e v e n - p o i n t L i k e r t s c a l e , t h e amount o f some a b i l i t y t h e s u b j e c t s f e l t t h e y p o s s e s s e d . The e n d - p o i n t s o f t h e L i k e r t s c a l e were 1 = " v e r y l o w " and 7 = " v e r y h i g h " a b i l i t y . A n e u t r a l p o i n t , l a b e l l e d " a v e r a g e " , was p r o v i d e d . The e n d o r s e m e n t s f o r t h e f o u r t e e n i t e m s were summed t o y i e l d a s i n g l e s c o r e . B e c a u s e o f a l a c k o f s u i t a b l e s u b j e c t s , no p i l o t - t e s t i n g was done f o r t h i s m e a s u r e , and c o n s e q u e n t l y no d a t a a r e a v a i l a b l e . Howeve r , some e v i d e n c e c a n be p r e s e n t e d f o r t h e r e l a t i o n s h i p o f a c a d e m i c s e l f - c o n c e p t t o a c h i e v e m e n t i n s t a t i s t i c s . F o r e x a m p l e , H a r t l e y and H a r t l e y (1976) r e p o r t e d t h a t t h e r a t i n g s o f a b i l i t i e s u s e d i n t h e i r s t u d y a c c o u n t e d f o r 1 0 . 5 % o f t h e e x p l a i n e d v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . T h e s e r a t i n g s a r e p a r t o f t h e m e a s u r e u s e d i n t h i s t h e s i s . F u r t h e r , F e i n b e r g and H a l p e r i n (1978) r e p o r t e d t h a t s e l f - r a t i n g s o f t h e s u b j e c t ' s p e r c e p t i o n o f h i s own a b i l i t y i n m a t h e m a t i c s , r e l a t i v e t o o t h e r s t u d e n t s , a c c o u n t e d f o r 1 0 . 1 % o f a c h i e v e m e n t i n s t a t i s t i c s . An i t e m m e a s u r i n g t h i s p e r c e p t i o n , t o o , i s p a r t o f t h e measu re u s e d i n t h i s i n v e s t i g a t i o n . A c h i e v e m e n t M o t i v a t i o n . The m e a s u r e o f a c h i e v e m e n t m o t i v a t i o n ( A p p e n d i x B) was t h e sum o f t h e s u b j e c t ' s r e s p o n s e s t o e i g h t e e n i t e m s d e v e l o p e d by Shye ( 1 9 7 8 ) . He i n v e s t i g a t e d t h e d i m e n s i o n s o f a c h i e v e m e n t m o t i v e i n a s a m p l e o f s u c c e s s - o r i e n t e d b u s i n e s s m e n . T h i s f o r m , w h i c h was c o n s t r u c t e d t o r e s e m b l e t h e s e m a n t i c d i f f e r e n t i a l i n f o r m a t , a s k s t h e s u b j e c t t o r a t e (on s i x s e v e n - p o i n t s c a l e s ) e a c h o f t h e t h r e e c o n c e p t s , " t a s k s I p r e f e r " , " t a s k s I u n d e r t a k e " , and " t a s k s a t w h i c h I s u c c e e d " . The s c o r e on t h i s measu re i s t h e sum o f t h e n u m e r i c e n d o r s e m e n t s 44 o f e a c h i t e m . A h i g h e r s c o r e r e f l e c t s a g r e a t e r d e g r e e o f a c h i e v e m e n t m o t i v a t i o n . No p s y c h o m e t r i c d a t a were r e p o r t e d by Shye f o r t h i s m e a s u r e . I t was s e l e c t e d b e c a u s e i t was t h e o n l y m e a s u r e o f a c h i e v e m e n t m o t i v e f o u n d i n t h e l i t e r a t u r e t h a t was n o t i n d i v i d u a l l y - a d m i n i s t e r e d . I t was n o t p i l o t - t e s t e d b e c a u s e a l l c l a s s e s f r o m w h i c h s u b j e c t s w o u l d be drawn h a d been c a n v a s s e d and c o n s e q u e n t l y , no s u b j e c t s were a v a i l a b l e . P e r c e i v e d U t i l i t y . L i k e t h a t o f S p e c i f i c M o t i v a t i o n , t h e m e a s u r e o f t h i s v a r i a b l e ( A p p e n d i x B) was b a s e d on R a y n o r ' s t h e o r y o f c o n t i n g e n t and n o n c o n t i n g e n t p a t h s . I t was m e a s u r e d by summing t h e r e s p o n s e s t o two q u e s t i o n s . The f i r s t q u e s t i o n e n q u i r e d a b o u t u t i l i t y o f t h e s t a t i s t i c s c o u r s e t o t h e s u b j e c t d u r i n g h i s c o u r s e o f s t u d i e s , w h i l e t h e s e c o n d i t e m a s k e d a b o u t p e r c e i v e d u t i l i t y w i t h r e g a r d t o t h e s u b j e c t ' s i n t e n d e d c a r e e r p a t h . E a c h i t e m was e n d o r s e d by t h e s u b j e c t on a f i v e - p o i n t s c a l e , w i t h e n d p o i n t s i n d i c a t i n g e x t r e m e d e g r e e s o f u t i l i t y and n o n u t i l i t y . A n e u t r a l p o i n t , l a b e l l e d " n e i t h e r u s e f u l no r o f no u s e " , was p r o v i d e d . The s c o r e on t h e measu re was s i m p l y t h e sum o f t h e i t e m s , when t h e r e s p o n s e t o e a c h i t e m o f n e g a t i v e p o l a r i t y was r e v e r s e d . The sum r e p r e s e n t e d t h e d e g r e e o f u t i l i t y p e r c e i v e d by t h e s u b j e c t . T h i s m e a s u r e was d e v e l o p e d b e c a u s e no g r o u p - a d m i n i s t e r e d m e a s u r e o f t h i s v a r i a b l e was i d e n t i f i e d i n t h e l i t e r a t u r e . B e c a u s e no s u b j e c t s were a v a i l a b l e f o r p i l o t - t e s t i n g , no p s y c h o m e t r i c d a t a were c a l c u l a t e d . 45 S p e c i f i c M o t i v a t i o n . The m e a s u r e o f t h i s v a r i a b l e ( A p p e n d i x B) c o n s i s t e d o f two i t e m s , b o t h o f w h i c h were drawn f r o m d e s c r i p t i o n s o f R a y n o r ' s (1978) t h e o r i z i n g a b o u t c o n t i n g e n t a n d n o n c o n t i n g e n t p a t h s and t h e i r r e l a t i o n s h i p t o a c h i e v e m e n t m o t i v a t i o n . They e n q u i r e d a b o u t t h e r e a s o n f o r t a k i n g t h e s t a t i s t i c s c o u r s e and t h e s t r e n g t h o f d e s i r e t o t a k e t h e c o u r s e , r e s p e c t i v e l y . E a c h i t e m was e n d o r s e d on a f i v e - p o i n t s c a l e , t h e e n d p o i n t s o f w h i c h i n d i c a t e d e x t r e m e l y p o s i t i v e and e x t r e m e l y n e g a t i v e a f f e c t . A n e u t r a l p o i n t was p r o v i d e d f o r b o t h i t e m s . T h i s p o i n t was l a b e l l e d " e q u a l l y b e c a u s e i t i s r e q u i r e d and b e c a u s e I wi.sh t o t a k e i t " and " n e i t h e r wan ted t o t a k e i t no r n o t t o t a k e i t " f o r t h e two i t e m s , r e s p e c t i v e l y . T h i s s c a l e was d e v e l o p e d b e c a u s e no g r o u p m e a s u r e s o f t h i s v a r i a b l e were i d e n t i f i e d . i n t h e l i t e r a t u r e . B e c a u s e no s u b j e c t s .were a v a i l a b l e , no p i l o t -t e s t i n g o f t h i s measu re was c a r r i e d o u t . E x p e r i e n c e . The measu re o f t h i s v a r i a b l e ( A p p e n d i x B) was t h e r e s p o n s e t o a s i n g l e i n q u i r y a b o u t t h e number o f m a t h e m a t i c s o r s t a t i s t i c s c o u r s e s p r e v i o u s l y c o m p l e t e d . The measu re i s t he same as t h a t u s e d by G i a m b r a ( 1 9 7 2 ) , F e i n b e r g and H a l p e r i n ( 1 9 7 8 ) , and E l m o r e and V a s u d 9 8 0 ) . G i a m b r a (1972) f o u n d t h a t 80% o f h i s s u b j e c t s , who l a t e r o b t a i n e d f i r s t c l a s s marks i n a s t a t i s t i c s c o u r s e , had t a k e n a t l e a s t one p o s t - a l g e b r a m a t h e m a t i c s c o u r s e . F e i n b e r g a n d H a l p e r i n (1978 ) r e p o r t e d t h a t t h e number o f p r e v i o u s m a t h e m a t i c s o r s t a t i s t i c s c o u r s e s c o m p l e t e d c o r r e l a t e d 0.31 w i t h c o u r s e marks i n s t a t i s t i c s . F i n a l l y , E l m o r e and V a s u (1980) f o u n d t h a t t h e number o f c o u r s e s 46 c o m p l e t e d i n m a t h e m a t i c s o r s t a t i s t i c s c o r r e l a t e d 0 .22 w i t h s t a t i s t i c s a c h i e v e m e n t . The M e a s u r e o f t h e D e p e n d e n t V a r i a b l e The f i n a l mark a c h i e v e d by t h e s t u d e n t on a common o n e - h o u r e x a m i n a t i o n was u s e d as t h e measu re o f t he d e p e n d e n t v a r i a b l e , s t a t i s t i c s a c h i e v e m e n t . T h i s t e s t was i n c o r p o r a t e d by e a c h c o u r s e i n s t r u c t o r i n t o h i s own f i n a l e x a m i n a t i o n . The e x a m i n a t i o n i t e m s were s e l e c t e d f rom a p o o l o f i t e m s d e v e l o p e d t o t e s t l e a r n i n g o f i n t r o d u c t o r y s t a t i s t i c s a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . No p i l o t t e s t i n g was c o m p l e t e d , and t h e e x a m i n a t i o n f o r m i s no t a p p e n d e d t o t h i s t h e s i s . The e x a m i n a t i o n was composed o f 27 i t e m s . T w e n t y - t h r e e i t e m s were f i x e d - c h o i c e i n f o r m a t . Of t h e f o u r o p e n - e n d e d i t e m s , one r e q u i r e d t h e s t a t e m e n t o f a s t a t i s t i c a l c o n c l u s i o n i n a s u b s t a n t i v e f o r m . The r e m a i n i n g t h r e e i t e m s r e q u i r e d e l e m e n t a r y c a l c u l a t i o n s b a s e d on a g r a p h d e p i c t i n g t h e a r e a s u n d e r t h e n o r m a l c u r v e , c o m b i n e d w i t h an u n d e r s t a n d i n g o f t h e mean , t h e s t a n d a r d d e v i a t i o n and t h e p e r c e n t i l e . The a r e a s e x a m i n e d by t h e t e s t i n c l u d e d d e s c r i p t i v e s t a t i s t i c s , c o r r e l a t i o n a l and i n f e r e n t i a l s t a t i s t i c s . No i t e m s r e q u i r i n g u s e o f t a b l e s o f s t a t i s t i c a l s i g n i f i c a n c e were i n c l u d e d . B e c a u s e t h e e x a m i n a t i o n e m p h a s i z e d u n d e r s t a n d i n g o f c o n c e p t s , i t c o u l d have been a d m i n i s t e r e d e i t h e r i n o p e n - o r c l o s e d - b o o k f o r m a t . A l l f o u r i n s t r u c t o r s c h o s e t h e o p e n - b o o k f o r m a t . 47 S u b j e c t s T a r g e t P o p u l a t i o n . The t a r g e t p o p u l a t i o n f o r t h i s s t u d y was t h e p o p u l a t i o n o f p e r s o n s r e g i s t e r e d i n i n t r o d u c t o r y s t a t i s t i c s c o u r s e s i n e d u c a t i o n . A c c e s s i b l e P o p u l a t i o n . S t u d e n t s r e g i s t e r e d i n an i n t r o d u c t o r y s t a t i s t i c s c o u r s e i n e d u c a t i o n d u r i n g t h e Summer S e s s i o n o f 1981 a t t h e U n i v e r s i t y o f A l b e r t a , t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a and t h e U n i v e r s i t y o f V i c t o r i a s e r v e d as t h e a c c e s s i b l e p o p u l a t i o n f o r t h i s r e s e a r c h . The c o u r s e s i n c l u d e d two t h r e e - w e e k i n t r o d u c t o r y s t a t i s t i c s c o u r s e s ( E d u c a t i o n 482 a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a a n d E d u c a t i o n 560 a t t h e U n i v e r s i t y o f V i c t o r i a ) , and one s i x - w e e k c o m b i n e d i n t r o d u c t o r y s t a t i s t i c s and e l e m e n t a r y r e s e a r c h d e s i g n c o u r s e ( E d u c a t i o n 502 a t t h e U n i v e r s i t y o f A l b e r t a ) . S a m p l e . V o l u n t e e r s f r o m t h e s a m p l e d c l a s s e s l i s t e d above s e r v e d a s s u b j e c t s . The c o o p e r a t i o n o f p o t e n t i a l s u b j e c t s was r e q u e s t e d d u r i n g c l a s s t i m e , o n c e d u r i n g e a c h c o u r s e . The p u r p o s e o f t h e s t u d y and a b r i e f e x p l a n a t i o n o f t h e t i m e i t w o u l d t a k e were d e s c r i b e d t o t h e c l a s s members , and c o o p e r a t i o n was r e q u e s t e d i m m e d i a t e l y f o l l o w i n g t h e e x p l a n a t i o n . D a t a C o l l e c t i o n and P r e p a r a t i o n D a t a C o l l e c t i o n . The m e a s u r e s o f e a c h i n d e p e n d e n t v a r i a b l e were c o l l e c t e d d u r i n g t h e f i r s t c l a s s p e r i o d o f e a c h c o u r s e a t t h e U n i v e r s i t i e s o f B r i t i s h C o l u m b i a and V i c t o r i a . B e c a u s e o f 48 u n e x p e c t e d p r o b l e m s w i t h t h e m a i l s e r v i c e , t h e t e s t s were a d m i n i s t e r e d t o t he U n i v e r s i t y o f A l b e r t a s u b j e c t s a f t e r a p p r o x i m a t e l y o n e - t h i r d o f t h e c o u r s e s e s s i o n s had t a k e n p l a c e . The t e s t s were a d m i n i s t e r e d i n a s i n g l e s e s s i o n o f a p p r o x i m a t e l y one and a q u a r t e r h o u r s i n a l l i n s t a n c e s . A t t h e b e g i n n i n g o f t h e s e s s i o n , e a c h s t u d e n t was g i v e n a t e s t p a c k e t , c o n t a i n i n g a b r i e f d e s c r i p t i o n o f t h e s t u d y , a c o n s e n t f o r m and a c o p y o f e a c h t e s t , s t a p l e d t o g e t h e r i n t h e o r d e r o f a d m i n i s t r a t i o n . A d m i n i s t r a t i o n i n s t r u c t i o n s ( A p p e n d i x D) were s t a n d a r d i z e d a c r o s s c l a s s e s . F i r s t , t h e e x p l a n a t i o n o f t h e s t u d y was r e a d t o t h e c l a s s . S e c o n d , t h o s e s t u d e n t s who w i s h e d t o p a r t i c i p a t e c o m p l e t e d t h e c o n s e n t f o r m . S t u d e n t s who d i d n o t w i s h t o p a r t i c i p a t e l e f t t h e r oom. O n l y t h e n d i d a d m i n i s t r a t i o n o f - t h e m e a s u r e s b e g i n . I n s t r u c t i o n s were r e a d a l o u d f o r e a c h t e s t . The a d m i n i s t r a t o r t i m e d e a c h , u s i n g a s t o p w a t c h . The t e s t s were a d m i n i s t e r e d i n t h e f o l l o w i n g s e q u e n c e : t h e e x p e r i e n t i a l / m o t i v a t i o n a l q u e s t i o n n a i r e ( c o n t a i n i n g t h e m e a s u r e s o f p e r c e i v e d u t i l i t y , s p e c i f i c m o t i v a t i o n , a c h i e v e m e n t m o t i v a t i o n , a c a d e m i c s e l f - e s t e e m , and p a s t e x p e r i e n c e ) (10 m i n u t e s ) , a t t i t u d e s t o w a r d s t a t i s t i c s / r e s e a r c h (5 m i n u t e s ) , A d v a n c e d V o c a b u l a r y T e s t (8 m i n u t e s ) , D i a g r a m m i n g R e l a t i o n s h i p s (8 m i n u t e s ) , S u b t r a c t i o n and M u l t i p l i c a t i o n (4 m i n u t e s ) , P a p e r F o l d i n g (6 m i n u t e s ) and t h e C o n c e p t L e a r n i n g T a s k (12 m i n u t e s ) . The o r d e r o f a d m i n i s t r a t i o n was s e l e c t e d , f i r s t , a s an a t t e m p t t o m i n i m i z e c o n t a m i n a t i o n o f t h e a t t i t u d i n a l and m o t i v a t i o n a l m e a s u r e s by p e r c e i v e d p e r f o r m a n c e on t h e c o g n i t i v e 49 t e s t s . S e c o n d , t he o n l y h i g h l y s p e e d e d c o g n i t i v e t a s k was a d m i n i s t e r e d i m m e d i a t e l y a f t e r a s h o r t b r e a k , t o a l l o w m i n i m a l i n t e r f e r e n c e f r o m f a t i g u e . F i n a l l y , t h e t e s t most l i k e l y t o a r o u s e a n x i e t y ( t h e C o n c e p t L e a r n i n g T a s k ) was p l a c e d l a s t i n t h e s e q u e n c e . The f i n a l e x a m i n a t i o n f o rms ( i . e . , t h e measu re o f t h e d e p e n d e n t v a r i a b l e ) were a d m i n i s t e r e d t o t h e s u b j e c t s by t h e c l a s s i n s t r u c t o r s as p a r t o f t h e f i n a l c o u r s e e x a m i n a t i o n s . D a t a P r e p a r a t i o n . I t em r e s p o n s e s f o r e a c h o f t h e p r e - t e s t s were k e y p u n c h e d d i r e c t l y f r o m t h e o r i g i n a l answer s h e e t o n t o a f i l e s t o r e d a t t h e C o m p u t i n g C e n t r e , U n i v e r s i t y o f B r i t i s h C o l u m b i a . In a d d i t i o n , i d e n t i f i c a t i o n f i e l d s c o n s i s t i n g o f a c o d e f o r e a c h c l a s s , a t w o - d i g i t number i d e n t i f y i n g t h e i n d i v i d u a l s u b j e c t and a s i n g l e d i g i t i d e n t i f y i n g t h e t e s t b e i n g k e y p u n c h e d , were a d d e d t o e a c h r e c o r d a s i t was e n t e r e d . E a c h i t e m r e s p o n s e on t h e f i n a l e x a m i n a t i o n was c o d e d and t h e c o d i n g v e r i f i e d by t h e i n v e s t i g a t o r . The r e s p o n s e s were t h e n k e y p u n c h e d o n t o a d i s k f i l e , a c c o m p a n i e d by i d e n t i f i c a t i o n f i e l d s . The k e y p u n c h i n g was v e r i f i e d by c h e c k i n g t h e e n t e r e d d a t a a g a i n s t t h e o r i g i n a l f o r m s ( f o r t h e p r e - t e s t s ) o r t h e c o d e d f o r m s ( f o r t h e f i n a l e x a m i n a t i o n ) . No d a t a e n t r y e r r o r s were t o l e r a t e d . Two k i n d s o f i n c o m p l e t e r e c o r d were s o u g h t o u t and d e l e t e d f r o m t h e d a t a p o o l . F i r s t , any s u b j e c t who had no t a t t e m p t e d e a c h measu re was i d e n t i f i e d and h i s / h e r r e c o r d d e l e t e d . S e c o n d , t h e d a t a o f any s u b j e c t who had c o m p l e t e d e i t h e r t h e p r e - t e s t s o r t h e f i n a l e x a m i n a t i o n , b u t n o t b o t h , were e l i m i n a t e d f r o m 50 f u r t h e r c o n s i d e r a t i o n . S c o r i n g P r o c e d u r e s . The s c o r e s on each of the f o u r c o g n i t i v e measures of V e r b a l Comprehension, Number F a c i l i t y , S p a t i a l V i s u a l i z a t i o n and L o g i c a l Reasoning were w e i g h t e d . A weight of " 0 " was a s s i g n e d i f an i n c o r r e c t response had been chosen f o r a g i v e n i t e m . C h o i c e s of c o r r e c t r e s p o n s e s were a s s i g n e d the weight " 1 " . The t o t a l s c o r e was the sum of the w e i g h t s f o r a p a r t i c u l a r measure. Each i t e m of the Concept L e a r n i n g Task was hand-scored " 0 " or " 1 " , i f the response t o t h a t i t e m was i n c o r r e c t or c o r r e c t , r e s p e c t i v e l y . The w e i g h t s were e n t e r e d i n t o the d a t a f i l e , the t o t a l s c o r e b e i n g the sum of the w e i g h t s . Responses t o the items of n e g a t i v e p o l a r i t y on the measures of A t t i t u d e Toward S t a t i s t i c s and A t t i t u d e Toward Research were r e v e r s e d b e f o r e the s c a l e s were s c o r e d . Because v e r y few responses were o m i t t e d by the s u b j e c t s , the n e u t r a l weight of "4" was a s s i g n e d t o each m i s s i n g r e s p o n s e . The t o t a l s c o r e f o r each a t t i t u d e measure was the sum of the w e i g h t s of the items of p o s i t i v e p o l a r i t y , p l u s the sum of the r e v e r s e d w e i g h t s of the items of n e g a t i v e p o l a r i t y . The measures of Academic S e l f - C o n c e p t , Achievement M o t i v a t i o n , P e r c e i v e d U t i l i t y and S p e c i f i c M o t i v a t i o n were s c o r e d s i m p l y by summing the numeric response t o each item of the s c a l e . Once a g a i n , because t h e r e were v e r y few m i s s i n g responses i n the d a t a p o o l , the m i d - s c a l e v a l u e of "4" was a s s i g n e d t o each o m i t t e d response. The measure of the v a r i a b l e , E x p e r i e n c e , was a s i n g l e i t e m . 51 T h u s , t h e r e s p o n s e t o t h i s i t e m c o n s t i t u t e d t h e " t o t a l " s c o r e . T h e r e were no m i s s i n g r e s p o n s e s o b s e r v e d f o r t h i s m e a s u r e . The m e a s u r e o f t h e d e p e n d e n t v a r i a b l e , S t a t i s t i c s A c h i e v e m e n t , was t h e s c o r e a t t a i n e d on t h e o n e - h o u r f i n a l e x a m i n a t i o n . E a c h i t e m was h a n d - s c o r e d by t h e i n v e s t i g a t o r b e f o r e t h e marks a t t a i n e d f o r e a c h i t e m were e n t e r e d i n t o t h e d a t a f i l e . The t o t a l s c o r e was t h e sum o f t h e i t e m m a r k s . P r e l i m i n a r y A n a l y s i s The p r e l i m i n a r y a n a l y s i s o f t h e d a t a was c o m p l e t e d i n two s t a g e s . The f i r s t s t e p was t h e i t e m a n a l y s i s o f t h e d a t a c o l l e c t e d f r o m t h e B r i t i s h C o l u m b i a and the A l b e r t a s a m p l e s . F o l l o w i n g t h i s s t e p , t h e d a t a f r o m t h e two s a m p l e s were c o m p a r e d i n o r d e r t o d e t e r m i n e w h e t h e r t h e y c o u l d be p o o l e d f o r t h e f i n a l a n a l y s i s . The r e s u l t s o f t h e s e a n a l y s e s , r e p o r t e d i n C h a p t e r 4, r e v e a l e d t h a t t h e two s a m p l e s c o u l d n o t be m e r g e d . The s i g n i f i c a n t d i f f e r e n c e s be tween t h e s a m p l e s n e c e s s i t a t e d t h e r e p h r a s i n g o f t h e r e s e a r c h q u e s t i o n s ( d i s c u s s e d i n C h a p t e r 4 ) , and t h e c o n s e q u e n t r e f o r m u l a t i o n o f t h e f i n a l a n a l y s i s p l a n . I t em A n a l y s i s I t em a n a l y s e s were c o m p u t e d f o r e a c h m e a s u r e o f t h e d e p e n d e n t and i n d e p e n d e n t v a r i a b l e s u s i n g t h e c o m p u t e r p r o g r a m LERTAP ( N e l s o n , 1 9 7 4 ) . The p r o g r a m c a l c u l a t e d , f o r e a c h m e a s u r e , t h e mean s c o r e , t h e s t a n d a r d d e v i a t i o n , t h e s t a n d a r d e r r o r and a H o y t i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t , i n a d d i t i o n 52 t o t h e o t h e r i t e m s t a t i s t i c s . The p r o c e d u r e s were i d e n t i c a l f o r t h e d a t a c o l l e c t e d f r o m t h e B r i t i s h C o l u m b i a and f r o m t h e A l b e r t a s a m p l e s . The r e s u l t s o f t h e s e a n a l y s e s a r e r e p o r t e d i n C h a p t e r 4 . T h i s a n a l y s i s , and a l l o t h e r a n a l y s e s w h i c h u s e d c o m p u t e r f a c i l i t i e s , were c a r r i e d ou t on t h e Amdahl 470 V/7 CPU i n s t a l l e d a t t h e C o m p u t i n g C e n t r e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . E q u i v a l e n c e o f t h e B r i t i s h C o l u m b i a and A l b e r t a S a m p l e s . The s a m p l e s f r o m B r i t i s h C o l u m b i a and A l b e r t a were c o m p a r e d i n o r d e r t o d e t e r m i n e whe the r o r n o t t h e y c o u l d be a n a l y z e d t o g e t h e r a s a s i n g l e s a m p l e . The mean v e c t o r s o f t h e 12 m e a s u r e s o f t h e i n d e p e n d e n t v a r i a b l e s were c o m p a r e d u s i n g H o t e l l i n g ' s T - s q u a r e (T imm, 1 9 7 5 ) . A t e s t o f t h e h o m o g e n e i t y o f t h e 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 was p e r f o r m e d u s i n g t h e B a r t l e t t - B o x t e s t (T imm, 1 9 7 5 ) . B o t h s t a t i s t i c s were c o m p u t e d u s i n g t h e m u l t i v a r i a t e a n a l y s i s o f v a r i a n c e c o m p u t e r p r o g r a m OWMAR ( H a k s t i a n , No te 1 ) . 