T H E R E L A T IO N S H IP B E T W E E N A C H IE V E D G R O W T H IN H E I G H T A N D T H E B E G IN N IN G O F G R O W T H IN R E A D IN G By TH O M A S P O M P H E R T F R A N C IS N A L L Y A T H E SIS S u b m i t t e d to th e S c h o o l of G r a d u a t e S t u d i e s of M i c h i g a n S ta te C o l l e g e of A g r i c u l t u r e a n d A p p lie d S c i e n c e i n p a r t i a l f u l f i l l m e n t of t h e r e q u i r e m e n t s f o r th e d e g r e e of D O C T O R O F P H IL O S O P H Y D e p a r t m e n t of E l e m e n t a r y E d u c a t i o n 1953 T A B L E OF CONTENTS CHAPTER I. Page PROBLEM AND D E F IN IT I O N O F T E R M S In tro d u c tio n . ......................... 1 ..................................................................................... 1 ............................................................................. 4 P ro b le m Im p o rta n c e of D e fin itio n o f II. R E V IE W OF th e S tu d y T erm s TH E In tro d u c tio n ...................................................... 6 ......................................' ........................ 7 L IT E R A T U R E ......................... ..................................................................................... 9 I n c i p i e n c y - - P h y s i c a l M a t u r a t i o n ................. t F o r m u l a - - G o m p e r z F u n c t i o n Y =k i ........................... 12 16 ........................................................................................... 22 R e a d in g III. PROCEDURE D a t a .................... M e th o d 22 ..................................................................................... L im ita tio n s IV. 9 ...................................................... 26 TH E DATA: . I T S ANA LY SIS AND I N T E R P R E T A T I O N .......................................................................... 29 .................................................................................... 29 ...............................................................................'. 29 In tro d u c tio n The D a ta A n a ly sis of the S tu d y 23 a n d . In te rp re ta tio n ............................................... 40 Ill CHAPTER V. Page SU M M A R Y A N D I M P L I C A T I O N S .................................................. 60 S u m m a r y ........................................................................... I m p l i c a t i o n s .................................... ■.............................................. 60 62 B I B L I O G R A P H Y ............................................................................................................ A P P E N D I C E S .....................■ 64 76 L IS T O F TABLES TABLE I. II. III. IV. Y. YI. Page D i s t r i b u t i o n of D e v i a t i o n s of A c t u a l P o i n t s F r o m E q u a t i o n P r e d i c t i o n f o r G r o w t h in H e i g h t .................................................................................................................. 35 D i s t r i b u t i o n of D e v i a t i o n s of A c t u a l S c o r e s F r o m E q u a t i o n P r e d i c t i o n - f o r G r o w t h in R e a d i n g ............................................................................................................... 36 B o y s ' R e a d i n g I n c i p i e n c y - - P e r c e n t a g e of D e v e lo p m e n t in H e ig h t an d C h ro n o lo g ic a l A g e a t R e a d i n g I n c i p i e n c y ................................................................... 43 G i r l s ' R e a d in g I n c i p i e n c y - - P e r c e n t a g e of D e v e lo p m e n t in H e ig h t and C h ro n o lo g ic a l A g e a t R e a d i n g I n c i p i e n c y ................................................................... 45 D i s t r i b u t i o n of P e r c e n t a g e o f D e v e l o p m e n t in H e i g h t a t W h ic h R e a d in g T h e o r e t i c a l l y B e g a n .................................................................................................................. 48 D i s t r i b u t i o n of C h r o n o l o g i c a l A ge a t W h ic h R e a d i n g T h e o r e t i c a l l y B e g a n ............................................................ 49 L IS T O F F IG U R E S F ig u r e 1. P age G r a p h i c s u m m a r y of c a s e 5 F . G r o w t h a g e s t a k e n f r o m H o u s e ................................................................... 17 C o m p a r a t i v e m a t u r a t i o n s in h e i g h t a n d re a d in g — c a se 58F 27 3. I l l u s t r a t i o n of A p p e n d i c e s A a n d B ........................................... 30 4. I l l u s t r a t i o n of A p p e n d ix C .............................................................. 32 5. I l l u s t r a t i o n o f A p p e n d ix E ............................................................. 32 6. C o m p a r i s o n of b o y s 1 and g i r l s 'c u rv e s o f c o n s t a n t s f o r g r o w t h in h e i g h t ............................................ 33 C o m p a r i s o n of b o y s ' a n d g i r l s ' c u r v e s of c o n s t a n t s f o r g r o w t h in r e a d i n g ......................................... 34 D i s t r i b u t i o n of d e v i a t i o n s o f a c t u a l p o i n t s f r o m e q u a t i o n p r e d i c t i o n f o r g r o w t h in h e i g h t ........................................................................................................... 38 D i s t r i b u t i o n of d e v i a t i o n s o f a c t u a l s c o r e s f r o m e q u a t i o n p r e d i c t i o n f o r g r o w t h in r e a d i n g ........................................................................................................ 39 10. F o u r s e l e c t e d c u r v e s of g r o w t h in h e i g h t ........................ 41 11. F o u r s e l e c t e d c u r v e s of g r o w t h in r e a d i n g ..................... 42 12. D i s t r i b u t i o n of p e r c e n t of d e v e l o p m e n t in h e i g h t a t w h ic h r e a d i n g t h e o r e t i c a l l y b e g a n .................... 50 D i s t r i b u t i o n of c h r o n o l o g i c a l age a t w h ic h r e a d i n g t h e o r e t i c a l l y b e g i n s ......................................................... 51 2. 7. 8. 9. 13. vi F ig u re Page 14. C o m p a r i s o n of c u r v e of c o n s t a n t s f o r grow th, in h e i g h t , b o y s a n d g i r l s , w ith t h o s e p r e s e n t e d b y B o y n to n a n d M e r e d i t h ........................................................................... 55 15. R e la tio n s h ip b e tw e e n p e r c e n t of d e v e lo p m e n t in h e i g h t (in i s o c h r o n s ) a n d c h r o n o l o g i c a l age a t r e a d i n g i n c i p i e n c y - - b o y s ............................................................... 16. R e l a t i o n s h i p b e t w e e n p e r c e n t of d e v e l o p m e n t in h e i g h t (in i s o c h r o n s ) a n d c h r o n o l o g i c a l age a t r e a d i n g i n c i p i e n c y - - g i r l s ..................................... 56 57 CHAPTER I P R O B L E M A N D D E F IN IT I O N O F T E R M S In tro d u ctio n T h e c o n c e p t of a s c i e n c e of e d u c a t i o n c o m p a r a b l e to th e s c i e n c e of p h y s i c s i s r e l a t i v e l y n e w . T h i s c o n c e p t of e d u c a t i o n h a s p r o g r e s s e d f r o m t h e s p e c u l a t i v e s t a g e of A r i s t o t l e a n d R o u s s e a u t h r o u g h t h e p s e u d o s c i e n t i f i c s t a g e of G. S ta n le y H a l l a n d B o b b i t t to th e r i g i d c o n t r o l c o n c e p t h e l d by C o u r t i s a n d M i l l a r d . 1 ,2 ,3 ’ ’ S im ilarly , th e s c i e n c e of p h y s i c s h a s p r o g r e s s e d f r o m th e s p e c u l a t i v e s t a g e of T h a l e s a n d L u c r e t i u s t h r o u g h th e p s e u d o s c i e n t i f i c s t a g e of th e a l ­ c h e m i s t s a n d a s t r o l o g e r s to th e m o r e a d v a n c e d ' ' s c i e n t i f i c " of N e w to n a n d B o l l e s . concept A lth o u g h s o m e i n v e s t i g a t o r s h a v e g i v e n lip S. A. C o u r t i s , T o w a r d a S c i e n c e of E d u c a t i o n , A n n A r b o r , M ic h i g a n . L i t h o - p r i n t e d . E d w a r d s B r o s . , 1951, C h. 2 - 4 . 2 S. A. C o u r t i s , " E d u c a t i o n - A P s e u d o S c i e n c e , " J . of E d . R e s . , X VII ( F e b . , 1928), p p . 1 3 0 -3 2 . “ C. V. M i l l a r d , C h ild D e v e l o p m e n t , B o s to n : 1951, p. 1. D. C. H e a th , s e r v i c e to t h e c o n c e p t of e d u c a t i o n a s a s c i e n c e , i t w a s th e C o u r t i s M i l l a r d s c h o o l of t h o u g h t t h a t l a i d th e f r a m e w o r k t h r o u g h w h ic h s u c h a c o n c e p t m a y e v e n t u a l l y b e c o m e a r e a l i t y . ^ ’^ ’^ T h i s c o n c e p t o f e d u c a t i o n w h ic h i s b a s e d o n th e s i n g l e v a r i ­ a b le t h e o r y m a k e s p o s s i b l e th e d e s c r i p t i o n a n d p r e d i c t i o n of g r o w t h a n d b e h a v i o r i n t e r m s of t h e ' ' L a w of t h e S in g le V a r i a b l e . ' ' 7 ,8 ,9 W. C. O l s e n , s p e a k i n g a t a m e e t i n g of t h e G r a d u a t e F a c u l t i e s of W ay n e U n i v e r s i t y , M i c h i g a n S t a t e C o l l e g e , a n d U n i v e r s i t y of M i c h i g a n in M ay, 1952, s t a t e d t h a t (1) b e h a v i o r o p e r a t e d a c c o r d i n g to la w , (2) f u t u r e b e h a v i o r c a n b e p r e d i c t e d , a n d (3) p r e d i c t i o n i s s u f f i c i e n t l y 4 S. A. C o u r t i s , M a t u r a t i o n U n its a n d H ow to U s e T h e m , A n n A rb o r, M ich ig an . L ith o - p r in te d . E d w a r d s B r o s . , 1950, p. ii. . 5 S. A. C o u r t i s , " F a c t a n d F a n c y i n E d u c a t i o n a l M e a s u r e ­ m e n t , " B u l l e t i n of th e S c h o o l o f E d u c a t i o n , U n i v e r s i t y of I n d ia n a , XVIII (S e p t., 1942), p p . 8 - 2 4 . 6 S. A . C o u r t i s , T o w a r d a S c i e n c e of E d u c a t i o n , op. c it., c h . 10. 7 „ S. A. C o u r t i s , m e n t , " l o c . c it. 8 " F a c t and F a n c y in E d u c a tio n a l M e a s u r e ­ . S. A . C o u r t i s , " D i s c i p l i n e U n d e r th e G r o w t h C o n c e p t , " C h ild G r o w t h in a n E r a of C o n f lic t,. 15th Y e a r b o o k , M i c h i g a n E d u ­ c a t i o n A s s o c i a t i o n a n d D e p a r t m e n t of E l e m e n t a r y P r i n c i p a l s , 1944, pp. 3 9 - 4 2 . 9 S. A . C o u r t i s , T o w a r d a S c i e n c e of E d u c a t i o n , o p. c i t . , c h . 7. 3 e x a c t to b e s u s c e p t i b l e to a m a t h e m a t i c a l f o r m u l a . T h ese sta te m e n ts c o n t a i n th e e s s e n c e o f th e c o n c e p t o f e d u c a t i o n a s a s c i e n c e . C o u r t i s a d h e r e s to t h i s t h e o r y w h e n h e p o s t u l a t e s th e t h e s i s t h a t e d u c a t i o n a l p h e n o m e n a c a n b e t r e a t e d m u c h th e s a m e a s p h y s i c a l phenom ena. B o th p h e n o m e n a a r e s u b j e c t to th e ' ' L a w o f th e S in g le V a r i a b l e .'1 • T h e re fo re , e d u c a tio n a l p h e n o m en a can be e x p r e s s e d in te rm s s i m i l a r to t h o s e of th e p h y s i c a l s c i e n c e s . C o u rtis sta te s: ''I n th e p a s t m a n , i n p h y s i c a l s c i e n c e s , h a s d e a l t w ith s i m p l e x s i t u a t i o n s i n v o lv in g only tw o v a r i a b l e s ( s u c h a s p r e s s u r e a n d v o l u m e i n g a s e s ) , one v a r i a b l e a t a t i m e , u n d e r th e 'L a w of th e S in g le V a r i a b l e . ' " c o n tin u e s: He " A t l a s t , h o w e v e r , th e f a c t o r c a u s i n g c o n f u s i o n h a s b e e n u n c o v e r e d a n d m e t h o d s d e v e l o p e d b y w h ic h th e o r g a n i z e d c o m p l e x i t i e s w ith w h ic h th e b i o l o g i s t s d e a l c a n a l s o b e s t u d i e d u n d e r t h e 'L a w of th e S in g l e V a r i a b l e . ' T h e la w s , w h o s e o p e r a t i o n s p e l l o r d e r in th e p h e n o m e n a of l i f e , m a y n o w b e i s o l a t e d a n d e x p r e s s e d i n m a t h e m a t i c a l l a n g u a g e . '' I n u n d e r t a k i n g t h i s w o r k , a n a t t e m p t h a s b e e n m a d e to a p p ly th e " L a w of th e S in g le V a r i a b l e " a n d t h e r e b y , c o n t r i b u t e to th e d e ­ v e l o p m e n t of a s c i e n c e of e d u c a t i o n . 10 c i t . , p. i i i . S. A . C o u r t i s , M a t u r a t i o n U n i t s a n d H o w to U s e T h e m , o p . 4 P ro b le m O n e of t h e b a s i c a s s u m p t i o n s on w h ic h th e c h i l d d e v e l o p m e n t m o v e m e n t r e s t s i s t h a t of c o n s t a n t c h a n g e . T h ere is an o v e r­ w h e lm in g b o d y o f e v i d e n c e , n o t o n ly i n t h e w o r k of C o u r t i s , ^ ^ M illa rd , 12 and O lso n , 13 b u t i n t h a t of m a n y o t h e r s a s w e ll, w h ic h s u ub s *t a n *• t i a t+e vut h i s a s s u m p t i o n . 1 4 ,1 5 ,1 6 T he stu d ie s 17 w h i c h h a v e b e e n p r e s e n t e d in t h e l i t e r a t u r e h a v e e s t a b l i s h e d t h e g e n e r a l p r i n c i p l e t h a t t h e c h ild d e v e l o p s a s a S. A. C o u r t i s , T o w a r d a S c i e n c e of E d u c a t i o n , op . c i t ., p p. 8 -9 . 12 C . V. M i l l a r d , C h ild D e v e l o p m e n t , op. c i t . , p . 11. 13 W. C ., O l s o n , C h ild D e v e l o p m e n t , B o s to n : 1949, p. 17, p. 36. D. C. H e a th , 14 F . K. M e r r y a n d R . V. M e r r y , T h e F i r s t T w o D e c a d e s of L i f e , N e w Y o r k : H a r p e r , 1950, p . 83. 15 " T h e T h r e e R ' s i n th e E l e m e n t a r y S c h o o l , " A s s o c i a t i o n fo r S u p e rv is io n a n d C u r ric u lu m D e v elo p m e n t o f 'th e N a tio n a l E d u c a ­ ti o n A s s o c i a t i o n , 1 952, p . 