53 C h a p t e r IV . -P r e l i m i n a r y R e s u l t s and F i n a l A n a l y t i c P r o c e d u r e s The r e s u l t s o f t he p r e l i m i n a r y a n a l y s e s d e s c r i b e d i n C h a p t e r I I I a r e p r e s e n t e d i n t h e f i r s t s e c t i o n o f t h i s c h a p t e r . As w i l l be d i s c u s s e d , t h e s e i n i t i a l f i n d i n g s r e v e a l e d t h a t t h e B r i t i s h C o l u m b i a s amp le and t h e A l b e r t a s amp l e c o u l d no t be p o o l e d . I n s t e a d , two s a m p l e s o f s m a l l e r s i z e were r e t a i n e d f o r f i n a l a n a l y s i s . The s m a l l e r s a m p l e s i z e s p r e v e n t e d e x p l o r a t i o n o f t h e q u e s t i o n s i n i t i a l l y p o s e d i n C h a p t e r I I . C o n s e q u e n t l y , t h e r e s e a r c h q u e s t i o n s were r e c a s t and t h e a n a l y s i s p r o c e d u r e s m o d i f i e d a c c o r d i n g l y . T h e s e l a s t two p h a s e s ( r e c a s t i n g t h e r e s e a r c h q u e s t i o n s and m o d i f y i n g t h e a n a l y s e s ) a r e p r e s e n t e d i n t h e s e c o n d and t h i r d s e c t i o n s o f t h e p r e s e n t c h a p t e r . R e s u l t s o f t h e P r e l i m i n a r y A n a l y s i s D e s c r i p t i o n o f t h e Sample The f o u r s t a t i s t i c s c l a s s e s f r o m w h i c h s u b j e c t s were drawn were t a u g h t d u r i n g t h e Summer S e s s i o n o f 1 9 8 1 . The c o u r s e s t o o k p l a c e a t one o f t h r e e u n i v e r s i t i e s - U n i v e r s i t y o f B r i t i s h C o l u m b i a ( two c l a s s e s ) , U n i v e r s i t y o f V i c t o r i a , and U n i v e r s i t y o f A l b e r t a . The f i r s t t h r e e c o u r s e s l i s t e d were o f t h r e e - w e e k d u r a t i o n , and were i n t r o d u c t o r y s t a t i s t i c s a t a m a g i s t r a l o r 54 h i g h e r l e v e l t o s t u d e n t s who were f o r t he most p a r t r e g i s t e r e d i n g r a d u a t e p r o g r a m s i n E d u c a t i o n . The f o u r t h c l a s s , h e l d a t t h e U n i v e r s i t y o f A l b e r t a , t o o k p l a c e o v e r a s i x - w e e k p e r i o d and was d e s i g n e d t o g i v e p r o f i c i e n c y no t o n l y i n i n t r o d u c t o r y s t a t i s t i c s , bu t a l s o i n e l e m e n t a r y r e s e a r c h d e s i g n s k i l l s . T h i s c l a s s , a g a i n , was a imed a t g r a d u a t e s t u d e n t s i n E d u c a t i o n . A l l f o u r c o u r s e s c o n t a i n e d a p p r o x i m a t e l y t h e same s t a t i s t i c a l c o n t e n t . D e s c r i p t i v e s t a t i s t i c s were t a u g h t f i r s t . T h i s s e c t i o n o f t he c o u r s e i n c l u d e d l e s s o n s on l e v e l s o f m e a s u r e m e n t , f r e q u e n c y d i s t r i b u t i o n s and h i s t o g r a m s , m e a s u r e s o f c e n t r a l t e n d e n c y a n d v a r i a b i l i t y , a n d m e a s u r e s o f r e l a t i o n s h i p ( c o r r e l a t i o n and s i m p l e r e g r e s s i o n ) . L e s s o n s on i n t r o d u c t o r y i n f e r e n t i a l s t a t i s t i c s f o l l o w e d . The l e s s o n s t a u g h t d u r i n g t h i s s e c t i o n o f t h e c o u r s e i n c l u d e d t h e t o p i c s o f p r o b a b i l i t y t h e o r y , b i n o m i a l d i s t r i b u t i o n , f o r m u l a t i o n o f r e s e a r c h a n d s t a t i s t i c a l h y p o t h e s e s , s a m p l i n g d i s t r i b u t i o n s , and t h e use o f t h e t - t e s t f o r i n d e p e n d e n t and d e p e n d e n t s a m p l e s . Two c o u r s e s c o n t a i n e d , i n a d d i t i o n , an i n t r o d u c t i o n t o one-way a n a l y s i s o f v a r i a n c e . A l m o s t a l l t h e c l a s s members i n t h r e e o f t h e f o u r c l a s s e s a g r e e d t o p a r t i c i p a t e i n t h e i n v e s t i g a t i o n by s i g n i n g t h e c o n s e n t f o r m s and c o m p l e t i n g t h e s e t o f p r e - t e s t s . S p e c i f i c a l l y , 16 , 11 and 32 c l a s s members i n c o u r s e s o f f e r e d a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , t h e U n i v e r s i t y o f V i c t o r i a and t h e U n i v e r s i t y o f A l b e r t a c o m p l e t e d t h e s e t o f p r e - t e s t s ( ou t o f 17 , 12 and 34 c l a s s members , r e s p e c t i v e l y ) . The e x c e p t i o n t o t h i s h i g h r a t e o f p a r t i c i p a t i o n (92% t o 94%) was one o f t h e two c l a s s e s f r o m t h e U n i v e r s i t y o f B r i t i s h , C o l u m b i a , 55 i n w h i c h o n l y 12 o f t h e 26 r e g i s t r a n t s (46%) c o m p l e t e d t h e c o n s e n t f o rms and p r e - t e s t s . The r e a s o n f o r t h i s a n o m a l y i s unknown . I n t e g r i t y o f t h e D a t a P o o l . The p r e l i m i n a r y e x a m i n a t i o n o f t h e d a t a p o o l h a d two o b j e c t i v e s , a s d i s c u s s e d i n C h a p t e r I I I . The f i r s t was t o e n s u r e t h a t e a c h s u b j e c t had a t t e m p t e d e a c h s u b - t e s t . The s e c o n d o b j e c t i v e was t o e n s u r e t h a t o n l y s u b j e c t s who had c o m p l e t e d b o t h p r e - t e s t s and t h e f i n a l e x a m i n a t i o n p o s t -t e s t were i n c l u d e d i n t h e f i n a l d a t a p o o l . T a b l e 5 c o n t a i n s t h e numbers o f s u b j e c t s who c o m p l e t e d t h e p r e - t e s t s , t h e p o s t - t e s t s , and t h e numbers o f s u b j e c t s f o r whom i t was p o s s i b l e t o m a t c h p r e - and p o s t - t e s t s . W i t h t h e - T a b l e 5 O b t a i n e d Sample S i z e s P r e - P o s t - P r e -T e s t s T e s t s and P o s t -T e s t s U n i v e r s i t y : ~ ~ ! B r i t i s h C o l u m b i a O ) 12 26 11 B r i t i s h C o l u m b i a ( 2 ) 16 17 13 V i c t o r i a 11 12 9 A l b e r t a 32 34 32 T o t a l 71 89 65 e x c e p t i o n o f one s u b j e c t f r o m t h e U n i v e r s i t y o f V i c t o r i a who had t o l e a v e t h e p r e - t e s t i n g s e s s i o n t o k e e p a m e d i c a l a p p o i n t m e n t , no s u b j e c t f a i l e d t o a t t e m p t a l l s u b t e s t s i n t h e p r e t e s t b a t t e r y . Of t h e s i x s u b j e c t s f o r whom p r e - t e s t r e s u l t s were a v a i l a b l e , b u t n o t p o s t - t e s t s c o r e s , a l l h ad f a i l e d t o c o m p l e t e 56 t h e r e s p e c t i v e c o u r s e s . I t em A n a l y s i s The B r i t i s h C o l u m b i a S a m p l e . T a b l e 6 c o n t a i n s t h e mean , s t a n d a r d d e v i a t i o n , s t a n d a r d e r r o r and Hoy t i n t e r n a l c o n s i s t e n c y T a b l e 6 S c a l e S t a t i s t i c s ( B r i t i s h C o l u m b i a Sample (n = 33 ) ) Mean S t a n d a r d S t a n d a r d Hoy t D e v i a t i o n E r r o r C o e f f . D e p e n d e n t V a r i a b l e : E x a m i n a t i o n S c o r e 32.61 7 .67 3 .63 0 . 7 7 I n d e p e n d e n t V a r i a b l e s : 1. E x p e r i e n c e 2 .36 1 .34 — -* 2 . C o g n i t i v e M e a s u r e s : A d v a n c e d V o c a b u l a r y T e s t 2 6 . 5 5 3 .58 2 . 1 6 0 .63 P a p e r F o l d i n g T e s t 1 1 .88 3 .84 1 .58 0 .82 M u l t i p l i c a t i o n and S u b t r a c t i o n 7 3 . 7 0 20.31 3 .70 0 .97 D i a g r a m m i n g R e l a t i o n s 2 0 . 7 3 5.88 2 .12 0 .87 C o n c e p t L e a r n i n g T a s k 5 .55 2 .85 1.27 0 .78 3 . A t t i t u d i n a l M e a s u r e s : A t t i t u d e Towa rd S t a t i s t i c s 8 7 . 7 6 18 .92 5 .60 0.91 A t t i t u d e Towa rd R e s e a r c h 9 5 . 7 6 1 7 . 2 5 5 .52 0 . 8 9 A c a d e m i c S e l f - C o n c e p t 6 7 . 4 2 1 4 . 0 7 2 . 9 9 0 .95 4 . M o t i v a t i o n a l M e a s u r e s : A c h i e v e m e n t M o t i v a t i o n 9 3 . 7 0 10 .24 4 . 0 3 0 .84 P e r c e i v e d U t i l i t y 8 .58 1 .54 0 . 7 2 0 .78 S p e c i f i c M o t i v a t i o n 5 .30 1 .98 1 . 0 9 0 .72 * T h i s m e a s u r e c o n t a i n e d a s i n g l e i t e m . c o e f f i c i e n t f o r e a c h o f t h e m e a s u r e s o f t h e i n d e p e n d e n t and d e p e n d e n t v a r i a b l e s f o r t h e B r i t i s h C o l u m b i a s a m p l e . A d d i t i o n a l 57' i t e m a n a l y s i s i n f o r m a t i o n i s p r e s e n t e d and d i s c u s s e d i n t h e t e x t . The i n t e r n a l c o n s i s t e n c y o f t h e f i n a l e x a m i n a t i o n was a c c e p t a b l e . T h i s j udgement i s b a s e d on t h e f a c t t h a t t h e o b t a i n e d Hoy t c o e f f i c i e n t was e q u a l t o 0 . 7 7 , a n d an a c c e p t a b l e v a l u e f o r u s i n g s c a l e s c o r e s on a g r o u p b a s i s i s o f t e n s e t a t 0 . 7 0 ( e . g . , by C r o n b a c h , 1 9 7 0 ) . The mean s c o r e o f 3 2 . 6 o u t o f a p o s s i b l e 55 marks ( 59 .3% ) i n d i c a t e s t h a t , on t h e a ve r age . , t h e e x a m i n a t i o n was f o u n d t o be o f medium d i f f i c u l t y . I t e m - t o t a l c o r r e l a t i o n s on t h i s measu re r a n g e d be tween - 0 . 1 7 and 0 . 7 2 , w i t h a mean v a l u e o f 0 . 3 3 . F o u r i t e m - t o t a l c o e f f i c i e n t s were o b s e r v e d t o be n e g a t i v e (mean v a l u e , - 0 . 0 9 ) . The a v e r a g e number o f p o s t - s e c o n d a r y m a t h e m a t i c s o r s t a t i s t i c s c o u r s e s c o m p l e t e d was 2 . 3 6 . Of t h e f i v e c o g n i t i v e m e a s u r e s , two were o b s e r v e d t o be c h a r a c t e r i z e d by h i g h l e v e l s o f i n t e r n a l c o n s i s t e n c y ( i . e . , a b o v e 0 . 8 0 ) . P a p e r F o l d i n g and D i a g r a m m i n g R e l a t i o n s h a d H o y t c o e f f i c i e n t s o f 0 .82 and 0 . 8 7 , r e s p e c t i v e l y . One o t h e r c o g n i t i v e m e a s u r e , t h e C o n c e p t L e a r n i n g T a s k , was r e v e a l e d t o be a c c e p t a b l y homogeneous (Hoyt c o e f f i c i e n t = 0 . 7 8 ) . The s p e e d e d t e s t , M u l t i p l i c a t i o n and S u b t r a c t i o n , was e x t r e m e l y i n t e r n a l l y c o n s i s t e n t , w i t h an a s s o c i a t e d c o e f f i c i e n t o f 0 . 9 7 . I t s h o u l d be n o t e d t h a t t h e H o y t c o e f f i c i e n t f o r t h e t e s t o f M u l t i p l i c a t i o n and S u b t r a c t i o n may be somewhat i n f l a t e d b e c a u s e o f t h e s p e e d e d n a t u r e o f t h e t e s t . An e s t i m a t e o f t e s t -r e t e s t o r o f p a r a l l e l f o r m r e l i a b i l i t y wou ld be more v a l i d , b u t t h e s e were o b t a i n a b l e n e i t h e r f r o m t h e r e s u l t s r e p o r t e d by 58 E k s t r o m e t a l . , n o r f r o m t h e d a t a s e t u n d e r d i s c u s s i o n . H o w e v e r , b e c a u s e t h e measu re i s d i v i d e d i n t o two s e p a r a t e l y t i m e d p a r t s o f e q u a l l e n g t h , t h e c o r r e l a t i o n be tween t h e p a r t s c o u l d s e r v e a s a r o u g h e s t i m a t e o f p a r a l l e l f o r m r e l i a b i l i t y . F o r t h e B r i t i s h C o l u m b i a s a m p l e , t h i s c o e f f i c i e n t was 0 . 8 9 . H o w e v e r , i t s h o u l d be n o t e d t h a t no a t t e m p t was made by E k s t r o m e t a l . t o a c h i e v e p a r a l l e l i s m i n t h e two h a l v e s o f any o f t h e m e a s u r e s i n t h e K i t . The i n t e r n a l c o n s i s t e n c y f o r t h e f i f t h c o g n i t i v e m e a s u r e , t h e A d v a n c e d V o c a b u l a r y T e s t , was somewhat l o w e r t h a n t h e o t h e r s ( 0 . 6 3 ) . T h i s low v a l u e may i n p a r t be due t o a c e i l i n g e f f e c t ; t h e mean mark o f 2 6 . 5 5 ( 7 3 . 8 % ) was h i g h e r t h a n t h e mean f o r any o t h e r c o g n i t i v e m e a s u r e . F u r t h e r , t h e d i s t r i b u t i o n o f s c o r e s was m a r k e d l y s k e w e d . Of t h e 33 s u b j e c t s i n t h e B r i t i s h C o l u m b i a s a m p l e , 20 o b t a i n e d s c o r e s o f 29 o r a b o v e ( i . e . 80% o r g r e a t e r ) . T h e s e r e s u l t s may be c o m p a r e d w i t h t h o s e o f E k s t r o m e t a l . ( 1 9 7 6 ) , who r e p o r t e d an o b t a i n e d mean on t h e A d v a n c e d V o c a b u l a r y T e s t o f 13 .8 and a s t a n d a r d d e v i a t i o n o f 5 . 2 , b a s e d on d a t a c o l l e c t e d f r o m a s amp le o f 46 c o l l e g e s t u d e n t s . The d a t a o b t a i n e d f r o m t h e B r i t i s h C o l u m b i a s amp le were l e s s v a r i a b l e , a n d d i s p l a y e d a s i g n i f i c a n t l y h i g h e r mean s c o r e ( t = 1 3 . 5 , d f = 2 l 2 , P < 0 . 0 0 1 ) . F o r t h e t e s t o f P a p e r F o l d i n g , r e s u l t s b a s e d on t h e B r i t i s h C o l u m b i a d a t a d i d n o t d i f f e r s i g n i f i c a n t l y f r o m t h o s e r e p o r t e d by E k s t r o m e t a l . . E k s t r o m e t a l . d i d n o t r e p o r t r e s u l t s b a s e d on c o l l e g e s t u d e n t d a t a f o r t h e r e m a i n i n g two m e a s u r e s ( t h e t e s t s o f D i a g r a m m i n g R e l a t i o n s a n d M u l t i p l i c a t i o n 59 and S u b t r a c t i o n ) . E x a m i n a t i o n o f t h e r e s p o n s e d i s t r i b u t i o n s and t h e r e s p o n s e / t o t a l p o i n t - b i s e r i a l c o e f f i c i e n t s f o r e a c h o f t h e f o u r c o g n i t i v e m e a s u r e s ( a l l bu t M u l t i p l i c a t i o n and S u b t r a c t i o n ) r e v e a l e d t h a t , w i t h t h e e x c e p t i o n o f s e v e n i t e m s f r o m t h e A d v a n c e d V o c a b u l a r y T e s t , no i t e m was a n s w e r e d c o r r e c t l y by a l l 33 s u b j e c t s . The l a s t - n a m e d measu re a l s o d i s p l a y e d t h e h i g h e s t f r e q u e n c y o f n e g a t i v e c o r r e l a t i o n s be tween t h e c o r r e c t r e s p o n s e c h o i c e and t h e t o t a l s c o r e ( 5 , o r 1 3 . 8 % , a s c o m p a r e d t o 1 0 . 0 % , 3 .3% and 0 . 0 % , f o r t h e m e a s u r e s o f P a p e r F o l d i n g , D i a g r a m m i n g R e l a t i o n s and N u m e r i c C o n c e p t L e a r n i n g , r e s p e c t i v e l y ) . L i k e t h e s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e r e p o r t e d a b o v e , t h e s e r e s u l t s s u g g e s t t h a t t h e A d v a n c e d V o c a b u l a r y T e s t may have been i n a p p r o p r i a t e f o r t h e B r i t i s h C o l u m b i a s a m p l e . The i n t e r n a l c o n s i s t e n c y f o r e a c h o f t h e m e a s u r e s o f a t t i t u d e and m o t i v a t i o n was 0 .78 o r h i g h e r , w i t h one e x c e p t i o n -S p e c i f i c M o t i v a t i o n ( 0 . 7 2 ) . The mean s c o r e s f o r A t t i t u d e T o w a r d S t a t i s t i c s and A t t i t u d e Towa rd R e s e a r c h ( 8 7 . 7 6 and 9 5 . 7 6 r e s p e c t i v e l y ) were n o t s i g n i f i c a n t l y h i g h e r t h a n t h o s e o b t a i n e d d u r i n g t h e i n s t r u m e n t d e v e l o p m e n t p r o c e s s ( 7 4 . 0 2 and 8 4 . 6 9 , r e s p e c t i v e l y ) . E x a m i n a t i o n o f t h e i t e m - t o t a l c o r r e l a t i o n c o e f f i c i e n t s r e v e a l e d t h a t no i t e m on e i t h e r m e a s u r e was n e g a t i v e l y c o r r e l a t e d w i t h t h e t o t a l s c o r e . Mean i t e m / t o t a l c o r r e l a t i o n c o e f f i c i e n t s were 0 . 5 5 a n d 0 .52 f o r t h e m e a s u r e s o f a t t i t u d e t o w a r d s t a t i s t i c s a n d r e s e a r c h , r e s p e c t i v e l y , w i t h t h e r e s p e c t i v e r a n g e s b e i n g 0 .32 t o 0 . 7 8 a n d 0 . 2 9 t o 0 . 7 4 . The mean s c o r e s o f t h e m e a s u r e s o f S e l f - C o n c e p t and 60 A c h i e v e m e n t M o t i v a t i o n i n d i c a t e t h a t t h e members o f t h e B r i t i s h C o l u m b i a s a m p l e , on t h e a v e r a g e , p e r c e i v e d t h e m s e l v e s t o be f a i r l y h i g h l y s k i l l e d (mean on S e l f - C o n c e p t , 6 7 . 4 2 o u t o f a maximum s c o r e o f 9 8 ) , and r e l a t i v e l y a c h i e v e m e n t - o r i e n t e d (mean 9 3 . 7 0 o u t o f a p o s s i b l e maximum s c o r e o f 1 2 6 ) . On t h e a v e r a g e , t h e members o f t h e s amp l e saw t h e c o u r s e a s b e i n g o f h i g h u t i l i t y (mean s c o r e on t h e measu re o f P e r c e i v e d U t i l i t y o f 8 .58 o u t a p o s s i b l e 1 0 ) . Howeve r , t h e i r s c o r e s on t h e measu re o f S p e c i f i c M o t i v a t i o n w e r e , on t h e a v e r a g e , much l o w e r ( 5 . 3 o u t o f a p o s s i b l e 1 0 ) . None o f t h e i t e m s on t h e S e l f - C o n c e p t m e a s u r e and on t h e t h r e e m o t i v a t i o n a l m e a s u r e s c o r r e l a t e d n e g a t i v e l y w i t h t h e i r r e s p e c t i v e t o t a l s c o r e . The mean i t e m - t o t a l c o r r e l a t i o n s were 0 . 7 5 and 0 .43 f o r t h e m e a s u r e s o f S e l f - C o n c e p t and A c h i e v e m e n t M o t i v e r e s p e c t i v e l y , w i t h r a n g e s o f 0 .60 t o 0 . 8 9 and 0 . 1 9 t o 0 .68 r e s p e c t i v e l y . The c o r r e l a t i o n s be tween t h e two i t e m s on e a c h o f t h e m e a s u r e s o f S p e c i f i c M o t i v a t i o n and P e r c e i v e d U t i l i t y were 0 .64 and 0 . 5 6 , r e s p e c t i v e l y . The A l b e r t a S a m p l e . The m e a n s , s t a n d a r d d e v i a t i o n s , s t a n d a r d e r r o r s and Hoy t i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t s c a l c u l a t e d f r o m t h e A l b e r t a d a t a a r e p r e s e n t e d i n T a b l e 7. A g a i n , a d d i t i o n a l r e s u l t s f r o m t h e i t e m a n a l y s e s a r e r e p o r t e d i n t h e t e x t . The i n t e r n a l c o n s i s t e n c y ( 0 . 7 3 ) o f t h e f i n a l e x a m i n a t i o n was w i t h i n a c c e p t a b l e l i m i t s . The mean s c o r e o f 3 4 . 8 ( 6 3 . 2 % ) i n d i c a t e s t h a t , on t h e a v e r a g e , t h e t e s t was f o u n d t o be o f 61 T a b l e 7 S c a l e S t a t i s t i c s ( A l b e r t a Sample (n = 32 ) ) Mean S t a n d a r d S t a n d a r d Hoy t D e v i a t i o n E r r o r C o e f f . D e p e n d e n t V a r i a b l e : E x a m i n a t i o n S c o r e 3 4 . 7 8 6 .98 3 .60 0 .73 I n d e p e n d e n t V a r i a b l e s : 1. E x p e r i e n c e 2 .00 1.14 - -* 2 . C o g n i t i v e M e a s u r e s : A d v a n c e d V o c a b u l a r y T e s t 2 3 . 9 7 5.61 2 .15 0 . 8 5 P a p e r F o l d i n g T e s t 10 .72 2 .82 1.61 0 . 6 6 M u l t i p l i c a t i o n and S u b t r a c t i o n 6 8 . 3 8 19 .17 3 .49 0 . 9 7 D i a g r a m m i n g R e l a t i o n s 1 7 . 1 9 6.31 2 .24 0 .87 C o n c e p t L e a r n i n g T a s k 7.31 2 .88 1 .42 0 .74 3 . A t t i t u d i n a l M e a s u r e s : A t t i t u d e Towa rd S t a t i s t i c s 7 7 . 0 9 2 3 . 4 5 5.32 0 . 9 5 A t t i t u d e Towa rd R e s e a r c h 8 5 . 9 7 2 3 . 9 7 5 .36 0 . 9 5 A c a d e m i c S e l f - C o n c e p t 6 7 . 6 6 8 .24 3 .02 0 .86 4 . M o t i v a t i o n a l M e a s u r e s : A c h i e v e m e n t M o t i v a t i o n 9 3 . 6 6 10 .64 3 .63 0 .88 P e r c e i v e d U t i l i t y 7 .72 1 .67 0 .60 0 . 8 7 S p e c i f i c M o t i v a t i o n 5 .00 2 .55 1 .37 0.71 * T h i s measu re c o n t a i n e d a s i n g l e i t e m . medium d i f f i c u l t y . The i t e m - t o t a l c o r r e l a t i o n s r a n g e d f r o m a v a l u e o f - 0 . 2 5 t o one o f 0 . 6 1 , w i t h a mean v a l u e o f 0 . 2 2 . F i v e c o e f f i c i e n t s were o b s e r v e d t o be n e g a t i v e , w i t h a mean v a l u e o f - 0 . 0 9 . The a v e r a g e number o f p o s t - s e c o n d a r y m a t h e m a t i c s o r s t a t i s t i c s c o u r s e s c o m p l e t e d was 2 . 0 . T h r e e o f t h e f i v e c o g n i t i v e m e a s u r e s were h i g h l y i n t e r n a l l y c o n s i s t e n t . A d v a n c e d V o c a b u l a r y , M u l t i p l i c a t i o n and S u b t r a c t i o n and D i a g r a m m i n g R e l a t i o n s had a s s o c i a t e d Hoy t c o e f f i c i e n t s o f 62 0 . 8 5 , 0 .97 and 0 . 8 7 r e s p e c t i v e l y . N u m e r i c C o n c e p t L e a r n i n g was o b s e r v e d t o show an i n t e r n a l c o e f f i c i e n t o f 0 . 7 4 . As was d i s c u s s e d a b o v e , t h e c o e f f i c i e n t o f i n t e r n a l c o n s i s t e n c y f o r t he s p e e d e d t e s t , M u l t i p l i c a t i o n and S u b t r a c t i o n , may have y i e l d e d an i n f l a t e d e s t i m a t e o f r e l i a b i l i t y . The a p p r o x i m a t e p a r a l l e l -f o r m c o e f f i c i e n t , b a s e d on t h e c o r r e l a t i o n be tween t h e two h a l v e s o f t h e t e s t , was 0 . 9 3 . T h i s v a l u e may be a more a c c u r a t e e s t i m a t e o f r e l i a b i l i t y o f t h e t e s t . The i n t e r n a l c o n s i s t e n c y f o r t h e f i f t h c o g n i t i v e m e a s u r e , P a p e r F o l d i n g , was somewhat l o w e r t h a n f o r t h e o t h e r f o u r -0 . 6 6 . T h i s may be due t o t h e r e l a t i v e l y low v a r i a b i l i t y - t h e s t a n d a r d d e v i a t i o n was 2 . 8 2 . The v a l u e o b t a i n e d i s l o w e r t h a n t h a t r e p o r t e d by E k s t r o m e t a l . E x a m i n a t i o n o f t h e r e s p o n s e d i s t r i b u t i o n s and t h e r e s p o n s e / t o t a l p o i n t - b i s e r i a l c o e f f i c i e n t s r e v e a l e d t h a t , e x c e p t f o r f i v e i t e m s on t h e A d v a n c e d V o c a b u l a r y t e s t and a s i n g l e i t e m on t h e measu re o f Pape r F o l d i n g , no i t e m was a n s w e r e d c o r r e c t l y by a l l 32 s u b j e c t s . O n l y one i t e m (on P a p e r F o l d i n g ) c o r r e l a t e d n e g a t i v e l y w i t h t h e t o t a l s c o r e . The i n t e r n a l c o n s i s t e n c y o f e a c h measu re o f a t t i t u d e and m o t i v a t i o n was 0 .86 o r h i g h e r , e x c e p t f o r S p e c i f i c M o t i v a t i o n ( i n t e r n a l c o n s i s t e n c y o f 0 . 7 1 ) . The mean s c o r e s f o r t h e m e a s u r e s o f a t t i t u d e t o w a r d s t a t i s t i c s and r e s e a r c h were no t s i g n i f i c a n t l y d i f f e r e n t f r o m t h o s e o b t a i n e d d u r i n g t h e i n s t r u m e n t d e v e l o p m e n t p r o c e d u r e . No i t e m on e i t h e r s c a l e was n e g a t i v e l y c o r r e l a t e d w i t h t h e t o t a l s c o r e f o r t h a t s c a l e . The mean i t e m - t o t a l c o r r e l a t i o n was 0 . 6 7 f o r e a c h m e a s u r e , w i t h 63 r e s p e c t i v e r a n g e s o f 0.11 t o 0 . 8 6 and 0 .47 t o 0 . 8 4 . The o b s e r v e d means on t h e m e a s u r e s o f S e l f - C o n c e p t and A c h i e v e m e n t M o t i v a t i o n i n d i c a t e t h a t , on t h e a v e r a g e , t h e A l b e r t a samp le f e l t t h a t t h e y were r e l a t i v e l y a b l e (mean on S e l f - C o n c e p t 6 7 . 7 ou t o f a p o s s i b l e s c o r e o f 98) and were a c h i e v e m e n t - o r i e n t e d (mean 9 3 . 7 ou t o f a p o s s i b l e t o t a l s c o r e o f 1 2 6 ) . The s u b j e c t s f e l t t h a t t he c o u r s e was o f f a i r l y h i g h u t i l i t y (mean on P e r c e i v e d U t i l i t y o f 7 .7 ou t o f a p o s s i b l e 1 0 ) . T h e i r s p e c i f i c m o t i v a t i o n was , h o w e v e r , r a t h e r low (mean o f 5.0 o u t o f a p o s s i b l e 1 0 ) . No i t e m on e i t h e r S e l f - C o n c e p t o r A c h i e v e m e n t M o t i v a t i o n c o r r e l a t e d n e g a t i v e l y w i t h t h e i r r e s p e c t i v e t o t a l s c o r e . The mean i t e m - t o t a l c o r r e l a t i o n s f o r t h e two m e a s u r e s were 0 .53 a n d 0 . 