19. 16 K. C. G a r r i s o n , G r o w t h a n d D e v e l o p m e n t , N e w Y o r k : L o n g m a n s G r e e n , 1952, p . 67. 17 T h e f o llo w in g a r e b u t a fe w o f a n a l m o s t u n l i m i t e d n u m ­ b er: S, A . C o u r t i s , c i t . , c h . 3. " D is c ip lin e U n d e r th e G ro w th C o n c e p t," op. w h o le , b u t no s t u d i e s c o u ld b e fo u n d t h a t a t t e m p t to e s t a b l i s h th e e x a c t r e l a t i o n s h i p b e t w e e n tw o s p e c i f i c d e v e l o p m e n t a l f a c t o r s o n a n in d iv id u a l b a s is . T h e p u r p o s e of t h i s s tu d y , t h e r e f o r e , i s to a t t e m p t to d e t e r ­ m i n e w ith p r e c i s i o n t h e r e l a t i o n s h i p b e t w e e n th e a c h i e v e d g r o w t h i n h e i g h t a n d th e b e g i n n i n g of g r o w t h i n r e a d i n g o n th e b e l i e f t h a t s u c h a r e la tio n s h ip , w h en o n ce e s ta b lis h e d , w ill e n ab le th e u s e r , u n d e r " c o n s ta n t c o n d i t i o n s , to p r e d i c t w ith in f a i r l y n a r r o w l i m i t s th e t i m e a t w h ic h a s p e c i f i c i n d i v i d u a l s h o u ld b e r e a d y to r e a d . W. C . O l s o n a n d B. O. H u g h e s , " T h e C h ild a s a W h o l e , " C h ild B e h a v i o r a n d D e v e l o p m e n t , N e w Y o r k : M c G r a w H i l l , 1943, p. 199" C . V. M i l l a r d , C h ild D e v e l o p m e n t , op. c i t . , pp. 5 - 7 . W. C. O l s o n , C h ild D e v e l o p m e n t , op. c i t . , p. 40. R a l p h W. H o u s e , " A S tu d y of F i v e P u p i l s W ho N e e d e d H e lp i n R e a d i n g , " J . E d . R e s . , 41, 1947, p p . 4 7 - 5 9 . A . W. B l a i r a n d W. H. B u r t o n , G r o w t h a n d D e v e l o p m e n t of th e P r e - A d o l e s c e n t , N e w Y o r k : A p p l e t o n - C e n t u r y - C r o f t s , 1951, ch. 4. E l i z a b e t h F u l l e r , " P e a s i n a P o d , " E d . L e a d e r s h i p , III ( A p r i l, 1946), p p . 3 0 2 - 7 . L o u i s T h o r p e , C h ild P s y c h o l o g y a n d D e v e l o p m e n t , N e w Y o rk : M c G r a w H ill, 1946, p . 272. R . N. S a n fo rd and o th e r s , P h y s iq u e , P e r s o n a l i t y and S c h o la r ­ s h ip , M o n o g . of t h e S o c ie ty f o r R e s e a r c h in C h ild D e v e l o p m e n t , Vol. VIII, N o. 1, S e r . N o . 34, 1943. I m p o r t a n c e of t h e S tu d y C o n v e n t i o n a l m e a s u r e s a n d s t a t i s t i c a l i n t e r p r e t a t i o n do n o t p e r m i t th e a n a l y s i s of t h e i n d i v i d u a l c h i l d ' s g r o w t h p a t t e r n . ^ ’ ^ S in c e t h e c h ild d e v e l o p m e n t m o v e m e n t i s i n t e r e s t e d p r i m a r i l y i n th e i n d i v i d u a l c h i l d ' s p a t t e r n of g r o w t h , t h e s e e x i s t e n t p r o c e d u r e s a r e in e ffe c tiv e. W h e n g r o w t h i s t a k e n in to c o n s i d e r a t i o n , a s i s t h e c a s e w ith t h e t e c h n i q u e d e v e l o p e d b y C o u r t i s , t h e c h i l d c a n b e d e a l t w ith as an in d iv id u a l. A c c o r d i n g to t h i s t e c h n i q u e , " a n i n d i v i d u a l ' s g r o w th m u s t b e d i a g n o s e d i n t e r m s o f h i s ow n p r o b a b l e m a t u r a t i o n a n d i n t e r m s of h is own r a te a n d in c ip ie n c y ." n iq u e i s 20 A m a x i m of t h i s t e c h ­ " n e v e r u s e a n y i n t e r p r e t a t i o n w h ic h l o s e s s i g h t of a s i n g l e c h ild ." 18 S. A. C o u r t i s , " V a l i d a t i o n of S t a t i s t i c a l P r o c e d u r e s , " J . of E d . R e s . , X L L ( J u n e , 1925), p. 3 1 - 4 0 . 19 L . K. F r a n k , " R e s e a r c h i n C h ild P s y c h o l o g y : H i s t o r y a n d P r o s p e c t , " C h ild B e h a v i o r a n d D e v e l o p m e n t , N . Y ., M c G r a w H i l l , 1943, p . 3. S. A . C o u r t i s , " M a t u r a t i o n a s a F a c t o r i n D i a g n o s i s , " 3 4 th Y e a r b o o k o f N a t i o n a l S o c ie ty f o r S tu d y of E d u c a t i o n , 1935, p p . 1 6 9 -8 7 . 7 T h e i m p o r t a n c e of t h i s s tu d y i s tw o fo ld : (1) to d e m o n s t r a t e th e v a lu e of a n e w a p p r o a c h to c h ild d e v e l o p m e n t , n a m e l y th e G o m p e r z F u n c t i o n a s a p p l i e d b y S. A . C o u r t i s , a n d (2) to p r e s e n t t h e d i f f e r e n t g r o w t h p a t t e r n s o f c h i l d r e n i n a m a n n e r w h ic h w ill e n a b l e e d u c a t o r s to a d j u s t t h e c u r r i c u l u m to t h e s e p a t t e r n s o n th e b a s i s o f s c i e n t i f i c a n a ly sis. D e f i n i t i o n of T e r m s F o r t h i s s tu d y , th e f o llo w in g t e r m s w ill b e a r t h e s e c o n n o t a ­ tio n s : 1. C hange is an o b s e rv e d se q u e n tia l d ifferen c e. 2. G ro w th 21 i s a g e n e r a l t e r m f o r c h a n g e i n liv in g o r g a n i s m s c a u s e d by t h e li f e p r o c e s s . 3. from D ev elo p m en t 21 i s a w a re n e s s th a t g ro w th is p ro c e e d in g s o m e l o w e r l e v e l to a h i g h e r l e v e l w ith o u t e m p h a s i s u p o n t h e u ltim a te s ta te . 4. M atu ratio n 21 i s p r o g r e s s t o w a r d a n u l t i m a t e s t a t e of c o n ­ d itio n . 1'In a c t u a l p r a c t i c e , g r o w th , d e v e l o p m e n t , a n d m a t u r a t i o n a r e u s e d i n t e r c h a n g e a b l y d e p e n d in g u p o n t h e e m p h a s i s d e s i r e d . ” S. A . C o u r t i s , M a t u r a t i o n U n i t s a n d H ow to U s e T h e m , op. c i t . , p. 22. 8 5. C y c l e o f G r o w t h i s p r o g r e s s t o w a r d a s p e c i f i c s t a t e of c o n d itio n m a d e b y a n i m m a t u r e o r g a n i s m , o t h e r t h i n g s b e i n g e q u a l. 6. L a w of G r o w th , y = k ^ r t ± i], i s a n a d o p t i o n of t h e t r G o m p e r z F u n c t i o n , y = ki , w h e r e y = a c h i e v e d g r o w t h , k = m a x i ­ m u m , i = in c ip ie n c y , r “ r a te , t = v a ria b le tim e , and ] = iso ­ c h ro n ic v a lu e. 7. M a x i m u m i s th e u l t i m a t e s t a t e o r c o n d itio n . 8. In c ip ie n c y i s m a g n itu d e a t th e b eg in n in g of a p e r io d of m a t u r a t i o n a n d i s c o n s t a n t t h r o u g h o u t th e g r o w t h c y c l e . 9. R ate is c o n sta n t p r o g r e s s to w a rd a m a x im u m e x p re s s e d in i s o c h r o n s . 10. Iso ch ro n is 1 p e r c e n t of th e t o t a l t i m e r e q u i r e d f o r a g r o w t h c u r v e to c h a n g e f r o m a d e v e l o p m e n t of 0 .0 0 0 0 0 0 1 8 9 p e r c e n t to a d e v e l o p m e n t of 9 9 .9 0 9 1 7 p e r c e n t. 11. . G r o w t h C o n s t a n t s a r e m a x i m vim, i n c i p i e n c y , a n d r a t e . 12. =£ ] m e a n s t h a t i n c l u d e d v a lu e i s e x p r e s s e d i n i s o c h r o n s . C H A P T E R II R E V IE W O F T H E L I T E R A T U R E In tro d u c tio n I n r e c e n t y e a r s , a s a b y - p r o d u c t of th e r e l a t i v e l y n e w c h ild d e v e l o p m e n t m o v e m e n t , d i s s a t i s f a c t i o n h a s b e e n e x p r e s s e d c o n c e r n i n g t h e ' ' n o r m a t i v e a p p r o a c h 1' i n h e r e n t i n c r o s s - s e c t i o n a l stu d ie s. ’^ 3 ,2 4 ^ y p e Qf i n t e r p r e t a t i o n l o s e s s i g h t of th e i n ­ d iv i d u a l c h ild w h ic h i s c o n t r a r y to c h ild d e v e l o p m e n t p r o c e d u r e s . A s a r e s u l t of t h i s s i t u a t i o n , th e l o n g i t u d i n a l s tu d y i s b e i n g g iv e n g re a te r c o n sid e ra tio n . T h e t i m e a n d e x p e n s e in v o lv e d i n s t u d i e s of t h i s n a t u r e a r e s e r i o u s o b s t a c l e s w h ic h h a v e l i m i t e d t h e n u m ­ b e r of s u c h s t u d i e s . 22 L . K. F r a n k , " R e s e a r c h i n C h ild P s y c h o l o g y : a n d P r o s p e c t , 1' o p. c i t . , p . 10. H isto ry 23 W. F . D e a r b o r n a n d J . W. M . R o th n e y , P r e d i c t i n g th e C h i l d 's D e v e l o p m e n t , C a m b r i d g e : S c i - A r t P u b l i s h e r s , 1941, p. 330. 24 W. M . K r o g m a n , " T r e n d s i n t h e S tu d y of t h e P h y s i c a l G r o w t h o f C h i l d r e n , " C h ild D e v e l o p m e n t , II , 1940, p p . 2 7 9 - 8 4 . 10 L o n g itu d in al s tu d ie s 25 fo u n d i n th e l i t e r a t u r e a r e c o n c e r n e d m a i n l y w ith t h e p h y s i c a l g r o w t h of th e c h ild . T h e r e a r e a fe w s t u d i e s w h ic h i n c l u d e m e n t a l g r o w t h a n d , i n r a r e i n s t a n c e s , o ne f in d s g r o w t h i n e d u c a t i o n a l a c h i e v e m e n t i n c l u d e d a s a p a r t of th e research . * * ^ 2 6 ,2 7 ,2 8 ,2 9 ,3 0 ,3 1 . . ^ _ T h e n u m b e r of s t u d i e s a p p e a rin g m th e l i t ­ e r a t u r e w h ic h u t i l i z e l o n g i t u d i n a l g r o w t h d a t a i s v e r y l i m i t e d in 25 C o m p l e t e b i b l i o g r a p h i e s of t h e s e s t u d i e s a r e p r e s e n t e d i n th e f o llo w in g R e v s . of E d . R e s . : V o l. Ill ( A p r i l , 1933); V ol. VI ( F e b . , 1936); V o l. I X ~ ( F e b ., 1939); V o l. XI ( D e c ., 1941); V o l. X IV ( D e c ., 1944); V o l. XX ( D e c ., 1950);' V ol. X XII ( D e c ., 1952). 26 H a r v a r d G r o w th S tu d y D a t a , M o n o g . of th e S o c i e t y f o r R e s . i n C h ild D e v . , V ol. 3, S e r . N o . 14, N o. 1, 1938. 27 K a t h e r i n e S i m m o n s , T h e B r u s h F o u n d a t i o n S tu d y o f C h ild G r o w t h a n d D e v e l o p m e n t , II, P h y s i c a l G r o w t h a n d D e v e l o p m e n t , M o n. of S o c . f o r R e s . i n C h ild D e v ., V o l. IX , S e r . N o. 37, N o. 1, 1944. 28 J e a n W. M c F a r l a n e , S t u d i e s of C h ild G u i d a n c e . I. M e t h ­ o d o lo g y of D a t a C o l l e c t i o n a n d O r g a n i z a t i o n , M o n o , of S o c . f o r R e s . i n C h ild " D e v . , V o l. I ll, S e r . N o. 19, N o. 6, 1938. 29 H . E. J o n e s a n d N a n c y B a y l e y , " T h e B e r k l e y G r o w t h S t u d y , " C h ild D e v e l o p m e n t 12 No. E ( J u n e , 1941), p p. 1 6 7 -7 3 . 30 B i r d T . B a ld w in , P h y s i c a l G r o w t h of C h i l d r e n f r o m B i r t h to M a t u r i t y , U n iv . of Io w a S tu d i e s i n C h ild W e l f a r e , V ol. 1, N o . 1, T92T 31 D e a r b o r n D a ta , E v e r e t t D a t a , H o l t D a t a - - u n p u b l i s h e d s t u d i e s of t h e C h i l d D e v e l o p m e n t L a b o r a t o r i e s of th e D e p a r t m e n t of E l e m e n t a r y E d u c a t i o n , M i c h i g a n S t a t e C o lle g e , , E a s t L a n s i n g , M ic h . 11 r e l a t i o n to t h o s e - o f a c r o s s - s e c t i o n a l n a t u r e . s i t u a t i o n i s tw o fo ld . The r e a s o n fo r th is (1) T h e p r e s e n t p r a c t i c e of s u r v e y i n g p o p u l a ­ tio n s on a c r o s s - s e c t i o n a l b a s is and i n te r p r e tin g th e r e s u l t s s t a t i s ­ t i c a l l y r e q u i r e s a m i n i m u m of t i m e a n d e x p e n s e . ' (2) No r e a l n e e d h a s b e e n f e lt f o r lo n g itu d in a l s tu d ie s u n til r e c e n t y e a r s . The tre n d , h o w e v e r , s e e m s to b e t o w a r d s s t u d i e s of th e l o n g i t u d i n a l t y p e . M i l l a r d s t a t e s t h a t l o n g i t u d i n a l s t u d i e s a r e r e p l a c i n g th e c r o s s s e c t i o n a l w h ic h t e n d to s m o o t h o u t c u r v e s . M illa rd : 32 G a r r i s o n c o n c u r s w ith M. . . t h e r e h a s b e e n a s h i f t t o w a r d th e l o n g i t u d i n a l m e th o d . . . . in r e c e n t y e a r s th e r e h a s b e e n a c o n tin u ed i n c r e a s e 33 i n th e u s e of th e l o n g i t u d i n a l a p p r o a c h . ' 1 S in c e t h e r e l a t i o n s h i p b e t w e e n d i f f e r e n t s t a g e s of m a t u r i t y a n d b e t w e e n d i f f e r e n t m a t u r a t i o n s m u s t b e s t u d i e d i n r e s p e c t to s i n g l e i n d i v i d u a l s , o n e f in d s i t n e c e s s a r y to r e s o r t to th e l o n g i t u d i n a l a p p r o a c h r a t h e r t h a n th e c r o s s - s e c t i o n a l . A c o m p re h en siv e su rv ey of t h e l i t e r a t u r e p r o d u c e s n o s u c h lo n g i t u d i n a l s tu d y d e a l i n g w ith m a t u r a t i o n i n h e i g h t a n d m a t u r a t i o n i n r e a d i n g , a lth o u g h s t u d i e s w e r e 32 W. C. O l s o n a n d B. O. H u g h e s , " T h e C h ild a s A W h o l e , " lo c . c i t . 33 11. K. C . G a r r i s o n , G r o w t h a n d D e v e l o p m e n t , o p . c i t . , p p . 1 0 “ 12 fo u n d w h ic h d e a l t w ith o n e o r th e o t h e r of t h e s e a r e a s , ^ ’^ ’^ ’^ ’^ T h e r e w e r e n o d a t a , o t h e r t h a n th e D e a r b o r n D a t a , u p o n w h ic h t h i s s tu d y i s b a s e d , p r e s e n t e d i n t h e l i t e r a t u r e w h ic h c o u ld b e d e a l t w ith o n th e b a s i s of t h e p r o c e s s o f m a t u r a t i o n . T h i s r e s e a r c h w a s u n d e r t a k e n to d e m o n s t r a t e th e e f f e c t o n th e re la tio n s h ip b e tw e e n d e v e lo p m e n t in h e ig h t and in re a d in g in c ip ie n c y w h e r e t h e p r o c e s s of m a t u r a t i o n i s t a k e n a s a f a c t o r . R ead in g I n c ip ie n c y - - P h y s ic a l M a tu ra tio n A fe w w r i t e r s h a v e a d v a n c e d th e t h e o r y of p h y s i c a l m a t u r a ­ tio n a s a fa c to r d e te rm in in g re a d in e ss to read . G e se ll and 34 F . L . K u n k le , G r o w th a n d P r e d i c t i o n i n R e a d i n g A c h i e v e ­ m e n t , U n p u b l i s h e d M a s t e r of A r t s T h e s i s , M i c h i g a n S t a t e C o l l e g e , 1950. 