5 2 , w i t h c o r r e s p o n d i n g r a n g e s o f 0 . 0 8 t o 0 .74 and 0 . 2 9 t o 0 . 6 7 r e s p e c t i v e l y . The c o r r e l a t i o n s be tween t h e two i t e m s on t h e m e a s u r e s o f P e r c e i v e d U t i l i t y and S p e c i f i c M o t i v a t i o n were 0 . 7 7 and 0 . 5 6 r e s p e c t i v e l y . E q u i v a l e n c e o f t h e S a m p l e s In o r d e r t o a s s e s s t h e i r e q u i v a l e n c e , t h e two s a m p l e s were c o m p a r e d i n two ways , as d e s c r i b e d i n C h a p t e r I I I . B o t h were s t a t i s t i c a l , a n d i n v o l v e d t h e c a l c u l a t i o n o f t h e H o t e l l i n g ' s T - s q u a r e and t h e B a r t l e t t - B o x s t a t i s t i c s . H o t e l l i n g ' s T - s q u a r e t e s t was p e r f o r m e d t o e x a m i n e c o m p a r a b i l i t y o f t h e B r i t i s h C o l u m b i a a n d A l b e r t a s a m p l e s (n=33 and 32 r e s p e c t i v e l y ) on t h e 12 i n d e p e n d e n t v a r i a b l e s and t h e d e p e n d e n t v a r i a b l e . The v a l u e o f T - s q u a r e ( 3 . 0 0 8 , d f = 1 2 , 5 2 , 64 p = 0 . 0 0 2 9 ) was s t a t i s t i c a l l y s i g n i f i c a n t . The B a r t l e t t - B o x t e s t was p e r f o r m e d t o t e s t t h e c o m p a r a b i l i t y o f t h e 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 . The r e s u l t i n g v a l u e was s t a t i s t i c a l l y s i g n i f i c a n t ( F = 1 . 3 3 , d f = 7 8 , 1 2 5 0 7 . 8 , p = . 0 2 6 ) . I t was c o n c l u d e d , t h e r e f o r e , t h a t t h e two s a m p l e s were no t c o m p a r a b l e and r e p r e s e n t e d two d i f f e r e n t p o p u l a t i o n s . B e c a u s e t h e v a l u e o f T - s q u a r e had a c h i e v e d s t a t i s t i c a l s i g n i f i c a n c e , , u n i v a r i a t e t e s t s were p e r f o r m e d on e a c h o f t h e m e a s u r e s o f t h e i n d e p e n d e n t v a r i a b l e s . T h i s p r o c e d u r e f o l l o w e d t h e r e c o m m e n d a t i o n s o f Timm (1975) and Hummel l and S l i g o ( 1 9 7 1 ) . Of t h e t h i r t e e n mean v a l u e s , f i v e were s i g n i f i c a n t l y d i f f e r e n t when u n i v a r i a t e t e s t s were p e r f o r m e d . B r i t i s h C o l u m b i a s u b j e c t s s c o r e d s i g n i f i c a n t l y h i g h e r on A d v a n c e d V o c a b u l a r y ( t = 2 . 2 l , d f = 6 3 , p = 0 . 0 3 1 ) and D i a g r a m m i n g R e l a t i o n s ( t = 2 . 3 4 , d f = 6 3 , p = 0 . 0 2 2 ) . T h e A l b e r t a s a m p l e s c o r e d , on t h e a v e r a g e , h i g h e r on t h e C o n c e p t L e a r n i n g T a s k ( t = 2 . 4 9 , d f = 6 3 , p = 0 . 0 l 6 ) . F i n a l l y , t h e B r i t i s h C o l u m b i a s a m p l e , on t h e a v e r a g e , f e l t more p o s i t i v e l y a b o u t s t a t i s t i c s and s t a t e d t h a t t h e c l a s s w o u l d be o f h i g h e r u t i l i t y t h a n d i d t h e A l b e r t a s a m p l e , a s i n f e r r e d f r o m t h e s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s f o r A t t i t u d e Towa rd S t a t i s t i c s ( t = 2 . 0 2 , d f = 6 3 , p = 0 . 0 4 8 ) a n d P e r c e i v e d U t i l i t y ( t = 2 . 1 5 , d f = 6 3 , p = 0 . 0 3 5 ) . The s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s were no t s u r p r i s i n g , g i v e n t h e l o g i c a l d i f f e r e n c e s be tween t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s . B e c a u s e o f t h e low s u b j e c t - t o -v a r i a b l e r a t i o s , s t a t i s t i c a l c o m p a r i s o n s among t h e t h r e e B r i t i s h C o l u m b i a c l a s s e s were n o t p o s s i b l e . H o w e v e r , t h e s a m p l e s 65 c o l l e c t e d f r o m w i t h i n B r i t i s h C o l u m b i a a p p e a r e d l o g i c a l l y c o m p a r a b l e . S p e c i f i c a l l y , e a c h o f t h e t h r e e c l a s s e s was o f t h e same d u r a t i o n , and was s i m i l a r t o t h e o t h e r s i n t e r m s o f c o n t e n t . The o r d e r o f p r e s e n t a t i o n o f m a t e r i a l and t h e c o n t e n t s o f l e s s o n s i n a l l t h r e e c o u r s e s were b a s e d on t h e t e x t by G l a s s and S t a n l e y ( 1 9 7 0 ) . On t h e o t h e r h a n d , t h e U n i v e r s i t y o f A l b e r t a c l a s s was o f s i x weeks d u r a t i o n and c o m b i n e d s t a t i s t i c s and r e s e a r c h . Some c o m p a r a b i l i t y i s f o u n d i n t h e f a c t t h a t t h e s t a t i s t i c a l l e s s o n s o f t h i s c o u r s e w e r e , t o o , b a s e d on G l a s s and S t a n l e y . • • A p l a u s i b l e r e a s o n f o r t h e o b s e r v e d s i g n i f i c a n t d i f f e r e n c e s i s t h e f a c t t h a t t h e t i m e s o f a d m i n i s t r a t i o n o f t h e p r e - t e s t s d i f f e r e d f o r t h e two s a m p l e s . A l t h o u g h e a c h o f t h e t h r e e B r i t i s h C o l u m b i a c l a s s e s r e c e i v e d p r e - t e s t s on t h e f i r s t day o f c l a s s , t h e A l b e r t a c l a s s d i d n o t . B e c a u s e o f t h e two-week d e l a y i n t h e r e c e i p t o f t h e p r e - t e s t s by t h e i n s t r u c t o r o f t h e c o u r s e ( s e e p. 4 7 , C h a p t e r I I I ) , t h e s e p r e - t e s t s were a d m i n i s t e r e d t o t h e A l b e r t a s u b j e c t s a t a p o i n t w h i c h was a p p r o x i m a t e l y two-t h i r d s o f t h e way t h r o u g h t h e c o u r s e . The r e s u l t s o f t h e p r e t e s t s , c o n s e q u e n t l y , m i g h t have been c o n t a m i n a t e d by p r i o r t r a i n i n g i n s t a t i s t i c s . L o g i c a l l y , t h e r e f o r e , t h e two s a m p l e s were n o t e q u i v a l e n t , j u s t a s t h e y were n o t s t a t i s t i c a l l y e q u i v a l e n t . The u n i v a r i a t e s i g n i f i c a n t d i f f e r e n c e i n C o n c e p t L e a r n i n g , r e p o r t e d a b o v e , may have been c a u s e d , i n p a r t , by t h e d i f f e r e n c e i n t i m e o f a d m i n i s t r a t i o n . T h i s t a s k r e q u i r e d t h e s u b j e c t s t o u s e and a p p l y t h e i d e a o f " s u m m a t i o n " , w i t h an a l t e r e d s y s t e m o f 66 s y m b o l s and t h e A l b e r t a s amp le w o u l d have been e x p o s e d t o t h i s c o n c e p t b e f o r e t h e t e s t i n g s e s s i o n . T h u s , C o n c e p t L e a r n i n g may have been an a c h i e v e m e n t t e s t , r a t h e r t h a n a c o n c e p t a t t a i n m e n t t e s t , f o r t h e A l b e r t a s u b j e c t s . F i n a l l y , t h e more p o s i t i v e a t t i t u d e s t o w a r d s t a t i s t i c s and t h e g r e a t e r f e e l i n g t h a t t h e c l a s s wou ld be u s e f u l , o b s e r v e d i n t h e B r i t i s h C o l u m b i a s a m p l e , may a l s o be t e n t a t i v e l y a t t r i b u t e d t o t h e f a c t t h a t t h e l a t t e r g r o u p had had v i r t u a l l y no e x p e r i e n c e w i t h s t a t i s t i c s a t t h e t i m e o f r e s p o n d i n g , u n l i k e t h e A l b e r t a s a m p l e . R e c a s t i n g o f t h e R e s e a r c h Q u e s t i o n s The p r e l i m i n a r y r e s u l t s r a i s e d a d i f f i c u l t i s s u e . S p e c i f i c a l l y , t h e n o n - e q u i v a l e n c e o f t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s meant t h a t , i n b o t h c a s e s , t h e s amp l e s i z e t o v a r i a b l e r a t i o s o f 3 3 : 1 2 and 3 2 : 1 2 were t o o s m a l l . The s m a l l n ' s w o u l d n o t a l l o w t h e c a l c u l a t i o n o f s t a b l e e s t i m a t e s o f e i t h e r t h e l a t e n t s t r u c t u r e o r t h e p a t h c o e f f i c i e n t s n e c e s s a r y t o answer t h e r e s e a r c h q u e s t i o n s p r e s e n t e d i n C h a p t e r I. T h u s , i t became n e c e s s a r y t o r e c a s t t h e r e s e a r c h q u e s t i o n s . The r e p h r a s e d r e s e a r c h q u e s t i o n s had t o f u l f i l l two c o n d i t i o n s . F i r s t , t h e y c o u l d n o t i m p l y t h e use o f an LVM p r o c e d u r e . S e c o n d , t h e y had t o r e m a i n w i t h i n t h e e x p l o r a t o r y s p i r i t o f t h e o r i g i n a l q u e s t i o n s , i n s o f a r a s p o s s i b l e a l l o w i n g e x p l o r a t i o n o f t h e d a t a w i t h o u t r e q u i r i n g t h e a p p l i c a t i o n o f i n a p p r o p r i a t e a n a l y t i c t e c h n i q u e s . The r e c a s t r e s e a r c h q u e s t i o n s w e r e : a) What i s t h e r e l a t i o n s h i p be tween a c h i e v e m e n t i n 67 e l e m e n t a r y s t a t i s t i c s a n d e a c h o f t h e t w e l v e m a n i f e s t v a r i a b l e s ? b) What a r e t h e c h a r a c t e r i s t i c s o f t h e c l u s t e r s r e v e a l e d by s u b j e c t i v e e x a m i n a t i o n o f t h e i n t e r c o r r e l a t i o n s among t h e i n d e p e n d e n t a n d d e p e n d e n t v a r i a b l e s ? c ) How much of t h e v a r i a n c e i n a c h i e v e m e n t i n i n t r o d u c t o r y s t a t i s t i c s c a n be a c c o u n t e d f o r by t h e t w e l v e m a n i f e s t v a r i a b l e s , t a k e n b o t h a s a g r o u p and c u m u l a t i v e l y ? The r e p h r a s e d r e s e a r c h q u e s t i o n s f u l l f i l l t h e c o n d i t i o n s o u t l i n e d a b o v e . F i r s t , o n l y m a n i f e s t v a r i a b l e s a r e c o n s i d e r e d i n t h e q u e s t i o n s . In a d d i t i o n , t h e s e t o f t h r e e q u e s t i o n s a l l o w s some c o m p a r i s o n o f t h e r e s u l t s w i t h t h o s e r e p o r t e d i n t h e l i t e r a t u r e a n d s u m m a r i z e d i n T a b l e 1 ( s ee C h a p t e r I ) . F i n a l l y , by d e m a n d i n g s u b j e c t i v e a n a l y s i s , t h e r e p h r a s e d q u e s t i o n s a l l o w some o f t h e e x p l o r a t o r y n a t u r e o f t h e s t u d y t o be r e t a i n e d . B e c a u s e o f t h e e x p l o r a t o r y n a t u r e o f t h e s t u d y , i t was d e c i d e d t o s e l e c t t h e 0 . 1 0 l e v e l o f s t a t i s t i c a l s i g n i f i c a n c e a s t h e c r i t e r i o n , r a t h e r t h a n t h e c o n v e n t i o n a l 0 . 0 5 l e v e l . T h i s r e l a x e d c r i t e r i o n w o u l d n o t o n l y a l l o w more s p e c u l a t i v e a n a l y s i s , b u t w o u l d t a k e i n t o c o n s i d e r a t i o n t h e s m a l l s amp l e s i z e s . T h a t i s , s m a l l s a m p l e s i z e s a r e s a i d ( e . g . , by G l a s s a n d S t a n l e y , 1970) t o make d e t e c t i o n o f e f f e c t s o f s m a l l m a g n i t u d e l e s s l i k e l y when t h e 0 .05 l e v e l i s r e t a i n e d . In i n v e s t i g a t i n g t h e s e t h r e e q u e s t i o n s , t h e B r i t i s h C o l u m b i a s a m p l e and t h e A l b e r t a s amp l e were a n a l y z e d s e p a r a t e l y , 68 t h e r e b y p r o v i d i n g , i n p a r t , a r e p l i c a t i o n . M e t h o d o l o g y o f t h e F i n a l A n a l y s i s I n c l u d e d i n t h i s s e c t i o n i s a d e s c r i p t i o n o f t h e p r o c e d u r e s u s e d t o i n v e s t i g a t e t h e r e c a s t r e s e a r c h q u e s t i o n s . The r e s u l t s a r e t h e n r e p o r t e d i n C h a p t e r V . C o r r e l a t i o n a l A n a l y s e s The B r i t i s h C o l u m b i a S a m p l e . The a n a l y s i s o f t h e s a m p l e o f d a t a f r o m B r i t i s h C o l u m b i a was c o m p l e t e d i n two s t e p s : t h e c a l c u l a t i o n and a n a l y s i s o f t h e m a t r i x o f i n t e r c o r r e l a t i o n s among t h e v a r i a b l e s , f o l l o w e d by a s t e p w i s e r e g r e s s i o n p r o c e d u r e . —- - - -The z e r o - o r d e r c o r r e l a t i o n s be tween e a c h p o s s i b l e p a i r o f t h e 12 i n d e p e n d e n t v a r i a b l e s , a n d be tween e a c h i n d e p e n d e n t v a r i a b l e and S t a t i s t i c s A c h i e v e m e n t , were c a l c u l a t e d . E a c h c o r r e l a t i o n c o e f f i c i e n t was e x a m i n e d , and w h e t h e r i t was s t a t i s t i c a l l y s i g n i f i c a n t was d e t e r m i n e d by c o m p a r i n g i t t o t h e t a b l e d v a l u e f o r t h e 0 .10 l e v e l , i . e . | 0 . 2 9 2 | ( G l a s s and S t a n l e y , 1970 , T a b l e I, p . 5 3 6 ) . The p a t t e r n o f s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s was t h e n e x a m i n e d a n d d e s c r i b e d s u b j e c t i v e l y . The s u b j e c t i v e p r o c e s s i n c l u d e d , f i r s t , an---examination and d e s c r i p t i o n o f t h e s i g n i f i c a n t r e l a t i o n s h i p s be tween t h e i n d e p e n d e n t v a r i a b l e s and s t a t i s t i c s a c h i e v e m e n t . T h i s was f o l l o w e d by an a t t e m p t t o " c l u s t e r " t h e s t a t i s t i c a l l y 69 s i g n i f i c a n t i n t e r - i n d e p e n d e n t v a r i a b l e c o e f f i c i e n t s i n a m e a n i n g f u l way. E a c h c l u s t e r w h i c h was i s o l a t e d f r o m t h e m a t r i x o f i n t e r c o r r e l a t i o n s was s u b j e c t i v e l y d e s c r i b e d , and an a t t e m p t was made t o r e l a t e i t t o a c h i e v e m e n t i n s t a t i s t i c s . The d a t a were t h e n s u b j e c t e d t o a f r e e f o r w a r d s t e p w i s e r e g r e s s i o n , u s i n g t h e s u b p r o g r a m REGRESSION o f t h e S t a t i s t i c a l P a c k a g e f o r t h e S o c i a l S c i e n c e s . P a r t i a l F - t e s t s were e x a m i n e d t o d e t e r m i n e t h e l e v e l o f s i g n i f i c a n c e o f any g i v e n i n d e p e n d e n t v a r i a b l e ' s c o n t r i b u t i o n . B e c a u s e o f t h e e x p l o r a t o r y n a t u r e o f t h e a n a l y s i s , h o w e v e r , n o n s i g n i f i c a n t c o n t r i b u t i o n s t o t h e v a r i a n c e i n t h e d e p e n d e n t v a r i a b l e were a l s o e x a m i n e d . The A l b e r t a S a m p l e . The a n a l y s i s o f t h e d a t a c o l l e c t e d f r o m t h e A l b e r t a s a m p l e was t h r e e - p a r t . F i r s t , t h e z e r o - o r d e r c o r r e l a t i o n m a t r i x was c a l c u l a t e d and e x a m i n e d a s d e s c r i b e d f o r t h e d a t a f r o m t h e B r i t i s h C o l u m b i a s a m p l e , u s i n g a c o r r e l a t i o n c o e f f i c i e n t o f | 0 . 2 9 6 | a s t h e c r i t e r i o n . T h i s i s t h e c r i t i c a l v a l u e f o r t h e 0 . 1 0 l e v e l o f s i g n i f i c a n c e f o r a s a m p l e o f 32 s u b j e c t s ( G l a s s and S t a n l e y , 1970 , T a b l e I, p . 5 3 6 ) . Two s t e p w i s e r e g r e s s i o n p r o c e d u r e s were c o m p u t e d a n d t h e r e s u l t s r e p o r t e d , a g a i n u s i n g t h e SPSS s u b p r o g r a m REGRESS ION. In t h e f i r s t p r o c e d u r e , t h e o r d e r o f e n t r y o f t h e i n d e p e n d e n t v a r i a b l e s was d i c t a t e d by t h e ou t come o f t h e f r e e s t e p w i s e r e g r e s s i o n p r o c e d u r e u s e d t o a n a l y z e t h e s amp l e o f d a t a f r o m B r i t i s h C o l u m b i a , as d e s c r i b e d a b o v e . The s e c o n d r e g r e s s i o n was a f r e e f o r w a r d s t e p w i s e p r o c e d u r e , i n w h i c h any i n d e p e n d e n t v a r i a b l e was a l l o w e d t o e n t e r a t w h i c h e v e r p o i n t t h e c h a r a c t e r i s t i c s o f t h e d a t a s e t m i g h t d i c t a t e . T h i r d , t h e 70 r e s u l t s of the a n a l y s e s of the A l b e r t a sample of data and the B r i t i s h Columbia sample were compared. 71 C h a p t e r V .  R e s u l t s o f t h e F i n a l A n a l y s i s In t h i s c h a p t e r , t h e f i n d i n g s f r om t h e e x a m i n a t i o n o f t h e z e r o - o r d e r c o r r e l a t i o n m a t r i x and the p a r s i m o n i o u s f o r w a r d r e g r e s s i o n p r o c e d u r e u s e d t o a n a l y z e t h e B r i t i s h C o l u m b i a d a t a a r e p r e s e n t e d f i r s t . S e c o n d , t h e r e s u l t s o f t h e c o r r e l a t i o n a l a n a l y s e s o f t h e A l b e r t a d a t a a r e r e p o r t e d , and t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s a r e c o m p a r e d b r i e f l y . F i n a l l y , t h e r e s u l t s o f t h e e x p l o r a t o r y r e g r e s s i o n p r o c e d u r e s a r e p r e s e n t e d f o r b o t h s a m p l e s . C o r r e l a t i o n a l A n a l y s e s The B r i t i s h C o l u m b i a Sample I n t e r c o r r e l a t i o n s . The l o w e r t r i a n g u l a r m a t r i x o f i n t e r c o r r e l a t i o n s among t h e m e a s u r e s o f t h e 12 i n d e p e n d e n t v a r i a b l e s and o f t h e d e p e n d e n t v a r i a b l e a r e p r e s e n t e d i n T a b l e 8 * . Of t h e 66 i n t e r c o r r e l a t i o n s among t h e i n d e p e n d e n t v a r i a b l e s , 23 were s t a t i s t i c a l l y s i g n i f i c a n t a t o r b e y o n d t h e 0 . 1 0 l e v e l . Of t h e 12 c o r r e l a t i o n s o f s t a t i s t i c s a c h i e v e m e n t w i t h t h e i n d e p e n d e n t v a r i a b l e s , f o u r were s t a t i s t i c a l l y s i g n i f i c a n t . A l l 27 s i g n i f i c a n t c o r r e l a t i o n s were p o s i t i v e . *Means and s t a n d a r d d e v i a t i o n s a r e p r e s e n t e d i n T a b l e 6 . 72 T a b l e 8 I n t e r - c o r r e l a t i o n s Among t h e V a r i a b l e s ( B r i t i s h C o l u m b i a Sample )-M e a s u r e Number* 1 2 3 4 5 6 7 8 9 10 1 1 1 2 M e a s u r e : * * * ~ E x p e r i e n c e : 1 . -C o g n i t i v e M e a s u r e s : 2. 0.41 0 . 6 3 * * 3. 0 . 37 0 . 18 0 .82 4. 0 . 02 0 . 01 0 .24 0. 89 5. 0 . 46 0 . 15 0 . 7 3 0. 35 0 . 87 6 . 0 . 64 0. 29 0 . 6 6 0. 24 0 . 59 0 .78 A f f e c t i v e M e a s u r e s : 7. 0 . 3 2 0 . 0 3 0 . 4 7 0 . 1 3 0 . 4 5 0 . 1 8 0 . 9 1 8. 0 . 1 5 - 0 . 0 8 0 . 0 4 - 0 . 1 0 0 . 0 5 - 0 . 1 9 0 . 6 6 0 . 8 9 9. 0 .32 0 . 1 7 0 . 0 5 0 .12 0 . 0 3 0 . 2 4 - 0 . 0 1 0 . 1 3 0 . 9 5 M o t i v a t i o n a l M e a s u r e s : 1 0 . - 0 . 0 3 0.30-0.28-0.12-0.09-0.14 0 . 0 8 0 .33 0 . 1 3 0 .84 1 1 . 0 . 3 3 0.21 0 . 1 4 0 . 1 7 0 . 1 4 0 . 1 0 0 . 3 2 0 . 5 3 0 . 3 7 0 . 2 5 0 . 7 8 12. 0 . 2 6 0.21 0 . 0 6 0 . 1 5 0 . 0 3 0 .12 0 .33 0 .38 0 .40 0 . 1 5 0 .40 0 .72 S t a t i s t i c s A c h i e v e m e n t : 13 . 0 . 5 3 0 .38 0 . 4 0 - 0 . 0 6 0 . 2 6 0 . 4 6 0 .20 0 .03 0.01 0 . 0 9 0.01 0 . 1 6 * 1 , = E x p e r i e n c e ; 2 . = A d v a n c e d V o c a b u l a r y T e s t ; 3 .=Pape r F o l d i n g T e s t ; 4 . = M u l t i p l i c a t i o n and S u b t r a c t i o n ; 5 .=D i ag r amming R e l a t i o n s ; 6 . = C o n c e p t L e a r n i n g ; 7. A t t i t u d e T o w a r d S t a t i s t i c s ; 8 . = A t t i t u d e Toward R e s e a r c h ; 9 . = A c a d e m i c S e l f - C o n c e p t ; 1 0 . = A c h i e v e m e n t M o t i v a t i o n ; 1 1 . = P e r c e i v e d U t i l i t y ; 1 2 . = S p e c i f i c M o t i v a t i o n ; 1 3 , = S t a t i s t i c s A c h i e v e m e n t . * * R e l i a b i l i t y c o e f f i c i e n t s e n t e r e d on t h e ma in d i a g o n a l . * * * U n d e r l i n e d v a l u e s were s t a t i s t i c a l l y s i g n i f i c a n t ( p < 0 . l 0 ) . T h r e e o f t h e f o u r i n d e p e n d e n t v a r i a b l e s w h i c h a c h i e v e d s i g n i f i c a n t c o r r e l a t i o n s w i t h S t a t i s t i c s A c h i e v e m e n t were c o g n i t i v e - A d v a n c e d V o c a b u l a r y ( r = 0 . 3 8 ) , P a p e r F o l d i n g ( r = 0 . 4 0 ) a n d C o n c e p t L e a r n i n g ( r = 0 . 4 6 ) . The f o u r t h s i g n i f i c a n t c o r r e l a t i o n was o b s e r v e d be tween A c h i e v e m e n t a n d P a s t E x p e r i e n c e ( r = 0 . 5 3 ) , a v a r i a b l e w h i c h c a n be s a i d t o be c l o s e l y r e l a t e d t o 73 c o g n i t i v e a b i l i t i e s . The a b s e n c e o f a r e l a t i o n s h i p be tween A c h i e v e m e n t and a t t i t u d i n a l o r m o t i v a t i o n a l v a r i a b l e s i s no t a u s u a l f i n d i n g i n t h e l i t e r a t u r e . A c o r r e l a t i o n be tween A t t i t u d e Towa rd S t a t i s t i c s and a c h i e v e m e n t has been r e p o r t e d s e v e r a l t i m e s . L a c k o f know ledge o f t h e s u b j e c t m a t t e r i n t h e B r i t i s h C o l u m b i a s a m p l e may have i n f l u e n c e d t h i s r e s u l t . Of t h e s i g n i f i c a n t c o r r e l a t i o n s , a g r o u p o f 12 f o r m e d an i n t e r p r e t a b l e c l u s t e r . F i v e o f t h e 12 c o r r e l a t i o n s i n c l u d e d E x p e r i e n c e . S p e c i f i c a l l y , E x p e r i e n c e was s i g n i f i c a n t l y c o r r e l a t e d w i t h A d v a n c e d V o c a b u l a r y ( r = 0 . 4 l ) , P ape r F o l d i n g ( r = 0 . 3 7 ) , D i a g r a m m i n g R e l a t i o n s ( r = 0 . 4 6 ) , C o n c e p t L e a r n i n g (r = 0 . 6 4 ) , a n d S t a t i s t i c s A c h i e v e m e n t . ( r = 0 . 5 3 ) . T h e s e r e l a t i o n s h i p s , when c o n s i d e r e d t o g e t h e r w i t h t h e t h r e e s i g n i f i c a n t c o r r e l a t i o n s o f P a s t E x p e r i e n c e w i t h n o n c o g n i t i v e v a r i a b l e s - A t t i t u d e Towa rd S t a t i s t i c s ( r = 0 . 3 2 ) , A c a d e m i c S e l f -C o n c e p t , ( r = 0 . 3 2 ) , and P e r c e i v e d U t i l i t y ( r = 0 . 3 3 ) - may be i n t e r p r e t e d a s a " p a s t a c h i e v e m e n t " s u b c l u s t e r r e l a t i n g e x p e r i e n c e , s t r o n g a b i l i t y , p o s i t i v e a t t i t u d e , and h i g h a c h i e v e m e n t . A f u r t h e r f o u r s i g n i f i c a n t c o r r e l a t i o n s were o b s e r v e d be tween p a i r s o f c o g n i t i v e v a r i a b l e s . D i a g r a m m i n g R e l a t i o n s c o r r e l a t e d s i g n i f i c a n t l y w i t h P a p e r F o l d i n g ( r = 0 . 7 3 ) , M u l t i p l i c a t i o n and S u b t r a c t i o n ( r = 0 . 3 5 ) and C o n c e p t L e a r n i n g ( r = 0 . 5 9 ) , w h i l e t h e o b s e r v e d c o r r e l a t i o n be tween C o n c e p t L e a r n i n g and P a p e r F o l d i n g was 0 . 6 6 . T h i s " h i g h e r c o g n i t i v e a b i l i t y " s u b c l u s t e r r e f l e c t e d l o g i c a l r e a s o n i n g and s p a t i a l v i s u a l i z a t i o n a b i l i t i e s , c o m b i n e d w i t h n u m e r i c s k i l l s . 74 The l a s t t h r e e s i g n i f i c a n t c o r r e l a t i o n s o f t h e 12 were A t t i t u d e Towa rd S t a t i s t i c s and P a p e r F o l d i n g ( r = 0 . 4 7 ) , A t t i t u d e Towa rd S t a t i s t i c s and D i a g r a m m i n g R e l a t i o n s ( r = 0 . 4 5 ) , and C o n c e p t L e a r n i n g and S t a t i s t i c s A c h i e v e m e n t ( r = 0 . 4 6 ) . The two s u b c l u s t e r s w i t h t h e a d d i t i o n o f t h e s e t h r e e c o r r e l a t i o n s may be me rged t o become a " s t a t i s t i c s a c h i e v e m e n t " c l u s t e r i n w h i c h , h o w e v e r , i t a p p e a r s t h a t A t t i t u d e Towa rd S t a t i s t i c s , Number F a c i l i t y and L o g i c a l R e a s o n i n g a r e o n l y i n d i r e c t l y r e l a t e d t o S t a t i s t i c s A c h i e v e m e n t . A s e c o n d c l u s t e r o f s i x s i g n i f i c a n t c o r r e l a t i o n s i n c l u d e d m o t i v a t i o n a l and a t t i t u d i n a l v a r i a b l e s . A t t i t u d e T o w a r d R e s e a r c h was c o r r e l a t e d w i t h S p e c i f i c M o t i v a t i o n ( r = 0 . 3 8 ) , P e r c e i v e d U t i l i t y ( r = 0 . 5 3 ) , and A c a d e m i c S e l f - E s t e e m ( r = 0 . 3 7 ) . S p e c i f i c M o t i v a t i o n and P e r c e i v e d U t i l i t y were c o r r e l a t e d s i g n i f i c a n t l y w i t h e a c h o t h e r ( r = 0 . 4 0 ) . S t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s were o b s e r v e d be tween A t t i t u d e T o w a r d S t a t i s t i c s and P e r c e i v e d U t i l i t y ( r = 0 . 3 2 ) and A t t i t u d e Toward S t a t i s t i c s and S p e c i f i c M o t i v a t i o n ( r = 0 . 3 3 ) . The c l u s t e r c o m b i n e d a t t i t u d i n a l and m o t i v a t i o n a l v a r i a b l e s , bu t was n o t r e l a t e d t o a c h i e v e m e n t i n s t a t i s t i c s . I t may h a v e r e p r e s e n t e d " a c a d e m i c o r i e n t a t i o n " . A h i g h s c o r e on t h i s c l u s t e r m i g h t be t y p i c a l o f s u b j e c t s who p o s s e s s a h i g h o p i n i o n o f t h e i r own a b i l i t i e s and a p o s i t i v e o r i e n t a t i o n t o w a r d s r e s e a r c h a n d s t a t i s t i c s . The a b s e n c e o f a r e l a t i o n s h i p be tween t h i s c l u s t e r and A c h i e v e m e n t may, a g a i n , have been due t o t h e s u b j e c t s ' l a c k o f e x p e r i e n c e w i t h t h e s u b j e c t m a t t e r . 75 P a r s i m o n i o u s F o r w a r d R e g r e s s i o n . When t h e m e a s u r e s o f a l l 12 i n d e p e n d e n t v a r i a b l e s were e n t e r e d i n t h e f r e e f o r w a r d f o r w a r d r e g r e s s i o n p r o c e d u r e , o n l y t h e measu re o f P a s t E x p e r i e n c e c o n t r i b u t e d s i g n i f i c a n t l y t o t h e v a r i a n c e i n A c h i e v e m e n t ( F = 1 1 . 9 0 , d f = l , 3 1 , p = . 0 0 l 6 ) . T h i s v a r i a b l e a c c o u n t e d f o r 2 7 . 7 % o f t h e o b s e r v e d v a r i a n c e i n a c h i e v e m e n t i n s t a t i s t i c s ( R = 0 . 5 7 7 ) . The p a r t i a l c o r r e l a t i o n s o f t h e r e m a i n i n g 11 i n d e p e n d e n t v a r i a b l e s w i t h s t a t i s t i c s a c h i e v e m e n t , and t h e F - r a t i o s a s s o c i a t e d w i t h t h e m , a r e p r e s e n t e d i n T a b l e 9. As may be s een T a b l e 9 P a r t i a l C o r r e l a t i o n s and F - R a t i o s f o r t h e N o n - C o n t r i b u t o r y I n d e p e n d e n t V a r i a b l e s ( B r i t i s h C o l u m b i a Samp le ) I n d e p e n d e n t V a r i a b l e P a r t i a 1 F - R a t i o C o r r e l a t i o n A d v a n c e d V o c a b u l a r y 0 . 2 0 8 1 .36 P a p e r F o l d i n g 0 . 2 5 7 2.11 M u l t i p l i c a t i o n and S u b t r a c t i o n - 0 . 0 8 9 0 .24 D i a g r a m m i n g R e l a t i o n s 0 . 0 1 3 0.01 C o n c e p t L e a r n i n g 0 .184 1.05 A t t i t u d e T o w a r d S t a t i s t i c s 0 . 0 3 9 0 . 0 5 A t t i t u d e Toward R e s e a r c h 0 . 0 5 0 0 .08 A c a d e m i c S e l f - C o n c e p t - 0 . 1 9 5 1.18 A c h i e v e m e n t M o t i v a t i o n 0 . 1 2 0 0 .44 S p e c i f i c M o t i v a t i o n 0 . 0 2 3 0 .02 P e r c e i v e d U t i l i t y - 0 . 1 8 3 1.04 i n t h e t a b l e , t h e h i g h e s t p a r t i a l c o r r e l a t i o n was t h a t be tween P a p e r F o l d i n g and A c h i e v e m e n t ( 0 . 2 5 7 ) - a v a l u e n o t s i g n i f i c a n t a t t h e 0 . 1 0 l e v e l . When t h e c o g n i t i v e a n d n o n c o g n i t i v e 76 v a r i a b l e s were e x a m i n e d , i t became e v i d e n t t h a t a l l 11 v a r i a b l e s made e q u a l l y low c o n t r i b u t i o n s t o s t a t i s t i c s a c h i e v e m e n t . H o w e v e r , t h e p o s s i b l e e f f e c t s o f s u p p r e s s i o n c a n n o t be j u d g e d f r o m t h i s t a b l e . The A l b e r t a Samp le I n t e r c o r r e l a t i o n s . The l o w e r t r i a n g u l a r m a t r i x o f i n t e r c o r r e l a t i o n s among t h e 12 m e a s u r e s o f t h e i n d e p e n d e n t v a r i a b l e s and o f t h e d e p e n d e n t v a r i a b l e i s p r e s e n t e d i n T a b l e 1 0 * . Of t h e 66 c o r r e l a t i o n s be tween p a i r s o f t h e i n d e p e n d e n t v a r i a b l e s , 20 were s t a t i s t i c a l l y s i g n i f i c a n t a t o r b e y o n d t h e 0 .10 l e v e l . A f u r t h e r f i v e c o r r e l a t i o n s be tween an i n d e p e n d e n t v a r i a b l e and s t a t i s t i c s a c h i e v e m e n t were s t a t i s t i c a l l y s i g n i f i c a n t . A l l s i g n i f i c a n t c o r r e l a t i o n s were p o s i t i v e . The t o t a l number o f s i g n i f i c a n t c o r r e l a t i o n s (25) i s s i m i l a r t o t h e number (27) o b s e r v e d i n t h e m a t r i x o f c o r r e l a t i o n s c a l c u l a t e d f r o m t h e B r i t i s h C o l u m b i a d a t a . T h r e e o f t h e i n d e p e n d e n t v a r i a b l e s w h i c h were s i g n i f i c a n t l y c o r r e l a t e d w i t h S t a t i s t i c s A c h i e v e m e n t were c o g n i t i v e - P a p e r F o l d i n g ( r = 0 . 3 6 ) , M u l t i p l i c a t i o n a n d S u b t r a c t i o n ( r = 0 . 3 7 ) and C o n c e p t L e a r n i n g (r = 0 . .48 ) . The r e m a i n i n g two s i g n i f i c a n t c o r r e l a t i o n s w i t h A c h i e v e m e n t i n v o l v e d A t t i t u d e Toward S t a t i s t i c s ( r = 0 . 4 4 ) and A t t i t u d e Towa rd R e s e a r c h ( r = 0 . 3 2 ) . T h i s p a t t e r n o f c o g n i t i v e and a t t i t u d i n a l z e r o - o r d e r c o r r e l a t i o n s was n o t o b s e r v e d i n t h e B r i t i s h C o l u m b i a d a t a . I t i s more t y p i c a l *Means and s t a n d a r d d e v i a t i o n s a r e p r e s e n t e d i n T a b l e 7. 77 T a b l e 10 I n t e r - c o r r e l a t i o n s among t h e V a r i a b l e s ( A l b e r t a Samp le ) M e a s u r e Number* 1 2 3 4 5 6 7 8 9 1 0 11 12 M e a s u r e : * * * E x p e r i e n c e : 1 . -C o g n i t i v e M e a s u r e s : 2. - o . 1 1 0 . 8 5 * * 3. - o . 1 3 0 .46 0 . 66 4 . 0 . 09 0 .52 0 . 26 0. 93 5. 0 . 09 0 . 3 5 0 . 29 0. 08 0 . 8 7 6. 0 . 3 3 0 .23 0 .23 0.31 0 .43 0 .74 A f f e c t i v e M e a s u r e s : 7. 0 . 2 9 0 .14 0 . 0 6 0 . 1 4 - 0 . 1 1 0.31 0 . 9 5 8. 0 . 2 8 0 .24 0 .03 0 . 0 2 - 0 . 0 6 0 .22 0.81 0 . 9 5 9. 0 . 1 9 0 . 1 0 - 0 . 0 3 - 0 . 0 1 - 0 . 1 4 0 . 1 7 0 . 3 5 0 .18 0 . 8 6 M o t i v a t i o n a l M e a s u r e s : 10 . 0.19 0 .33 0 .10 0.41 0 . 1 5 0 . 4 6 0 . 2 5 0 .34 0 . 1 6 0 . 8 8 1 1 • 0-32 0 .02 0 .12 0 .18 0 . 0 9 0 .03 0 . 4 6 0 . 4 9 0 .04 0.11 0 .87 12 . 0 . 1 9 0 .14 0 .04 0 . 1 9 0 . 2 7 0 .03 0 . 5 5 0 . 5 6 0 .33 0 .03 0 .62 0.71 S t a t i s t i c s A c h i e v e m e n t : 13 . 0 . 2 8 0.21 0 . 3 6 0 . 3 7 0 .18 0 .48 0 .44 0 .32 0 . 0 7 0 .08 0 .25 0 . 2 6 * 1 . = E x p e r i e n c e ; 2 . = A d v a n c e d V o c a b u l a r y T e s t ; 3 .=Pape r F o l d i n g T e s t ; 4 . = M u l t i p l i c a t i o n and S u b t r a c t i o n ; 5 .=D i ag r amming R e l a t i o n s ; 6 . = C o n c e p t L e a r n i n g ; 7. A t t i t u d e Towa rd S t a t i s t i c s ; 8 . = A t t i t u d e Towa rd R e s e a r c h ; 9 . = A c a d e m i c S e l f - C o n c e p t ; 1 0 . = A c h i e v e m e n t M o t i v a t i o n ; 1 1 . = P e r c e i v e d U t i l i t y ; 1 2 . = S p e c i f i c M o t i v a t i o n ; 1 3 . = S t a t i s t i c s A c h i e v e m e n t . * * R e l i a b i l i t y c o e f f i c i e n t s a r e e n t e r e d on t h e ma in d i a g o n a l . * * * U n d e r l i n e d v a l u e s were s t a t i s t i c a l l y s i g n i f i c a n t ( p < 0 . 1 0 ) . o f t h e p a t t e r n s r e p o r t e d i n t h e l i t e r a t u r e ( e . g . , E l m o r e and V a s u , 1980). . Of t h e 25 s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s , two were o b t a i n e d be tween P a s t E x p e r i e n c e a n d e a c h o f C o n c e p t L e a r n i n g ( r = 0 . 3 3 ) a n d P e r c e i v e d U t i l i t y ( r = 0 . 3 2 ) . B o t h c o r r e l a t e d s i g n i f i c a n t l y w i t h P a s t E x p e r i e n c e i n t h e B r i t i s h C o l u m b i a d a t a . 78 H o w e v e r , o t h e r e v i d e n c e f o r t h e " s t a t i s t i c s a c h i e v e m e n t " c l u s t e r o f c o g n i t i v e and n o n c o g n i t i v e v a r i a b l e s r e l a t e d t o E x p e r i e n c e w h i c h was a b s t r a c t e d f r o m t h e B r i t i s h C o l u m b i a d a t a was no t f o u n d i n t h e A l b e r t a d a t a s e t . One p o s s i b l e e x p l a n a t i o n f o r t h i s d i f f e r e n c e i s t h a t t h e d i f f e r e n t a d m i n i s t r a t i o n t i m e s o f t h e p r e - t e s t s i n f l u e n c e d t h e r e l a t i o n s h i p s among t h e v a r i a b l e s . Of t h e s i g n i f i c a n t c o r r e l a t i o n s among t h e c o g n i t i v e v a r i a b l e s , t h r e e were o b s e r v e d be tween A d v a n c e d V o c a b u l a r y and e a c h o f P a p e r F o l d i n g ( r = 0 . 4 6 ) , M u l t i p l i c a t i o n and S u b t r a c t i o n ( r = 0 . 5 2 ) a n d D i a g r a m m i n g R e l a t i o n s ( r = 0 . 3 5 ) . A f o u r t h s i g n i f i c a n t c o r r e l a t i o n was o b s e r v e d be tween D i a g r a m m i n g R e l a t i o n s and C o n c e p t L e a r n i n g ( r = 0 . 4 3 ) . S i n c e t h i s s u b c l u s t e r i n c l u d e d v e r b a l a b i l i t y , number f a c i l i t y , s p a t i a l v i s u a l i z a t i o n a n d l o g i c a l r e a s o n i n g , i t may r e p r e s e n t " g e n e r a l a b i l i t y " . The s u b c l u s t e r was no t o b s e r v e d i n t h e a n a l y s i s o f t h e B r i t i s h C o l u m b i a d a t a . In f a c t , o n l y one o f t h e f o u r c o r r e l a t i o n s was s t a t i s t i c a l l y s i g n i f i c a n t i n t h e a n a l y s i s o f t h e l a t t e r d a t a be tween D i a g r a m m i n g R e l a t i o n s and C o n c e p t L e a r n i n g . T h r e e s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s were o b s e r v e d be tween A c h i e v e m e n t M o t i v a t i o n and e a c h o f M u l t i p l i c a t i o n and S u b t r a c t i o n ( r = 0 . 4 l ) , C o n c e p t L e a r n i n g ( r = 0 . 4 6 ) a n d A d v a n c e d V o c a b u l a r y ( r = 0 . 3 3 ) . T h i s s e t may be i n t e r p r e t e d as an " a c h i e v e m e n t m o t i v a t i o n " s u b c l u s t e r , c o n s i s t i n g n o t o n l y o f a c h i e v e m e n t m o t i v a t i o n , b u t a l s o o f two v a r i a b l e s i n w h i c h s p e e d i s an i n t e g r a l c o m p o n e n t , and a t h i r d v a r i a b l e i n w h i c h p r o f i c i e n c y i s o f t e n e q u a t e d w i t h a h i g h d e g r e e o f s u c c e s s . The f a c t t h a t b o t h t h e " a c h i e v e m e n t m o t i v a t i o n " and t h e " s t a t i s t i c s " 79 s u b c l u s t e r s i n c l u d e t h e same t h r e e c o g n i t i v e v a r i a b l e s a l l o w s a f u r t h e r i n t e r p r e t a t i o n o f t h e " g e n e r a l a b i l i t y " c l u s t e r . T h a t i s , i t may be t h a t a c h i e v e m e n t m o t i v a t i o n e x e r t s an i n d i r e c t i n f l u e n c e on A c h i e v e m e n t t h r o u g h c o g n i t i v e v a r i a b l e s w h i c h a r e t h e m s e l v e s d i r e c t l y r e l a t e d t o a c h i e v e m e n t . In t h i s c a s e , A c h i e v e m e n t M o t i v e was r e l a t e d t o M u l t i p l i c a t i o n and S u b t r a c t i o n , and t o C o n c e p t L e a r n i n g , b o t h o f w h i c h were c o r r e l a t e d w i t h A c h i e v e m e n t . A s e c o n d c l u s t e r o f e i g h t s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n c o e f f i c i e n t s l i n k S t a t i s t i c s A c h i e v e m e n t , A t t i t u d e and M o t i v a t i o n . S t a t i s t i c s A c h i e v e m e n t was s i g n i f i c a n t l y c o r r e l a t e d w i t h A t t i t u d e Towa rd S t a t i s t i c s ( r = 0 . 4 4 ) and w i t h A t t i t u d e Toward R e s e a r c h ( r = 0 . 3 2 ) . A l l s i x p o s s i b l e c o r r e l a t i o n s among P e r c e i v e d U t i l i t y , S p e c i f i c M o t i v a t i o n , A t t i t u d e Towa rd S t a t i s t i c s and A t t i t u d e Toward R e s e a r c h a c h i e v e d s t a t i s t i c a l s i g n i f i c a n c e ( r ' s be tween 0 . 4 6 and 0 . 8 1 ) . L a s t , t h e c o r r e l a t i o n s be tween S e l f - C o n c e p t and A t t i t u d e Towa rd S t a t i s t i c s ( r = 0 . 3 5 ) and S e l f - C o n c e p t and S p e c i f i c M o t i v a t i o n ( r = 0 . 3 3 ) were b o t h s i g n i f i c a n t . The " a t t i t u d e - m o t i v a t i o n a l " c l u s t e r may be i n t e r p r e t e d a s r e p r e s e n t i n g t h e a t t i t u d i n a l c o n t r i b u t i o n t o a c h i e v e m e n t , s i n c e a l l t h e n o n c o g n i t i v e m e a s u r e s i n t e r c o r r e l a t e d s i g n i f i c a n t l y w i t h e a c h o t h e r , a n d t h e two a t t i t u d e m e a s u r e s c o r r e l a t e d w i t h S t a t i s t i c s A c h i e v e m e n t . T h i s c l u s t e r was v e r y s i m i l a r t o t h e a t t i t u d i n a l - m o t i v a t i o n a l c l u s t e r o b s e r v e d i n t h e B r i t i s h C o l u m b i a d a t a , e x c e p t t h a t , i n t h e A l b e r t a s a m p l e , t h e c l u s t e r was r e l a t e d t o a c h i e v e m e n t . No s u c h r e l a t i o n s h i p was o b s e r v e d 80 i n t h e B r i t i s h C o l u m b i a s a m p l e . P a r s i m o n i o u s F o r w a r d R e g r e s s i o n . Two f o r w a r d r e g r e s s i o n p r o c e d u r e s were c o m p u t e d . The f i r s t p r o c e d u r e , i n w h i c h o n l y E x p e r i e n c e was e n t e r e d , d i d no t y i e l d t h e same o r d e r o f m u l t i p l e R a s was o b s e r v e d i n t h e a n a l y s i s o f t h e B r i t i s h C o l u m b i a d a t a . The s e c o n d r e g r e s s i o n p r o c e d u r e was a f r e e f o r w a r d r e g r e s s i o n , i n w h i c h t he i n d e p e n d e n t v a r i a b l e s were f r e e t o e n t e r where t h e s t a t i s t i c a l p r o p e r t i e s o f t h e d a t a s e t w o u l d d i c t a t e . T a b l e 11 P a r t i a l C o r r e l a t i o n s and F - R a t i o s f o r t h e N o n - C o n t r i b u t o r y I n d e p e n d e n t V a r i a b l e s ( A l b e r t a S amp le ) I n d e p e n d e n t V a r i a b l e P a r t i a l F - R a t i o C o r r e l a t i o n ~ A d v a n c e d V o c a b u l a r y 0 . 2 6 2 2 .14 Pape r F o l d i n g 0 .422 6 . 2 8 * M u l t i p l i c a t i o n and S u b t r a c t i o n 0 . 3 5 6 4 . 2 0 * D i a g r a m m i n g R e l a t i o n s 0 . 1 6 2 0 . 7 6 C o n c e p t L e a r n i n g 0.431 6 . 6 2 * A t t i t u d e Towa rd S t a t i s t i c s 0 . 3 8 7 5 . 1 1 * A t t i t u d e Towa rd R e s e a r c h 0 . 2 6 6 2 .20 A c a d e m i c S e l f C o n c e p t 0 . 0 2 0 0 .12 A c h i e v e m e n t M o t i v e 0 . 0 2 4 0 .02 S p e c i f i c M o t i v a t i o n 0 . 2 1 8 1 .44 P e r c e i v e d U t i l i t y 0 . 170 0 . 8 6 * p < 0 . 0 5 When E x p e r i e n c e was e n t e r e d i n t o t h e r e g r e s s i o n e q u a t i o n , o n l y 8 . 1 1 % o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t was a c c o u n t e d f o r . The l e v e l o f s i g n i f i c a n c e a s s o c i a t e d w i t h t h i s v a l u e was 0.11 - h i g h e r t h a n t h e c h o s e n c r i t e r i o n o f 0 . 1 0 . The 81 p a r t i a l c o r r e l a t i o n s o f t h e r e m a i n i n g 11 i n d e p e n d e n t v a r i a b l e s w i t h s t a t i s t i c s a c h i e v e m e n t , and t h e F - r a t i o s a s s o c i a t e d w i t h t h e c o e f f i c i e n t s , a r e p r e s e n t e d i n T a b l e 11 . As may be s een i n t h e t a b l e , f o u r o f t h e 11 i n d e p e n d e n t v a r i a b l e s made s t a t i s t i c a l l y s i g n i f i c a n t c o n t r i b u t i o n s b e y o n d t h a t o f E x p e r i e n c e - P a p e r F o l d i n g ( p a r t i a l r = 0 . 4 2 2 ) , M u l t i p l i c a t i o n and S u b t r a c t i o n ( p a r t i a l r = 0 . 3 5 6 ) , C o n c e p t L e a r n i n g ( p a r t i a l r = 0 . 4 3 O and A t t i t u d e Towa rd S t a t i s t i c s ( p a r t i a l r = 0 . 3 8 7 ) . T h r e e v a r i a b l e s were c o g n i t i v e , t h e r e m a i n i n g o n e , a t t i t u d i n a l . I t w i l l be r e c a l l e d t h a t , b a s e d on t h e B r i t i s h C o l u m b i a d a t a , E x p e r i e n c e a c c o u n t e d f o r 2 7 . 7 % o f t h e e x p l a i n e d v a r i a n c e , w i t h no s i g n i f i c a n t c o n t r i b u t i o n f r o m any o t h e r i n d e p e n d e n t v a r i a b l e . When t h e d a t a c o l l e c t e d f r o m t h e A l b e r t a samp le were s u b j e c t e d t o a f r e e f o r w a r d - r e g r e s s i o n p r o c e d u r e , t h r e e i n d e p e n d e n t v a r i a b l e s c o n t r i b u t e d s i g n i f i c a n t l y t o t h e e x p l a n a t i o n o f t h e v a r i a n c e i n A c h i e v e m e n t , a s i n d i c a t e d by t h e p a r t i a l F - r a t i o s . The t h r e e v a r i a b l e s were C o n c e p t L e a r n i n g ( 2 3 . 4 % o f t h e v a r i a n c e ; F = 9 . 1 4 6 , d f = 1 , 3 0 ) , A t t i t u d e Toward S t a t i s t i c s ( f u r t h e r 9 . 1 % o f t h e v a r i a n c e ; F = 3 . 9 1 8 , d f = 2 , 2 9 ) and P a p e r F o l d i n g ( f u r t h e r 6 . 8% o f t h e v a r i a n c e ; F = 3 . 1 5 9 , d f = 3 , 2 8 ) . The t h r e e v a r i a b l e s , t h e n , a c c o u n t e d f o r a t o t a l o f 3 9 . 3 % o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . The p a r t i a l c o r r e l a t i o n s and t h e c o r r e s p o n d i n g F - r a t i o s f o r t h e r e m a i n i n g n i n e i n d e p e n d e n t v a r i a b l e s a r e p r e s e n t e d in^- T a b l e 12 . I t w i l l be n o t e d t h a t t h e h i g h e s t p a r t i a l c o r r e l a t i o n , be tween A c h i e v e m e n t and A c h i e v e m e n t M o t i v a t i o n ( p a r t i a l r = 0 . 2 5 7 ) was n o t s i g n i f i c a n t a t o r b e y o n d t h e 0 .10 l e v e l . I n s p e c t i o n o f 82 T a b l e 12 P a r t i a l C o r r e l a t i o n s and F - R a t i o s f o r 9 N o n - C o n t r i b u t o r y I n d e p e n d e n t V a r i a b l e s ( A l b e r t a S amp le ) I n d e p e n d e n t V a r i a b l e P a r t i a l F - R a t i o C o r r e l a t i o n A d v a n c e d V o c a b u l a r y - 0 . 0 3 5 0 . 0 3 M u l t i p l i c a t i o n and S u b t r a c t i o n 0 . 2 1 4 1 . 2 9 D i a g r a m m i n g R e l a t i o n s - 0 . 0 0 6 0.001 A t t i t u d e Toward R e s e a r c h - 0 . 0 3 0 0 . 0 2 8 A c a d e m i c S e l f C o n c e p t - 0 . 1 1 6 0 . 3 6 7 A c h i e v e m e n t M o t i v a t i o n - 0 . 2 5 7 1 .92 S p e c i f i c M o t i v a t i o n 0 . 1 02 0 . 2 8 4 P e r c e i v e d U t i l i t y - 0 . 157 0 . 3 7 9 t h e t a b l e r e v e a l s t h a t c o g n i t i v e and n o n c o g n i t i v e v a r i a b l e s were e q u a l l y n o n - c o n t r i b u t o r y , b u t , o f t h e s e t o f 12 i n d e p e n d e n t v a r i a b l e s t a k e n a s a w h o l e , t h e c o g n i t i v e v a r i a b l e s c o n t r i b u t e d more h i g h l y t h a n t h e n o n c o g n i t i v e . E x p l o r a t o r y F o r w a r d R e g r e s s i o n . The r e s u l t s f r o m t h e f r e e f o r w a r d r e g r e s s i o n s f o r b o t h s a m p l e s i n w h i c h a l l 12 i n d e p e n d e n t v a r i a b l e s were a l l o w e d t o e n t e r a s l o n g as t h e p a r t i a l F - r a t i o was no t v e r y c l o s e t o 0 . 0 a r e p r e s e n t e d i n T a b l e 13 . F rom t h e t a b l e i t i s a p p a r e n t t h a t , a l t h o u g h t h e t o t a l v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t e x p l a i n e d by e a c h s e t o f v a r i a b l e s i s a l m o s t e q u a l , t h e r e l a t i v e c o n t r i b u t i o n s , o r d e r s o f e n t r y , a n d b e t a w e i g h t s a t t h e l a s t s t e p , f o r e a c h o f t h e i n d e p e n d e n t v a r i a b l e s a r e a l m o s t t o t a l l y d i s s i m i l a r i n t h e two s a m p l e s . F rom t h e r e s u l t s b a s e d on t h e B r i t i s h C o l u m b i a s a m p l e , i t may be s e e n t h a t t h e v a r i a b l e s w h i c h a r e e n t e r e d i n t o t h e r e g r e s s i o n e q u a t i o n a f t e r E x p e r i e n c e ( t h e o n l y s t a t i s t i c a l l y s i g n i f i c a n t v a r i a b l e ) a n d w h i c h c o n t r i b u t e more t h a n 1% t o t h e 83 T a b l e 13 O r d e r o f E n t r y , R-Squa re Change and B e t a W e i g h t s f o r E x p l o r a t o r y F o r w a r d R e g r e s s i o n s B r i t i s h C o l u m b i a A l b e r t a 0 R- B 0 R- B r S q u a r e r S q u a r e d e r Change d e r Change A d v a n c e d V o c a b u l a r y .6 0 . 075 0, . 3 3 5 1 1 0 . 002 - o . 073 P a p e r F o l d i n g 2 0 . 047 0, . 5 9 8 3 0 . 068 0 . 261 M u l t i p l i c a t i o n and S u b t r a c t i o n 9 0 . 002 0, . 0 3 2 5 0 . 060 0 . 408 D i a g r a m m i n g R e l a t i o n s 3 0 . 034 -•o, . 4 6 5 -* - -C o n c e p t L e a r n i n g 10 0 . 001 0, . 047 1 0 . 234 0 . 346 A t t i t u d e Towa rd S t a t i s t i c s -* - - 2 0 . 091 0 . 146 A t t i t u d e Towa rd R e s e a r c h -* - - 10 0 . 003 0 . 167 A c a d e m i c S e l f - C o n c e p t 7 0 . 022 -•0. , 169 8 0 . 008 - 0 . 093 A c h i e v e m e n t M o t i v a t i o n 4 0 . 040 0. ,404 4 0 . 040 - o . 353 P e r c e i v e d U t i l i t y 5 0 . 056 -•0. , 253 9 0 . 007 - o . 147 S p e c i f i c M o t i v a t i o n 8 0 . 001 - 0. , 049 6 0 . 021 0 . 235 E x p e r i e n c e 1 0 . 277 0 . ,531 7 0 . 014 0 . 