35 C. V. M i l l a r d , " T h e N a t u r e a n d C h a r a c t e r i s t i c s of P r e A d o l e s c e n t G r o w t h i n R e a d i n g A c h i e v e m e n t , " C h ild D e v e l o p m e n t , V o l. II, N o . 2, 1940, p p . 7 1 - 1 1 4 . 36 F . K. S c h u t t l e w o r t h , T h e P h y s i c a l a n d M e n t a l G r o w t h of G i r l s a n d B o y s A g e 6 - 1 9 i n R e l a t i o n to A g e a t M a x i m u m G r o w th , M o n o , o f th e S o c i e t y f o r R e s e a r c h i n C h i l d D e v e l o p m e n t , V o l. IV , S e r . N o . 22, N o . 3, 1939. 37 H . V. M e r e d i t h , R h y th m of P h y s i c a l G r o w th , U n i v e r s i t y of Io w a S t u d i e s i n C h ild W e l f a r e , V ol. X I, N o . 3, 1935. 38 N a n c y B a y l e y , " T a b l e s f o r P r e d i c t i n g A d u lt H e i g h t f r o m S k e l e t a l A g e a n d P r e s e n t H e i g h t , " J . P e d i a t r i c s , 28 ( J a n . - J u n e , 1946), pp. 49-64. 13 Ilg 39 s t a t e t h a t r e a d i n e s s to r e a d a n d r e a d i n e s s to w a lk a r e b a s e d o n a s i m i l a r c o n c e p t of m a t u r i t y , s i n c e r e a d i n g d e p e n d s on m o t o r s k i l l s , a s d o e s w a lk in g , w h i c h a r e s u b j e c t to th e s a m e l a w s of g r o w t h t h a t g o v ern c re e p in g and g ra sp in g . To M c G r a w , " m a tu r a tio n and le arn in g a r e n o t d i f f e r e n t p r o c e s s e s , m e r e l y d i f f e r e n t f a c e t s o f th e f u n d a ­ m e n t a l p r o c e s s of g r o w t h . " She g o e s o n to s a y " c h r o n o l o g i c a l age and m e n ta l age s ta n d a r d s h a v e b e e n c a s t a sid e as a d eq u a te c r i t e r i o n fo r in a u g u ra tin g a p r o g r a m of t o i l e t t r a i n i n g . I t is n o w p o s s i b l e to s a y t h a t w h e n a n i n f a n t b e h a v e s in a p a r t i c u l a r w a y h i s n e u r a l f u n c ­ t i o n in g is s u c h t h a t h e c a n p r o f i t b y a t o i l e t t r a i n i n g p r o g r a m , a n d it i s p o s s i b l e to p r e d i c t w h a t th e p r o b a b l e c o u r s e of a c h i e v e m e n t w ill b e . T h e r e i s no r e a s o n w h y s i m i l a r b e h a v i o r c r i t e r i o n c a n n o t b e f o r m u l a t e d so t h a t t e a c h e r s a n d p a r e n t s w i l l be a b le to d e t e c t w h e n a p a r t i c u l a r c h i l d is p r e p a r i n g f o r r e a d i n g , w r i t i n g , a n d a r i t h • ,,40 m e t i c . 11 A c r o s s - s e c t i o n a l s t u d y w h ic h a c t u a l l y r e l a t e d d e v e l o p m e n t in r e a d ­ in g to p h y s i c a l d e v e l o p m e n t w a s m a d e b y B e t t s . B e t t s , i n a s t u d y of th e 39 A . G e s e l l a n d F . Ilg , C h ild D e v e l o p m e n t , N e w Y o r k : H a r p e r B r o s . , 1949, p . 389. 40 M y r t l e B . M c G r a w , T h e N e u r o m u s c u l a r M a t u r a t i o n of the H u m an In fa n t, N ew Y ork: C o l u m b i a U n i v e r s i t y P r e s s , 1943, p p . 1 3 0 -3 1 , 14 i n c r e a s e of i n t e r p u p i l l a r y d i s t a n c e , f in d s th e g r e a t e s t g a i n b e t w e e n th e a g e s of s i x a n d s e v e n . He s ta te s : " T h e m a t u r a t i o n of t h e p h y s i o l o g i c a l p r o c e s s e s in v o l v e d i n r e a d i n g , u n d o u b te d ly a f a c t o r of p a r a m o u n t i m p o r t a n c e a n d d e s e r v i n g of f i r s t r a n k , h a s r e c e i v e d to o l i t t l e a t t e n t i o n . . . m a t u r i t y of f u n c t i o n , a s w e ll a s f r e e d o m f r o m p h y s i o l o g i c a l d e f e c t s , c o n t r i b u t e s d i r e c t l y to p s y c h o l o g i c a l r e a d i n e s s to r e a d . " 41 A s e v e r e d e f e c t of s t u d i e s of t h i s t y p e b a s e d on c r o s s - s e c t i o n a l d a t a i s w e ll i l l u s t r a t e d i n t h i s r e s e a r c h . B e tts u s e d m e a n a n d m e d i a n g r o w t h n o r m s to d e s c r i b e th e d a ta , c o n s i s t i n g of 684 c a s e s f r o m K i n d e r g a r t e n to S ix th G r a d e . D u r i n g th e o n e - h a l f y e a r i n t e r v a l s f r o m K i n d e r g a r t e n B to K i n d e r g a r t e n A a n d G r a d e 1 A to IB , t h e m e d i a n d e c r e a s e d r a t h e r t h a n i n c r e a s e d . The m e a n s r e ­ a c t e d i n a s i m i l a r f a s h i o n b e t w e e n G r a d e s 4B a n d 4A a n d G r a d e s 5A a n d 6B. I n a d d itio n , n o i n c r e a s e w a s r e p o r t e d f o r th e m e d i a n s b e t w e e n G r a d e s 3B a n d 3A, a n d G r a d e s 6B a n d 6A . L i k e w i s e , no i n c r e a s e w as o b t a i n e d f o r th e m e a n s a t K i n d e r g a r t e n B a n d K i n d e r ­ g a r t e n A o r a t G r a d e s 3B and 3A . I t w o u ld s e e m o b v io u s to a s s u m e th a t g r o w t h , o n a n i n d i v i d u a l b a s i s , a c t u a l l y did o c c u r f o r th e a b o v e E. A . B e t t s , " A P h y s i o l o g i c a l A p p r o a c h to t h e A n a l y s i s of R e a d i n g D i s a b i l i t i e s , " O hio S t a t e U n i v e r s i t y E d u c a t i o n R e s e a r c h B u l l e t i n (S ept. 19, 1934), V ol. X III, N o. 6, p . 138. 15 m e n tio n e d in t e r v a l s b u t th a t its e ffe c t w a s o b lite r a te d by th e c r o s s se c tio n a l a n a ly sis. T h e s e d a t a l o s e s i g h t o f th e i n d i v i d u a l c h ild a n d , th e r e f o r e , t h e i r v a lu e s e e m s m o r e a c a d e m ic th an r e a l in t e r m s of c la s s ro o m p ra c tic a lity . E am es, 42 i n h i s s tu d y of 25 c a s e s of r e a d i n g d i s a b i l i t y w h o s e a v e r a g e I .Q ., a s d e t e r m i n e d by a S t a n f o r d - B i n e t t e s t , w a s 0.91 fo u n d t h a t 62 p e r c e n t h a d s k e l e t a l d e f e c t s . O lso n 43 a n d D a v i s s t r e s s th e i n t e r r e l a t i o n s h i p of g r o w t h t h r o u g h t h e c o n c e p t o f o r g a n i s m i c a g e w h i c h i s a n a v e r a g e of s e v e r a l s p e c ific g ro w th a g e s . O ne c a s e is p r e s e n t e d in w h ic h re a d in g ag e c o i n c i d e d c l o s e l y w ith th e o r g a n i s m i c a g e a lth o u g h t h e m e n t a l a g e w a s h ig h a n d th e r e a d i n g a g e low . H ouse, 44 i n a s tu d y of f iv e p u p i l s w ho n e e d e d h e l p i n r e a d i n g , r e l i e d o n m a t u r i t y a g e s to p l a n a r e a d i n g p r o g r a m w h ic h w o u ld m a k e l e a r n i n g to r e a d p o s s i b l e . H o u s e 's s tu d y u t i l i z e d O l s o n ' s o r g a n i s m i c 42 T. H . E a m e s , "R ea d in g D is a b ility ," A rc h iv e s of P e d i ­ a t r i c s , 54, 1940, p . 487. 43 W. C. O l s o n a n d W. I. D a v i s , " T h e A d a p t i o n . of I n s t r u c ­ t i o n i n R e a d in g to th e G r o w t h o f C h i l d r e n , " E d . M e t h o d s , 20 (N o v ., 1940), N o . 2, p p . 7 1 - 7 9 . 44 R a l p h W. H o u s e , " A S tu d y of F i v e P u p i l s Who N e e d e d H e lp i n R e a d i n g , " lo c . c it. 16 age p rin c ip le s u p p le m e n te d b y o th e r in d ic e s of m a tu r ity . s e n t e d g r a p h i c a l l y ( F i g u r e 1). One c a s e is p r e ­ The c lo s e re la tio n s h ip b e tw e e n re a d in g a g e , 8 .3 y e a r s , a n d o r g a n i s m i c a g e s , 8 .2 y e a r s , is q u ite a p p a r e n t . I t is th e o p in io n o f H o u s e t h a t a c h i e v e m e n t i s a n e x p r e s s i o n o f t o t a l g r o w t h . T h e s t u d i e s w h ic h h a v e b e e n p r e s e n t e d l e n d c r e d u l e n c e to B o y n ­ t o n ' s s t a t e m e n t c o n c e r n i n g th e r e l a t i o n s h i p b e t w e e n r e a d i n g a n d p h y s i c a l m a t u r a t i o n o r g r o w th . B o y n to n s t a t e s : " W e k n o w so l i t t l e a b o u t i t [ r e a d - in g ] in c o n n e c t i o n w i t h p h y s i c a l m a t u r a t i o n o r g r o w t h . " 45 T h is s t a t e ­ m e n t i n d i c a t e s t h a t r e s e a r c h in th is a r e a m i g h t w e ll b e f r u i t f u l . F o r m u la - - G o m p e r z F u n c tio n Y = ki r 46 A t t e m p t s to i s o l a t e a g e n e r a l m a t h e m a t i c a l c u r v e w h ic h w ill d e s c r i b e a n d p r e d i c t th e c o u r s e o f g r o w t h p h e n o m e n o n h a v e b e e n n u m ero u s. Shock 47 p r e s e n t s a n e x c e l l e n t a n a l y s i s o f th e v a r i e d ty p e o f f o r m u l a w h ic h h a v e b e e n u t i l i z e d w ith v a r y i n g d e g r e e s o f s u c c e s s . 45 P . L . B o y n to n , " R e l a t i o n o f R e a d i n g to M a t u r a t i o n , " P e a b o d y J o u r n a l of E d u c a t i o n , 16, p p . 1 5 5 -5 9 (N ov., 1 93 8), p . 157. 46 B e n j a m i n G o m p e r z , P h i l o s o p h i c a l T r a n s a c t i o n s of th e R o y a l S o c i e t y of L o n d o n f o r the y e a r M D C C C X X Y , P a r t I, L o n d o n , W. N i c o l , P r i n t e r s to th e R o y a l S o c ie ty , M D C C C X X V . 47 N . S. S h o c k , " G r o w t h C u r v e s , " H a n d b o o k o f E x p e r i m e n t a l P s y c h o l o g y , N e w Y o r k : J o h n W ile y , 1951, c h . 10. gtrqwth fitCrB. ca se \ 5 f m 10 7 ---- '\ tv p e s F ig u re 1. o f - ag-es G ra p h ic s u m m a ry of c a s e 5 F . a g e s ta k e n fr o m H o u se . G ro w th 18 P e a r s o n , w r i t i n g i n 1901, s t a t e s : " I b e l i e v e th e d a y m u s t c o m e w h e n th e b i o l o g i s t w ill, w i t h o u t b e in g a m a t h e m a t i c i a n , n o t h e s i t a t e to u s e m a t h e m a t i c a l a n a l y s i s w h e n h e r e q u i r e d i t . 11 48 The w r i t e r i s i n c o m p l e t e a g r e e m e n t w ith t h i s s t a t e m e n t . M a n y r e s e a r c h w o r k e r s r e p o r t s u c c e s s i n d e s c r i b i n g a nd p r e d i c t i n g th e p a t t e r n s of i n d i v i d u a l g r o w t h p h e n o m e n a . e n c o u r a g i n g of t h e s e i s th e G o m p e r z F u n c t i o n , y = k i r 49 The m o st t , a d a p t e d by C o u r t i s to p r e d i c t a n d d e s c r i b e g r o w t h i n a l l a r e a s - - p h y s i c a l and e d u c a tio n a l. M i l l a r d p r e s e n t s a d e s c r i p t i o n of s e v e r a l s t u d i e s w h ic h s u c c e s s f u l l y u t i l i z e d th e G o m p e r z F u n c t i o n i n d e s c r i b i n g a n d p r e d i e tin g g r o w t h p h e n o m e n a . C o u rtis and is, up s ta te s to t h i s 50 th a t tim e , th is th e fu n c tio n is o n ly fu n c tio n "T he w h ic h Law of G r o w t h " w ill w o r k in 48 K a r l P e a r s o n , N a t u r e ( J a n . 17, 1901), q u o te d f r o m D 'A r c y , G r o w t h a n d F o r m , N e w Y o r k : H a r p e r B r o s . , 1942, p. 72. 49 T . P . N a l l y a n d A. R . D e L o n g , A n A p p r a i s a l o f a M e th o d o f P r e d i c t i n g G r o w t h , E a s t L a n s i n g , M i c h i g a n , C h ild D e v e l o p m e n t L a b o r a t o r i e s , M i c h i g a n S t a t e C o l l e g e , 1952, S e r i e s II, N o. 1. 50 C . V. M i l l a r d , A n A n a l y s i s of F a c t o r s C o n d itio n in g P e r ­ f o r m a n c e i n S p e llin g , u n p u b l i s h e d . P h . D . T h e s i s #1235, E d u c a t i o n , U n i v e r s i t y of M i c h i g a n , 1937. 19 d e sc rib in g is and p re d ic tin g g ro w th f o r a ll areas w here m a tu ra tio n a ff a c t*o r . 5 1 ) 5 2 S e v e r a l r e v i e w s of s u c h m a t h e m a t i c a l f o r m u l a s a p p e a r in th e fo llo w in g m a n u s c r i p t s - - C a r m i c h a e l , M a n u a l of C h ild P s y c h o l o g y , S t e v e n s , H a n d b o o k of E x p e r i m e n t a l P s y c h o l o g y , R o th n e y , P r e d i c t i n g t h e C h i l d 1s D e v e l o p m e n t . 54 55 53 and D e a r b o r n and A ll of t h e s e g iv e s p e c i a l a t t e n t i o n , to th e G o m p e r z F u n c a t i o n ; D e a r b o r n a n d R o th n e y c i t e i t a s p o s s e s s i n g m e r i t s b e y o n d t h o s e of t h e o t h e r f u n c t i o n s r e ­ v ie w e d . S. A . C o u r t i s , " G r o w t h a n d D e v e l o p m e n t i n C h i l d r e n , ' ' A d ­ v a n c e s i n H e a l t h E d u c a t i o n , P r o c e e d i n g s of S e v e n t h H e a l t h E d u c a t i o n C o n f e r e n c e , A n n A r b o r , M i c h i g a n , 19 33 , N e w Y o r k : A m e r i c a n C h ild H e a l t h A s s o c i a t i o n , 1934, p p . 1 8 0 -2 0 6 . 52 S. A . C o u r t i s , " P r e d i c t i o n of G r o w th , J . of E d . R e s . , X X V I ( M a r . , 1933), p p . 4 8 1 - 9 2 . “ 53 H e l e n T h o m p s o n , " P h y s i c a l G r o w t h , " M a n u a l of C h ild P sy c h o lo g y , N ew Y ork: J o h n W ile y , 1951, p. 26 1. 54 N. S. S h o c k , " G r o w t h C u r v e s , " lo c . c it. W. F . D e a r b o r n a n d J . W. M . R o th n e y , P r e d i c t i n g th e C h i l d ' s D e v e l o p m e n t , op. c i t . , p. 218. 20 T he G o m p e rz F u n c tio n , a s a p p lie d by C o u rtis , y = k ^ r t ± is a d e q u a te ly d e s c r ib e d in h is w o rk s . c a l a c c o u n t of t h i s f u n c t i o n . 57 56 M illa rd p re s e n ts an h is to r i- 58 A t th e p r e s e n t t i m e , t h e r e a r e f e w s t u d i e s r e p o r t e d i n th e l i t e r a t u r e w h ic h e m p l o y t h e G o m p e r z F u n c t i o n o r C o u r t i s ' a d a p t i o n of it . 5 9 ,6 0 , 61 L o n g and D e a r b o r n h a v e u t i l i z e d i t to e s t a b l i s h g r o w t h tre n d s in m e n ta l d e v e lo p m e n t. M illa rd 6 2 63 ’ e m p lo y e d th is , fu n c tio n in a s tu d y of s p e l l i n g m a t u r a t i o n a n d a l s o w ith r e s e a r c h o n p r e a d o l e s c e n t 56 , . r^ T h i s i s th e s a m e e q u a t i o n a s y = ki w h ic h h a s b e e n s im p lifie d by C o u r tis f o r p r a c t i c a l p u r p o s e s . 57 S. A . C o u r t i s , M a t u r a t i o n U n its a n d H o w to U s e T h e m , lo c . c i t . 