161 * F<0 .001 f o r t h i s s a m p l e . i n c r e a s e i n t h e p e r c e n t a g e o f v a r i a n c e e x p l a i n e d a r e f i r s t , c o g n i t i v e , s e c o n d , m o t i v a t i o n a l , and t h i r d , c o g n i t i v e a g a i n . The o n l y a t t i t u d i n a l v a r i a b l e t o be e n t e r e d i s A c a d e m i c S e l f -C o n c e p t , a g l o b a l r a t i n g . The c o g n i t i v e v a r i a b l e s w h i c h c o n t r i b u t e more t h a n 1% i n c l u d e P a p e r F o l d i n g and A d v a n c e d V o c a b u l a r y , b o t h o f w h i c h had been f o u n d t o c o r r e l a t e s i g n i f i c a n t l y w i t h A c h i e v e m e n t a n d D i a g r a m m i n g R e l a t i o n s , w h i c h d i d n o t c o n t r i b u t e . The two m o t i v a t i o n a l v a r i a b l e s w h i c h c o n t r i b u t e d more t h a n 1% were A c h i e v e m e n t M o t i v a t i o n and P e r c e i v e d U t i l i t y . Of t h e a b o v e - l i s t e d v a r i a b l e s , o n l y two ( P a p e r F o l d i n g and 84 A c h i e v e m e n t M o t i v a t i o n ) c o n t r i b u t e d more t han 1% t o t h e change i n v a r i a n c e e x p l a i n e d i n t h e A l b e r t a s a m p l e . O t h e r v a r i a b l e s w h i c h c o n t r i b u t e d more t h a n 1% i n t h e A l b e r t a s a m p l e bu t d i d n o t i n t h e B r i t i s h C o l u m b i a s a m p l e i n c l u d e d M u l t i p l i c a t i o n and S u b t r a c t i o n , C o n c e p t L e a r n i n g , A t t i t u d e T o w a r d S t a t i s t i c s , and S p e c i f i c M o t i v a t i o n . I t w i l l be r e c a l l e d t h a t P a p e r F o l d i n g , A t t i t u d e T o w a r d S t a t i s t i c s and C o n c e p t L e a r n i n g c o n t r i b u t e d s i g n i f i c a n t l y t o t h e e x p l a i n e d v a r i a n c e i n a c h i e v e m e n t f o r t h e A l b e r t a s a m p l e (as r e p o r t e d a b o v e ) . 85 C h a p t e r V I .  Summary and C o n c l u s i o n s In t h i s c h a p t e r , a summary o f t h e i n v e s t i g a t i o n i s p r e s e n t e d f i r s t , f o l l o w e d by a d i s c u s s i o n o f t h e r e s u l t s d e s c r i b e d i n C h a p t e r V . T h e n , t h e l i m i t a t i o n s o f t h e s t u d y a r e d e l i n e a t e d . The c h a p t e r i s t e r m i n a t e d by t h e c o n c l u s i o n s o f t h e i n v e s t i g a t i o n and some i m p l i c a t i o n s f o r f u t u r e r e s e a r c h . Summary o f t h e I n v e s t i g a t i o n A l t h o u g h much a t t e n t i o n has been f o c u s e d on t h e c o r r e l a t e s and d e t e r m i n a n t s b o t h o f g e n e r a l a c a d e m i c a c h i e v e m e n t and o f a c h i e v e m e n t i n some s p e c i f i c s u b j e c t s ( e . g . , m a t h e m a t i c s ) , v e r y few i n v e s t i g a t i o n s have r e p o r t e d t h e s t u d y o f t h e c o r r e l a t e s o f s t a t i s t i c s a c h i e v e m e n t among s t u d e n t s e n r o l l e d i n p r o g r a m s i n t h e s o c i a l s c i e n c e s . T h i s t h e s i s i s a r e p o r t o f s u c h an i n v e s t i g a t i o n . M e a s u r e s o f t w e l v e i n d e p e n d e n t v a r i a b l e s , s e l e c t e d on t h e b a s i s o f t h e l i t e r a t u r e i n t h e a r e a , were c o l l e c t e d f r o m v o l u n t e e r s u b j e c t s d u r i n g a c l a s s s e s s i o n o f e a c h o f f o u r c l a s s e s a t t h e U n i v e r s i t i e s o f A l b e r t a , B r i t i s h C o l u m b i a and V i c t o r i a . Among t h e c o g n i t i v e v a r i a b l e s i n v e s t i g a t e d were Number F a c i l i t y and N u m e r i c C o n c e p t L e a r n i n g ( b a s e d on f i n d i n g s o f M i c h a e l and M i c h a e l , 1 9 6 9 ) , v e r b a l r e a s o n i n g ( F e i n b e r g and H a l p e r i n , 1 9 7 8 ) , a b s t r a c t o r l o g i c a l r e a s o n i n g ( H a r t l e y and 86 H a r t l e y , 1976) and s p a t i a l v i s u a l i z a t i o n ( E l m o r e and V a s u , 1 9 8 0 ) . N o n c o g n i t i v e v a r i a b l e s w h i c h had p r e v i o u s l y been f o u n d t o c o r r e l a t e w i t h s t a t i s t i c s a c h i e v e m e n t and w h i c h were i n v e s t i g a t e d i n c l u d e d a t t i t u d e t o w a r d s t a t i s t i c s ( R o b e r t s and B i l d e r b a c k , 1 9 8 0 ) , a c a d e m i c s e l f - e s t e e m ( H a r t l e y and H a r t l e y , 1 9 7 6 ) , and p r e v i o u s p o s t - s e c o n d a r y e x p e r i e n c e w i t h m a t h e m a t i c s o r s t a t i s t i c s ( F e i n b e r g a n d H a r p e r i n , 1 9 7 8 ) . In a d d i t i o n t o t h e a b o v e - m e n t i o n e d v a r i a b l e s , t h e r e l a t i o n s h i p s o f a t t i t u d e t o w a r d r e s e a r c h , a c h i e v e m e n t m o t i v a t i o n , s p e c i f i c m o t i v a t i o n , and p e r c e i v e d u t i l i t y o f t h e s t a t i s t i c s c o u r s e t o a c h i e v e m e n t i n s t a t i s t i c s were i n v e s t i g a t e d . The i n c l u s i o n o f a m e a s u r e o f a t t i t u d e t o w a r d r e s e a r c h was b a s e d on f i n d i n g s r e p o r t e d by H a r t l e y and H a r t l e y ( 1 9 7 6 ) , who r e p o r t e d t h a t a measu re o f a t t i t u d e t o w a r d p s y c h o l o g y a s a s c i e n t i f i c e n d e a v o u r was r e l a t e d t o a c h i e v e m e n t i n s t a t i s t i c s . W i t h r e g a r d t o t h e m o t i v a t i o n a l v a r i a b l e s , i t was h y p o t h e s i z e d t h a t m o t i v a t i o n c o u l d a c c o u n t f o r an a d d i t i o n a l , unknown, p r o p o r t i o n o f t h e e x p l a i n e d v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . T h i s s p e c u l a t i o n was b a s e d on t h e t h e o r e t i c a l and e m p i r i c a l f i n d i n g s o f A t k i n s o n ( 1 9 7 8 ) , Rayno r (1978) and H a k s t i a n a n d G a l e ( 1 9 7 9 ) , who have s t a t e d t h a t m o t i v a t i o n a l v a r i a b l e s may a c c o u n t f o r a s much a s 25% o f t h e v a r i a n c e i n a c a d e m i c a c h i e v e m e n t . The m e a s u r e o f t h e d e p e n d e n t v a r i a b l e , s t a t i s t i c s a c h i e v e m e n t , was t h e s c o r e o b t a i n e d on a o n e - h o u r common e x a m i n a t i o n . T h i s m e a s u r e was a d m i n i s t e r e d by e a c h c o u r s e i n s t r u c t o r a s p a r t o f t h e f i n a l e x a m i n a t i o n . 87 The o r i g i n a l i n t e n t was t o i n v e s t i g a t e t h e d e t e r m i n a n t s o f s t a t i s t i c s a c h i e v e m e n t t h r o u g h t h e a p p l i c a t i o n o f B e n t l e r ' s (1980) " c a u s a l m o d e l i n g w i t h l a t e n t v a r i a b l e s " a p p r o a c h . A l a t e n t s t r u c t u r e w h i c h was t h o u g h t p l a u s i b l y t o u n d e r l i e t h e s e t o f i n d e p e n d e n t v a r i a b l e s was s p e c i f i e d , and t h r e e e x p l o r a t o r y m o d e l s d e l i n e a t e d . E a c h mode l m i g h t , i t was s p e c u l a t e d , a c c o u n t f o r t h e o b s e r v e d c o r r e l a t i o n m a t r i x . The i n v e s t i g a t i o n was p l a n n e d a s a p a r t i a l r e p l i c a t i o n o f two s t u d i e s i n t h e l i t e r a t u r e c o n c e r n i n g t h e c o n t r i b u t i o n s o f b o t h a b i l i t y and a t t i t u d i n a l v a r i a b l e s t o s t a t i s t i c s a c h i e v e m e n t . B o t h s t u d i e s b a s e d t h e i r c o n c l u s i o n s on t h e r e s u l t s o f s t e p w i s e r e g r e s s i o n p r o c e d u r e s p e r f o r m e d on m a n i f e s t v a r i a b l e s ( H a r t l e y and H a r t l e y , 1976 ; E l m o r e and V a s u , 1 9 8 0 ) , w h e r e a s t h e p r e s e n t s t u d y p r o p o s e d t o t e s t m o d e l s o f s t a t i s t i c s a c h i e v e m e n t u s i n g l a t e n t v a r i a b l e s . S t u d e n t s i n e d u c a t i o n , one o f t h e s o c i a l s c i e n c e s , were c h o s e n a s t h e a c c e s s i b l e p o p u l a t i o n r a t h e r t h a n m a t h e m a t i c s o r s c i e n c e s t u d e n t s b e c a u s e d i f f i c u l t i e s w i t h s t a t i s t i c s a p p e a r t o be more common among p o p u l a t i o n s o f s o c i a l s c i e n c e s t u d e n t s . In a d d i t i o n , i t was h o p e d t h a t t h e i n v e s t i g a t i o n w o u l d have a d e g r e e o f p r a c t i c a l u t i l i t y . T h a t i s , i t c o u l d have y i e l d e d i n f o r m a t i o n a b o u t t h e d i r e c t i o n s f u t u r e r e s e a r c h i n t o t h e e a r l y d i a g n o s i s and t r e a t m e n t o f p r o b l e m s w i t h s t a t i s t i c s c o u l d t a k e . F u r t h e r , t h e i n v e s t i g a t i o n c o u l d h a v e s h e d some l i g h t on t h e a d e q u a c y o f a s e t o f r a t h e r s i m p l e m o d e l s t o e x p l a i n t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . I t had been i n t e n d e d i n i t i a l l y t o i n v e s t i g a t e t h e l a t e n t 88 s t r u c t u r e and e a c h mode l by u s i n g t h e c o m b i n e d s a m p l e s o f i n t r o d u c t o r y s t a t i s t i c s s t u d e n t s f r o m a l l t h r e e u n i v e r s i t i e s . U n f o r s e e n d e l a y s i n a d m i n i s t e r i n g t h e m e a s u r e s o f t h e i n d e p e n d e n t v a r i a b l e s a t t h e U n i v e r s i t y o f A l b e r t a r e s u l t e d i n s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s be tween t h e B r i t i s h C o l u m b i a and A l b e r t a d a t a p o o l s . The r e s u l t i n g s p l i t o f t h e t o t a l s amp l e o f 65 i n t o two s a m p l e s o f 33 and 32 ( f r o m B r i t i s h C o l u m b i a and A l b e r t a , r e s p e c t i v e l y ) meant t h a t e a c h s amp l e was t o o s m a l l t o p e r m i t s t a b i l i t y i n e s t i m a t e s o f t h e l a t e n t s t r u c t u r e a n d o f t h e p a t h c o e f f i c i e n t s . C o n s e q u e n t l y , t h e r e s e a r c h q u e s t i o n s were r e d e v e l o p e d i n o r d e r t o e x c l u d e f r o m t h e a n a l y s i s p l a n a l l c o n s i d e r a t i o n o f t h e " l a t e n t v a r i a b l e " a p p r o a c h and e x p l o r a t i o n o f m o d e l s i n c o r p o r a t i n g l a t e n t v a r i a b l e s . The method o f a n a l y s i s was , t h e n , l i m i t e d t o t h e e x a m i n a t i o n o f z e r o - o r d e r c o r r e l a t i o n s and t o t h e c o m p u t a t i o n and a n a l y s i s o f f o r w a r d f o r w a r d r e g r e s s i o n p r o c e d u r e s . The B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s were a n a l y z e d s e p a r a t e l y , and t h e r e s u l t s f r o m e a c h c o m p a r e d . B e c a u s e o f t h e e x p l o r a t o r y n a t u r e o f t h e i n v e s t i g a t i o n , t h e 0 . 1 0 l e v e l o f s t a t i s t i c a l s i g n i f i c a n c e was a d o p t e d a s t h e c r i t e r i o n r a t h e r t h a n t h e more c o n v e n t i o n a l 0 . 0 5 l e v e l . The r e v i s e d r e s e a r c h q u e s t i o n s e n q u i r e d a b o u t t h e r e l a t i o n s h i p o f e a c h i n d e p e n d e n t v a r i a b l e t o s t a t i s t i c s a ch i e vemen t ,^- a b o u t t h e c l u s t e r s o f v a r i a b l e s r e v e a l e d by s u b j e c t i v e e x a m i n a t i o n o f t h e c o r r e l a t i o n m a t r i x , a n d a b o u t t h e c o n t r i b u t i o n t o o b s e r v e d v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t made by t h e t o t a l s e t o f 12 v a r i a b l e s . E a c h q u e s t i o n was a n s w e r e d 89 i n d e p e n d e n t l y o f t h e o t h e r two . C o r r e l a t i o n a l a n a l y s i s o f t h e B r i t i s h C o l u m b i a s a m p l e r e v e a l e d t h a t p a s t e x p e r i e n c e , v e r b a l r e a s o n i n g , s p a t i a l v i s u a l i z a t i o n a n d a t t i t u d e t o w a r d s t a t i s t i c s were s i g n i f i c a n t l y c o r r e l a t e d w i t h a c h i e v e m e n t . Two c l u s t e r s o f i n t e r c o r r e l a t i o n s ( c o g n i t i v e - e x p e r i e n t i a l and a t t i t u d i n a l - m o t i v a t i o n a l ) were i d e n t i f i e d . O n l y t he f i r s t c l u s t e r was r e l a t e d t o s t a t i s t i c s a c h i e v e m e n t . A p p l i c a t i o n o f f o r w a r d r e g r e s s i o n r e v e a l e d t h a t o n l y p r e v i o u s c o u r s e w o r k a c c o u n t e d f o r a s t a t i s t i c a l l y s i g n i f i c a n t p r o p o r t i o n o f t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . The s e t o f 12 v a r i a b l e s t a k e n t o g e t h e r a c c o u n t e d f o r 5 5 . 5 % o f t h e v a r i a n c e . S i m i l a r a n a l y s i s o f t h e A l b e r t a d a t a r e v e a l e d t h a t s p a t i a l v i s u a l i z a t i o n , number f a c i l i t y , c o n c e p t l e a r n i n g , a t t i t u d e t o w a r d s t a t i s t i c s and a t t i t u d e t o w a r d r e s e a r c h s i g n i f i c a n t l y c o r r e l a t e d w i t h s t a t i s t i c s a c h i e v e m e n t . C o g n i t i v e - m o t i v a t i o n a l and a t t i t u d i n a l - m o t i v a t i o n a l c l u s t e r s o f i n d e p e n d e n t v a r i a b l e s were i d e n t i f i e d i n t h e c o r r e l a t i o n m a t r i x . B o t h c l u s t e r s a p p e a r e d t o be r e l a t e d t o s t a t i s t i c s a c h i e v e m e n t . The r e s u l t s o f a f o r w a r d r e g r e s s i o n r e v e a l e d t h a t 5 4 . 9 % o f t h e v a r i a n c e i n a c h i e v e m e n t was a c c o u n t e d f o r by t h e s e t o f 12 i n d e p e n d e n t v a r i a b l e s . T h r e e ( c o n c e p t l e a r n i n g , a t t i t u d e t o w a r d s t a t i s t i c s and s p a t i a l v i s u a l i z a t i o n ) c o n t r i b u t e d s i g n i f i c a n t l y . The o r d e r o f e n t r y was n o t s i m i l a r t o t h a t o b s e r v e d i n t h e r e s u l t s f o r t h e B r i t i s h C o l u m b i a s a m p l e . N o n - p a r s i m o n i o u s f o r w a r d r e g r e s s i o n a n a l y s e s o f t h e B r i t i s h C o l u m b i a and A l b e r t a d a t a s e t s were c o m p u t e d i n o r d e r t o y i e l d 90 " h i n t s and c l u e s " ( B e n t l e r , 1980) a b o u t t he r e l a t i o n s h i p s among t h e v a r i a b l e s i n t h e two d a t a s e t s . O r d e r o f e n t r y o f t h e i n d e p e n d e n t v a r i a b l e s was n o t s i m i l a r f o r t h e two s a m p l e s , and t h e r e l a t i v e c o n t r i b u t i o n s o f c o g n i t i v e , . a t t i t u d i n a l a n d m o t i v a t i o n a l v a r i a b l e s were e q u a l l y d i s s i m i l a r . D i s c u s s i o n o f t h e R e s u l t s The d i s c u s s i o n i n c l u d e s , f i r s t , a g e n e r a l comment on t h e p s y c h o m e t r i c c h a r a c t e r i s t i c s o f t h e B r i t i s h C o l u m b i a and A l b e r t a d a t a s e t s , f o l l o w e d by a b r i e f d i s c u s s i o n o f t h e n o n - e q u i v a l e n c e o f t h e two s a m p l e s . S e c t i o n s d i s c u s s i n g e a c h o f t h e t h r e e r e c a s t r e s e a r c h q u e s t i o n s a r e t h e n p r e s e n t e d . W i t h two e x c e p t i o n s , t h e r e s u l t s o f t h e i t e m a n a l y s e s o f t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s were m a r k e d l y s i m i l a r . T h e s e e x c e p t i o n s i n v o l v e d t h e i n t e r n a l c o n s i s t e n c y c o e f f i c i e n t s o f two o f t h e c o g n i t i v e m e a s u r e s ( A d v a n c e d V o c a b u l a r y and P a p e r F o l d i n g ) . In t h e B r i t i s h C o l u m b i a d a t a , A d v a n c e d V o c a b u l a r y d i s p l a y e d a r e l a t i v e l y low Hoy t c o e f f i c i e n t o f 0 . 6 3 , w h i l e P ape r F o l d i n g was o b s e r v e d t o have an i n t e r n a l c o n s i s t e n c y o f 0 . 8 2 . The r e v e r s e s i t u a t i o n o b t a i n e d i n t h e A l b e r t a d a t a , w i t h A d v a n c e d V o c a b u l a r y b e i n g t h e more i n t e r n a l l y c o n s i s t e n t (Hoy t c o e f f i c i e n t o f 0 . 8 5 a s c o m p a r e d t o one o f 0 . 6 6 f o r P a p e r F o l d i n g ) . In b o t h s i t u a t i o n s i n w h i c h i n t e r n a l c o n s i s t e n c y was l o w , t h e v a r i a n c e was a l s o l o w . T h i s f a c t may have been r e s p o n s i b l e f o r t h e low r e l i a b i l i t y i n b o t h c a s e s . In t h e B r i t i s h C o l u m b i a d a t a , t h e skewed d i s t r i b u t i o n a n d l i m i t e d r a n g e o f s c o r e s (19 t o 36 ou t o f a t o t a l o f 36- p o s s i b l e m a r k s ) may 91 a l s o have c o n t r i b u t e d t o t h e l o w e r r e l i a b i l i t y . The s i m i l a r i t y o f t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s on t h e p s y c h o m e t r i c p r o p e r t i e s o f t h e m e a s u r e s d i d n o t e x t e n d e i t h e r t o t h e p r o f i l e s o f mean v a l u e s , o r t o t h e 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 w h i c h were s i g n i f i c a n t l y d i f f e r e n t f r o m e a c h o t h e r . As d e s c r i b e d i n C h a p t e r IV , t h e m u l t i v a r i a t e d i f f e r e n c e be tween s a m p l e s and a t l e a s t t h r e e o f t h e f i v e u n i v a r i a t e s i g n i f i c a n t d i f f e r e n c e s may be t h e r e s u l t o f t h e two weeks o f i n s t r u c t i o n i n s t a t i s t i c s w h i c h o c c u r r e d p r i o r t o t h e a d m i n i s t r a t i o n o f t h e p r e - t e s t s t o t h e A l b e r t a s a m p l e . P e r f o r m a n c e on t h e C o n c e p t L e a r n i n g t a s k c o u l d have been a f f e c t e d by i n s t r u c t i o n a b o u t t h e " s u m m a t i o n " o p e r a t o r d u r i n g c l a s s t i m e , and b o t h o f t h e n o n c o g n i t i v e m e a s u r e s ( A t t i t u d e T o w a r d S t a t i s t i c s and P e r c e i v e d U t i l i t y ) . c o u l d . h ave b e e n i n f l u e n c e d by t h e s u b j e c t s ' e x p o s u r e t o t h e s u b j e c t m a t t e r . The d i f f e r e n t i a l p e r f o r m a n c e on A d v a n c e d V o c a b u l a r y and D i a g r a m m i n g R e l a t i o n s i s more d i f f i c u l t t o j u s t i f y a s b e i n g i n f l u e n c e d by i n - c l a s s e x p e r i e n c e . As was r e p o r t e d i n C h a p t e r IV ( p . 6 4 ) , t h e s a m p l e o f B r i t i s h C o l u m b i a s t u d e n t s p e r f o r m e d s i g n i f i c a n t l y b e t t e r on b o t h m e a s u r e s . I t i s u n l i k e l y t h a t s t a t i s t i c a l i n s t r u c t i o n w o u l d r e s u l t i n d e c r e a s e d p e r f o r m a n c e on e i t h e r t e s t . D i f f e r e n c e s be tween t h e B r i t i s h C o l u m b i a a n d A l b e r t a s a m p l e s c o u l d be due t o s a m p l i n g f l u c t u a t i o n o r t h e y c o u l d be t h e r e s u l t o f t h e two s a m p l e s b e i n g r e p r e s e n t a t i v e o f d i f f e r e n t p o p u l a t i o n s . S t i l l a t h i r d 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 t h e t i m e o f a d m i n i s t r a t i o n i n f l u e n c e d t h e m o t i v a t i o n a l l e v e l o f t h e s t u d e n t s a n d , i n a d d i t i o n , t h e i r a t t i t u d e s t o w a r d 92 p a r t i c i p a t i n g i n t h e s t u d y . I t seems l i k e l y t h a t t h e A l b e r t a s a m p l e were no t a s h i g h l y m o t i v a t e d t o p e r f o r m w e l l on s e e m i n g l y i r r e l e v a n t t a s k s . R e s e a r c h Q u e s t i o n O n e . The f i r s t r e s e a r c h q u e s t i o n e n q u i r e d a b o u t t h e r e l a t i o n s h i p be tween s t a t i s t i c s a c h i e v e m e n t a n d e a c h o f t h e t w e l v e m a n i f e s t v a r i a b l e s . The answer t o t h i s q u e s t i o n , as r e p o r t e d i n C h a p t e r V , was d e v e l o p e d f rom t h e a n a l y s i s o f z e r o - o r d e r c o r r e l a t i o n s be tween e a c h o f t h e i n d e p e n d e n t v a r i a b l e s and s t a t i s t i c s a c h i e v e m e n t . No p a r t i a l o r m u l t i p l e c o r r e l a t i o n s were c o n s i d e r e d . Two v a r i a b l e s a c h i e v e d a s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n w i t h A c h i e v e m e n t ( P a p e r F o l d i n g and C o n c e p t L e a r n i n g ) i n b o t h t h e B r i t i s h C o l u m b i a and A l b e r t a d a t a s e t s , w h i l e f i v e d i d no t ( D i a g r a m m i n g R e l a t i o n s , A c a d e m i c S e l f -C o n c e p t , A c h i e v m e n t M o t i v a t i o n , S p e c i f i c M o t i v a t i o n and P e r c e i v e d U t i l i t y ) . In t h e B r i t i s h C o l u m b i a s a m p l e , P a s t E x p e r i e n c e a n d A d v a n c e d V o c a b u l a r y c o r r e l a t e d s i g n i f i c a n t l y w i t h S t a t i s t i c s A c h i e v e m e n t ; t h e s e s i g n i f i c a n t c o r r e l a t i o n s were n o t o b s e r v e d i n t h e A l b e r t a d a t a . M u l t i p l i c a t i o n and S u b t r a c t i o n , A t t i t u d e T o w a r d S t a t i s t i c s a n d A t t i t u d e Towa rd R e s e a r c h were s i g n i f i c a n t l y c o r r e l a t e d w i t h A c h i e v e m e n t i n t h e A l b e r t a d a t a b u t n o t i n t h e B r i t i s h C o l u m b i a d a t a s e t . A l t h o u g h d r a w i n g f a l s e c o n c l u s i o n s due t o s a m p l i n g e r r o r i s a d a n g e r when a n a l y z i n g s m a l l s a m p l e s s u c h a s t h e B r i t i s h C o l u m b i a and A l b e r t a o n e s , some c o n f i d e n c e c a n be p l a c e d i n t h e r e s u l t s , s i n c e s e v e n o f t h e 12 z e r o - o r d e r c o r r e l a t i o n s were s i g n i f i c a n t ( o r n o t ) i n b o t h d a t a s e t s . In a d d i t i o n , t h e two 93 s i g n i f i c a n t c o e f f i c i e n t s r e p l i c a t e d t h o s e r e p o r t e d i n t h e l i t e r a t u r e ( s e e T a b l e 2 ) . F o u r o f t h e f i v e v a r i a b l e s w h i c h f a i l e d t o a c h i e v e a s i g n i f i c a n t c o r r e l a t i o n w i t h s t a t i s t i c s a c h i e v e m e n t were n o n c o g n i t i v e . T h r e e v a r i a b l e s were m o t i v a t i o n a l . T h i s f i n d i n g a r g u e s a g a i n s t A t k i n s o n ' s and R a y n o r ' s s p e c u l a t i o n s , and i s i n c o n f l i c t w i t h H a k s t i a n and G a l e ' s r e s u l t s w i t h r e g a r d t o t h e d i r e c t c o n t r i b u t i o n o f m o t i v a t i o n a l v a r i a b l e s t o t h e v a r i a n c e i n g e n e r a l a c a d e m i c a c h i e v e m e n t , b u t i s i n a g r e e m e n t w i t h t h e c o n s e n s u s o f o p i n i o n r e p o r t e d i n t h e l i t e r a t u r e ( V i d l e r , 1 9 7 7 ) . F i n a l l y , t h e a b s e n c e o f s i g n i f i c a n t r e l a t i o n s h i p s be tween A c h i e v e m e n t and D i a g r a m m i n g R e l a t i o n s , and be tween A c h i e v e m e n t and A c a d e m i c S e l f - C o n c e p t , a r e d i f f i c u l t t o e x p l a i n . M e t h o d v a r i a n c e , a r i s i n g f r o m v a r i a b l e s s u c h a s t h e s p e c i f i c t a s k r e q u i r e d , may p r o v i d e a p a r t i a l e x p l a n a t i o n o f t h e s e f i n d i n g s . The s a m p l e - s p e c i f i c s t a t i s t i c a l l y s i g n i f i c a n t r e l a t i o n s h i p s a r e w i t h two e x c e p t i o n s l e s s c l e a r l y i n t e r p r e t a b l e . A r e l a t i o n s h i p be tween A t t i t u d e Towa rd S t a t i s t i c s and A c h i e v e m e n t , and be tween A t t i t u d e T o w a r d R e s e a r c h and A c h i e v e m e n t was o b s e r v e d i n t h e A l b e r t a d a t a b u t no t i n t h a t f r o m B r i t i s h C o l u m b i a . The d i s c r e p a n c y may be e x p l a i n e d a s a f u n c t i o n o f e x p o s u r e t o t h e s u b j e c t m a t t e r . One e x p l a n a t i o n f o r t h e s e d i s c r e p a n t f i n d i n g s i s t h a t a t t i t u d e had n o t d e v e l o p e d s u f f i c i e n t l y i n t h e B r i t i s h C o l u m b i a s amp l e ( i n whom i t was m e a s u r e d on t h e f i r s t day o f c l a s s ) , whe reas a t t i t u d e m i g h t have become more c r y s t a l l i z e d i n t h e A l b e r t a s a m p l e , a f t e r two weeks o f r e l a t i v e l y i n t e n s e e x p o s u r e t o t h e s u b j e c t m a t t e r . 