58 C. V. M i l l a r d , A n A n a l y s i s of F a c t o r s C o n d itio n in g P e r ­ f o r m a n c e i n S p e l l i n g , op. c i t ., c h . 3. 59 C. V. M i l l a r d , lo c . c i t . 60 B e n j a m i n G o m p e r z , P h i l o s o p h i c a l T r a n s a c t i o n s of th e R o y a l S o c i e t y of L o n d o n f o r t h e y e a r M D C C C X X V , P a r t I, lo c . c i t . 61 H . H . L o n g a n d W. F . D e a r b o r n , 1'T h e C u r v e of M e n t a l G r o w t h , ' 1 P r e d i c t i n g t h e C h i l d 's G r o w t h , " o.p. c i t . , p p . 2 0 1 - 3 7 . , 62 C. V. M i l l a r d , A n A n a l y s i s o f F a c t o r s C o n d itio n in g P e r ­ fo r m a n c e in S p e llin g , l o c . c i t . 63 C. V. M i l l a r d , " T h e N a t u r e a n d C h a r a c t e r i s t i c s of P r e A d o l e s c e n t G r o w t h i n R e a d i n g A c h i e v e m e n t , " lo c . c it. 21 re a d in g m a tu ra tio n . M ered ith 65 K u n k le 64 h a s a p p l i e d i t to r e a d i n g m a t u r a t i o n . t e s t e d t h i s t e c h n i q u e , u n s u c c e s s f u l l y , i n p r e d i c t i n g th e s t a t u r e of s i x Io w a m a l e s s e l e c t e d f r o m t h e Io w a S t u d i e s . a nd D e lo n g 66 N ally h a v e p r e s e n t e d a r e f u t a t i o n of M e r e d i t h ' s d a t a i n d i ­ c a tin g g r o s s e r r o r s i n t h e a p p l i c a t i o n of th e f u n c t i o n . p o rts n u m e ro u s stu d ie s 67 C o u rtis r e - s u p p o r t i n g th e v a l i d i t y of th e f u n c t i o n i n w h ic h d e s c r i p t i o n a n d p r e d i c t i o n f a l l w ith in a n a v e r a g e e r r o r of ±2 p e r c e n t . T h e C h i l d D e v e l o p m e n t L a b o r a t o r i e s of M i c h i g a n S ta te C o lle g e h a v e u t i l i z e d t h i s f u n c t i o n w i t h a c o n s i d e r a b l e a m o u n t of success. F. m e n t , lo c . c i t . 65 L . K u n k le , G r o w t h a n d P r e d i c t i o n i n R e a d i n g A c h i e v e ­ H . V. M e r e d i t h , R h y th m o f G r o w th , op. c i t . , p . 107. 66 T . P . N a l l y a n d A. R . D e L o n g , A n A p p r a i s a l of a M e th o d of P r e d i c t i n g G r o w th , l o c . c it. S. A. C o u r t i s , " T h e F a c t o r C o n c e p t , " U n i v e r s i t y of M i c h i g a n S c h o o l of E d u c a t i o n B u l l e t i n IV (D e c ., 1932), p p . 3 6 - 3 8 . C H A P T E R III PROCEDURE D a ta T h e v a l u e of d a t a w h ic h c a n b e a n a l y z e d in t e r m s o f t h e i n ­ d iv id u a l c h i l d w a s r e c o g n i z e d i n th e 1 9 2 0 's b y C. V. M i l l a r d , th e n S u p e r i n t e n d e n t of S c h o o l s , D e a r b o r n , M i c h i g a n . S in c e t h a t t i m e D r . M i l l a r d h a s d e v o t e d h i s e f f o r t s to r e s e a r c h w h i c h t r e a t s th e c h i l d a s a n i n d i v i d u a l a n d w h i c h s e e k s to d e s c r i b e th e g r o w t h p a t t e r n of in d iv id u a l c h ild r e n . U n d e r h i s s u p e r v i s i o n , th e t e a c h e r s of th e H e n r y F o r d S c h o o l w e r e i n s t r u c t e d in th e c o l l e c t i o n of d a t a a n d m a i n t e n a n c e of l o n g i ­ tu d in a l r e c o r d s . T he c o m b i n e d e f f o r t s o f a d m i n i s t r a t o r s a n d t e a c h ­ e r s p r o d u c e d t h e s e d a t a w h ic h a r e a v a i l a b l e a t th e C h i l d D e v e l o p ­ m e n t L a b o r a t o r i e s of M i c h i g a n S ta te C o l l e g e u n d e r th e t i t l e , D e a r b o r n D a ta . T h e c h i l d r e n o f t h e H e n r y F o r d S c h o o l, D e a r b o r n , M ic h i g a n , w ere u tiliz e d as s u b je c ts. T h e s e c h i l d r e n w e r e m e a s u r e d in c o n s e c u ­ tiv e y e a r s f o r a p e r i o d e x t e n d i n g f r o m K i n d e r g a r t e n to N in th G r a d e . In s o m e i n s t a n c e s th e s p a n of y e a r s i s l e s s ; th e n u m b e r of s t u d e n t s 23 m e a s u r e d v a r i e d w i t h th e n o r m a l f l u c t u a t i o n s in s c h o o l p o p u l a t i o n s u c h a s a b s e n c e s , m o v i n g a w a y , e n t e r i n g s c h o o l in t h e m i d d l e g r a d e s , a n d th e l i k e . M illa rd s ta te s : " T h e c h i l d r e n in t h i s s c h o o l a r e , i n g e n e r a l , t y p i c a l of t h e h i g h e r l e v e l of s o c i a l s t a t u s f o u n d in a n i n d u s t r i a l co m m u n ity . , ,68 V e r y f e w of th e c a s e s r e p r e s e n t s o c i a l e x t r e m e s . 11 T he p r e s e n t d a t a c o n s i s t of s e v e n t y - s e v e n c a s e s - - t h i r t y - f i v e g irls and fo rty -tw o boys. dred cases. T h ese w e re s e le c te d fro m o v er th re e hun­ A ll of t h e c a s e s w h ic h w e r e c o m p l e t e w e r e p l o t t e d o n l o g a r i t h m i c p a p e r a n d t h o s e f o u n d to c o n t a i n t h r e e o r m o r e m e a s u r e s in th e p r e a d o l e s c e n t c y c l e of g r o w t h b o t h in r e a d i n g a n d in h e i g h t w e r e s e l e c t e d f o r t h i s s tu d y . T w o o f th e c a s e s w h ic h f i t t h e s a m ­ p lin g c r i t e r i a w e r e o m itte d f r o m th e f i n a l s tu d y , a s th e g r e a t v a r i ­ a b i l i t y of th e m e a s u r e s m a d e c o m p u t a t i o n of g r o w t h e q u a t i o n s i m ­ p o ssib le . M e th o d S in c e th e v a l u e of l o n g i t u d i n a l d a t a s t e m s f r o m th e a n a l y s i s o f th e g r o w t h p a t t e r n of t h e i n d i v i d u a l c h ild , i t is n e c e s s a r y to u t i l i z e 68 C. V . M i l l a r d , " T h e N a t u r e a n d C h a r a c t e r i s t i c s of P r e A d o l e s c e n t G r o w t h in R e a d i n g A c h i e v e m e n t , " o p . c i t ., p p . 7 2 - 7 3 . 24 p r o c e d u r e s w h ic h w i l l n o t d i s t o r t t h i s p a t t e r n . Such a m e th o d has b e e n d e v e l o p e d b y D r . S. A . C o u r t i s , w h o s e a p p l i c a t i o n of t h e G o m p e r z F u n c tio n , 69 y = k =j;rt ± i b w h e r e y = a c h i e v e d g r o w t h , k = m a x im u m , r = r a t e , t = v a r ia b le tim e , i = in c ip ie n cy , and 4 ] = iso ch ro n ic v a lu e, su c c e ssfu lly a v e r a g e e r r o r of ± 2 p e r c e n t . d e sc rib e s g ro w th d a ta w ith in an T h is m e t h o d y i e l d s e q u a l u n i t s of g r o w t h w h i c h l e n d t h e m s e l v e s to c o m p a r a t i v e i n t e r p r e t a t i o n a n d a n a ly s is s in c e is o c h ro n ic u n its a r e e q u a l and c o m p a ra b le . 70 • E x a c t e x p l a n a t i o n of t h e t e c h n i q u e u t i l i z e d in f o r m u l a t i n g g r o w t h e q u a t i o n s i s p r e s e n t e d in C o u r t i s ' m a n u a l , M a t u r a t i o n U n its a n d H o w to U s e T h e m . p e a r s in M i l l a r d ' s 71 A n i l l u s t r a t i o n of t h i s t e c h n i q u e a l s o a p - C h ild D e v e lo p m e n t. 72 E q u a t i o n s w e r e f o r m u l a t e d f o r t h e p r e a d o l e s c e n t c y c l e of m a t u r a t i o n in r e a d i n g a n d in h e i g h t . The eq u atio n s of h e ig h t w e re w r i t t e n a s th o u g h t h e y w e r e th e i n i t i a l c y c l e of g r o w t h w h i c h d o e s 69 , . rt y = k ii . 70 S. A. C o u r t i s , " M a t u r a t i o n U n its f o r th e M e a s u r e m e n t of G r o w t h , " S c h o o l a n d S o c i e t y , X X X (N o v. 16, 1939), p p . 6 8 3 - 9 0 . 71 T h is m a n u a l i s a v a i l a b l e f r o m S. A . C o u r t i s , 9110 D w ig h t A v e ., D e t r o i t 14, M i c h i g a n . 72 C . V. M i l l a r d , C h i l d D e v e l o p m e n t , o p . c i t ., p p . 4 0 - 4 4 . 25 n o t a p p e a r to b e th e c a s e . A t l e a s t tw o e a r l i e r c y c l e s of g r o w t h 7 3 ,7 4 and p o s s ib ly th r e e c a n be id e n tifie d . ’ M o re e x a c t eq u atio n s m i g h t h a v e b e e n d e r i v e d if d a t a w e r e a v a i l a b l e f o r t h e s e e a r l i e r c y cle s. A lth o u g h th e p r e s e n t d a t a o m i t t h e s e e a r l i e r c y c l e s , the a d e q u a c y of th e g r o w t h e q u a t i o n s tif ic p r o c e d u r e . 75 s t i l l f a l l s w i t h i n th e l i m i t s of s c i e n - T h e a v e r a g e d e v i a t i o n s of t h e s e e q u a t i o n s of h e ig h t a r e w e ll w ith in ± 2 p e r c e n t e r r o r . T h e r e a d i n g e q u a t i o n s w e r e s o l v e d f o r 0 .1 p e r c e n t of d e v e l ­ o p m e n t i n o r d e r to d e t e r m i n e w h ic h r e a d i n g t h e o r e t i c a l l y 76 " t," i . e . , th e c h r o n o l o g i c a l a g e a t b e g in s. The eq u atio n s w e re so lv ed a t 0.1 p e r c e n t o f d e v e l o p m e n t r a t h e r t h a n 0 .0 p e r c e n t of d e v e l o p m e n t , a s 0 .1 p e r c e n t is a p p r o x i m a t e l y th e s m a l l e s t l e v e l to w h i c h th e g r o w t h p o i n t s in r e a d i n g c a n b e i n t e r p o l a t e d , i . e . , b e t w e e n 0.0 5 a n d 0 .1 0 of a p o i n t s c o r e o n th e R e v i s e d S t a n f o r d R e a d i n g A c h i e v e m e n t Tes1 73 R i c h a r d S c a m m o n , 11 T h e F i r s t S e r i a t i m S tu d y o f H u m a n G r o w t h , " A m e r i c a n J o u r n a l o f P h y s i c a l A n t h r o p o l o g y , V o l. X, N o . 3 ( J u n e - S e p t . , 1927), p . 332. 74 S. A. C o u r t i s , M a t u r a t i o n U n its a n d H o w to U s e T h e m , o p . c i t ., p . 93. 75 T. P . N a l l y a n d A . R . D e L o n g , A n A p p r a i s a l of a M e th o d f o r P r e d i c t i n g G r o w t h , l o c . c it. *7^ R e a d i n g i n c i p i e n c y w h e n r e f e r r e d to i n t h i s p a p e r w ill m e an as th e o re tic a lly d e te rm in e d . 26 T h i s c h r o n o l o g i c a l a g e , " t , 11 F i g u r e 2, P o i n t A, w a s th e n s u b ­ s t i t u t e d in to th e e q u a t i o n o f h e i g h t a n d s a i d e q u a t i o n w a s s o l v e d f o r p e r c e n t of d e v e l o p m e n t i n h e i g h t ( F ig . 2, P o i n t B) f o r t h e p r e a d o l e s c e n t c y c l e of g r o w t h . 77 (See F i g . 2.) D is trib u tio n s w e re m ade of re a d in g in c ip ie n c y and p e r c en t o f d e v e l o p m e n t i n h e i g h t a t the t i m e of r e a d i n g i n c i p i e n c y , s e g r e g a t ­ in g s e x e s . T h e s e d i s t r i b u t i o n s w e r e a n a l y z e d to d e t e r m i n e th e i n t e r r e ­ l a t i o n s h i p a n d i n t e r d e p e n d e n c y of d e v e l o p m e n t in h e i g h t a n d d e v e l o p ­ m e n t in r e a d i n g . L i m i t a t i o n s o f th e S tu d y T h e u n d e r l y i n g c o n c e p t u p o n w h ic h t h i s s t u d y r e s t s is t h a t th e c h i l d g r o w s a s a w h o l e . p ro cess. T h e g r o w t h o f th e c h i l d i s a n i n t e g r a t e d S in c e a s t u d y o f the e n t i r e i n t e g r a t e d p a t t e r n o f .the c h i l d w o u ld r e q u i r e m o r e t i m e t h a n i s a v a i l a b l e f o r t h i s p r o j e c t , o n e p h a s e of t h a t i n t e g r a t i o n w a s s e l e c t e d f o r a n a l y s i s . T h i s s tu d y , t h e r e f o r e , d e a l s w ith t h e r e l a t i o n s h i p of tw o m a ­ tu r a tio n p a t t e r n s , th a t of re a d in g and th a t of h eig h t. Two s p e c i f i c P e r c e n t of d e v e l o p m e n t in h e i g h t w h e n r e f e r r e d to in t h i s p a p e r w i l l m e a n w i t h i n t h e p r e a d o l e s c e n t c y c l e of g r o w th . 27 ? I * Q luw SQ U kuj a j^ o a r^ i 'k tS l° 5 $ ^ $ ! ^ £ s 8 & l | ^h C h !2. « '! ‘ ~ S ^ S s L s 'Peiz'Eefi'r Figure o& 2. C o m p a ra tiv e m a tu r a tio n s in height ^ ^ S;? re a d in g --c ase 58F. ^ j and 5 28 p o i n t s (F ig . 2, P o i n t s A a n d B) in th e d e v e l o p m e n t o f t h e s e m a t u r a ­ tio n p a t t e r n s w e r e s e l e c t e d f o r s tu d y . T h e p e r c e n t of d e v e l o p m e n t in h e i g h t s e r v e s a s o n e ( P o i n t B ) , w h ile r e a d i n g i n c i p i e n c y s e r v e s a s th e o t h e r ( P o i n t A ). The r e l a t i o n s h i p b e t w e e n t h e s e p o i n t s is t r e a t e d on a n i n d i v i d u a l b a s i s . T h e c o n c u r r e n c e of t h e s e d a t a w ith t h o s e f o u n d in th e l i t e r a t u r e a n d w i t h g e n e r a l l y a c c e p t e d c o n c e p t s c o n c e r n i n g th e g r o w t h of c h i l d ­ r e n i s t r e a t e d b r i e f l y b u t d o e s n o t c o n s t i t u t e a m a j o r p o r t i o n of t h i s research . S in c e n o o t h e r r e s e a r c h , u t i l i z i n g th e p r e s e n t c o n c e p t a n d r e l a t e d to t h i s a r e a , c o u l d b e f o u n d in th e l i t e r a t u r e , t h i s r e s e a r c h m u s t b e c o n s i d e r e d a s p i o n e e r i n g in n a t u r e . T h e te c h n i q u e of a n a l y ­ s i s e m p l o y e d c o n s t i t u t e s a m a j o r c o n t r i b u t i o n of t h i s s t u d y to r e ­ search . C H A P T E R IV TH E DATA: IT S A N A L Y S IS A N D I N T E R P R E T A T I O N I n t r o d u c tio n T h e a n a l y s i s a n d i n t e r p r e t a t i o n of t h e s e d a t a a r e b a s e d on t h e p r e m i s e th e o n e m u s t n e v e r l o s e s i g h t of th e i n d i v i d u a l c h ild . S t a t i s t i c a l p r o c e d u r e s a r e e m p l o y e d to d e s c r i b e d i s t r i b u t i o n s of s c o r e s d e riv e d f r o m an a n a ly s is of in d iv id u a l c h ild re n . A n a tte m p t has b een m a d e to p r e s e r v e th e i n d i v i d u a l i t y of th e d a t a a t a l l t i m e s . The D a ta T h e o r i g i n a l d a t a f r o m w h i c h th e g r o w t h e q u a t i o n s w e r e f o r m u la te d w e re c o lle c te d by C. V. M illa rd . 