94 The r e m a i n i n g t h r e e d i s c r e p a n t f i n d i n g s a r e l e s s i n t e r p r e t a b l e . The r e l a t i o n s h i p be tween A d v a n c e d V o c a b u l a r y and A c h i e v e m e n t o b s e r v e d i n t h e a n a l y s i s o f t h e B r i t i s h C o l u m b i a s amp le was no t a s l a r g e a s t h a t r e p o r t e d by H a r t l e y and H a r t l e y ( 1 9 7 6 ) , a n d , f u r t h e r , was a b s e n t i n t h e r e s u l t s o f t h e a n a l y s i s o f t h e A l b e r t a d a t a s e t . The r e l a t i o n s h i p be tween A c h i e v e m e n t and E x p e r i e n c e , r e p o r t e d by E l m o r e and V a s u ( 1 9 8 0 ) , was o b s e r v e d i n t h e B r i t i s h C o l u m b i a s amp l e b u t n o t i n t h e A l b e r t a . S a m p l i n g f l u c t u a t i o n i s one e x p l a n a t i o n o f t h i s d i s c r e p a n c y ; o t h e r s u b j e c t and c o u r s e v a r i a b l e s c o u l d s e r v e t o e x p l a i n t h e m . In summary , t h e r e l a t i o n s h i p s be tween t h e c o g n i t i v e v a r i a b l e s and a c h i e v e m e n t r e p o r t e d i n t h e l i t e r a t u r e were t o some e x t e n t r e p l i c a t e d i n t h e p r e s e n t i n v e s t i g a t i o n . In t h e c a s e o f t h e n o n c o g n i t i v e v a r i a b l e s , t h e " f i t " be tween t h e r e s u l t s o f t h e p r e s e n t i n v e s t i g a t i o n and t h o s e r e p o r t e d i n t h e l i t e r a t u r e was much w o r s e . R e s e a r c h Q u e s t i o n Two. The s e c o n d r e s e a r c h q u e s t i o n e n q u i r e d a b o u t c l u s t e r s o f v a r i a b l e s r e v e a l e d by s u b j e c t i v e a n a l y s i s o f t h e c o r r e l a t i o n m a t r i x . The answer t o t h i s q u e s t i o n , a s r e p o r t e d i n C h a p t e r V , was b a s e d upon z e r o - o r d e r c o r r e l a t i o n s . No p a r t i a l o r m u l t i p l e c o r r e l a t i o n s were e x a m i n e d . Two c l u s t e r s were a b s t r a c t e d f r o m t h e i n t e r c o r r e l a t i o n m a t r i x c a l c u l a t e d f r o m t h e B r i t i s h C o l u m b i a d a t a . T h e s e c l u s t e r s were i n t e r p r e t e d a s a - c o g n i t i v e - e x p e r i e n t i a l c l u s t e r , f o u n d t o be r e l a t e d t o a c h i e v e m e n t , a n d an a t t i t u d e - m o t i v a t i o n a l 95 c l u s t e r , w h i c h was n o t . B o t h c l u s t e r s o f v a r i a b l e s a b s t r a c t e d f r o m t h e A l b e r t a s a m p l e ' s c o r r e l a t i o n m a t r i x were r e l a t e d t o a c h i e v e m e n t . The f i r s t c l u s t e r was i n t e r p r e t e d as g e n e r a l a b i l i t y and m o t i v a t i o n . The s e c o n d was an a t t i t u d i n a l -m o t i v a t i o n a l c l u s t e r . The d i f f e r e n c e s be tween t h e c l u s t e r s i d e n t i f i e d i n t h e B r i t i s h C o l u m b i a and A l b e r t a d a t a s e t s c a n be t e n t a t i v e l y r e l a t e d t o t h e m o d e l s d e l i n e a t e d i n C h a p t e r II a n d d r o p p e d f r o m t h e f i n a l a n a l y s i s b e c a u s e o f s m a l l s amp le s i z e s . The r e s u l t s o f t h e e x a m i n a t i o n o f t h e B r i t i s h C o l u m b i a i n t e r c o r r e l a t i o n m a t r i x s u g g e s t t h a t , when m e a s u r e d a t t h e o u t s e t o f a c o u r s e , E x p e r i e n c e may c o n t r i b u t e b o t h d i r e c t l y and i n d i r e c t l y ( t h r o u g h c o g n i t i v e a b i l i t i e s ) t o t h e v a r i a n c e i n S t a t i s t i c s A c h i e v e m e n t . The a b s e n c e o f s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s i n . w h i c h E x p e r i e n c e i s one o f t h e v a r i a b l e s i n t h e A l b e r t a s amp le s u g g e s t s t h a t t h e d i r e c t e f f e c t d i s a p p e a r s a s c o u r s e - t i m e p a s s e s and s t u d e n t s a r e e x p o s e d t o t h e s u b j e c t m a t t e r . F u r t h e r , t h e l a c k o f a z e r o - o r d e r r e l a t i o n s h i p be tween a t t i t u d e o r m o t i v a t i o n a n d a c h i e v e m e n t i n t h e B r i t i s h C o l u m b i a s a m p l e , c o m b i n e d w i t h t h e o c c u r r a n c e o f s e v e r a l s i g n i f i c a n t c o r r e l a t i o n s be tween e i t h e r E x p e r i e n c e o r a c o g n i t i v e v a r i a b l e and a n o n c o g n i t i v e o n e , t e n t a t i v e l y s u g g e s t s t h a t a t t h e b e g i n n i n g o f a c o u r s e t h e c o n t r i b u t i o n t o t h e v a r i a n c e i n a c h i e v e m e n t by t h e n o n c o g n i t i v e v a r i a b l e s i s i n d i r e c t t h r o u g h b o t h E x p e r i e n c e a n d c o g n i t i o n . H o w e v e r , when s t u d e n t s have had some e x p o s u r e t o t h e s u b j e c t m a t t e r , a s d i d t h e A l b e r t a s u b j e c t s , a t t i t u d e may c o n t r i b u t e d i r e c t l y and i n d i r e c t l y t o t h e 96 v a r i a n c e i n a c h i e v e m e n t . The i n f l u e n c e o f m o t i v a t i o n may r e m a i n i n d i r e c t . When c o n s i d e r i n g t h e p r e d i c t i o n o f A c h i e v e m e n t i n t h e n a i v e s u b j e c t , a mode l w h i c h r e t a i n s t h e d i r e c t e f f e c t o f E x p e r i e n c e and c o g n i t i v e v a r i a b l e s , s u c h a s M o d e l " A " , d e s c r i b e d i n C h a p t e r I I , ( w i t h t h e r e p l a c e m e n t o f t h e d i r e c t e f f e c t o f a t t i t u d e and m o t i v a t i o n w i t h i n d i r e c t e f f e c t s o f b o t h on b o t h e x p e r i e n c e and c o g n i t i o n ) may p l a u s i b l y e x p l a i n t h e o b s e r v e d c o r r e l a t i o n m a t r i x . The above a n a l y s i s s u g g e s t s t h a t a mode l s u c h a s M o d e l " C " , d e s c r i b e d i n C h a p t e r I I , may be more p l a u s i b l e a s an e x p l a n a t i o n o f s t a t i s t i c s a c h i e v e m e n t when some e x p o s u r e t o t h e s u b j e c t m a t t e r has a l r e a d y o c c u r r e d ( w i t h t h e a d d i t i o n o f an i n d i r e c t i n f l u e n c e o f m o t i v a t i o n on c o g n i t i o n ) . I t s h o u l d be n o t e d t h a t t h e r e s u l t s o f t h e s u b j e c t i v e e x a m i n a t i o n o f t h e c o r r e l a t i o n m a t r i c e s do n o t y i e l d any " h u n c h e s a n d g u e s s e s " ( i n B e n t l e r ' s s e n s e ) a b o u t t h e p o s s i b l e v a l u e s t h e p a t h c o e f f i c i e n t s m i g h t t a k e . R e s e a r c h Q u e s t i o n T h r e e . The t h i r d r e s e a r c h q u e s t i o n e n q u i r e d a b o u t t h e c o n t r i b u t i o n o f t h e s e t o f 12 i n d e p e n d e n t v a r i a b l e s t o t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t . The answer t o t h e q u e s t i o n , a s r e p o r t e d i n C h a p t e r V , was d e v e l o p e d t h r o u g h t h e a p p l i c a t i o n o f b o t h p a r s i m o n i o u s and e x p l o r a t o r y r e g r e s s i o n p r o c e d u r e s . O n l y E x p e r i e n c e s i g n i f i c a n t l y c o n t r i b u t e d t o t h e v a r i a n c e i n s t a t i s t i c s a c h i e v e m e n t i n t h e B r i t i s h C o l u m b i a s a m p l e , w h i l e t h r e e v a r i a b l e s ( P ape r F o l d i n g , A t t i t u d e Toward S t a t i s t i c s and 97 C o n c e p t L e a r n i n g ) d i d so i n t h e A l b e r t a s a m p l e . In a d d i t i o n , e x p l o r a t o r y a n a l y s i s r e v e a l e d t h a t t h e r e l a t i v e c o n t r i b u t i o n s t o t h e v a r i a n c e f o r t h e n o n s i g n i f i c a n t l y c o n t r i b u t i n g v a r i a b l e s were v e r y d i f f e r e n t i n t h e two s a m p l e s . U n l i k e t h e r e s u l t s o f a n a l y s i s o f t h e A l b e r t a s a m p l e , t h e r e s u l t s y i e l d e d by t h e B r i t i s h C o l u m b i a s a m p l e do n o t r e s e m b l e t h o s e o f H a r t l e y and H a r t l e y ( 1 9 7 6 ) , o r t h o s e o f E l m o r e and V a s u ( 1 9 8 0 ) . In t h e A l b e r t a s a m p l e , b o t h s p a t i a l v i s u a l i z a t i o n and m a t h e m a t i c a l s k i l l s among t h e c o g n i t i v e v a r i a b l e s , and A t t i t u d e T o w a r d S t a t i s t i c s , s i g n i f i c a n t l y c o n t r i b u t e d t o t h e v a r i a n c e i n A c h i e v e m e n t . B o t h H a r t l e y and H a r t l e y and E l m o r e and V a s u r e p o r t e d t h a t a t t i t u d e was r e l a t e d t o A c h i e v e m e n t . The f o r m e r f o u n d t h a t m a t h e m a t i c a l s k i l l c o r r e l a t e d w i t h s t a t i s t i c s a c h i e v e m e n t , w h i l e E l m o r e and V a s u r e p o r t e d a s i g n i f i c a n t r e l a t i o n s h i p be tween A c h i e v e m e n t and S p a t i a l V i s u a l i z a t i o n . A f o u r t h v a r i a b l e , E x p e r i e n c e had been f o u n d by E l m o r e and V a s u t o be r e l a t e d t o S t a t i s t i c s A c h i e v e m e n t . T h i s r e l a t i o n s h i p was o b s e r v e d o n l y i n t h e B r i t i s h C o l u m b i a s a m p l e , and was s t r o n g e r t h a n t h a t r e p o r t e d by t h e s e a u t h o r s . H o w e v e r , t h e c o n t r i b u t i o n s o f s p a t i a l v i s u a l i z a t i o n and m a t h e m a t i c s s k i l l s were n o t s i g n i f i c a n t , and t h a t o f a t t i t u d e was e x t r e m e l y s m a l l . The c o n t r i b u t i o n o f t h e v a r i a b l e , A c a d e m i c S e l f - C o n c e p t , was l o w e r f o r b o t h s a m p l e s t h a n t h a t r e p o r t e d by H a r t l e y and H a r t l e y . B o t h t h e p a r s i m o n i o u s a n d e x p l o r a t o r y r e g r e s s i o n p r o c e d u r e s y i e l d some e v i d e n c e a b o u t t h e d i r e c t e f f e c t s o f t h e i n d e p e n d e n t v a r i a b l e s on A c h i e v e m e n t . The r e s u l t s o f t h e a n a l y s e s o f t h e 98 B r i t i s h C o l u m b i a s amp le r e v e a l t h a t E x p e r i e n c e d i d i n d e e d e x e r t a d i r e c t i n f l u e n c e on A c h i e v e m e n t . When c o n s i d e r e d i n t h e o r d e r o f e n t r y , t h e n e x t v a r i a b l e s t o c o n t r i b u t e t o t h e v a r i a n c e i n A c h i e v e m e n t were c o g n i t i v e . As was n o t e d i n t h e d i s c u s s i o n o f R e s e a r c h Q u e s t i o n Two, t h e i n f l u e n c e o f c o g n i t i v e v a r i a b l e s was h y p o t h e s i z e d t o be d i r e c t . Howeve r , t h e n e x t e n t r y was t h e m o t i v a t i o n a l v a r i a b l e A c h i e v e m e n t M o t i v a t i o n . T h i s f i n d i n g may i n d i c a t e t h a t m o t i v a t i o n e x e r t s a d i r e c t e f f e c t . Whether t h e s e v e r a l o b s e r v e d c o n t r i b u t i o n s t o t h e v a r i a n c e i n a c h i e v e m e n t w o u l d w i t h s t a n d c r o s s - v a l i d a t i o n i s n o t c e r t a i n , g i v e n t h e s m a l l s a m p l e s i z e s and t h e o t h e r l i m i t a t i o n s d i s c u s s e d b e l o w . J u s t a s some o f t h e s p e c u l a t i o n c o n c e r n i n g t h e d i r e c t e f f e c t s o f E x p e r i e n c e and c o g n i t i o n were r e f l e c t e d i n t h e d i s c u s s i o n o f t h e r e s u l t s o f a n a l y s i s o f t h e B r i t i s h C o l u m b i a d a t a , so d i r e c t e f f e c t s o f c o g n i t i o n and a t t i t u d e , d i s c u s s e d a b o v e , were r e f l e c t e d i n t h e r e s u l t s o f t h e e x p l o r a t o r y and p a r s i m o n i o u s a n a l y s e s o f t h e A l b e r t a d a t a . S p a t i a l v i s u a l i z a t i o n and c o n c e p t l e a r n i n g made s i g n i f i c a n t c o n t r i b u t i o n s t o t h e v a r i a n c e i n a c h i e v e m e n t . Once a g a i n , A c h i e v e m e n t M o t i v a t i o n was e n t e r e d n e x t , c o n t r i b u t i n g 4 . 0 4 % t o t h e c h a n g e i n R - s q u a r e . L i m i t a t i o n s o f t h e S t u d y T h e most s e r i o u s l i m i t a t i o n o f t h i s i n v e s t i g a t i o n a r o s e a s t h e r e s u l t o f t h e n o n e q u i v a l e n c e o f t h e B r i t i s h C o l u m b i a and A l b e r t a s a m p l e s . T h i s s t a t i s t i c a l and l o g i c a l f i n d i n g meant t h a t t h e s a m p l e s c o u l d n o t be p o o l e d , and c o n s e q u e n t l y two s m a l l 99 s a m p l e s r a t h e r t h a n a s i n g l e l a r g e r one were a v a i l a b l e f o r a n a l y s i s . The r e f o r m u l a t i o n o f t h e r e s e a r c h q u e s t i o n s became n e c e s s a r y , and t h e t h r e e m o d e l s w h i c h were o r i g i n a l l y p o s t u l a t e d c o u l d no t be e v a l u a t e d . F o r t h e same r e a s o n , no i n v e s t i g a t i o n i n t o t h e l a t e n t s t r u c t u r e u n d e r l y i n g t h e s e t o f t w e l v e m a n i f e s t v a r i a b l e s was c a r r i e d o u t . F i n a l l y , t h e s m a l l s amp l e s i z e s , b e i n g g e n e r a l l y s u b j e c t t o g r e a t e r f l u c t u a t i o n due t o c h a n c e , c a s t t h e e n t i r e s e t o f r e s u l t s i n t o d o u b t . A s e c o n d s e r i o u s l i m i t a t i o n o f t h i s s t u d y was t h a t o f low g e n e r a l i z a b i l i t y f r o m t h e s amp l e t o t h e t a r g e t p o p u l a t i o n . I t i s by no means c e r t a i n t h a t t h e s u b j e c t s , who were s t u d e n t s i n E d u c a t i o n , were r e p r e s e n t a t i v e o f a l l s o c i a l s c i e n c e s s t u d e n t s e n r o l l e d i n i n t r o d u c t o r y s t a t i s t i c s c o u r s e s . F u r t h e r , t h e s t u d e n t s were e n r o l l e d i n Summer S e s s i o n c o u r s e s r a t h e r t h a n r e g u l a r w i n t e r s e s s i o n c l a s s e s . V o l u n t e e r s were b e i n g t e s t e d , a l t h o u g h p a r t i c i p a t i o n f r o m t h r e e o f t h e f o u r c o u r s e s was v e r y h i g h . T h e s e c o n s i d e r a t i o n s must be t a k e n i n t o a c c o u n t when e v a l u a t i n g t h e r e s u l t s o f t h e i n v e s t i g a t i o n . F i n a l l y , t h e t e s t s were l i m i t e d i n r a n g e o f a b i l i t i e s t e s t e d and i n p s y c h o m e t r i c p r o p e r t i e s . The r e s t r i c t i o n s p l a c e d on t e s t i n g t i m e so a s n o t t o t a k e up t o o much c l a s s t i m e i n a Summer S c h o o l c o u r s e n e c e s s i t a t e d s h o r t t e s t l e n g t h s , and a r e l a t i v e l y r e s t r i c t e d r a n g e o f v a r i a b l e s t e s t e d . In a d d i t i o n , i t was i m p o s s i b l e t o a s k t h e i n s t r u c t o r s o f t h e c o u r s e s t o g i v e up more t h a n one c l a s s p e r i o d . C o n s e q u e n t l y , any c o n c l u s i o n s a b o u t t h e r a n g e o f a b i l i t i e s w h i c h r e l a t e t o S t a t i s t i c s A c h i e v e m e n t a r e e ven more l i m i t e d . The ma in a l t e r n a t i v e , t h a t 1 00 o f t e s t i n g o u t s i d e o f c l a s s t i m e , c o u l d have r e s u l t e d i n an even l e s s r e p r e s e n t a t i v e s a m p l e . C o n c l u s i o n s and I m p l i c a t i o n s The r e s u l t s o f t h i s i n v e s t i g a t i o n a r e i n c o n c l u s i v e . The s m a l l s amp l e s i z e s r e s t r i c t t h e power o f t h e i n v e s t i g a t i o n . F u r t h e r , t h e f a c t t h a t t h e s u b j e c t s were Summer S c h o o l s t u d e n t s r a t h e r t h a n w i n t e r s e s s i o n s t u d e n t s r e s t r i c t s e x t e r n a l v a l i d i t y . H o w e v e r , some " h u n c h e s and g u e s s e s " ( i n B e n t l e r ' s u s a g e ) may be d rawn f r o m t h e r e s u l t s . F i r s t , w i t h r e g a r d t o t h e c o r r e l a t e s o f S t a t i s t i c s A c h i e v e m e n t , i t may be c o n c l u d e d t h a t t h e two v a r i a b l e s , s p a t i a l v i s u a l i z a t i o n and m a t h e m a t i c a l s k i l l s , do c o r r e l a t e w i t h S t a t i s t i c s A c h i e v e m e n t . T h i s c o n c l u s i o n i s b a s e d upon t h e f a c t t h a t t h i s f i n d i n g r e p l i c a t e s r e s u l t s r e p o r t e d i n t h e l i t e r a t u r e . E x p e r i e n c e and A c h i e v e m e n t were r e l a t e d o n l y i n t h e l e s s e x p e r i e n c e d s a m p l e . T h i s f i n d i n g h a s n o t been r e p o r t e d i n t h e l i t e r a t u r e . I t may be t h a t t h e n o n c o g n i t i v e v a r i a b l e , A t t i t u d e Towa rd S t a t i s t i c s , i s r e l a t e d t o a c h i e v e m e n t i n s t a t i s t i c s o n l y i n t h e s u b j e c t who has had some e x p o s u r e t o t h e s u b j e c t m a t t e r . S e c o n d , t h e r e s u l t s o f t h e e x a m i n a t i o n o f t h e i n t e r c o r r e l a t i o n m a t r i c e s s u g g e s t s t h a t t h e i n v e s t i g a t i o n o f two d i f f e r e n t m o d e l s m i g h t y i e l d p l a u s i b l e e x p l a n a t i o n s o f a c h i e v e m e n t i n t h e i n e x p e r i e n c e d and t h e e x p o s e d s u b j e c t , r e s p e c t i v e l y . F i g u r e 6 p o r t r a y s a mode l w h i c h may " f i t " d a t a c o l l e c t e d f r o m t h e i n e x p e r i e n c e d s u b j e c t . As d i s c u s s e d a b o v e , t h e 101 F i g u r e 6 M o d e l o f A c h i e v e m e n t ( L e s s E x p e r i e n c e d S t u d e n t ) i n d i r e c t r o l e o f m o t i v a t i o n a l v a r i a b l e s may be s u p p l e m e n t e d by some d i r e c t e f f e c t . The p o s s i b l e d i r e c t e f f e c t i s i n d i c a t e d by t h e d o t t e d l i n e i n F i g u r e 6. O n l y f u r t h e r r e s e a r c h c a n c l a r i f y t h i s i s s u e , and t e s t o r r e f i n e t h e m o d e l . The s t a n d a r d i z e d b e t a w e i g h t s , c a l c u l a t e d f r o m t h e B r i t i s h C o l u m b i a s a m p l e , c o u l d be t a k e n as a g u i d e f o r s p e c i f i c a t i o n o f t he p a t h c o e f f i c i e n t s . Howeve r , t h e s amp le i s so s m a l l t h a t t h e w e i g h t s may be e x t r e m e l y i n a c c u r a t e . E x p e r i e n c e >• Cogn i t i on-^___^ /A t t i t u d e A c h i e v e m e n t t M o t i v a t i o n - ' ' F i g u r e 7 M o d e l o f A c h i e v e m e n t (More E x p e r i e n c e d S t u d e n t ) The mode l d e p i c t e d i n F i g u r e 7, i s v e r y s i m i l a r t o m o d e l " C " d e l i n e a t e d i n C h a p t e r I I , a n d may p l a u s i b l y a c c o u n t f o r t h e o b s e r v e d r e l a t i o n s h i p s among v a r i a b l e s c o l l e c t e d f r o m e x p e r i e n c e d s t u d e n t s , who have been e x p o s e d t o i n s t r u c t i o n i n s t a t i s t i c s . A g a i n , t h e m o d e l was d i s c u s s e d a b o v e . A l t h o u g h t h e 1 02 b e t a w e i g h t s r e p o r t e d above c o u l d s e r v e as i n i t i a l e s t i m a t e s o f t h e p a t h c o e f f i c i e n t s , s p e c i f i c a t i o n s s u c h a s t h e s e may be s u b j e c t t o e x t r e m e f l u c t u a t i o n on c r o s s - v a l i d a t i o n . F i n a l l y , i t may be c o n c l u d e d t h a t , w i t h t h e s e t o f m e a s u r e s i n v e s t i g a t e d i n t h i s s t u d y , a p p r o x i m a t e l y 55% o f t h e v a r i a n c e i n a c h i e v e m e n t i n s t a t i s t i c s i s e x p l a i n e d . Howeve r , t h e c o n t r i b u t i o n s o f t h e s e v e r a l i n d e p e n d e n t v a r i a b l e s v a r i e s w i t h t h e amount o f s t a t i s t i c s i n s t r u c t i o n t o w h i c h t h e s u b j e c t s have been e x p o s e d . S e v e r a l i m p l i c a t i o n s f o r f u t u r e r e s e a r c h may be drawn f r o m t h e r e s u l t s o f t h i s i n v e s t i g a t i o n . F i r s t , f u r t h e r i n v e s t i g a t i o n s i n t o t h e e f f e c t o f e x p o s u r e t o s t a t i s t i c s on t h e c o r r e l a t e s and d e t e r m i n a n t s o f s t a t i s t i c s a c h i e v e m e n t a r e d e s i r a b l e . S e c o n d , t h e m o d e l s o f a c h i e v e m e n t , w h i c h were d e v e l o p e d f r o m s u b j e c t i v e a n a l y s i s a n d e x p l o r a t o r y r e g r e s s i o n a n a l y s i s , s h o u l d be s u b j e c t t o more s t r i n g e n t i n v e s t i g a t i o n . F i n a l l y , t h e p o t e n t i a l e x p l a n a t o r y power o f i n d e p e n d e n t v a r i a b l e s w h i c h were e x c l u d e d f r o m c o n s i d e r a t i o n i n t h e p r e s e n t i n v e s t i g a t i o n s h o u l d be e m p i r i c a l l y d e t e r m i n e d . The a r e a o f t h e c o r r e l a t e s and d e t e r m i n a n t s o f m a t h e m a t i c s a c h i e v e m e n t w o u l d a p p e a r t o be a f r u i t f u l s o u r c e o f p o s s i b l e p r e d i c t o r s . 1 03 N o t e s H a k s t i a n , R. OWMAR: One-way m u l t i v a r i a t e a n a l y s i s o f v a r i a n c e . U n p u b l i s h e d memorandum. 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S a n d e r s , J . R . and W o r t h e n , B .R .• An A n a l y s i s o f E m p l o y e r s '  P e r c e p t i o n s o f t h e R e l a t i v e I m p o r t a n c e o f S e l e c t e d R e s e a r c h  and R e s e a r c h - R e l a t e d C o m p e t e n c i e s and S h o r t a g e s o f  P e r s o n n e l w i t h s u c h C o m p e t e n c i e s . U n i v e r s i t y o f C o l o r a d o , 1970 . S e p i e , A . C . and K e e l i n g , B. The r e l a t i o n s h i p be tween t y p e s o f a n x i e t y and u n d e r - a c h i e v e m e n t i n m a t h e m a t i c s . J o u r n a l o f  E d u c a t i o n a l R e s e a r c h , 1978 , 7_2, 1 5 - 1 9 . S h e r m a n , J . M a t h e m a t i c s , s p a t i a l v i s u a l i z a t i o n and r e l a t e d f a c t o r s : c h a n g e s i n g i r l s and b o y s , g r a d e s 8 - 1 1 . J o u r n a l  o f E d u c a t i o n a l P s y c h o l o g y , 1980 , 7 2 , 4 7 6 - 4 8 2 . S h y e , S. A c h i e v e m e n t m o t i v e : a f a c e t e d d e f i n i t i o n and s t r u c t u r a l a n a l y s i s . M u l t i v a r i a t e B e h a v i o r a l R e s e a r c h , 1978 , J_3, 3 2 7 - 4 6 . S i n g h , B .K . N o n - I n t e l l e c t i v e C o r r e l a t e s o f A c a d e m i c A c h i e v e m e n t . A l l a h b a d : I n d i a n I n t e r n a t i o n a l P u b l i c a t i o n s , 1976 . T imm, N . H . M u l t i v a r i a t e A n a l y s i s . B e l m o n t , C a l . : Wadswor th 107 C o . , 1975 . T r o u t m a n , J . G . C o g n i t i v e p r e d i c t o r s o f f i n a l g r a d e s i n f i n i t e m a t h e m a t i c 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 M e a s u r e m e n t , 1978 , 3 8 , 4 0 1 - 4 0 4 . V i d l e r , D . C . A c h i e v e m e n t m o t i v a t i o n . i n S . B a l l ( e d . ) , M o t i v a t i o n In E d u c a t i o n . New Y o r k : A c a d e m i c P r e s s , 1977 . W h i t e , K .R . The r e l a t i o n s h i p be tween s o c i o e c o n o m i c s t a t u s and  a c a d e m i c a c h i e v e m e n t . P a p e r p r e s e n t e d a t t h e A n n u a l M e e t i n g o f t he A m e r i c a n E d u c a t i o n a l R e s e a r c h A s s o c i a t i o n (San F r a n c i s c o , C a l i f o r n i a , A p r i l 12, 1979) W o l f l e , L . M. S t r a t e g i e s o f p a t h a n a l y s i s . A m e r i c a n E d u c a t i o n  R e s e a r c h J o u r n a l , 1980 , _T7, 1 8 3 - 2 0 9 . 108 A p p e n d i x A I n i t i a l Form o f t h e  C o n c e p t L e a r n i n g T a s k T a s k I n s t r u c t i o n s T h i s f o r m i s a m e a s u r e o f how q u i c k l y and w e l l you c a n l e a r n an u n f a m i l i a r m a t h e m a t i c a l c o n c e p t . F i r s t , t h e c o n c e p t i s d e s c r i b e d a n d s e c o n d , n i n e q u e s t i o n s a r e a s k e d t o t e s t y o u r a b i l i t y t o u s e t h e c o n c e p t . You c a n r e f e r back t o t h e c o n c e p t d e s c r i p t i o n s w h i l e a n s w e r i n g t h e q u e s t i o n s and you c a n do t h e q u e s t i o n s i n any o r d e r y o u w i s h . The t i m e l i m i t i s t w e l v e (12) m i n u t e s . I w i l l t e l l y o u when f o u r m i n u t e s and e i g h t m i n u t e s have p a s s e d . F i r s t , p l e a s e answe r t h i s q u e s t i o n . Do y o u know what t he s y m b o l {i = 1 }*{5} X,j means? I f y ou a n s w e r e d " Y e s " , p l e a s e w r i t e what you t h i n k i t means h e r e : P l e a s e t u r n t h e page and b e g i n when I t e l l y o u t o " t u r n a n d b e g i n now " . 109 C o n c e p t D e s c r i p t i o n . A . S u b s c r i p t N o t a t i o n . I f we have a " m a t r i x " c o n t a i n i n g " e l e m e n t s " , we can r e f e r t o any e l e m e n t by i t s p o s i t i o n i n t h e m a t r i x . I f we have a m a t r i x w i t h 12 e l e m e n t s ( i . e . , n u m b e r s ) , s u c h a s : 1 2 Row 1 2 3 Row 2 0 - 1 Row 3 4 7 o lumn 3 4 1 5 6 2 0 -6 we c a n c a l l any o f i t s numbers o r e l e m e n t s Xjj . " i " i s t h e number o f t h e ROW o f t h e m a t r i x and " j " i s t h e number o f t h e COLUMN o f t h e m a t r i x . F o r e x a m p l e , X 4 2 , r e f e r s t o t h e e l e m e n t i n t h e f i r s t row and t h e s e c o n d c o l u m n , o r t h e number 3. S o , X 1 2 , = 3, and X z i = 0 , e t c . 110 B. A d d i t i o n N o t a t i o n . In t h i s t a s k , t h e s y m b o l " • " means " a d d i t i o n " . When y o u see t h i s s y m b o l , you a r e t o ADD numbers t o g e t h e r . The d i a g r a m g i v e n be low w i l l t e l l y o u how t o d e c i d e w h i c h numbers a r e t o be a d d e d t o g e t h e r . where t o b e g i n a d d i n g where t o s t o p a d d i n g - a d d i t i o n s i g n s u b s c r i p t t o a d d o v e r {i=m} • {n} Xjj t h e 1st s u b s c r i p t (ROW) t he 2nd s u b s c r i p t (COLUMN) -the e l e m e n t t o a d d B a s e d on t h e d i a g r a m and t h e m a t r i x g i v e n a b o v e , an e x a m p l e m i g h t b e : {i = U • {2} X,-3 = X 1 3 + X Z 3 = 1 + 6 = 7 111 T e s t Q u e s t i o n s . P l e a s e w r i t e y o u r answe r f o r e a c h i t e m i n t h e s p a c e f o l l o w i n g t h e i t e m . Use any b l a n k s p a c e you w i s h f o r y o u r r o u g h w o r k . Use t h e m a t r i x f r o m t h e " C o n c e p t D e s c r i p t i o n " t o c a l c u l a t e y o u r a n s w e r s . 1 • X ± 2 , =  2. { j = 1 } • { 4} X^j = 3. { i = 2 } » { 3 } Kit = 4 . { i = 2 } « { 3 } X i 3 X i a , = 5. { i = 2 } » { 2 } Xj^ = 6 . {j = 2 } « { 4 } XAj XZJ- X 3 j = 7. i f c = 3, {j = 2 } » { 4 } c X 4 j = 8 . i f c = 2, { J = 1 } « { 3 } ( X i j -c ) = 9 . d o e s {k=1}•{3} X f e t X k f c e q u a l [ { k = l } » { 3 } X k l ] [ { k = l } « { 3 } X k t , ] ? 1 1 2 A p p e n d i x B. N o n - C o p y r i g h t T e s t M a t e r i a l s I n t r o d u c t o r y S t a t e m e n t . "My name i s Sheena S e l k i r k and I am a g r a d u a t e s t u d e n t i n Measu remen t a n d R e s e a r c h M e t h o d o l o g y a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . T h i s s t u d y i s an i n v e s t i g a t i o n i n t o t h e e x t e n t t o w h i c h a b i l i t i e s and a t t i t u d e s a r e r e l a t e d t o t h e p e r f o r m a n c e i n i n t r o d u c t o r y s t a t i s t i c s . You r p a r t i c i p a t i o n i s v o l u n t a r y , b u t I w o u l d c e r t a i n l y a p p r e c i a t e y o u r c o - o p e r a t i o n . The more c o m p l e t e my d a t a a r e , t h e b e t t e r I c a n t a l k a b o u t how w e l l t h e m e a s u r e s p r e d i c t marks i n t h e c l a s s . The c o m p l e t e s e t o f m e a s u r e s w i l l be a d m i n i s t e r e d i n t o d a y ' s c l a s s and w i l l t a k e a b o u t one and o n e - q u a r t e r h o u r s , w i t h a s h o r t b r e a k h a l f - w a y t h r o u g h . The q u e s t i o n n a i r e s w i l l i n c l u d e s e l f - r a t i n g s , an a t t i t u d e m e a s u r e , and s e v e r a l c o g n i t i v e m e a s u r e s . In a d d i t i o n , I w o u l d l i k e y o u t o g i v e me p e r m i s s i o n t o r e c e i v e y o u r mark i n t h e f i n a l exam f rom y o u r i n s t r u c t o r . A l l r e p o r t i n g o f r e s u l t s w i l l be done o n l y on a g r o u p b a s i s . A l l i n f o r m a t i o n w i l l be t r e a t e d a s c o n f i d e n t i a l and w i l l be s h a r e d w i t h n o - o n e . I f y o u w o u l d l i k e t o know a b o u t t h e r e s u l t s o f t h i s s t u d y , p l e a s e c o n t a c t me i n t h e f a l l and I w i l l t e l l y o u a b o u t t h e m . I f y ou a r e w i l l i n g t o p a r t i c i p a t e , p l e a s e r e a d and s i g n t h e l e t t e r o f c o n s e n t , a n d we w i l l b e g i n w i t h t h e f i r s t q u e s t i o n n a i r e . " 1 13 L e t t e r o f C o n s e n t . I g i v e , t h e i n s t r u c t o r o f t h e c o u r s e , , i n w h i c h I am c u r r e n t l y r e g i s t e r e d , p e r m i s s i o n t o g i v e my f i n a l mark t o Sheena S e l k i r k , on t h e c o n d i t i o n t h a t she w i l l n o t r e v e a l t h e mark t o any o t h e r p e r s o n . I u n d e r s t a n d t h a t t h e marks w i l l be r e p o r t e d a s g r o u p s t a t i s t i c s o n l y . F u r t h e r , I u n d e r s t a n d t h a t I may r e f u s e t o p a r t i c i p a t e o r w i t h d r a w f r o m t h e s t u d y a t a l a t e r d a t e and t h a t e i t h e r a c t i o n , i f t a k e n , w i l l i n no way i n f l u e n c e my f i n a l s t a n d i n g i n t h i s c o u r s e . S i g n e d , 1 1 4 C o n c e p t L e a r n i n g T a s k . T h i s f o r m i s a measu re o f how q u i c k l y and w e l l you c a n l e a r n an u n f a m i l i a r m a t h e m a t i c a l c o n c e p t . F i r s t , t h e c o n c e p t i s d e s c r i b e d and s e c o n d , 13 q u e s t i o n s a r e a s k e d t o t e s t y o u r a b i l i t y t o u s e t h e c o n c e p t . You may r e f e r back t o t h e c o n c e p t d e s c r i p t i o n w h i l e a n s w e r i n g t h e q u e s t i o n s and you may do t h e q u e s t i o n s i n any o r d e r you w i s h . THERE ARE NO TRICK QUESTIONS. ALL THE INFORMATION YOU NEED TO ANSWER THE QUESTIONS IS CONTAINED IN THE CONCEPT DESCR IPT ION, EXCEPT FOR BAS IC ARITHMETIC AND ALGEBRAIC S K I L L S . The t i m e l i m i t f o r t h i s t a s k i s t w e l v e (12) m i n u t e s . I w i l l t e l l y o u when f o u r m i n u t e s and e i g h t m i n u t e s have p a s s e d . P l e a s e t u r n t h e page and b e g i n when I s a y , " T u r n and b e g i n now. " CONCEPT DESCRIPT ION S u b s c r i p t N o t a t i o n . I f we have a " v e c t o r " c o n t a i n i n g numbers o r " e l e m e n t s " , we may r e f e r t o any e l e m e n t i n t h e v e c t o r , u s i n g s u b s c r i p t s . F o r e x a m p l e , i f we have t h e f o l l o w i n g v e c t o r : E l e m e n t Number 1 - 2 3 4 5 6 7 8 9 U ) S c o r e : 0 5 3 9 1 0 4 7 0 6 We may c a l l any o f i t s e l e m e n t s Xj , where i = 1 , 2 , 3 and so on up t o 1 0 . F o r t h i s e x a m p l e , i f i = 4 , X; =9 . S i m i l a r l y , i f i = 9 , t h e n X; =0 and X,, =XL =X 4 =0. Summat ion N o t a t i o n . In t h i s t a s k , t h e s y m b o l " • " means ADD IT ION . When y o u see t h e s y m b o l " • " , you a r e t o ADD numbers t o g e t h e r . The f o l l o w i n g d i a g r a m w i l l h e l p y o u t o l e a r n t o know WHICH NUMBERS you a r e t o a d d . where t o b e g i n a d d i n g ^ _^-whe re t o s t o p a d d i n g In} • {irt t t h e a d d i t i o n s i g n t h e e l e m e n t t o a d d B a s e d on t h e v e c t o r o f numbers g i v e n a b o v e , a n d on t h e d i a g r a m , an e x a m p l e o f t h e use o f t h i s n o t a t i o n m i g h t b e : {2} • {5} X-, = X^ + X s + X^ + X r = 5 + 3 + 9 + 1 = 18 1 15 TEST QUESTIONS P l e a s e w r i t e y o u r answer f o r e a c h q u e s t i o n i n t he s p a c e f o l l o w i n g t h e q u e s t i o n . Use any b l a n k s p a c e y o u w i s h f o r y o u r r o u g h wo rk . The two v e c t o r s t o use i n a n s w e r i n g t h e s e q u e s t i o n s a r e : V e c t o r E l e m e n t Number : 1 2 3 4 5 6 7 8 V e c t o r X : 5 8 3 2 1 9 4 7 V e c t o r Y : 7 1 6 0 4 5 8 3 1. X 3 + Y + = 2. Xf + 5Y-, = 3. 4 ( Y ? + 4 X Z ) = 4 . 3 ( X 3 Yz + X^ ) = 5. 2 ( X * - Y 5 )* + X j = 6 . {1} • (8} Xk = 7. {4} • {7} Yk = 8. {2} • {6} X,- Y; = 9 . {7} • {7} Y * = 10 . {3} • {6} ( X k + 2) = 11 . (4} • {5} (Yj - 5) = 12 . {6} • {8} 3Xj = 13 . d o e s {1} • {3} X,- Y; e q u a l [{1} • (3} Xj ] [{1} • {3} Yj ] ? 116 A t t i t u d e M e a s u r e . ATT ITUDES ABOUT STAT I ST ICS AND RESEARCH DESIGN T h i s q u e s t i o n n a i r e c o n s i s t s o f q u e s t i o n s a b o u t d o i n g r e s e a r c h and s t a t i s t i c s . You r t a s k i s t o d e c i d e how much you a g r e e o r d i s a g r e e w i t h e a c h s t a t e m e n t , a n d t h e n t o mark an " X " t h r o u g h t h e number t h a t i n d i c a t e s y o u r d e g r e e o f a g r e e m e n t . The s c a l e t o be u s e d f o r e a c h s t a t e m e n t i s : 1- s t r o n g l y d i s a g r e e 2- d i s a g r e e 3- d i s a g r e e a l i t t l e 4- n e i t h e r a g r e e n o r d i s a g r e e 5- a g r e e a l i t t l e 6- a g r e e 7- s t r o n g l y a g r e e . F o r e x a m p l e : I l i k e s t a t i s t i c s I f y ou " d i s a g r e e a l i t t l e " w i t h t h i s s t a t e m e n t , y o u w o u l d mark an " X " t h r o u g h " 3 " , o r i f y o u " s t r o n g l y a g r e e " w i t h t h e s t a t e m e n t , y o u w o u l d mark an " X " t h r o u g h " 7 " . T h e r e a r e 40 s t a t e m e n t s . P l e a s e r e s p o n d t o e a c h o n e , and o n l y mark one " X " f o r e a c h s t a t e m e n t . P r e v i o u s use o f t h i s q u e s t i o n n a i r e h a s shown t h a t most s u b j e c t s f i n i s h i n a b o u t f i v e m i n u t e s . N o t e t h a t on t h e f o r m u s e d by t h e s u b j e c t , e a c h q u e s t i o n was f o l l o w e d by t h e numbers " 1 " t h r o u g h " 7 " . 1. P l a n n i n g r e s e a r c h w o u l d be a r e w a r d i n g a c t i v i t y f o r me. 2. I t h i n k t h a t i t w o u l d be i n t e r e s t i n g t o t h i n k a b o u t w h i c h r e s e a r c h m e t h o d m i g h t be b e s t t o s o l v e a g i v e n p r o b l e m . 3. I w o u l d e n j o y t a l k i n g a b o u t r e s e a r c h p r o b l e m s w i t h my f r i e n d s . 4 . T h i n k i n g a b o u t s t a t i s t i c s makes me f e e l s i c k . 5. I d o n ' t l i k e t o have t o d e c i d e a b o u t w h e t h e r some p i e c e o f r e s e a r c h i s good o r b a d . 6 . A l m o s t a n y t h i n g i s more i n t e r e s t i n g t h a n s t a t i s t i c s . 7. The s y m b o l s u s e d i n s t a t i s t i c s a r e h a r d f o r me t o u n d e r s t a n d . 8 . I f i n d t h e d i f f e r e n t ways i n w h i c h one c o u l d do r e s e a r c h v e r y c o n f u s i n g . 9 . The a s s i g n m e n t s I w i l l e n j o y mos t a r e t h o s e w h i c h i n v o l v e 1 1 7 s t a t i s t i c s . 10 . S t a t i s t i c s makes me no more a n x i o u s t h a n any o t h e r s u b j e c t d o e s . 1 1 . E v a l u a t i n g r e s e a r c h i s c h a l l e n g i n g and s t i m u l a t i n g . 12. I w o u l d n e v e r buy a s t a t i s t i c s book i f I d i d n ' t have t o . 13 . I o n l y t h i n k a b o u t d o i n g r e s e a r c h when I h ave t o . 14. I am l o o k i n g f o r w a r d t o d o i n g my own r e s e a r c h some d a y . 15 . I f i n d i t e a s y t o u n d e r s t a n d t h e d i f f e r e n t ways o f p l a n n i n g r e s e a r c h . 16 . I wou ld e n j o y t h i n k i n g a b o u t what t o c o n c l u d e f r o m s t a t i s t i c a l c a l c u l a t i o n s . 17 . D o i n g r e s e a r c h wou ld be a was te o f t i m e f o r me. 18 . I w o u l d l i k e t o r e a d a b o u t how t o do r e s e a r c h . 1 9 . The w o r s t exams a r e t h o s e i n w h i c h y o u have t o use s t a t i s t i c s t o g e t t h e r i g h t a n s w e r s . 2 0 . T h e r e i s t o o much e m p h a s i s i n u n i v e r s i t y on r e s e a r c h and how t o do i t . 2 1 . W o r k i n g a s a r e s e a r c h c o n s u l t a n t i s a j o b I ' d l i k e t o do someday . 2 2 . An i n t e r e s t i n g a s s i g n m e n t m i g h t be t o do some s t a t i s t i c s i n d i f f e r e n t ways and t h e n compa re t h e r e s u l t s . 2 3 . I e n j o y t h i n k i n g a b o u t s t a t i s t i c a l p r o b l e m s . 2 4 . I f I e v e r had t o do r e s e a r c h I w o u l d l i k e i t i f someone e l s e p l a n n e d how t o c a r r y i t o u t . 2 5 . D o i n g s t a t i s t i c s w o u l d make me f e e l a n x i o u s . 2 6 . I w o u l d r a t h e r r e a d a b o u t t h e c o n c l u s i o n s f r o m some r e s e a r c h t h a n a b o u t how i t was d o n e . 2 7 . I f i n d s t a t i s t i c s e x c i t i n g and e n j o y a b l e . 2 8 . The ways i n w h i c h s t a t i s t i c a l f o r m u l a s a r e d e r i v e d w o u l d be e a s y t o u n d e r s t a n d . 2 9 . D o i n g s t a t i s t i c s i s a l m o s t a l w a y s b o r i n g . 3 0 . E ven when I am i n t e r e s t e d i n t h e s u b j e c t , I r a r e l y t h i n k a b o u t how t o do r e s e a r c h i n i t . 1 18 3 1 . I s o m e t i m e s do s t a t i s t i c a l c a l c u l a t i o n s f o r f u n . 3 2 . I t r y t o a v o i d t a k i n g s t a t i s t i c s c l a s s e s . 3 3 . I t i s b o r i n g t o t a l k a b o u t r e s e a r c h w i t h o t h e r p e o p l e . 3 4 . My f a v o u r i t e a s s i g n m e n t s i n v o l v e e v a l u a t i n g r e s e a r c h . 3 5 . I am l o o k i n g f o r w a r d t o l e a r n i n g l o t s a b o u t s t a t i s t i c s . 3 6 . I w o u l d a l w a y s p u t o f f d o i n g a s s i g n m e n t s w h i c h i n v o l v e d d o i n g s t a t i s t i c s . 3 7 . I w i l l f i n d s t a t i s t i c s t o be v e r y l o g i c a l . 3 8 . I l i k e t o r e a d t h e s e c t i o n on m e t h o d o l o g y i n r e s e a r c h r e p o r t s . 3 9 . I n e v e r t a l k t o o t h e r s a b o u t how t o do r e s e a r c h . 4 0 . I h a t e d o i n g s t a t i s t i c a l c a l c u l a t i o n s . 1 19 A c a d e m i c S e l f - C o n c e p t . P l e a s e r a t e y o u r a b i l i t y on e a c h o f t h e f o l l o w i n g . Mark t h e p o i n t on t h e s c a l e t h a t i n d i c a t e s t h e amount o f e a c h a b i l i t y y o u f e e l y o u p o s s e s s . The s c a l e t o be u s e d f o r e a c h a b i l i t y i s : 1 2 3 4 5 6 v e r y a l i t t l e a v e r a g e a l i t t l e low low be low above h i g h a v e r a g e a v e r a g e F o r e x a m p l e , i f y o u f e l t t h a t y o u h a d " v e r y h i g h " g e n e r a l m e n t a l a b i l i t y , r e l a t i v e t o t h e p o p u l a t i o n o f g r a d u a t e s t u d e n t s , you wou ld p u t a mark (a c i r c l e , an " X " , e t c . ) on t h e " 7 " f o r t h a t a b i l i t y . a . G e n e r a l m e n t a l a b i l i t y b . R e t e n t i o n o f m a t e r i a l l e a r n e d c . C o m p r e h e n s i o n o f m a t e r i a l r e a d d . T e c h n i c a l w r i t i n g a b i l i t y e . S k i l l a t o r a l p r e s e n t a t i o n s f . D e a l i n g w i t h c o m p l e x s u b j e c t m a t t e r g . E x p l a i n i n g t h i n g s a t a l e v e l t o s u i t some g i v e n a u d i e n c e h . A p p l y i n g t h e o r y t o some p r a c t i c a l p r o b l e m i . S e l e c t i n g some s i g n i f i c a n t p r o b l e m f r o m a g r o u p o f p o s s i b l e p r o b l e m s j . P e r c e i v i n g and d e a l i n g w i t h "human r e l a t i o n s " p r o b l e m s k. G e n e r a l m a t h e m a t i c a l a b i l i t y 1. A b i l i t y t o work s w i f t l y and a c c u r a t e l y m. A b i l i t y t o remember many d e t a i l s o f a p r o b l e m n . A b i l i t y t o v i s u a l i z e a p r o b l e m m e n t a l l y 7 v e r y h i g h 120 A c h i e v e m e n t M o t i v a t i o n . F o r t h e n e x t t h r e e q u e s t i o n s , p l e a s e c i r c l e t h e number on e a c h o f t h e s c a l e s t h a t r e p r e s e n t s y o u r c h o i c e o f r e s p o n s e . Use t h e f o l l o w i n g a s a g u i d e : 1 v e r y much p r e f e r op t i o n " A " 2 much p r e f e r o p t i o n " A " 3 p r e f e r o p t i o n " A " 4 pe r f e r n e i t h e r o p t i o n 5 p e r f e r o p t i o n " B " 6 much p r e f e r o p t i o n " B " 7 v e r y much p r e f e r o p t i o n " B " F o r e x a m p l e , i f y ou "much p r e f e r " d i f f i c u l t t a s k s i n i t e m a . f o r t h e f i r s t q u e s t i o n , y o u w o u l d c i r c l e o r c r o s s ou t t h e " 1 " f o r t h a t i t e m . 1 . a , b, c . d . e . a , b, c , d , e, f . I PREFER TASKS WHICH: i n v o l v e u n c e r t a i n t y . 1 a r e d i f f i c u l t . 1 I do m y s e l f . 1 have some r i s k . 1 r e q u i r e p r o b l e m s o l v i n g 1 f u l f i l l n eed t o s u c c e e d . . . 2 . 3 . 4 . 5 . 6 . 7 . h a v e s u r e o u t c o m e s , 2 . 3 .4 . 5 . 6 . 7 . a r e e a s y 2 . 3 . 4 . 5 . 6 . 7 . 1 do as p a r t o f a g r o u p , 2 . 3 . 4 . 5 . 6 . 7 . h a v e no o r e x c e s s i v e r i s k r e q u i r e m e r e l y 2 . 3 . 4 . 5 . 6 . 7 . . . f o l l o w i n g d i r e c t i o n s f u l f i l l n eed t o . . 1 . 2 . 3 . 4 . 5 . 6 . 7 a v o i d f a i l u r e I AM MOST SAT I SF I ED WITH TASKS WHICH: i n v o l v e u n c e r t a i n t y . 1 . 2 , a r e d i f f i c u l t . 1 . 2 I do m y s e l f . 1 . 2 , have some r i s k . 1 . 2 , r e q u i r e p r o b l e m s o l v i n g 1.2, f u l f i l l n e e d t o 3 . 4 . 5 . 6 . 7 . h a v e s u r e o u t c o m e s 3 . 4 . 5 . 6 . 7 . a r e e a s y 3 . 4 . 5 . 6 . 7 . 1 do a s p a r t o f a g r o u p 3 . 4 . 5 . 6 . 7 . h a v e no o r e x c e s s i v e r i s k r e q u i r e m e r e l y 3 . 4 . 5 . 6 . 7 . . . f o l l o w i n g d i r e c t i o n s f u l f i l l n eed t o s u c c e e d 1 . 2 . 3 . 4 . 5 . 6 . 7 a v o i d f a i l u r e 3. I OFTEN UNDERTAKE TASKS WHICH: a . b . c . d . e . i n v o l v e u n c e r t a i n t y . 1 . 2 . 3 . 4 . 5 . 6 . 7 . h a v e s u r e o u t c o m e s a r e d i f f i c u l t . 1 . 2 . 3 . 4 . 5 . 6 . 7 . a r e e a s y I do m y s e l f . 1 . 2 . 3 . 4 . 5 . 6 . 7 . I do a s p a r t o f a g r o u p have some r i s k . 1 . 2 . 3 . 4 . 5 . 6 . 7 . h a v e no o r e x c e s s i v e r i s k r e q u i r e m e r e l y . 2 . 3 . 4 . 5 . 6 . 7 . . . f o l l o w i n g d i r e c t i o n s f u l f i l l n e e d t o r e q u i r e p r o b l e m s o l v i n g 1 f u l f i l l n e e d t o s u c c e e d 1 . 2 . 3 . 4 . 5 . 6 . 7 a v o i d f a i l u r e 121 S p e c i f i c M o t i v a t i o n . 1. Why a r e y o u t a k i n g t h i s c o u r s e ? a . o n l y b e c a u s e i t i s r e q u i r e d b. more b e c a u s e i t i s r e q u i r e d t h a n b e c a u s e I want t o c . e q u a l l y b e c a u s e i t i s r e q u i r e d and b e c a u s e I w i s h t o t a k e i t d . more b e c a u s e I w i s h t o t h a n b e c a u s e i t i s r e q u i r e d e . o n l y b e c a u s e I w i s h t o 2. How much d i d y o u want t o t a k e t h i s c o u r s e ? a . v e r y much b. some c . a l i t t l e d . I n e i t h e r wan ted t o t a k e i t n o r no t t o t a k e i t e . I d e f i n i t e l y d i d no t want t o t a k e t h i s c o u r s e P e r c e i v e d U t i l i t y . 1. How u s e f u l do you t h i n k t h i s c o u r s e w i l l be t o y o u , i n y o u r f u t u r e c o u r s e o f s t u d i e s ? a . v e r y u s e f u l b . somewhat u s e f u l c . s l i g h t l y u s e f u l d . n e i t h e r u s e f u l n o r o f ' n o use e . d e f i n i t e l y o f no use t o me 2. How u s e f u l do y o u t h i n k t h i s c o u r s e w i l l be t o y o u , i n y o u r c h o s e n c a r e e r p a t h ? E x p e r i e n c e . a . v e r y u s e f u l b . somewhat u s e f u l c . s l i g h t l y u s e f u l d . n e i t h e r u s e f u l n o r o f no use e . d e f i n i t e l y o f no use t o me I f y o u have s t u d i e d m a t h e m a t i c s o r s t a t i s t i c s i n a p o s t -s e c o n d a r y i n s t i t u t i o n b e f o r e , p l e a s e l i s t a n d d e s c r i b e t h e c o u r s e s t a k e n : N o t e : s c o r e d a c c o r d i n g t o number o f c o u r s e s t a k e n w i t h 1=none and 5 = f o u r o r more 122 A p p e n d i x C . I n i t i a l Fo rm of A t t i t u d e S c a l e s T a s k I n s t r u c t i o n s . A t t i t u d e s A b o u t S t a t i s t i c s and R e s e a r c h . T h i s q u e s t i o n n a i r e c o n s i s t s o f s t a t e m e n t s a b o u t d o i n g r e s e a r c h and s t a t i s t i c s . You r t a s k i s t o d e c i d e how much y o u a g r e e o r d i s a g r e e w i t h e a c h s t a t e m e n t , and t h e n t o mark an " X " t h r o u g h t h e number t h a t i n d i c a t e s y o u r d e g r e e o f a g r e e m e n t . The s c a l e t o be u s e d f o r e a c h s t a t e m e n t i s : 1 2 3 s t r o n g l y d i s a g r e e d i s a g r e e d i s a g r e e a l i t t l e F o r e x a m p l e : I l i k e s t a t i s t i c s 1 2 3 4 5 6 7 I f y o u " d i s a g r e e a l i t t l e " w i t h t h i s s t a t e m e n t , you wou ld mark an " X " t h r o u g h " 3 " , o r i f y ou " s t r o n g l y a g r e e " w i t h t h e s t a t e m e n t , y o u wou ld mark an " X " t h r o u g h " 7 " . T h e r e a r e 69 s t a t e m e n t s . P l e a s e r e s p o n d t o e a c h o n e , and o n l y mark one " X " f o r e a c h s t a t e m e n t . N o t e : O n l y 65 s t a t e m e n t s a r e i n c l u d e d i n t h i s a p p e n d i x b e c a u s e f o u r a d d i t i o n a l i t e m s w h i c h e n q u i r e d a b o u t b o t h a r e a s were i n c l u d e d i n t h e o r i g i n a l f o r m o f t h e m e a s u r e . They were d e l e t e d f r o m a n a l y s i s f o r t h i s t h e s i s . S t a t e m e n t s a b o u t S t a t i s t i c s . N o t e : i n t h i s and a p p e n d i x , a l l i t e m s w i t h i n s e c t i o n a r e l i s t e d i n o r d e r o f o b s e r v e d i t e m - t o t a l c o r r e l a t i o n , c a l c u l a t e d f r o m t h e p i l o t - s t u d y d a t a . The i t e m - t o t a l c o r r e l a t i o n f o l l o w s t h e i t e m , e n c l o s e d i n p a r e n t h e s e s . E a c h i t e m c h o s e n f o r i n c l u s i o n i n t h e f i n a l s c a l e i s m a r k e d by an a s t e r i s k . The o r d e r o f t h e i t e m i n t h e i n i t i a l f o r m i s i n d i c a t e d by t h e i t e m number p r e c e e d i n g t h e i t e m i t s e l f . A . S t a t e m e n t s o f P o s i t i v e P o l a r i t y . 