78 He r e p o r t e d h e i g h t in i n c h e s a n d r e a d i n g a c h i e v e m e n t in t e r m s o f R e v i s e d S t a n f o r d s c o r e s . T h e r e f o r e , h is u n i t s w e r e u s e d in t h i s s tu d y . T h e se d a ta a r e found i n A p p e n d i c e s A a n d B , a s a m p l e of w h ic h is p r e s e n t e d in F i g u r e 3. D e a r b o r n D a t a i s a v a i l a b l e a t th e C h i l d D e v e l o p m e n t L a b ­ o r a t o r i e s of 'th e D e p a r t m e n t of E l e m e n t a r y E d u c a t i o n , M i c h i g a n S ta te C o lle g e. 30 A p p e n d ix A D a t a - - B o y s (42 c a s e s ) C ase CA A p p e n d ix B D a t a - - G i r l s (35 c a s e s ) 1M H e ig h t C ase R e a d in g CA H e ig h t IF R e a d in g 83 4 7 .5 - 101 4 8.7 - 88 48.0 14.5 106 4 9 .2 9.5 92 4 8 .7 21.0 110 - 31.5 95 4 9 .1 - 113 50 .5 - 100 5 0 .2 39.0 118 50.7 4 0 .0 104 51.0 4 6.0 122 51 .5 49.0 107 5 1 .5 - 125 - 52.0 - 112 5 2 .4 60.0 130 52.7 5 3.5 116 5 3 .5 58 .5 134 54.0 60.5 124 5 4 .6 69.0 137 54.5 - 128 5 5 .2 7 6 .5 142 5 5 .5 67.0 131 5 5 .7 - 146 56.7 7 3 ,5 136 57.0 - 149 57.7 - 140 5 7.2 8 2.5 154 5 8 .6 - 158 5 9 .6 84.0 F ig u re 3. I l l u s t r a t i o n of A p p e n d i c e s A a n d B . 31 The g ro w th c o n s t a n t s - - r a t e , in c ip ie n c y , and m a x im u m - - f o r t h e p r e a d o l e s c e n t c y c le o f g r o w t h i n h e i g h t , th e a v e r a g e d e v i a t i o n o f the e q u a t i o n , th e n u m b e r of m e a s u r e s a v a i l a b l e , a n d th e a p p r o x i ­ m a t e a g e s p a n of t h e s e m e a s u r e s a n d D. a r e p r e s e n t e d in A p p e n d i c e s C F i g u r e 4 is a s a m p l e of A p p e n d ix C, w h ic h c o n t a i n s th e fo rty -tw o boy c a s e s . A p p e n d ix D p r e s e n t s s i m i l a r d a t a f o r th e th irty -fiv e g irl c a se s. T he g ro w th c o n s t a n t s - - r a t e , in c ip ie n cy , and m a x im u m - - f o r t h e p r e a d o l e s c e n t c y c le of g r o w t h i n r e a d i n g a c h i e v e m e n t , t h e a v e r ­ a g e d e v i a t i o n of th e e q u a t i o n , th e n u m b e r of m e a s u r e s a v a i l a b l e , a n d th e a p p ro x im a te age sp a n of th e se m e a s u r e s p e n d ice s E and F . a re p r e s e n t e d in A p ­ F i g u r e 5 is a s a m p l e o f A p p e n d ix E , w h i c h c o n ­ t a i n s th e f o r t y - t w o b o y c a s e s . A p p e n d ix F p r e s e n t s s i m i l a r d a ta f o r the t h i r t y - f i v e g i r l c a s e s . F ig u re 6 i l l u s t r a t e s th e c o m p a r i s o n b e t w e e n g i r l s ' a n d b o y s ' c u r v e s of c o n s ta n ts f o r g ro w th in h eig h t. F i g u r e 7 i l l u s t r a t e s th e c u r v e s of c o n s t a n t s f o r th e r e a d i n g d e v e l o p m e n t of b o y s a n d g i r l s . T h e d i s t r i b u t i o n o f th e d e v i a t i o n s o f t h e s e g r o w t h e q u 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 s I a n d II. T h e m e a n d e v i a t i o n of th e e q u a t i o n s o f h e i g h t b a s e d o n a n a v e r a g e n u m b e r of te n g r o w t h p o i n t s f o r t h e f o r t y - t w o b o y c a s e s 32 A p p e n d ix C B o y s 1 G ro w th C o n sta n t H e ig h t E q u a tio n y = K =§ r t ± i] ± AD C ase 1M M ax­ im u m K R ate r 5 4 .8 0 .3 6 0 0 F i g u r e 4. In C ip ie n c y l Avg. Dev. Span AD J 11s . Mo No. of M ea­ su res + 1 8 .5 3 0 .2 0 8 3-124 11 -A-ge c I l l u s t r a t i o n of A p p e n d ix C . A p p e n d ix C B oys 1 G ro w th C o n sta n ts R e a d in g E q u a t i o n y = K =§ r t ± i] ± AD C ase M ax­ im u m K 1M 92.0 R ate r In c ip ie n c y i A vg. D ev. AD Age Span in M os. No. of M ea­ sures 0 .5 9 4 2 - 3 1 .0 0 2 .3 8 8 -1 4 0 9 F ig u re 5. I l l u s t r a t i o n of A p p e n d ix E . 33 HEIG-HT IN IN C H E S BOVS = 6 0 ^ € a . z y < f z t •+ 2 2 . 19} t o . a G rlfLS* 5 r . z f o . 2 .J 2 ? t -f- 22'J 7 j t 0 . 2 0 // fh&E ) N Y E A l Z S F i g u r e 6. C o m p a r i s o n of b o y s ’ a n d g i r l s ' c u r v e s of c o n s t a n t s f o r g r o w t h i n h e i g h t . [ C u r v e s p r o j e c t e d w ith o u t c o n s i d e r a t i o n of a d o l e s c e n t b r e a k . ] S tanford scopes 80V S « — GIRLS = 7 S .Z £ I .0 7 4 & t - ± 2^ 7 A / £ ! ,U 4 & t - 2 3 * 0 t 2 . 2 (G) (oO 40 Jo tz . a g -b F ig u re 7. / n yeA £ s C o m p a r i s o n of b o y s ' a n d g i r l s ' c u r v e s of c o n s t a n t s f o r g r o w t h in r e a d i n g . [C u rv e s p r o j e c t e d w ith o u t c o n s i d e r a ­ t i o n of a d o l e s c e n t b r e a k . ] 35 TABLE I D IS T R IB U T IO N O F D E V IA T IO N S O F A C T U A L P O I N T S F R O M E Q U A T IO N P R E D I C T I O N F O R G R O W T H IN H E IG H T B o y s - - N = 42 G i r l s - -N = 35 In te rv a l (in c h e s ) F requency I n te r v a l (in c h e s ) F requency 0 .0 0 -0 .0 5 1 0 .0 0 -0 .0 5 2 0 . 06 - 0.10 3 0 . 06 - 0.10 2 0 .1 1 -0 .1 5 9 0 .1 1 -0 .1 5 3 0 . 16- 0.20 19 0 . 16- 0.20 10 0 .2 1 -0 .2 5 4 0 .2 1 -0 .2 5 10 0 .2 6 - 0 .3 0 3 0 .2 6 - 0 .3 0 5 0 .3 1 -0 .3 5 3 0 .3 1 -0 .3 5 1 0 .3 6 - 0 .4 0 2 T A B L E II D IS T R IB U T IO N O F D E V IA T IO N S O F A C T U A L S C O R E S F R O M E Q U A T IO N P R E D I C T I O N F O R G R O W T H IN R E A D IN G B o y s - - N = 42 G irls--N = 35 In te r v a l (sco res) F requency In te rv a l (sco res) F req u en cy 0.0-0.9 5 0.0-0.9 4 1.0-1.9 12 1.0-1.9 7 2.0-2.9 9 2 ."o - 2 .9 9 3.0-3.9 10 3.0-3.9 8 4.0-4.9 4 4.0-4.9 3 5.0-5.9 0 5.0-5.9 3 6.0-6.9 2 6.0-6.9 1 37 ( F i g . 8) w a s 0 .1 8 ± 0.01 i n c h 79 w i t h a s t a n d a r d d e v i a t i o n o f 0 .0 68 i n c h a n d a r a n g e o f 0.0 3 to 0 .3 5 in c h . S i m i l a r l y , t h a t o f th e t h i r t y - f i v e g i r l c a s e s ( F i g . 8) b a s e d o n a n a v e r a g e . n u m b e r of 8.2 g r o w th p o i n t s w a s 0.20 ± 0 .0 1 i n c h w i t h a s t a n d a r d d e v i a t i o n o f 0 .0 7 6 a n d a r a n g e of 0 .0 4 to 0 .3 8 in c h . S in c e s t u d i e s o f p h y s i c a l g r o w t h g e n ­ e r a l l y p r o d u c e a n a v e r a g e e r r o r of m e a s u r e m e n t in th e m a g n i t u d e o f 0 .4 3 in c h , 80 t h e d e v i a t i o n s of t h e s e e q u a t i o n s a p p e a r to f a l l w ith in n a rro w lim its. T h e m e a n d e v i a t i o n of th e r e a d i n g e q u a t i o n s b a s e d o n a v e r a g e n u m b e r of 6.0 g r o w t h p o i n t s f o r th e f o r t y - t w o b o y c a s e s ( F ig . 9) w a s 2 .5 3 ± 0 .2 3 p o i n t s w ith a s t a n d a r d d e v i a t i o n of 1.5 p o i n t s a n d a r a n g e of 0.0 to 6.9 p o i n t s . S i m i l a r l y , t h a t of th e t h i r t y - f i v e g i r l c a s e s ( F i g . 9) b a s e d o n a n a v e r a g e n u m b e r of 5.5 g r o w t h p o i n t s w a s 2.8 ± 0 .2 5 p o i n t s w ith a s t a n d a r d d e v i a t i o n o f 1.47 p o i n t s a n d a r a n g e of 0;1 to 6.2 p o i n t s . S in c e th e p r o b a b l e e r r o r of m e a s u r e m e n t of th e N e w S t a n f o r d A c h i e v e m e n t R e a d i n g T e s t i s a p p r o x i m a t e l y 1.95 p o i n t s , 81 t h e s e d e v i a t i o n s a l s o a p p e a r to f a l l w i t h i n n a r r o w l i m i t s . 79 T he s t a n d a r d e r r o r s o f th e m e a n s w e r e c o m p u t e d a t th e 1 p e r c e n t le v e l of co n fid en ce. 80 81 H a r y a r . d G r o w t h S tu d y D a t a , o p . c i t . , 11. T. K e l l e y , G . M . F u c h , L . M . T e r m a n , S t a n f o r d A c h i e v e ­ m e n t T e s t s , D i r e c t i o n s of A d m i n i s t r a t i n g , W o r l d B o o k C o ., 1940, p . 10. NO, Of? CASES H - 42- M E A N t - - - ) - Oi i 8 AVER.AG-E POits/TS* 1 0 STbNDAUP J>£MT/ON - O. O t g I 1 -i--------- r 0,62 S' 0.075" GANG-E = 0 .0 3 - 0 , J 5 r 0 ,7 1 5 0 .,7 S 0 ,7 .2 5 0 ,2 7 5 6,&XS~ H E IG H T I,A L O * S SOYS ho. o r OASES N = 3S~ MEAfv(— ) = 0 . ZO AVERAGE POINTS* 8 .2 . srAvj>/>ei> 3>E m r/oN s o ,o it> 8A N G E - o m - 0 ,3 8 0 ,0 7 5 0.0 7 5 0.1X5 0,»75 0 ,225 0 ,2 7 5 H&ICrAT 1/Ai.aES 0.325 0 ,$ 7 5 . G/ELS F i g u r e 8. D i s t r i b u t i o n of d e v i a t i o n s of a c t u a l p o i n t s f r o m e q u atio n p re d ic tio n f o r g ro w th in h e ig h t. /V r. 4-2. M E A N ( ---- )= 2 - S J A V egA G B POINTS = 6 , 0 S t* n Da p J> j>EirmrioN^ !> so /?ANGE - O - L,*} o is /■ S 2.S' <3>S 4*S s c o e e ^A LO E 'S sBoVS s. s ’ t* s NO. OF CAS FS /V= 3 S M e p N (— ) ~ W E G P tO rE P O /rffS s 2 ,8 v57S ’ smn2>Ae> deviations A V 7 - £' 2- os F i g u r e 9. /•£~ 2. S ' S 'S 4 'S S7SS C O ^ C V *\*-O SS GUSLS i.s D i s t r i b u t i o n of d e v i a t i o n s of a c t u a l s c o r e s f r o m e q u a ti o n p r e d i c t i o n f o r g ro w th in re a d in g . 4° F ig u re 10 c o n t a i n s f o u r c a s e s s e l e c t e d f o r g o o d n e s s o f f i t i l ­ l u s t r a t i n g th e d e v i a t i o n of th e a c t u a l g r o w t h p o i n t s f r o m th e p r e d i c t e d g r o w t h c u r v e s of h e i g h t . F ig u re 11 i l l u s t r a t e s th e d e v i a t i o n s of th e a c t u a l g r o w t h p o i n t s f r o m th e p r e d i c t e d g r o w t h c u r v e s of r e a d i n g f o r f o u r c a s e s se le c te d f o r g o o d n e s s of f i t . A n a ly sis and I n te r p r e ta tio n I n a c c o r d a n c e w i t h th e p r o c e d u r e d e s c r i b e d i n C h a p t e r III, t h e g ro w th e q u a tio n s f o r re a d in g w e re 0.1 p e r c e n t of d e v e l o p m e n t . so lv ed f o r v a r ia b le tim e , The re s u ltin g v a r ia b le tim e , th e c h r o n o l o g i c a l a g e a t w h i c h r e a d i n g t h e o r e t i c a l l y b e g i n s . c h ro n o lo g ic a l age w as th e n s u b s titu te d f o r v a ria b le tim e , th e e q u a t i o n s of h e i g h t . " t , 11 a t " t," is T h is Mt , 11 in T h e s e e q u a t i o n s w e r e s o l v e d to d e t e r m i n e th e p e r c e n t of d e v e l o p m e n t in h e i g h t in th e p r e a d o l e s c e n t c y c le of g ro w th a t v a r ia b le tim e , 1' t . 11 The r e s u l t s a re p r e s e n t e d in T ab les III a n d IV , a lo n g w ith t h e a v e r a g e .I.Q . s c o r e f o r e a c h c a s e a s o b ­ t a i n e d f r o m a n a v e r a g e of th e K u h l m a n - A n d e r s o n T e s t s c o r e s a v a i l ­ a b le f o r e a c h in d i v i d u a l . T h e m e a n p e r c e n t of d e v e l o p m e n t in h e i g h t f o r th e f o r t y - t w o b o y c a s e s w a s 7 2 .4 ± 1.2 p e r c e n t w ith a s t a n d a r d d e v i a t i o n of 2 .7 4 p e r c e n t a n d a r a n g e o f 1 0 .6 p e r c e n t . 41 INCHES INCHES y = 'S’? . 7 & £ o l i < 4 £ s - t + 1 3 ' 7 $ J - t O . O f y = . L O £ o , t S l l t + Z9.ZJ] ± o - O J C ASE 44M 1 9E 1--------- 1 “I /S 3 , CASE ZOM /£ £ - /S S C H R .D N O L .O G /C A L * A& -E /// MO-S. IS T ~ I-------- 1 fS~ l/E /3A ' CHeoNOLOStCAL. AGE ■W MO S . SCOPE'S too S 3 £ o , C>SO$ t - 3 ¥ . ¥ a j ± /. / foo y ~ Z o £ o .b & > S t-3 g ,< i3 3 ± . /./ So 2o too G,H*a/*Oi-OG*>A*~ s& £ J/V Ato s , CU#.aHOLae>/CA*~ * & e MoS., £TfiNPO*& scoecs SCOAES too ‘ to o y = 7 0 ,g£ I . Z 2 .3 It - 7 j . s £ J ± / y * 7 z£ a , Oe) / y t - ¥ s n j ± o .3 r t>C 2d to o /20 / no CHeonauoefCAi- +< f/v F ig u re 1 1. M as* /OO yVfl A&ff /V A/O-T' /3J3 CH 60W O LO & rc * i- F o u r s e l e c t e d c u r v e s of g r o w th in r e a d i n g . 43 T A B L E III B O Y S 1 R E A D IN G I N C I P I E N C Y - - P E R C E N T A G E O F D E V E L O P M E N T IN H E I G H T A N D C H R O N O L O G IC A L A G E A T R E A D IN G IN C I P I E N C Y R ead in g In c ip ie n c y C ase Avg. I .Q . 1 1 0 .6 N o. of M easu res o f I.Q . CA P e t . of D e v iatio n in H e i g h t 1 0 2 .4 8 9 9 70.1 77.9 81 .9 7 7.7 7 0 .3 7 1 .5 85.1 9 4 .3 1 14.7 8 8 9 86 .5 8 1 .6 7 4.9 74.0 7 1 .2 6 8 .8 10M 11M 12M 119.5 111.2 1 1 8 .4 : 8 8 9 6 8 .6 79.6. 72.0 7 4.7 7 8 .6 7 0 .4 13M 15M 17M 105.9 1 04 .4 120.0 10 9 9 8 1 .3 7 7 .3 7 9 .3 70.0 7 3 .4 72.7 18M 19M 20 M 11 6.2 10 9.3 1 1 3 .3 9 10 9 7 6 .8 6 9 .4 8 4 .4 73 .5 71.1 7 4 .3 21M 22M 23M 9 5 .8 11 0.4 9 0 .6 9 5 10 7 9 .2 7 4 .4 7 7 .6 74.0 70.9 24M 40 M 41M 8 9 .7 1 11 .2 113.1 10 7 9 .7 7 .9 61.8 7 4.9 7 5.7 70.0 42M 44 M 45M 1 1 1 .4 1 1 7.2 110.2 11 9 13 8 2 .6 77.1 82.1 7 4.9 75.1 7 0.7 1M 3M 4M 5M 7M 9M 109.2 92.6 91.0 44 T A B L E IB (C o n tin u ed ) R ead in g In c ip ie n c y C ase Avg. I.Q . 4 8M 5 0M 51M 100.1 52M 55M 94M 125.0 1 0 4 .8 9 9 .1 9 8M 103M 112M 116.6 9 7 .3 1 2 0 .5 1 2 6 .2 1 0 7 .8 96.8 N o . of M easu res o f I.Q . CA P e t . of D e v iatio n in H e i g h t 8 11 11 85.7 90.1 89.1 69.7 72.5 7 3.6 6 8 79 .4 8 4 .3 75.1 69.O 69.7 68.9 10 77 .5 7 3 .3 71.0 76 .6 71.5 68.2 78.8 69.3 78 .3 73.2 68.0 71.1 9 10 11 144M 170M 173M 9 9 .7 1 1 6 .5 10 9 9 176M 194M 197M 1 0 1 .2 1 1 6 .9 10 3.1 9 10 9 63.2 8 7 .6 80.1 71.2 74 .4 72.0 199M 214M 217M 1 1 5 .3 1 1 1 .3 9 7 .7 9 10 9 66.5 79.7 78 .8 69 .I 76.7 72 .6 N = 42 108.1 94 77.7 72 .4 29.2 10.6 R ange SD SE qm 6 .8 4 . 2.7 4 2.91 1.17 45 T A B L E IV G IR L S ' R E A D IN G I N C I P I E N C Y - - P E R C E N T A G E O F D E V E L O P M E N T IN H E I G H T AND C H R O N O L O G IC A L A G E A T R E A D IN G IN C I P I E N C Y R ea d in g In c ip ie n c y _ C ase A vg. *“ • No. of M easu res of I.Q . CA 2 P e t . of D e v iatio n in H e i g h t IF 2F 3F 98.1 128 110.1 9 11 7 84 .4 70.9 7 6 .6 7 9 .3 7 2 .5 7 5.0 4F 5F 6F 111.8 107.6 97.5 9 9 6 77.7 78.5 80.8 7 8 .6 7 3 .6 77.1 8F 1I F 12F 117.1 86.8 112.2 10 11 9 74.2 88 .8 72.8 7 4 .2 8 0 .7 7 2 .7 110.3 105.5 118.9 9 LI 10 79.7 80.4 74.1 7 6 .9 7 8 .6 7 4 .3 21F 22F 24F 106 133.3 126.7 9 9 10 75.8 64.5 67.8 80.1 7 5 .8 7 8 .6 25F 28F 29F 125.9 111.9 101.8 10 10 10 67.3 65.6 83.5 7 6 .3 7 3 .4 7 3 .6 31F 32F 35 F 99.1 107.7 117.7 10 9 8 80.1 78.7 71 .9 7 6 .7 7 8 .8 7 7 .7 38F 58F 62F 119.6 10 10 10 82.1 83.7 94.1 7 7 .3 7 5 .2 7 4 .6 13F 18F 19F - 94.5 106.8 46 T A B L E IV ( C o n t i n u e d ) R e a d in g I n c i p i e n c y C ase Avg. I .Q . N o. of M easu res of I .Q . CA P e t . of D ev iatio n in H e i g h t 63 F 64 F 65F 153.0 10 8.2 107.2 10 9 10 7 3 .6 9 0 .8 6 3 .6 78.1 7 7 .9 74.1 70F 129F 13 I F 1 08 .7 95.0 112.8 7 9 10 7 9 .8 8 1 .5 7 1 .5 7 9 .3 79 .5 80 .9 146F 173F 179F 113.7 105.0 1 1 1 .6 8 9 9 7 4 .6 8 4 .6 8 0 .6 7 2 .5 7 2 .2 7 2 .2 213F 218F 1 1 2 .8 11 9.2 6 9 76 .7 80.1 74 .2 77.1 N = 35 111.5 9.2 7 7 .5 7 6 .3 31 .5 8.7 Range SD SE qm 7 .0 3 2 .6 2 3.2 9 1.22 47 The m e a n c h ro n o lo g ic a l age a t w h ic h re a d in g th e o r e t ic a ll y b e g a n f o r th e f o r t y - t w o b o y c a s e s w a s 7 7 .7 ± 2.9 m o n t h s w ith a s t a n d a r d d e v i a t i o n of 6 .8 4 m o n t h s a n d a r a n g e of 2 9 .2 m o n t h s . T h is g r o u p o f f o r t y - t w o b o y s h a d a n a v e r a g e I .Q . s c o r e , a s d e t e r m i n e d b y th e K u h l m a n - A n d e r s o n T e s t , o f 108.1 b a s e d on 9.1 m easures. T h e m e a n p e r c e n t o f d e v e l o p m e n t in h e i g h t f o r th e t h i r t y fiv e g i r l c a s e s w a s 7 6 .3 ± 1.2 p e r c e n t w i t h a s t a n d a r d d e v i a t i o n of 2 .6 2 p e r c e n t a n d a r a n g e o f 8.7 p e r c e n t . The m e a n c h ro n o lo g ic a l age a t w h ic h re a d in g th e o r e tic a lly began and w a s 7 7 .5 ± 3.3 m o n t h s w i t h a s t a n d a r d d e v i a t i o n of 7 .0 3 m o n t h s a r a n g e of 31.5 m o n t h s . T h is g r o u p o f t h i r t y - f i v e g i r l s h a d a n a v e r a g e I.Q . s c o r e , a s d e t e r m i n e d b y th e K u h l m a n - A n d e r s o n T e s t , of 1 1 1 .5 b a s e d on 9.2 m e a s u r e s . " T a b l e s V a n d V I p r e s e n t th e d i s t r i b u t i o n s of p e r c e n t of d e v e l o p m e n t i n h e i g h t a n d th e c h r o n o l o g i c a l a g e a t w h i c h r e a d i n g th e o re tic a lly began. F i g u r e s 12 a n d 13 p r e s e n t th e d a t a g r a p h i c a l l y . T h e s e d a t a a p p e a r to b e in a g r e e m e n t w ith d a t a p r e s e n t e d th e g e n e r a l l i t e r a t u r e in th e f o ll o w i n g a s p e c t s : in 48 TABLE Y D IS T R IB U T IO N O F P E R C E N T A G E O F D E V E L O P M E N T IN H E IG H T A T W H IC H R E A D IN G T H E O R E T I C A L L Y B E G A N B o y s - - N = 42 G i r l s — N = 35 In te r v a l F requency In te r v al F requency 6 8 .4 3 72 .3 5 6 9 .4 5 7 3 .3 3 7 0 .4 5 74.3 5 7 1 .4 7 75 .3 2 7 2 .4 4 7 6 .3 3 7 3 .4 4 7 7 .3 5 7 4 .4 5 7 9 .3 4 7 5 .4 4 8 0 .3 2 7 6 .4 2 8 1 .3 1 7 7 .4 2 7 8 .4 1 49 T A B L E VI D IS T R IB U T IO N O F C H R O N O L O G IC A L A G E A T W H ICH R E A D IN G T H E O R E T IC A L L Y BEG A N B o y s - - N = 42 G i r l s —N = 35 In te rv a l F requency In te rv a l F requency 62.2 1 64 2 6 4 .2 1 66 1 6 6 .2 1 68 2 6 8 .2 2 70 1 7 0 .2 5 72 3 7 2 .2 1 74 4 7 4 .2 4 76 3 7 6 .2 2 78 3 7 8 .2 7 80 7 8 0 .2 6 82 2 8 2 .2 4 84 4 8 4 .2 2 86 0 8 6 .2 2 88 1 8 8 .2 2 90 9 0 .2 2 92 0 94 1 • 1 WU. ^ • - - M & W r H * 1/ ---------j--------- 1---------,-------- J---------1---------1---Li.>f- <;*?, 3 N = s3iT 73 .-3 ?yks /AJTEevAU * r .# I *7 ***— 7H C S N T O G /Z L S F i g u r e 12. D i s t r i b u t i o n o f p e r c e n t of d e v e l o p m e n t in h e i g h t a t w h ic h r e a d i n g t h e o r e t i c a l l y b e g a n . MEfiN c: 77.7 N = 4*2- 6 2 A 4 V.2 66-2 ^ . 2 76.272,2 7 ^ 2 7*.2 7 ? .2 ft),* «.i C H G O N O l - O & t C A L. f*e>E 7 2 ,1 -W 2 f».Z 7 2 - 2 * £ossN Q .O F - - M£AW= 77.3" /V = 3 3 - 6V 66 6 f 70 73- 7V 76 7/ fo ITH - So y s & - S o y w r o N - Gr 'fELs C■ - n a l l y - -B o y s J) - N A L L y - G-/RLS, 7 /o //V F ig u re 14. u C H e o w o i - o & / C A t. Mo-S- C o m p a r i s o n of c u r v e of c o n s t a n t s f o r g r o w t h i n h e ig h t, b o y s a n d g i r l s , w ith t h o s e p r e s e n t e d by B o y n to n a n d M e re d ith . ^ V a lu e s e s tim a te d f r o m G r o w t h ," op. c it., p. 267. H e le n T h o m p so n , "P h y sic a l 56 /SoCM&OMS EQUATION OP #E&fNNIN6 y ^ (>Ot £ £o. 2M ?2.'t-P 2 2 2 $ ] OF c y c L B C *7a) * - * 9 / ? M a s . £/V2> O F C i C L £ L/ME A& frlV a ) 2 . / S : CH PO W O LO & /C AL A G E O P REObtNG iNapiEHcy meam= 7 7 /7 PtCS‘ + IO JO 70 fo t/o C .H JSOnyO t-O & f /*V F ig u re 15. C *- M O-Ss + 1“ too tOT> 17 O /9 o F & F R e l a t i o n s h i p b e t w e e n p e r c e n t of d e v e l o p m e n t i n h e i g h t (in i s o c h r o n s ) a n d c h r o n o l o g i c a l a g e a t r e a d i n g i n c i p i ­ en cy - -b o y s. 57 ISOCHftOHS ~2& E^OETION OF H£!6HT~ —^ B E G I N N I N G O P C Y C ,L E * •S t,L 0 % )* E/yJ> o f C.VC.U& ( 9 ei ' 7 o ) - _Z2 U ty F A& + 2 2 , / jJ - 3 ^ 9 •+ M #S< s, -£c> , 2 7 2 * 7 ■+ 2.2. .l~}J i£ J£. pee c e n t oFj>Ft/eiofiM6A/r = 7 (t.S'fo M HEIGHT- C h &o n o *-o &/c.*u. h &e o f REF&'rlZ iNCIPte/Jcy m ean -~ I7.E M n 3/ -n F ig u re 1----- i— I---------h0 -f? 2? 16. — I— V? ■44? -4, ^ /&? C M / e o N o F o a / c / i t . *<&£ IN MO£ , /*-? g s . **7 R e l a t i o n s h i p b e t w e e n p e r c e n t of d e v e l o p m e n t i n h e i g h t (in i s o c h r o n s ) a nd c h r o n o l o g i c a l a g e a t r e a d i n g i n c i p i e n c y --g irls. 58 T h is r e s t r i c t e d r a n g e i n d i c a t e s a h ig h d e g r e e of c o r r e l a t i o n b e t w e e n t h e a m o u n t o f g r o w t h a c h i e v e d in h e i g h t a s m e a s u r e d in u n i t s of p e r c e n t a g e of d e v e l o p m e n t in h e i g h t w ith in th e p r e a d o l e s c e n t c y c l e an d th e o r e tic a lly d e te r m in e d b eg in n in g re a d in g . In o r d e r to i n v e s t i g a t e th e r e l a t i o n s h i p b e t w e e n th e r a n g e s o f th e d i s t r i b u t i o n s o f p e r c e n t a g e of d e v e l o p m e n t in h e i g h t a t w h ic h r e a d i n g b e g a n a n d th e c h r o n o l o g i c a l a g e a t w h i c h r e a d i n g b e g a n , i t w a s n e c e s s a r y to e q u a t e th e u n i t s . T h e u n its f o r th e r a n g e o f p e r ­ c e n t a g e s o f d e v e l o p m e n t in h e i g h t w e r e c h a n g e d to m o n t h u n i t s c o r ­ r e s p o n d i n g to t h o s e of c h r o n o l o g i c a l a g e . T h i s w a s d o n e in th e f o l ­ lo w in g m a n n e r : 1. U t i l i z i n g th e c u r v e of c o n s t a n t s a t th e m e a n p e r c e n t a g e of d e v e l o p m e n t in h e i g h t , 7 2 .4 p e r c e n t , f o r th e f o r t y - t w o b o y c a s e s , 4 .5 8 i s o c h r o n s a r e n e c e s s a r y to c o m p l e t e th e r a n g e of 10.6 p e r c e n t of g r o w th . .2 . S in c e th e a v e r a g e i n d i v i d u a l w a s g r o w i n g a t a r a t e of 0 .2 4 9 2 i s o c h r o n s p e r m o n t h , th e t i m e r e q u i r e d to g r o w 4 .5 8 i s o ­ c h r o n s c a n b e d e t e r m i n e d b y d iv id in g 4 .5 8 i s o c h r o n s b y 0 .2 4 9 2 i s o ­ chrons. T h i s d i v i s i o n y i e l d s a v a lu e of 18.4 m o n t h s . 3. T h u s , th e r a n g e of p e r c e n t a g e of d e v e l o p m e n t in h e i g h t w h e n c h a n g e d in to u n i t s of m o n t h s i s o n ly 1 8 .4 m o n t h s a s c o m p a r e d 59 w ith t h e 29.2 m o n t h r a n g e f o r c h r o n o l o g i c a l a g e i n the c a s e of th e fo rty -tw o boy c a s e s . 4. S im ila r p ro c e d u re s a p p l i e d to th e t h i r t y - f i v e g i r l c a s e s p r o d u c e d r a n g e s of 1 5 .5 m o n t h s a n d 31.5 m o n t h s , r e s p e c t i v e l y . T h u s , i t m a y b e s t a t e d t h a t o n t h e b a s i s of e q u a t e d u n its , e q u a t e d a c c o r d i n g to t h e p r o c e d u r e s d e s c r i b e d a b o v e , th e p e r c e n t a g e of d e v e l o p m e n t in h e i g h t a t w h i c h r e a d i n g t h e o r e t i c a l l y b e g i n s h a s a m o r e r e s t r i c t e d r a n g e t h a n t h a t o f th e c h r o n o l o g i c a l a g e . I t w o u ld t h e n a p p e a r t h a t p e r c e n t a g e o f d e v e l o p m e n t in h e i g h t is a b e t t e r i n ­ d i c a t o r o f r e a d i n e s s to b e g i n r e a d i n g t h a n c h r o n o l o g i c a l a g e . CHAPTER V SU M M A R Y A N D IM P L IC A T IO N S S um m ary 1. The s e v e n ty - s e v e n lo n g itu d in a l c a s e s , fo r ty -tw o boys an d t h i r t y - f i v e g i r l s , w e r e s e l e c t e d f r o m th e m o r e t h a n t h r e e h u n d r e d c a s e s w h i c h c o m p r i s e th e D e a r b o r n D a t a . 2. T h e s a m p l i n g c r i t e r i o n e m p l o y e d w a s t h a t th e d a t a m u s t c o n t a i n a t l e a s t t h r e e m e a s u r e s in th e p r e a d o l e s c e n t c y c le o f m a t u r a ­ ti o n in b o t h r e a d i n g a n d h e i g h t . 3. G r o w t h e q u a t i o n s r e p r e s e n t i n g a c h i e v e d g r o w t h i n b o th r e a d i n g a n d h e i g h t w i t h i n th e p r e a d o l e s c e n t c y c l e w e r e w r i t t e n u t i l i z ­ in g th e C o u r t i s a d a p t a t i o n of t h e G o m p e r z F u n c t i o n . T h is a d a p t a t i o n i s e x p r e s s e d b y th e e q u a t i o n y = k =§rt ± i] w h e r e y = a c h i e v e d g ro w th , k = m a x im u m , r = r a t e , t = v a r i a b l e tim e , i = in c ip ie n c y , an d ^ ] = is o c h r o n ic v a lu e. 4. T h e r e a d i n g e q u a t i o n s w e r e s o l v e d f o r 0.1 p e r c e n t of d e v e l o p m e n t to d e t e r m i n e th e c h r o n o l o g i c a l a g e s a t w h ic h r e a d i n g th e o re tic a lly began. T h e s m a l l e s t R e v i s e d S t a n f o r d R e a d i n g u n it of 61 m e a s u r e , 0 .0 5 to 0 .1 p o i n t , t h a t c a n b e e x p r e s s e d in i s o c h r o n i c u n its is 0 .1 p e r c e n t . p o s e s of t h i s 5. T h e r e f o r e , th is f i g u r e h a s b e e n c h o s e n f o r th e p u r ­ s tu d y . T h e c h r o n o l o g i c a l age of r e a d i n g i n c i p i e n c y w a s s u b s t i t u t e d in th e e q u a t i o n s o f h e i g h t . T h ese e q u a tio n s w e re th e n so lv ed in o r d e r to d e t e r m i n e th e a c h ie v e d ' p e r c e n t a g e of d e v e l o p m e n t in h e i g h t w ith in th e p r e a d o l e s c e n t c y c l e of g r o w t h a t w h ic h r e a d i n g t h e o r e t i c a l l y b e ­ g an. 6. T h e s e d i s t r i b u t i o n s of c h r o n o l o g i c a l a g e a t w h ic h r e a d i n g b e g a n a n d a c h i e v e d p e r c e n t a g e of d e v e l o p m e n t in h e i g h t w ith in th e p r e a d o l e s c e n t c y c l e w e r e a n a l y z e d a n d th e f o llo w in g r e s u l t s w e r e o b ­ t a in e d : asp e c ts: (a) T h e s e d a t a c o n c u r w ith th e g e n e r a l l i t e r a t u r e in tw o (1) a b e g i n n i n g r e a d i n g a g e of 7 7 .5 ± 1.2 m o n t h s f o r g i r l s a n d 7 7 .7 ± 1.2 m o n t h s f o r b o y s w a s o b t a i n e d , a s c o m p a r e d to th e 78 m o n t h s f o u n d in th e l i t e r a t u r e ; ( 2) t h e . r a t e o f g r o w t h of the g i r l s e x c e e d s t h a t o f th e b o y s . T h is d i f f e r e n c e i s s i g n i f i c a n t a t th e 10 p e r c e n t l e v e l of c o n f i d e n c e . (b) A r e l a t i o n s h i p d o e s e x i s t b e t w e e n th e p o i n t of t h e o r e t i c a l l y d e t e r m i n e d b e g i n n i n g r e a d i n g a n d p e r c e n t a g e of d e v e l o p m e n t i n h e i g h t w i t h i n th e p r e a d o l e s c e n t c y c l e of g r o w t h . (c) L i t t l e r e l a t i o n s h i p e x i s t s b e t w e e n p e r c e n t a g e of d e v e l o p m e n t in h e i g h t a n d t h e c h r o n o l o g i c a l a g e a t w h ic h r e a d i n g t h e o r e t i c a l l y b e g i n s . 62 (d) T h e r a n g e o f p e r c e n t a g e of d e v e l o p m e n t in h e i g h t w h e n c h a n g e d to e q u a t e d u n i t s (m o n th s ) i s m u c h s m a l l e r t h a n t h a t of c h r o n o l o g i c a l age a t th e t i m e w h i c h r e a d i n g t h e o r e t i c a l l y b e g i n s . Im p lic a tio n s 1. T h e r e s u l t s of t h i s s tu d y , w h ile h i g h l y t h e o r e t i c a l in n a ­ t u r e , i n d i c a t e t h e n e e d f o r th e i n v e s t i g a t i o n of th e r e l a t i o n s h i p of g e n e r a l p h y s i c a l m a t u r i t y a s e x h i b i t e d b y d e v e l o p m e n t in s t a t u r e to o b s e r v a b le re a d in g in c ip ie n c y . 2. A s t u d y c o r r e s p o n d i n g to t h a t of S h u t t l e w o r t h 9 3 ,9 4 ’ in w h ic h th e r e l a t i o n s h i p of m e n a r c h i a l a g e a n d M a x i m u m G r o w t h A ge w a s d e te rm in e d m ig h t p ro v e fru itfu l. I t is p o s s i b l e t h a t th e r e l a t i o n s h i p of i n c r e a s e s o r d e c r e a s e s in g r o w t h i n c r e m e n t s o f h e i g h t to r e a d i n g r e a d i n e s s m i g h t p r o v e v a l u a b l e in p r e d i c t i n g r e a d i n g i n c i p i e n c y . 3. P e r c e n t a g e o f d e v e l o p m e n t i n h e i g h t s h o u ld b e i n c o r p o r a t e d in to th e o v e r - a l l o b s e r v a t i o n p r o g r a m of c h i l d r e n who f a i l to r e a d 93 of G i r l s in, S e r. ^ F . K. S h u t t l e w o r t h , Sexual- M a t u r a t i o n a n d S k e l e t a l G r o w t h A ge 6 - 1 9 Y e a r s , M o n o , of S o c . f o r R e s . in C h ild D e v ., Vol. N o. 18, N o . 5, 1938. F . K. S h u ttle w o rth , The A d o le s c e n t P e r i o d - A P i c t o r i a l A t l a s , o p . c i t ., p . 4. 63 in o r d e r to d e t e r m i n e i t s u s e f u l n e s s in d i a g n o s i s a n d t r e a t m e n t of th is g ro w th f a i l u r e . 4. The f e a s i b i l i t y and p r a c t i c a l i t y of g ro u p in g c h ild r e n fo r r e a d i n g i n s t r u c t i o n o n a b a s i s of p h y s i c a l m a t u r i t y m i g h t b e c o n s i d ­ e r e d by c u r r ic u lu m - m a k e r s and a d m in is tr a to r s as a m e an s of re d u c ­ in g r e a d i n g f a i l u r e s i n th e e a r l y g r a d e s . 