4 5 6 7 n e i t h e r a g r e e a g r e e s t r o n g l y a g r e e a l i t t l e a g r e e n o r d i s a g r e e * 4 0 . I f i n d s t a t i s t i c s e x c i t i n g and e n j o y a b l e . ( 0 . 8 3 1 ) 1 23 5 4 . I am l o o k i n g f o r w a r d t o l e a r n i n g l o t s a b o u t s t a t i s t i c s ( 0 . 7 3 3 ) 3 2 . I e n j o y t h i n k i n g a b o u t s t a t i s t i c a l p r o b l e m s . ( 0 . 6 9 3 ) 2 2 . I w o u l d e n j o y t h i n k i n g a b o u t what t o c o n c l u d e f r o m s t a t i s t i c a l c a l c u l a t i o n s . ( 0 . 6 2 8 ) 12 . The a s s i g n m e n t s I w o u l d e n j o y most a r e t h o s e w h i c h i n v o l v e s t a t i s t i c s . ( 0 . 6 2 8 ) 4 7 . I s o m e t i m e s do s t a t i s t i c a l c a l c u l a t i o n s f o r f u n . ( 0 . 6 0 8 ) 4 4 . The ways i n w h i c h s t a t i s t i c a l f o r m u l a s a r e d e r i v e d a r e e a s y t o u n d e r s t a n d . ( 0 . 5 9 6 ) 2 7 . An i n t e r e s t i n g a s s i g n m e n t m i g h t be t o do some s t a t i s t i c s i n d i f f e r e n t ways and t h e n compare t h e r e s u l t s . ( 0 . 5 6 0 ) 6 4 . I f i n d s t a t i s t i c s t o be v e r y l o g i c a l . ( 0 . 5 5 2 ) . 14 . S t a t i s t i c s makes me no more a n x i o u s t h a n any o t h e r s u b j e c t d o e s . ( 0 . 5 5 1 ) 7. I f i n d s t a t i s t i c a l p r o o f s e a s y t o u n d e r s t a n d . ( 0 . 4 9 8 ) 3 5 . B e i n g a s t a t i s t i c i a n w o u l d be a r e w a r d i n g j o b f o r me. ( 0 . 4 6 0 ) 2. I make v e r y few m i s t a k e s when I do s t a t i s t i c a l c a l c u l a t i o n s . ( 0 . 4 4 5 ) 2 9 . I f i n d i t e a s y t o remember t h e m e a n i n g o f t h e v a r i o u s s t a t i s t i c a l t e r m s . ( 0 . 3 8 1 ) 6 9 . N o t e s f r o m s t a t i s t i c s c l a s s e s s h o u l d be s a v e d f o r f u t u r e r e f e r e n c e . ( 0 . 0 9 8 ) _^ S t a t e m e n t s o f N e g a t i v e P o l a r i t y . 5 2 . I t r y t o a v o i d t a k i n g c l a s s e s i n s t a t i s t i c s . ( 0 . 7 4 5 ) 10 . The s y m b o l s u s e d i n s t a t i s t i c s a r e h a r d f o r me t o u n d e r s t a n d . ( 0 . 7 1 4 ) 9 . A l m o s t a n y t h i n g i s more i n t e r e s t i n g t h a n s t a t i s t i c s . ( 0 . 7 0 6 ) 2 5 . The w o r s t exams a r e t h o s e i n w h i c h y o u h a v e t o u s e s t a t i s t i c s t o ge t t h e r i g h t a n s w e r s . ( 0 . 6 6 8 ) 6 8 . I h a t e d o i n g s t a t i s t i c a l c a l c u l a t i o n s . ( 0 . 6 5 6 ) 3 9 . D o i n g s t a t i s t i c s makes me f e e l a n x i o u s . ( 0 . 6 5 5 ) 124 * 4 5 . D o i n g s t a t i s t i c s i s a l m o s t a l w a y s b o r i n g . ( 0 . 6 5 4 ) * 5 6 . I w o u l d a l w a y s p u t o f f d o i n g any a s s i g n m e n t w h i c h i n v o l v e d d o i n g s t a t i s t i c s . ( 0 . 6 5 1 ) * 6 . T h i n k i n g a b o u t d o i n g s t a t i s t i c s makes me f e e l s i c k . ( 0 . 6 3 9 ) 6 0 . I n e v e r know what t o c o n c l u d e f r o m s t a t i s t i c a l c a l c u l a t i o n s . ( 0 . 6 1 6 ) 4 2 . I o n l y t h i n k a b o u t d o i n g s t a t i s t i c s when I have t o . (0 .551 ) 2 8 . I c a n ' t f i g u r e ou t how p e o p l e draw c o n c l u s i o n s f r o m s t a t i s t i c a l c a l c u l a t i o n s . ( 0 . 5 2 7 ) * 1 7 . I w o u l d n e v e r buy a s t a t i s t i c s book i f I d i d n ' t have t o . ( 0 . 5 0 7 ) 5 0 . I t i s f r u s t r a t i n g and p o i n t l e s s t o was t e t i m e s t u d y i n g s t a t i s t i c s . ( 0 . 4 6 9 ) 3 6 . When I do s t a t i s t i c a l c a l c u l a t i o n s , I make l o t s o f m i s t a k e s . ( 0 . 3 9 9 ) 6 2 . I w o u l d n e v e r s a ve my n o t e s f r o m a s t a t i s t i c s c l a s s . ( 0 . 3 7 4 ) 2 4 . T h i n k i n g a b o u t s t u d y i n g s t a t i s t i c s makes me a n x i o u s . ( 0 . 3 6 3 ) 3. S t a t e m e n t s a b o u t R e s e a r c h . A . S t a t e m e n t s o f P o s i t i v e P o l a r i t y . * 3 3 . I w o u l d l i k e t o r e a d a b o u t how t o do r e s e a r c h . ( 0 . 7 6 3 ) * 6 7 . I l i k e t o r e a d t h e s e c t i o n s on m e t h o d o l o g y i n r e s e a r c h r e p o r t s . ( 0 . 7 1 8 ) * 1 6 . E v a l u a t i n g r e s e a r c h i s c h a l l e n g i n g and s t i m u l a t i n g . ( 0 . 6 9 1 ) * 5. P l a n n i n g r e s e a r c h w o u l d be a r e w a r d i n g a c t i v i t y f o r me. ( 0 . 6 2 7 ) * 2 1 . I am l o o k i n g f o r w a r d t o d o i n g my own r e s e a r c h . ( 0 . 6 0 7 ) * 3 8 . W o r k i n g a s a r e s e a r c h c o n s u l t a n t i s a j o b I ' d l i k e t o do someday . ( 0 . 5 9 3 ) * 1 1 . I w o u l d e n j o y t a l k i n g a b o u t r e s e a r c h me thods w i t h my 1 25 f r i e n d s . ( 0 . 5 5 9 ) 8. I f i n d i t i n t e r e s t i n g t o t h i n k a b o u t w h i c h r e s e a r c h method m i g h t be b e s t t o s o l v e a g i v e n p r o b l e m . ( 0 . 5 5 8 ) 2 3 . I f i n d i t e a s y t o u n d e r s t a n d t h e d i f f e r e n t ways o f p l a n n i n g r e s e a r c h . ( 0 . 5 4 6 ) 5 8 . My f a v o u r i t e a s s i g n m e n t s i n v o l v e e v a l u a t i n g r e s e a r c h . ( 0 . 5 4 4 ) 4 8 . T h i n k i n g a b o u t r e s e a r c h i s one o f my f a v o u r i t e a c t i v i t i e s . ( 0 . 5 3 7 ) 53 66 I l i k e t o p l a n r e s e a r c h p r o j e c t s " i n my h e a d " . ( 0 . 5 3 3 ) I o f t e n t h i n k a b o u t t h e ways t o i n v e s t i g a t e p r o b l e m s w h i c h i n t e r e s t me. ( 0 . 5 3 2 ) 43 3. I l i k e t o t h i n k a b o u t d o i n g r e s e a r c h i n a l m o s t e v e r y s u b j e c t I s t u d y . ( 0 . 4 9 2 ) I w o u l d r a t h e r d e s i g n a r e s e a r c h p r o j e c t t h a n f o l l o w someone e l s e ' s p l a n . ( 0 . 4 1 9 ) 1. Whenever I w r i t e a p a p e r a b o u t s o m e t h i n g , I t h i n k a b o u t how I m i g h t do r e s e a r c h i n t h a t s u b j e c t . ( 0 . 3 5 3 ) -L S t a t e m e n t s o f N e g a t i v e P o l a r i t y . 19 . I o n l y t h i n k a b o u t d o i n g r e s e a r c h when I have t o . ( 0 . 7 3 3 ) 3 1 . D o i n g r e s e a r c h i s a was t e o f t i m e f o r me. ( 0 . 7 2 6 ) 5 7 . I t i s b o r i n g t o t a l k a b o u t r e s e a r c h w i t h o t h e r p e o p l e . ( 0 . 7 1 3 ) 4 6 . I w o u l d r a t h e r r e a d a b o u t t h e c o n c l u s i o n s f r o m some p i e c e o f r e s e a r c h t h a n a b o u t how i t was d o n e . ( 0 . 6 8 0 ) 4 1 . I f I e v e r h a d t o do r e s e a r c h I w o u l d l i k e i t i f someone e l s e p l a n n e d how t o c a r r y i t o u t . ( 0 . 6 6 8 ) 5 5 . E ven when I an i n t e r e s t e d i n t h e s u b j e c t , I r a r e l y t h i n k a b o u t how you c o u l d do r e s e a r c h i n i t . ( 0 . 6 5 6 ) 13 . I d o n ' t l i k e t o have t o d e c i d e a b o u t w h e t h e r some p i e c e o f r e s e a r c h i s g o o d o r b a d . ( 0 . 5 7 9 ) 6 1 . I n e v e r t a l k t o o t h e r p e o p l e a b o u t how t o do r e s e a r c h . ( 0 . 5 6 6 ) 1 5 . I f i n d t h e d i f f e r e n t ways i n w h i c h one c o u l d do r e s e a r c h v e r y c o n f u s i n g . ( 0 . 5 4 5 ) 1 26 * 3 7 . T h e r e i s t o o much e m p h a s i s i n u n i v e r s i t y on r e s e a r c h and how t o do i t . (0.52.9) 6 3 . When I r e a d any r e s e a r c h , I u s u a l l y s k i p t h e s e c t i o n t h a t d e s c r i b e s how t h e r e s e a r c h was c a r r i e d o u t . ( 0 . 5 3 3 ) 4 9 . The w o r s t a s s i g n m e n t s a r e t h o s e t h a t i n v o l v e a d e c i s i o n a b o u t whe the r some r e s e a r c h i s good o r b a d . ( 0 . 5 2 8 ) 1 8 . H a v i n g t o p l a n t o do r e s e a r c h i s b o r i n g . ( 0 . 5 0 7 ) 4. T h i n k i n g a b o u t d o i n g r e s e a r c h g i v e s me b u t t e r f l i e s i n my s t o m a c h . ( 0 . 4 8 7 ) 3 4 . I h a ve t r o u b l e u n d e r s t a n d i n g why p e o p l e u s e d i f f e r e n t r e s e a r c h me thods t o s o l v e t h e same p r o b l e m . ( 0 . 4 5 6 ) 6 5 . I w o u l d r a t h e r w r i t e a t e r m p a p e r a b o u t what I t h i n k t h a n one a b o u t t h e r e s e a r c h i n a p a r t i c u l a r s u b j e c t . ( 0 . 3 8 1 ) 2 6 . I n e v e r r e a d b o o k s o r a r t i c l e s on how t o do r e s e a r c h . ( 0 . 3 7 4 ) 1 27 A p p e n d i x D.  A d m i n i s t r a t i o n I n s t r u c t i o n s HAND OUT BOOKLETS (+/- 2 m i n . ) I n t r o d u c e t h e s t u d y i n y o u r own way. F o r e x a m p l e , " t o d a y t h e r e i s a s p e c i a l s e t o f t e s t s w h i c h I have been r e q u e s t e d t o a d m i n i s t e r . He r e i s a s t a t e m e n t a b o u t t h e p r o j e c t , w h i c h i s a l s o on t h e c o v e r s h e e t o f y o u r t e s t b o o k l e t . " READ (+/- 2 m i n . ) "My name i s Sheena S e l k i r k and I am a g r a d u a t e s t u d e n t i n Measu remen t a n d R e s e a r c h M e t h o d o l o g y a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . T h i s s t u d y i s an i n v e s t i g a t i o n i n t o t h e e x t e n t t o w h i c h a b i l i t i e s a n d a t t i t u d e s a r e r e l a t e d t o t h e p e r f o r m a n c e i n i n t r o d u c t o r y s t a t i s t i c s . You r p a r t i c i p a t i o n i s v o l u n t a r y , bu t I w o u l d c e r t a i n l y a p p r e c i a t e y o u r c o -o p e r a t i o n . The more c o m p l e t e my d a t a a r e , t h e b e t t e r I c a n t a l k a b o u t how w e l l t h e m e a s u r e s p r e d i c t marks i n t h e c l a s s . The c o m p l e t e s e t o f m e a s u r e s w i l l be a d m i n i s t e r e d i n t o d a y ' s c l a s s and w i l l t a k e a b o u t one and o n e - q u a r t e r h o u r s , w i t h a s h o r t b r e a k h a l f - w a y . t h r o u g h . The q u e s t i o n n a i r e s w i l l i n c l u d e s e l f - r a t i n g s , an a t t i t u d e m e a s u r e , and s e v e r a l c o g n i t i v e m e a s u r e s . In a d d i t i o n , I w o u l d l i k e y o u t o g i v e me p e r m i s s i o n t o r e c e i v e y o u r mark i n t h e f i n a l exam f r o m y o u r i n s t r u c t o r . A l l r e p o r t i n g o f r e s u l t s w i l l be done o n l y on a g r o u p b a s i s . A l l i n f o r m a t i o n w i l l be t r e a t e d a s c o n f i d e n t i a l a n d w i l l be s h a r e d w i t h n o - o n e . I f y ou w o u l d l i k e t o know a b o u t t h e r e s u l t s o f t h i s s tudy,- p l e a s e c o n t a c t me i n t h e f a l l and I w i l l t e l l you a b o u t t h e m . I f y o u a r e w i l l i n g t o p a r t i c i p a t e , p l e a s e r e a d a n d s i g n t h e l e t t e r o f c o n s e n t , and we w i l l b e g i n w i t h t h e f i r s t q u e s t i o n n a i r e . " ALLOW TIME FOR PEOPLE TO LEAVE THE ROOM IF THEY WISH. (+/- 1 m i n . ) READ (+/- 1 m i n . ) " B e s i d e s s i g n i n g y o u r name and f i l l i n g i n y o u r name a n d s t u d e n t number on t h e l e t t e r o f p e r m i s s i o n , you s h o u l d a l s o w r i t e i n t h e number o f t h e c l a s s ( t h a t i s ) . " T E L L THE STUDENTS THE NUMBER OF THE C L A S S . READ (+/- 1 m i n . ) " T h e f i r s t t a s k i s t o f i l l i n a q u e s t i o n n a i r e , w h i c h c o n s i s t s o f t h r e e p a g e s . The f i r s t i s o p e n - e n d e d q u e s t i o n s and r a t i n g s , and t h e o t h e r two a r e r a t i n g s . T h i s f o r m t a k e s a b o u t 10 m i n u t e s t o f i l l i n . P l e a s e b e g i n n o w . " T IME TEN MINUTES . READ (+/- 3 m i n . ) " P l e a s e go on t o t h e n e x t f o r m now. T h i s i s t h e a t t i t u d e q u e s t i o n n a i r e . I s h a l l r e a d t h e i n s t r u c t i o n s a l o u d w h i l e you r e a d them s i l e n t l y . T h i s q u e s t i o n n a i r e c o n s i s t s o f q u e s t i o n s a b o u t d o i n g r e s e a r c h and s t a t i s t i c s . Y o u r t a s k i s t o d e c i d e how much y o u a g r e e o r d i s a g r e e w i t h e a c h s t a t e m e n t , and t h e n t o mark an " X " t h r o u g h t h e number t h a t i n d i c a t e s y o u r d e g r e e o f a g r e e m e n t . The s c a l e t o be -used f o r e a c h s t a t e m e n t i s : 1 - s t r o n g l y d i s a g r e e , 2-d i s a g r e e , 3 - d i s a g r e e a l i t t l e , 4 - n e i t h e r a g r e e no r d i s a g r e e , 5-agree a l i t t l e , 6 - a g r e e , a n d 7 - s t r o n g l y a g r e e . 128 F o r e x a m p l e : I l i k e s t a t i s t i c s I f y o u " d i s a g r e e a l i t t l e " w i t h t h i s s t a t e m e n t , you wou ld mark an " X " t h r o u g h " 3 " , o r i f y ou " s t r o n g l y a g r e e " w i t h t h e s t a t e m e n t , y o u w o u l d mark an " X " t h r o u g h " 7 " . T h e r e a r e 40 s t a t e m e n t s . P l e a s e r e s p o n d t o e a c h o n e , and o n l y mark one " X " f o r e a c h s t a t e m e n t . P r e v i o u s use o f t h i s q u e s t i o n n a i r e has shown t h a t mos t s u b j e c t s f i n i s h i n a b o u t f i v e m i n u t e s . P l e a s e b e g i n now. T IME F I V E MINUTES. READ (+/- 3 m i n . ) P l e a s e t u r n t o t h e n e x t q u e s t i o n n a i r e now. F o r t h e r e s t o f t h e q u e s t i o n n a i r e s , I s h a l l r e a d t h e i n s t r u c t i o n s , a l o u d and t h e n t i m e e a c h p a r t o f t he t e s t q u i t e c l o s e l y . The n e x t t e s t , an A d v a n c e d V o c a b u l a r y T e s t , i s a m e a s u r e o f y o u r know ledge o f word m e a n i n g s . In t h e e x a m p l e b e l o w , one s t i m u l u s word i s p r i n t e d above f i v e r e s p o n s e w o r d s . You r t a s k i s t o c i r c l e t h e number o f t h e r e s p o n s e word t h a t h a s t h e same o r n e a r l y t h e same m e a n i n g a s t h e s t i m u l u s w o r d . T r y t h e e x a m p l e now. ALLOW 10 SECS . FOR THE EXAMPLE The c o r r e c t answer i s " j o l l y " , so y o u s h o u l d have c i r c l e d t h e number 5. You r s c o r e w i l l be t h e number o f i t e m s you have a n s w e r e d c o r r e c t l y . T h e r e i s no c o r r e c t i o n f o r g u e s s i n g . You w i l l have 4 m i n u t e s f o r e a c h p a r t o f t h i s t e s t . T h e r e a r e two p a r t s , and e a c h p a r t ha s 18 i t e m s . When y o u have f i n i s h e d p a r t 1, s t o p and do no t go o n t o p a r t 2 u n t i l a s k e d t o do s o . T u r n and b e g i n -- n o w . " TIME FOUR MINUTES. " T u r n and b e g i n p a r t 2 — n o w . " T IME FOUR MINUTES. READ (+/- 3 m i n . ) " P l e a s e t u r n t o t h e n e x t t e s t now. T h i s measu re i s a P a p e r F o l d i n g T e s t . In t h i s t e s t you a r e t o i m a g i n e t h e f o l d i n g and u n f o l d i n g o f s q u a r e p i e c e s o f p a p e r . In e a c h p r o b l e m , t h e f i g u r e s a t t h e l e f t o f t h e v e r t i c a l l i n e r e p r e s e n t a s q u a r e o f p a p e r b e i n g f o l d e d . The l a s t o f t h e f i g u r e s has one o r two s m a l l c i r c l e s drawn on i t t o show where t h e p a p e r has been p u n c h e d . E a c h h o l e has been p u n c h e d t h r o u g h a l l t h i c k n e s s e s o f t h e p a p e r a t t h a t p o i n t . The f i v e f i g u r e s t o t h e r i g h t o f t h e v e r t i c a l l i n e show where t h e h o l e s m i g h t be when t h e p a p e r i s c o m p l e t e l y u n f o l d e d . You a r e t o d e c i d e w h i c h one o f t h e f i g u r e s i s c o r r e c t a n d draw an X t h r o u g h t h a t f i g u r e . T r y t h i s s amp l e p r o b l e m . ALLOW 15 S E C S . FOR PROBLEM ATTEMPT. The c o r r e c t answer i s " C " - y o u s h o u l d h a v e m a r k e d " C " w i t h an X . The f i g u r e s be low show y o u how t h e p a p e r was f o l d e d and why " C " i s c o r r e c t . As y o u c a n s e e , t h e p a p e r i s f o l d e d i n h a l f a n d a h o l e p u n c h e d i n t h e l e f t - h a n d a r e a . When i t i s u n f o l d e d , t h e r e a r e two h o l e s i n t h e p a p e r . In t h e s e p r o b l e m s , a l l t h e f o l d s a r e shown i n t h e f i g u r e s t o t h e l e f t o f t h e v e r t i c a l l i n e , and t h e p a p e r i s n o t t u r n e d o r moved i n any way e x c e p t t o make t h e f o l d s shown . Remember, t h e c o r r e c t answe r i s t h e f i g u r e t h a t shows how t h e p a p e r l o o k s when i t i s c o m p l e t e l y u n f o l d e d . You w i l l have t h r e e m i n u t e s t o c o m p l e t e e a c h o f t h e two p a r t s o f t h i s t e s t . 1 29 E a c h p a r t ha s 1 p a g e . You r s c o r e w i l l be t h e number o f c o r r e c t r e s p o n s e s . When y o u have f i n i s h e d p a r t 1, s t o p . Do no t go on t o P a r t 2 u n t i l a s k e d t o do s o . T u r n and b e g i n -- now. TIME THREE MINUTES " T u r n and b e g i n p a r t 2 — now. TIME THREE MINUTES READ (+/- 3 m i n . ) "We a r e now more t h a n h a l f - f i n i s h e d w i t h t h e b a t t e r y o f t e s t s . I f y o u w i s h we w i l l t a k e a s h o r t " s t r e t c h " b r e a k , b u t p l e a s e d o n ' t l e a v e t h e room s i n c e t h e b r e a k w i l l o n l y be a few m i n u t e s l o n g . ALLOW TWO MINUTES FOR BREAK. READ (+/- 2 m i n . ) OK c o u l d we g e t s t a r t e d a g a i n ? . . . . The n e x t t e s t i s S u b t r a c t i o n and M u l t i p l i c a t i o n . T h i s i s a t e s t t o see how q u i c k l y a n d a c c u r a t e l y you can s u b t r a c t and m u l t i p l y . I t i s n o t e x p e c t e d t h a t you w i l l f i n i s h a l l t he p r o b l e m s i n t h e t i m e a l l o t t e d . You a r e t o w r i t e t h e a n s w e r s i n t h e b o x e s be low t h e p r o b l e m s . S e v e r a l p r a c t i c e p r o b l e m s a r e g i v e n be low w i t h -the f i r s t one c o r r e c t l y w o r k e d . P r a c t i c e f o r s p e e d on t h e o t h e r s . T h i s p r a c t i c e may h e l p y o u r s c o r e . ALLOW 20 S E C S . FOR PROBLEMS. You r s c o r e on t h i s t e s t w i l l be t h e number o f p r o b l e m s s o l v e d c o r r e c t l y . Work a s r a p i d l y a s y o u c a n w i t h o u t s a c r i f i c i n g a c c u r a c y . Be s u r e t h a t you a r e u s i n g t h e c o r r e c t p r o c e s s ; c h e c k t h e s i g n f o r e a c h row. You w i l l have 2 m i n u t e s f o r e a c h o f t h e two p a r t s o f t h e t e s t . E a c h p a r t has one p a g e . When y o u have f i n i s h e d p a r t 1, s t o p . Do no t b e g i n p a r t 2 u n t i l a s k e d t o do s o . T u r n a n d b e g i n -- now. T IME TWO MINUTES. T u r n and b e g i n p a r t 2 — now. T IME TWO MINUTES. READ (+/- 2 m i n . ) The n e x t measu re i s a t e s t c a l l e d D i a g r a m m i n g R e l a t i o n s . Somet imes t h e r e l a t i o n s h i p s among g r o u p s o f t h i n g s a r e b e s t e x p l a i n e d by d i a g r a m s t h a t c o n s i s t o f o v e r l a p p i n g c i r c l e s . In t h e d i a g r a m s i n t h i s t e s t , we do n o t c a r e a b o u t t h e r e l a t i v e s i z e s o f t h e c i r c l e s . F o r e x a m p l e , t a k e t h e r e l a t i o n s h i p s among t h r e e g r o u p s o f d i f f e r e n t t h i n g s - b i r d s , p e t s and t r e e s . The d i a g r a m shows t h a t no t r e e s a r e e i t h e r p e t s o r b i r d s , b u t some b i r d s a r e p e t s and some p e t s a r e b i r d s . E a c h i t e m i n t h i s t e s t names t h r e e g r o u p s o f t h i n g s . You a r e t o c h o o s e f rom t h e l e t t e r e d d i a g r a m s a t t h e t o p o f t h e t e s t page t h e one d i a g r a m t h a t shows t h e c o r r e c t r e l a t i o n s h i p among t h e t h r e e g r o u p s o f t h i n g s i n e a c h i t e m . Mark t h e l e t t e r o f t he d i a g r a m t h a t you s e l e c t . T r y t h e s e s amp l e i t e m s . ALLOW 20 SECONDS FOR SAMPLE ITEMS. You s h o u l d h a v e m a r k e d A f o r e x a m p l e 1 a n d E f o r e x a m p l e 2. You r s c o r e on t h i s t e s t w i l l be t h e number o f c o r r e c t c h o i c e s y o u have made . T h e r e a r e two p a r t s t o t h i s t e s t , and y o u a r e g i v e n 4 m i n u t e s t o c o m p l e t e e a c h p a r t . When y o u have f i n i s h e d p a r t 1, s t o p . Do n o t b e g i n p a r t 2 u n t i l a s k e d t o do s o . T u r n and b e g i n now. 1 30 TIME FOUR MINUTES. T u r n and b e g i n p a r t 2 — now. TIME FOUR MINUTES. READ (+/- 2 m i n . ) The l a s t t e s t i s a c o n c e p t l e a r n i n g t a s k . T h i s f o r m i s a measu re o f how q u i c k l y and w e l l y o u c a n l e a r n an u n f a m i l i a r m a t h e m a t i c a l c o n c e p t . F i r s t , t h e c o n c e p t i s d e s c r i b e d and s e c o n d , 13 q u e s t i o n s a r e a s k e d t o t e s t y o u r a b i l i t y t o use t h e c o n c e p t . You may r e f e r back t o t h e c o n c e p t d e s c r i p t i o n s w h i l e a n s w e r i n g t h e q u e s t i o n s and you may do t h e q u e s t i o n s i n any o r d e r y o u w i s h . T h e r e a r e no t r i c k q u e s t i o n s . A l l t h e i n f o r m a t i o n y o u n e e d t o answer t h e q u e s t i o n s i s c o n t a i n e d ' i n t h e c o n c e p t d e s c r i p t i o n , e x c e p t f o r b a s i c a r i t h m e t i c and a l g e b r a i c s k i l l s . The t i m e l i m i t f o r t h i s t a s k i s t w e l v e (12) m i n u t e s . I w i l l t e l l y o u when f o u r m i n u t e s and e i g h t m i n u t e s have p a s s e d . P l e a s e t u r n t h e page and b e g i n when I s a y , " T u r n and b e g i n — n o w . " TIME TWELVE MINUTES . ANNOUNCE FOUR AND E IGHT MINUTES. READ (+/- 1 m i n . ) T h a t ' s i t . Ms . S e l k i r k wou ld l i k e me t o t h a n k you a g a i n f o r y o u r c o o p e r a t i o n . I f y o u want h e r a d d r e s s , y o u may ask me f o r i t . P l e a s e hand i n y o u r t e s t b o o k l e t s t o me. $SIG 

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