5. S in c e th e G o m p e r z F u n c t i o n , a s a p p l i e d b y C o u r t i s , a p ­ p e a r s to d e s c r i b e r e l a t i o n s h i p s a n d m a t u r a t i o n s in b o th e d u c a t i o n a l and p h y s ic a l d a ta , th is fu n c tio n sh o u ld r e c e iv e g r e a t e r a tte n tio n and u tiliz a tio n . \ B I B L IO G R A P H Y F o rm u la B ald w in , B i r d T. " R e l a t i o n B e t w e e n M e n t a l a n d P h y s i c a l G r o w t h , 11 J . o f E d . P s y ., 1 3 :1 9 3 - 2 0 3 ( A p r i l , 1922). B ro d y , S a m u e l. " R e la tiv ity of P h y s io lo g ic T im e and P h y s io lo g ic W e i g h t , " G r o w t h 1: N o . 5. P a p e r s 1 -6 ( A p r i l, 1937). C a rm ic h a e l, L e o n a rd . M a n u a l of C h i l d P s y c h o l o g y . J o h n W ile y a n d S o n s , 1946. N e w Y o rk : C o u n t, E a r l W . " G r o w t h P a t t e r n s o f th e H u m a n P h y s i q u e : . A n A p ­ p r o a c h to K i n e t i c A n t h r o p o m e t r y , " H u m a n B i o l . 1 5 :1 - 3 2 (19 4 3 ). C o u r t i s , S. A . " D i s c i p l i n e U n d e r t h e G r o w t h C o n c e p t , " C h ild G r o w t h in a n E r a o f C o n f l i c t , C h . 3, 1 5 th Y e a r b o o k of t h e M i c h i g a n E d u c a t i o n A s s o c i a t i o n a n d D e p a r t m e n t of E l e m e n t a r y P r i n ­ c i p a l s , 1944. C o u r t i s , S. A . " E d u c a t i o n - A P s e u d o S c i e n c e , " J . of E d . R e s ., X V II ( F e b . , 19 28 ), 1 3 0 - 2 . C o u r t i s , S. A . " F a c t a n d F a n c y in E d u c a t i o n a l M e a s u r e m e n t , " B u l l e t i n of t h e S c h o o l of E d u c a t i o n , U n i v e r s i t y of I n d i a n a , X V H I (S e p t., 1942), 8 - 2 4 . C o u r t i s , S. A . " G r o w t h a n d D e v e l o p m e n t o f C h i l d r e n , " A d v a n c e s in H e a l t h E d u c a t i o n , P r o c e e d i n g s of S e v e n th H e a l t h E d u c a t i o n C o n ­ f e r e n c e , A n n A r b o r , M i c h i g a n , 1 9 3 3 . N e w Y o rk : A m e ric an C h i l d H e a l t h A s s o c i a t i o n , 1 934. p p . 1 8 0 -2 0 4 . C o u r t i s , S. A . " M a t u r a t i o n a s a F a c t o r i n D i a g n o s i s , " 3 4 th Y e a r b o o k o f N a t i o n a l S o c i e t y f o r th e S tu d y of E d u c a t i o n . 1935, p p . 169787. 65 C o u r t i s , S. A. M a t u r a t i o n U n its a n d H o w to U se T h e m . M ic h ig a n (L ith o -p rin te d ): E d w a r d s B r o s . , 1950. Ann A rb o r, C o u r t i s , S. A. " M a t u r a t i o n U n its f o r th e M e a s u r e m e n t of S c h o o l a n d S o c i e t y , X X X (Nov. 1 6, 1929), 6 8 3 - 6 9 0 . G r o w th ," C o u r t i s , S. A. " T h e F a c t o r C o n c e p t , " U n i v e r s i t y of M i c h i g a n S c h o o l of E d u c a t i o n B u l l e t i n , IV (D e c ., 1932), 3 6 - 3 8 . C o u r t i s , S. A. T h e M e a s u r e m e n t of G r o w t h , A n n A r b o r , M ic h i g a n , B r u m f i e l d a n d B r u m f i e l d , 1952. C o u r t i s , S. A . " T h e P r e d i c t i o n o f G r o w t h , " J_. of_ E d . R e s . V ol. 26 ( M a r c h 19, 1 93 3), 4 8 1 - 9 2 . C o u r t i s , S. A. T o w a rd s a S c ie n c e of E d u c a tio n , A nn A r b o r , M ich ig an ( L i t h o - p r i n t e d ) , E d w a r d s B r o s . , 1951. C o u r t i s , S. A. " V a l i d a t i o n of S t a t i s t i c a l P r o c e d u r e s , " J_. o f E d . R e s . X II ( J u n e , 1925), 3 1 - 4 0 . C o u r t i s , S. A. " W h a t D o e s th e I.Q . 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" A M a t h e m a t i c a l M e th o d f o r S tu d y in g G r o w t h of a C h i l d , " H u m a n B i o l ., 9 :5 5 6 - 5 6 3 (1943). 66 J o n e s , H. E ., and B ay ley , N ancy. " T h e B e r k e l e y G r o w t h S tu d y , 11 C h i l d D e v ., 1 2 :1 6 7 - 1 7 3 (1 94 3 ). Long, H. H . , a n d D e a r b o r n , W. F . " T h e C u r v e of M e n ta l G r o w t h , " P r e d i c t i n g th e C h ild 's D e v e lo p m e n t. C a m b r id g e , M a s s a c h u ­ se tts: S c i - A r t P u b l i s h e r s , 1941, p p . 2 0 1 - 2 3 7 . M i l l a r d , C . V. A n A n a l y s i s of F a c t o r s C o n d itio n in g P e r f o r m a n c e in S p e l l i n g . U n p u b l i s h e d P h . D . T h e s i s #1235 E d u c a t i o n , U n i v e r ­ s i t y of M i c h i g a n , 1937. N a lly , T . P . , a nd D e L o n g , A. R. 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" P h y s i c a l and M en ta l G r o w th ," R e v , of E d . R e s . , 1 1 :5 3 1 - 5 5 2 (1941). S t a n f o r d , R . N ., a n d o t h e r s . " P h y s iq u e , P e r s o n a lity , and S c h o la rsh ip , M o n o , of S o c . f o r R e s , in C h ild D e v ., V o l. VIII, N o . 1, S e r . N o . 34 (1943). S t e w a r t , S. F . " P h y s i c a l G r o w t h a n d S c h o o l S ta n d in g of B o y s , " J . o f E d . P s y ., 7 : 4 1 4 - 4 2 6 (1916). C h ild D e v e l o p m e n t - - G e n e r a l B a r k e r , R ., K o u n in , J . , a n d W r ig h t, H . C h i l d B e h a v i o r a n d D e v e l o p ­ m e n t . N e w Y o r k : M c G r a w H i l l , 1943. B o y n to n , P a u l , e t a l. P r e n t i s s H a ll, E le m e n ta ry E d u c a tio n a l P s y c h o lo g y . 1945. B r e c k e n r i d g e , M i r i a m , a n d V in c e n t, E . L . S a u n d e r s a n d C o ., 1947. N ew Y ork C h ild D e v e l o p m e n t . P h il.: 74 B r u c e , W. F . , a n d F r e e m a n , F . S. D e v e l o p m e n t a n d L e a r n i n g . Y o r k : H o u g h t o n - M i f f l i n C o ., 1942. New C a s w e l l , H. L . " P r a c t i c a l S u g g e s t i o n s f o r T e a c h i n g , 11 C o l u m b i a T e a c h e r s C o l l e g e B u l l e t i n , N o . 2 (19 4 1). C h ild G r o w t h a n d D e v e l o p m e n t in T e a c h e r E d u c a t i o n , A m e r i c a n A s ­ s o c i a t i o n of T e a c h e r s C o l l e g e s (1944). D e a r b o r n , W. F . , a n d R o th n e y , J . W. M . P r e d i c t i n g th e C h i l d 's D e v e l o p m e n t . C a m b r i d g e : S c i - A r t P u b l i s h e r s , 1941. F o r e s t, Isle . 1949. E a r ly Y e a r s a t S c h o o l. N ew Y ork: M cG ra w H ill, G a r r i s o n , K a r l C. G ro w th and D e v e lo p m e n t. G r e e n , 1952. N ew Y o rk : Longm ans G a t e s , A . I ., e t a l. C o ., 1948. N ew Y ork: M cM illa n E d u c a tio n a l P sy c h o lo g y . G e s e l l , A ., a n d Ilg , F . B r o s . , 1949. C h ild D e v e l o p m e n t . N ew Y ork: G e s e l l , A ., a n d Ilg , F . T h e C h i l d F r o m F i v e to T e n . H a r p e r s B r o s . , 1946. H u rlo c k , E liz a b e th . 1942. C h ild D e v e l o p m e n t . N e w Y o rk : H arp ers N ew Y o r k : M c G r a w H ill, M c F a r l e n e , J e a n W. " S t u d i e s i n C h ild D e v e l o p m e n t I. M e th o d o lo g y of D a ta C o lle c tio n an d O r g a n i z a t i o n ." M o n o , of S o c . f o r R e s , in C h i l d D e v . , V o l. I ll, N o . 6, S e r . No. 19 (1 93 8 ). M e r r y , F . K ., a n d M e r r y , R . V . T he F i r s t Tw o D e c a d e s of L i f e . N e w Y o r k : H a r p e r s B r o s . , 1950. M i l l a r d , C. V . C h i l d G r o w t h a n d D e v e l o p m e n t . H e a t h , 1951.O ls o n , W. C . C h ild D e v e l o p m e n t . B o s to n : B o s to n : D. C. D . C. H e a t h , 1950. 75 P r y o r , H. B . 1943. A s t h e C h ild G r o w s . N ew Y ork: S ilv e r B u rd e tt, Rand, W S w e e n y , M ., a n d V in c e n t, E . E. G r o w t h a n d D e v e l o p m e n t of th e Y oung C h i l d . P h i l . : S a u n d e r s C o ., 1946. S ta ff of th e D i v i s i o n of C h i l d D e v e l o p m e n t a n d T e a c h e r P e r s o n n e l . H e l p i n g T e a c h e r s to U n d e r s t a n d C h i l d r e n , A m e r i c a n C o u n c il of E d u c a t i o n , 1945. S t r a n g , R u th . C h ild S tu d y . N ew Y ork: M c M i l l a n C o ., 1951. T h e T h r e e R ' s in t h e E l e m e n t a r y S c h o o l . A s s o c i a t i o n of S u p e r v i s o r s a n d C u r r i c u l u m D e v e l o p m e n t of the N a t i o n a l E d u c a t i o n A s s o ­ c i a t i o n , 1952. T horpe, L o u is. C h ild P s y c h o lo g y a n d D e v e lo p m e n t. R o n a l d P r e s s , 1946. N ew Y ork: A P P E N D IC E S 77 A P P E N D IX A D A T A - - B O Y S (42 c a s e s ) 1M CA HT 83 4 7 .5 88 48 92 4 8 .7 95 49 .1 100 104 3M CA HT 101 . 42.0 14.5 106 50.0 21 110 - 5 0 .2 .51 R 4M CA HT 94 42.0 - 38 99 4 2.5 16 50 .7 51 103 4 3 .2 21 113 51.0 - 106 4 3 .7 - 39 118 52.1 65 111 4 4.2 37 46 122 5 2.7 75 115 4 4.4 53 118 4 5 .6 — R — 107 5 1 .5 - 149 56.2 - 112 5 2 .4 60 154 57.1 - 116 5 3 .5 5 8 .5 158 5 7 .4 105.5 124 5 4 .6 69 128 5 5 .2 7 6 .5 131 5 5 .7 - 136 5 7.0 - 140 5 7 .2 82.5 -- R - 78 A P P E N D I X A (C o n tin u ed ) 5M CA HT 7M R CA HT CA HT 88 51.7 — 31 92 52.7 - 27 93 R R 105 51 - 110 5 2 .2 9 .5 114 5 2 .5 23 104 4 8 .7 117 5 3 .5 - 107 49.1 122 5 4 .4 37 112 4 9 .5 33.5 100 54 .6 126 55 4 4 .5 116 50 .7 45 .5 105 56 55 129 5 5 .5 - 119 51 - 109 56 .2 62 134 5 6 .4 4 6 .5 124 5 1 .8 44 112 57 .3 - 138 5 7 .1 6 0 .5 128 5 2 .6 55 117 58 70 141 5 7 .5 - 131 53 121 59 7 0 .5 146 5 7 .7 64 136 5 3 .8 58 124 59.5 - 150 5 8 .4 65 140 5 4 .4 58 129 60.2 83 153 5 8 .5 - 143 5 4 .6 - 133 6 1 .4 87.5 158 5 9 .5 148 5 5 .6 - 136 61.8 - 162 60 152 5 5 .8 141 63 145 63.1 61 .5 95 100 47 9M - - - - 63.5 97 - 54 33 47 - 88 79 A P P E N D I X A (C o n tin u e d ) 10M 11M 12M CA HT R CA HT R CA 90 47.1 - 88 51.7 - 88 49 95 4 7 .7 46 95 5 3 .6 93 4 9 .5 30 99 4 8 .2 51 100 55.0 30 97 50 .7 4 6 .5 102 4 8 .5 - 103 55.5 31.5 107 4 9 .5 7 2 .5 10-7 55.8 85 112 57.1 111 ' HT R - 100 51 - 105 52 56 52 109 5 2 .6 68 .5 114 5 0 .7 - 116 5 7 .6 67.5 112 52.7 - 119 5 1 .4 85 .5 119 5 8 .3 - 117 5 3 .6 7 3 .5 123 5 2 .2 9 1 .5 124 58 .7 72.5 121 5 4 .7 7 4 .5 126 52.7 128 59.5 64 124 55 - 131 5 3 .4 95 131 60.2 - 129 56 79 .5 135 5 3 .8 103 136 61.5 7 2.5 133 5 6.4 94 138 5 4 .4 - 140 61.5 85 136 56.5 - 142 55 .0 - 143 62.4 - 141 5 7 .2 - 146 55.5 104 148 63.0 - 145 57.5 9 6 .5 152 63.2 9 3.5 80 A P P E N D I X A (C o n tin u ed ) 13M CA HT 84 4 8 .5 89 15M CA HT - 87 4 7 .5 4 9 .0 11 92 4 8 .2 93 5 0 .2 2 8 .5 96 4 9 .5 96 5 0 .5 - 99 4 9 .7 101 5 7 .7 42 104 105 5 2 .2 46 108 5 2 .7 113 R 17M CA HT 91 4 9 .2 - 19 .5 96 50.0 31 32 .5 100 51.0 - - 103 51.0 - 5 1 .0 40 108 52.1 57 108 5 1 .6 45 112 5 2 .6 65 - 111 5 1 .7 - 115 53.0 - 5 3 .6 5 2 .5 116 5 2 .8 55 120 54.0 73 117 5 4 .5 62 120 5 4 .2 55 124 5 4 .6 74.5 120 5 4 .7 - 128 55 .0 6 1 .5 127 55.0 - 125 5 5 .6 66 132 5 5 .7 65 132 5 5.7 81 129 5 6 .4 7 4 .5 135 56.0 - 135 5 6 .4 87 132 5 6 .5 - 140 5 6 .7 - 139 56.1 - 137 5 7 .2 - 144 5 6 .8 144 57.1 - 141 5 7 .5 88 148 5 7 .5 89.5 R - 7 1 .5 R 81 A P P E N D I X A (C o n tin u e d ) 18M 19M CA HT — 65 4 3 .5 4 2 .4 - 77 90 4 5 .0 - -95 4 5 .4 99 CA HT 66 4 0 .6 78 R 20M CA HT R - 75 4 2 .6 — 4 6 .5 - 87 . 45 - 89 5 0 .4 - 104 - 39 - 94 51.0 - 108 - 4 8 .5 - 52.5 98 - 35.5 111 4 9 .4 - 102 4 7 .0 - 101 5 2.2 - 116 50 63 107 4 8 .6 56 106 53.1 42 120 5 0 .4 62 111 4 8 .4 72 110 54.1 58 123 5 0.6 - 114 4 8 .7 - 118 5 5 .3 65.5 128 5 1.4 95 119 4 9 .2 88 122 5 5 .6 60 132 52.1 89 123 5 0 .3 83 125 56.1 - 135 5 2 .3 - 126 5 0 .6 - 130 56.8 74.5 140 5 3 .8 8 9 .5 131 51.1 90 134 5 7 .4 79 144 5 3 .8 90 135 5 1 .4 93 137 57.5 - 147 54 143 53.2 101 142 59.0 85 152 5 4 .6 147 54.1 100 146 5 9 .4 87 156 55 150 5 4 .6 - 149 5 9 .4 - 159 5 5 .4 - 155 55.1 . 106.5 154 60.4 - 164 5 6 .2 100 169 5 5 .5 102 158 61.0 88 168 57 104 R 97 103 82 A P P E N D I X A (C o n tin u ed ) 2 1M 22M CA HT R CA HT 86 4 9 .4 — 56 4 0.5 98 52.0 - 68 103 5 2 .4 - 107 - 110 23M CA HT R - 68 44.1 — 4 1 .6 - 80 46 .4 - 80 4 5.0 - 92 49.1 - 30 85 46 - 101 - 20 5 3 .6 - 89 - 22.5 104 51.1 - 119 5 5 .2 54 92 4 7 .4 - 109 52 24 122 5 5 .4 - 97 4 8 .4 29 113 52.4 36.5 127 5 6 .4 61 101 49.0 48.5 116 . 53.4 131 5 7 .3 64 .5 104 4 9 .4 - ,134 5 7 .4 - 109 5 0 .4 139 5 8.7 6 8.5 113 143 59 .2 6 2.5 146 5 9 .5 151 R - 121 54 4 3 .5 65.5 125 54.7 45 51.0 - 128 55.4 - 121 5 2 .4 - 133 56.1 54 - 123 53.0 - 137 57 54 60.0 81 .5 133 5 3.'5 88.5 140 57.1 - 155 60.7 82 137 54.1 91 145 5 8.6 61 158 61.2 - 140 5 4.7 - 149 59.2 70.5 163 61.6 83 .5 145 55.0 91.5 152 60.5 - 167 62.5 81 149 56.1 91 157 61.1 67.5 161 61.5 68.5 83 A P P E N D I X A ( C o n ti n u e d ) 2 4M 40 M. CA HT R CA HT 110 50 .1 — 64 4 2 .6 115 51.1 - 76 119 - 122 5 2 .4 127 5 3 .3 131 41M CA HT - 60 4 3 .0 - 4 4 .7 - 72 4 5 .4 - 88 4 7 .3 - 84 4 7 .4 - 97 - 31 93 - 3 3 .5 4 2 .5 100 5 0 .2 - 96 4 9 .4 - - .5 3 .5 109 - 67.5 105 - 7 0 .5 134 54.1 - 112 5 2 .4 - 108 52.0 - 139 55 59 117 53.1 - 113 5 2 .6 - 143 5 5 .3 5 7 .5 121 - 82.5 - 83 146 5 5 .5 - 124 54.1 - 120 53 .5 - 151 5 5 .6 66 129 - 85 125 54.1 88 155 5 7 .4 65.5 133 - 89 129 5 4 .6 9 1 .5 158 58 - 136 56.2 - 132 5 4 .7 - 163 5 9 .4 6 9 .5 141 - 9 4 .5 137 56.1 9 9 .5 167 61.1 69 145 - 87 .5 141 5 6 .3 8 7 .5 170 61.7 - 148 5 7 .6 - 144 57 .0 - 175 62.7 7 9 .5 153 5 8 .5 97 149 ' 5 7 .6 1 0 3 .5 179 6 3 .2 87 157 5 9 .2 99 153 58.1 1 0 0 .5 156 5 8 .4 - 161 59-2 1 0 4 .5 165 5 9.7 108 3 3 .5 - R 117 . R A P P E N D I X A (C o n tin u ed ) 42M 4 4M CA HT R CA HT 59 44.0 - 68 4 2 .6 64 46 .7 - 80 71 4 6 .6 - 83 49.0 95 45M CA HT - 66 45.0 - 4 5 .2 - 78 4 7 .4 - 92 4 8 .2 - 90 4 9 .4 - - 101 - 35 99 - 33 5 1 .4 - 104 51 .0 - 102 52.1 - 104 - 29 113 - 58 111 - 64 107 54.0 - 116 5 2 .7 - 114 5 4.4 - 112 54 .3 - 121 5 3 .3 - 119 5 5 .4 - 116 - 71 125 - 8 2 .5 123 55 .4 75 119 5 5 .2 - 128 5 4 .3 - 126 5 6 .4 - 124 5 5 .5 80 133 5 4 .7 85 .5 131 5 6 .4 83.5 131 57.1 - 137 5 5 .5 83 135 57.1 88 136 58.0 96 145 57.0. 9 5 .5 138 58.0 - 140 - 101.5 149 5 7 .5 97 143 5 8 .6 94 143 5 8 .6 - 152 58 .0 - 147 5 8 .6 85.5 148 5 9 .4 .9 3 157 59 .0 103 150 59.5 - 152 6 0 .5 1 07.5 161 6 0 .4 10 3.5 155 60.4 89 155 60 .7 - 164 6 0 .4 - ■159 61.7 96 160 62.2 107.5 169 6 2 .5 10 5.5 162 62.4 - 164 63.0 106.5 173 - 110 167 63 .6 98 167 65.0 - 176 6 3 .5 - 171 64.7 100 172 66.1 - 181 6 5 .6 109 174 65.2 - 176 66.5 107 185 6 5 .7 - 179 66,7 - 183 67.1 102 R R 85 A P P E N D I X A (C o n tin u ed ) 48M CA HT - 74 42.0 45 .7 - 86 47.6 - 98 CA HT 67 43.4 79 91 92 103 112 50M - 49.7 - R 25 107 51M CA HT — 71 43.7 — 44 .3 - 83 4 6 .4 - 45 .4 - 95 48.7 - - R 31 104 - R 30 110 47.6 - 107 51.1 - 56 119 - 59.5 116 - 68 51.0 - 119 53.7 - 124 5 4.4 - - 115 52 .3 - 127 120 53.0 - 131 124 - 69.5 134 51.7 - 128 127 54.0 - 139 52.3 76 131 55.4 - 132 55.1 74 143 53.0 76.5 136 56 .6 86 136 5 5 .4 74 146 53 .4 140 57.0 97.5 139 56 .2 - 151 54.2 81.5 143 57.5 - 144 57.1 85 155 54.7 84.5 148 59.0 99 148 57.7 77 158 55 .3 - 152 60.1 99 151 5 8 .4 - 163 56.4 86.5 155 61.0 - 156 60.1 85 167 58.0 93.5 160 62.4 103.5 160 62.5 84.5 170 •58.6 - 164 64.0 102 175 60.1 92.5 167 64.2 102 179 60.6 92.5 172 65.2 106.5 182 61.2 176 65.7 106 179 66.0 •- 184 67.0 - 188 67.0 - 66.5 - - - 82 113 86 A P P E N D I X A (C o n tin u e d ) 52M ' 55M 94M CA HT R CA HT R CA HT R 61 42.2 — 64 44 .4 - 84 48.6 — 73 44 - 76 46 .5 - 89 4 9 .5 - 85 46.3 - 88 4917 - 93 50.0 9 .5 94 - 20 97 - 24 96 50.5 - 97 49.3 - 100 5 2 .6 - 101 5 1 .2 23 106 - 48 109 - 43 105 52.0 24 109 5 1 .5 - 112 55.3 - 108 5 2 .3 - 114 5 2 .3 - 113 - 44 113 52.6 35 118 - 67 117 56.2 - 117 54 .5 52 121 53 - 124 57.5 - 120 54.7 - 126 54 71 129 58.2 81.5 1*25 55 .7 62 130 55 73 133 59 .3 66.5 129 5 6 .2 65 .5 133 55.1 - 141 ■ 60.5 79.5 132 56 .7 - 138 56.2 78 .5 145 61.7 77.5 137 5 7 .7 74 142 56 .7 89 .5 148 62.6 - 141 5 7 .8 79 145 57 .1 - 153 62.8 87.5 150 5 7 .6 85.5 157 65.0 92 154 58.7 89 160 65.4 165 67.4 89.5 169 68.0 95.5 87 A P P E N D I X A (C o n tin u ed ) 98M CA HT 77 48 .5 82 49 86 49 .7 89 50 94 10 3M CA HT - 80 46 .1 - 85 47 .0 24 89 47.7 - 92 48.2 50.7 37.5 97 49.2 98 51.1 38 101 101 5 1 .6 - 106 5 2 .4 110 53.4 113 53.5 118 112M CA HT — 71 48.0 - - 76 49.0 - 80 50.0 - 83 50.5 - 42 88 51.2 49.7 37.5 95 52.5 104 5 0 .4 - 100 5 3 .6 28 .5 49 109 5 1 .4 55 104 5 4 .6 30 1 68.5 113 52.0 65 107 55.0 - 116 5 2 .4 112 55.8 51.5 54 .2 73.5 121 53 .2 66 116 56.7 60.5 122 54 .8 74 125 5 3 .8 75.5 119 56.7 - 125 54 .8 - 128 54.6 - 124 58.2 73. 5 130 55.5 77.5 133 5 5 .2 75 128 58.8 78.5 134 55 .6 85 137 5 5 .4 84.5 R R 28.5 - - R 17 - - A 88 A P P E N D I X A (C o n tin u ed ) 1 4 4M 1 7 0M . 173M CA HT R CA HT R CA HT R 76 43 .7 - 72 42.7 - 76 47.2 - 81 44 .2 - 77 43 .5 - 85 49.2 - 85 45 - 81 44.5 - 88 49.5 - 88 45.2 - 84 45 .5 - 93 50.5 38 93 46 21 89 46 11 97 50.7 46 97 46 .7 19 93 4 6 .2 19 100 51.7 - 47 - 105 52.4 54 100 47 - 96 105 48 22 101 48 .2 33.5 109 53.2 59 109 48 .8 22.5 105 49 43 112 53.7 - 112 49 .4 - 108 49 - 117 54.4 73 117 50.1 42 113 50 55.5 121 55.4 75 121 50.5 52.5 117 50.8 63.5 124 55.5 . 124 51 - 120 50.5 - 129 56.2 81 129 51.7 54 125 51.8 66 133 56.7 84, 133 52.1 58 129 , 51.8 72 - 89 A P P E N D I X A ( C o n ti n u e d ) 176M CA HT 85 19 4M CA HT 48.0 93 .50.5 97 50.0 90 - 109 53.4 98 50.7 R 197M R 44.5 CA HT R 75 45 .5 - 80 46 - 84 47.2 - 87 48 - 92 48 13 26 118 53.5 102 51.7 130 66.5 105 52.0 110 53.2 60 96 48 .7 65*5 114 54.1 73.5 99 49 - 74.5 117 54.6 104 50 4 1 .5 122 55 .4 86 108 50 .5 44 85 111 51 116 5 1 .6 50.5 57 133 55.1 138 55 .3 142 48 145 56.5 150 57.0 78.5 126 56.2 154 57.0 80 129 5 6 .6 157 57.7 134 57.5 90.5 120 5 2 .4 162 58.0 138 5 7 .6 88 123 52 .5 - 166 58.8 128 53 .2 66 169 59.2 132 54 63.5 174 60.0 94 178 60.0 99 181 60.8 92.5 - A P P E N D I X A ( C o n ti n u e d ) 199M CA HT 214M 217M R CA HT R CA HT 72 45 - 75 46.0 - 86 48 77 47.7 - 80 47.2 - 91 48 .2 81 46.7 - 84 4 8.0 - 95 - 84 47.2 - 87 4 8 .7 - 98 49 .2 89 48 3 0.5 92 49.2 27 103 50.2 93 49 40 96 50 .2 32 107 50 .7 96 49.3 - 99 60.6 - 110 51 101 50.1 52.5 104 51.1 34.5 115 52 105 50 .7 60 108 52.0 40 .5 119 52.7 108 51.2 - 111 53.0 - 122 53.1 113 52 .1 - 116 5 3 .4 59.5 127 54.7 117 5 3 .2 72 120 54.1 69 131 54.7 120 53.4 - 123 54.1 - 134 5 5 .4 125 5 3 .8 69 128 54 .8 70.5 139 56 .7 129 54.7 ' 76 132 5 5 .4 77.5 143 56.8 91 A PPEN D IX B D A T A — G I R L S (35 c a s e s ) IF CA HT 101 4 8 .7 106 49 .2 110 - 2F R 3F CA . HT R CA HT R - 79 48 - 95 48.0 - 9.5 84 49 33 100 49.0 34 31.5 88 49 .7 50 104 49 .7 43 91 50.7 - 107 50.5 51 .2 62 112 51.2 56.5 71 116 51.7 57 - 119 52.2 - „ 113 50.5 118 50 .7 40 96 122 51.5 49 100 52 125 52 - 103 5 2 .5 130 52.7 53.5 108 53.5 83.5 124 52.7 69 134 54 60.5 112 54 .5 88 128 54.5 69.5 137 54.5 - 115 54 .8 - 131 55.0 142 55.5 67 120 55.7 92 136 56.5 83.5 146 56.7 73.5 124 56 .5 94.5 140 57.1 87.5 149 57.7 - 127 57 .2 - 143 58.2 154 5 8 .6 - 132 58.5 - 152 59.2 158 5 9 .6 84 136 59 .4 102 - - - - 88.5 92 A P P E N D I X B ( C o n ti n u e d ) 4F 5F 6f CA HT R CA HT R CA HT R 85 46.6 - 89 49.5 - 104 49.7 - 90 48.0 42 . 94 50.2 30 109 50.5 27 94 49 .0 52.5 98 51 48 113 51.0 33.5 97 4 9.5 116 51.5 102 50.7 106 51 109 51.5 114 52.5 118 101 51.2 57.5 106 • 52 .2 52.5 121 52.2 48.0 56 110 53 65.5 125 53.0 52 - 113 53 .6 - 128 53.7 - 65.5 118 55 67 133 54.7 59.0 53.5 77.5 122 56.2 75 137 55.5 62.5 121 53.7 - 125 57 - 140 57.2 126 54.2 78.5 134 59.1 84 145 58.2 62.5 130 55 88 137 60 - 149 59.4 69.5 133 5 5 .6 - 142 67.8 147 138 5 6 .4 146 68 154 142 57 .4 - 97.5 - ' - - 93 A P P E N D IX B (C o n tin u ed ) 8F CA HT 89 46.7 94 47 98 48.5 101 48.7 106 49.7 110 50.7 113 51 118 i if CA HT 100 50.7 43 105 54 12F CA HT R - 91 46 .5 39 51.0 13 95 48 .2 - 109 52.2 19 98 4 8 .5 - 112 53.2 - 103 49.0 47 54.5 117 53.5 21.5 107 50.0 55 59.5 121 54.0 35 110 49 .7 - 124 54.4 115 51.0 61 5i.7 69 129 55.5 40 119 51.5 68.5 122 52.5 ■ 77.5 133 56.2 46.5 ' 122 52.2 - 125 52.6 136 56.5 - 127 52.5 71.5 130 53.7 83 141 57.5 54.5 134 53.4 82 134 54.4 91.5 145 58.0 60.5 135 54.2 - 137 54.4 - 148 58.4 - 139 55.7 - 142 55 - 153 59.2 - 143 56.5 146 55 89.5 157 59.4 67 R - - - R - - 87 94 A P P E N D I X B (C o n tin u e d ) 13F 18F CA HT 47.7 66 4 3.2 95 49.5 78 100 5 0 .2 33 104 51.0 40 107 5 1.7 112 52 .5 1 16 5 3 .5 119 54.6 124 55 .5 128 5 6 .5 131 57.1 136 58 .7 140 59 .5 143 CA HT 88 19F CA HT R — 61 42.0 — 45.7 - 73 4 3 .6 - 90 4 9 .6 - 85 46.2 - 99 - 36 90 46 .6 - 102 51.2 - 94 57 107 52.2 54 97 48.0 62.5 111 53 .4 59 102 48.2 54 114 53 .6 106 49 .2 67 66.5 119 54 .4 67 109 49.6 71 123 55 .4 62 114 5 0 .4 126 .56.1 80.5 131 56.5 74.5 121 51.1 89.5 135 57.7 67 126 51.7 76.5 60 .4 138 58.2 130 52.5 88 148 61.5 143 58.8 81.5 133 52.6 - 152 61.6 147 59.1 75.5 138 53.2 97 150 60.2 - 142 53.6 95.5 155 61.5 83.5 145 54.6 159 61.7 82 150 54.8 93 .5 154 55.5 90.5 R 90 ' R - - - 118 - - 49 - - 73.5 78 - - A P P E N D I X B (C o n tin u ed ) 2 IF . 22F 24F CA HT R CA HT — 75 45.6 - 71 44.0 — 46.3 - 79 - 41 .5 76 44.6 * 92 4 9 .5 - 82 47 .6 - 80 - 28.5 97 50 40.5 87 48.4 52.5 83 46.0 - 101 - 4 8 .5 91 4 9 .4 61 88 46.4 47 104 51 94 49.6 - 92 47.6 57.5 109 52 64.5 99 51.0 65.5 95 4 8 .2 - 113 53 62 103 51.5 65.5 100 49.0 78 116 53 .2 - 106' 51 .6 - 104 49.6 - 121 5 3 .4 60 111 52 .5 76.5 112 50.2 73 125 54.4 64.5 115 53.7 78 116 51 .2 74 128 5 5 .2 - 118 54.1 - 119 5 1 .6 - 133 56 .2 72.5 123 55 .5 86 124 52 .5 90 137 57 .7 75.5 127 56.2 88 128 53.2 86.5 140 57.6 - 130 57.2 - 131 53.7 - 145 58.5 79.5 135 58.4 86 136 54.7 90.5 149 59.1 85.5 139 59.7 88 .5 140 55.5 93.5 152 60.4 - 157 6 1 .6 92.5 l6 l 63.1 86.5 CA HT 68 43.3 80 R R 96 A P P E N D I X B (C o n tin u ed ) 25F 28F 29F CA HT - 57 43.2 _ 73 45 - 4 9 .4 - 69 45 - 85 46.7 - 94 - 55.5 81 48 - 9T 4 9 .2 - 97 5 0.4 - 86 49 51 102 - 25 102 51 .4 49.5 90 - 54 106 - 39.5 106 52.0 67.5 93 49.6 - 109 5 1 .6 - 109 53.0 - 98 50 .6 62.5 114 52 .4 50 114 54.0 80 102 51.6 78.5 118 54.2 54 118 55.0 84 105 52.4 - 121 54 .6 - 121 55.5 - 110 53 83.5 126 56 .4 70 126 56.5 92 114 54.4 94 130 57.3 67.5 130 58.0 94 117 55.3 - 133 58 .3 133 59.1 - 122 57 102.5 138 59 76.5 138 60.0 106 126 52.5 105.5 142 60 74.5 142 60.1 - 129 59.1 - 145 60 - 145 61.7 - 134 60.1 104 150 60.2 84.5 150 61.3 109.5 138 - .106 154 60.1 85 154 62.8 105.5 141 61.2 - 157 60.5 - 162 - 110.5 146 61.5 112.5 162 60.5 89.5 150 61.8 110 166 60.8 96 CA HT 85 49.0 90 R R CA HT R - A P P E N D I X B ( C o n ti n u e d ) 31F 32F 35F CA HT R CA HT R CA HT 65 4 2 .1 - 67 42.2 - 64 42.6 77 42.4 - 79 43.4 - 76 45 89 4 5 .0 - 91 46 - 88 4 7 .6 94 45.6 - 96 46.6 - '93 4 8 .6 - 38.5 97 - 100 50.2 98 26 .5 100 101 47.2 - 106 47.6 42 108 48.6 44.5 105 51 110 49.0 50 .5 112 50 57 109 51.6 113 49.4 - 115 5 0 .2 - 112 52 .4 118 5 0 .0 63.5 120 50.6 58.5 117 53.4 122 50.2 7 0.5 124 51 .2 63 121 54 .6 125 50.6 127 51 .3 - 124 55.3 130 5 1 .5 64.5 132 52 .5 67 129 57.5 134 53 .0 62.5 136 53 72 133 59 137 53.4 - 139 53.6 - 136 59 142 55 .0 7 4 .5 144 5 5 .2 75 141 60.5 146 56 .0 83 148 55.7 76 145 60.6 149 56.5 151 56.6 - 148 61 154 57.6 80 .5 156 58.6 84 158 5 8 .5 90 1 60 58 .5 78.5 - - 10 3 ■' 4 8 .2 - 98 A P P E N D I X B (C o n tin u e d ) 38F 58F 62F CA HT R CA HT R CA HT R 55 40.6 - 67 43.2 - 64 43.5 - 67 43.1 - 72 43.7 - 69 45.0 - 79 45 .6 - 79 45.4 - 76 46.1 - 91 48 - 91 4 7.6 - 88 49.4 - 97 49 - 100 - 22.5 100 51.6 - 100 - 46 103 50.2 - 109 - 33.5 103 49.2 - 112 - 39.5 112 54.0 - 108 50 .4 63.5 115 52.4 - 117 55.0 - 112 51 62.5 120 53.5 - 121 - 61.5 115 51.4 124 - 61.5 124 55 .6 - 120 52.2 ■ 69 127 54.2 129 56.3^ 69.5 124 52 .4 74 132 - 62.5 133 57.2 72 127 53.5 - 136 - 64 136 58.2 - 131 53.7 - 139 56.0 - 141 59.0 75.5 132 - 76 144 56.6 69.5 145 - 70.5 135 - 73.5 148 - 64 148 60.0 - 136 54.5 - 151 57.4 - 153 61.2 80 139 55.5 - 156 58.7 69.5 157 62.2 75 142 - 81 160 59.5 78.5 160 64.2 - 143 55.6 - 163 60.2 - 165 64.2 87 146 - 85 .5 168 61.0 88.5 169 64.4 92.5 148 56.8 - 172 61.7 95 172 64.4 - 154 - 92 175 62.5 - 177 65.2 - 158 - 99 180 63.4 - 181 65.2 105.5 184 64.0 85 - A .99 A P P E N D I X B ( C o n ti n u e d ) 63F 64F CA HT - 90 45.6 - 80 97 50.1 5 3 .4 - 106 CA HT 63 45.6 75 99 R 65 F CA HT - 81 48.0 - 90 R 21.5 - 104 55 96 109 53 108 56 93.5 118 - 111 5 6 .4 - 121 116- 5 7 .6 97 126 120 5 9 .4 95 130 123 60 - 133 57.2 127 60.7 - 138 58 128 - 102.5 142 5 9 .6 131 - 110.5 145 60.4 93 R - 30 - 50 .3 . - 102 - 56.5 105 52 .4 - 55.2 - 110 53.0 - 56 - 114 67.5 117 54.2 - 122 54 .4 77.5 70 126 56.0 69 ■ 96.5 129 56.2 - 134 57 .4 74.5 - - - 49 67.5 - 132 62.2 - 150 6l.6 80.5 138 135 62.7 - 154 62.4 80 141 59.1 138 - 112.5 157 63 146 60.0 72.5 139 64.1 - 162 63.5 85 150 61.0 83.5 142 - 115.5 166 63.7 92.5 153 61.1 144 64.1 - 169 63.8 - 158 62.0 87.5 115.5 174 63.6 98 162 61.5 88.5 178 63.8 102 165 62.0 181 63.8 170 62.2 174 62.4 154 - - 80.5 - - - - ' 100 A P P E N D I X B (C o n tin u ed ) 70F CA HT 129F . 1 31 F R CA HT R CA HT R 53 40 — 87 46 .0 - 74 46.5 _ 65 41.6 - 92 4 6 .5 - 79 47 .2 - 70 43 - 96 47 .7 21 83 48 .5 - 77 44.2 - 99 48.2 - 86 49 - 89 46.5 - 104 4 9 .0 18 91 .49.7 27 98 - 43 108 49.7 21 95 - 34 101 49 .1 - 111 4 9 .5 - 98 51.1 - 106 49.6 - 116 50 .2 22 103 52. 40 110 - 72.5 120 5 1 .2 36.5 107 52.7 56 113 51 - 123 51.6 - 110 53.2 - 122 - 77 128 52 .2 4 1 .5 115 53 .4 71 125 53.1 - 132 52 .5 45 119 54.7 73 130 54 80 135 52.7 - 122 55.1 - 134 5 4 .2 - 140 53.7 42. 5 127 56 73 137 55 .2 84.5 144 5 4 .4 57 131 56.8 83 146 57 88 149 58.1 - 153 59.2 - 154 - 94 158 60 99.5 101 A P P E N D I X B (C o n tin u ed ) 1 46F 173F CA HT - 85 44.2 44 .2 - 90 83 45 .5 - 86 4 5 .7 - 91 46.7 95 CA HT 74 43 .4 79 R 179F CA HT - 71 43 .2 - 44.7 - 76 4 3 .7 - 94 45.7 - 80 44 .7 - 97 46.5 - 83 45 .5 - 26 102 47.2 38.5 88 4 6 .2 17 47 .7 35 106 47.2 46 92 47 .2 21.5 98 47.5 - 109 48 95 47.4 103 48.7 44 .5 114 48.7 100 48.2 32.5 107 49.7 48 .5 121 50 104 50.2 42 110 50.2 - 126 50.5 76.5 107 50 .2 - 115 50.7 - 130 51.2 78 112 50.2 59 119 5 1 .6 66 133 51 .6 - 116 51 .4 61.5 122 52.2 - 138 52.4 79.5 119 51.8 - 127 52.8 72 142 53.2 89 124 5 2 .6 61.5 131 54.2 96 .5 128 ' 5 3 .6 68.5 R - 57.5 - R - 102 A P P E N D I X B ( C o n ti n u e d ) 213F 218F CA HT R CA HT R 78 4 5 .5 - 77 46 .7 - 83 4 7 .7 - 82 47.5 - 87 48.0 - 86 48.7 - 90 48.0 - 89 4 9 .2 - 95 49 .7 28 .5 94 50.0 23 .5 99 50.7 41 98 51.0 42.5 102 50.7 - 101 51.2 - 107 52.2 53.5 106 52.5 57.5 114 53.5 - 110 53.5 66.5 119 54 .2 72 113 53.5 - 123 55.4 76 .5 118 54.5 90 126 55.7 - 122 5 5.4 99.5 131 56.7 80 125 55.2 - 135 57 .7 94 130 56.4 98.5 134 56.8 99.5 103 A P P E N D IX C G R O W TH C O N S T A N T S — BOYS: H E I G H T E Q U A T IO N S (y = K =£ r t + i] ± AD) Rate r I n c ip iency i A v g. D e v. AD A ge Span in Mo s. No. of M ea­ sures 54 .8 5 2 .6 55.0 0.3600 0.6980 0.1542 + 18.53 -13.96 + 2 8 .3 1 0.20 0.20 0.2 0 83-124 101-118 99-151 11 -5 15 5M 7M 9M 57.8 60.5 0.4610 0.1812 0.4640 + 2.11 + 2 5.9 5 + 5.10 0.13 0.23 0. 3 5 95-152 95-152 88-124 5 14 10 10M 11M 12M 52.4 60.7 62.0 0.4240 0.4210 0.2100 + 13.25 10.75 + 2 5 .3 6 0.3 0 0.20 90-123 '8 4 -1 2 8 93-145 7 10 14 13M 15M 17M 60.0 0.3320 0.2195 0.2244 , + 1 4 .9 3 + 24. 77 + 2 3 .6 3 0.16 1 0 1 -1 4 1 87-144 103-148 11 15 12 18M 19M 20 M 55.0 + 21 .8 7 + 2 5 .3 4 + 29.27 0. 2 9 62.0 60.0 0.2590 0.2223 0.1526 90-138 77-137 75-135 11 13 10 21 M 22M 23M 62.0 59.0 61.0 0.1914 0.1924 0.2058 +28.54 +2 7 . 6 7 + 26.4 7 0.16 0.16 0. 2 9 86-127 68-137 80-133 7 12 10 2 4M 40 M 41M 57.1 58 .4 57.0 0.3990 0.2745 0.2981 + 6.11 + 21.41 + 21.2 9 0 .1 3 0.03 0.14 110-151 88-124 84- 132 9 5 8 42M 44 M 45M 65.0 58.8 67.0 0.1617 0.2455 0.1527 + 2 9 .0 6 + 2 3. 73 + 2 7.7 2 0 .2 2 0 .0 9 0 .2 5 83-143 80-140 78-150 9 9 13 4 8M 50M 51M 65.0 0.1697 0.1815 0.1550 + 2 5 .6 4 +25 .0 0 +28. 01 0.17 0 .1 9 0 .1 7 103-148 98-155 71-131 9 9 7 M ax­ im um K 1M 3M 4M Case 61.0 61.0 61.5 60.0 65.0 0.16 0.31 0 .1 5 0.16 0. 0 9 104 A P P E N D I X C (C o n tin u ed ) Case M ax­ im um K Rate r Incipiency i Avg. Dev. AD A ge Sp a n in Mo s. No. of M ea­ sures 52M 55M 94M 65.0 65.0 64.5 0.1588 0.2089 0.1855 + 2 7. 30 +25.04 +'25.93 0.13 0.14 0 .1 9 85-150 76-129 101-141 12 7 11 98M 10 3M 112M 61.0 65.5 0.1976 0.1647 0.2229 + 27.92 +28.83 + 2 3 .7 6 0.13 0.13 0.18 98-134 80-125 92-128 10 12 9 144M 170M 173M 55 .8 59 .5 65.5 0.2800 0.1845 0.1621 +1 9.6 0 +26.74 + 2 8 .3 2 0.06 97-133 93-129 88-133 9 10 12 176M 194M 197M 56.5 62.5 63 .4 0.3842 0.2728 0.1383 + 16.51 + 18.29 + 30.07 0.34 0.16 85-138 98-138 92-132 5 10 11 199M 214M 217M 62.3 61.3 63.0 0.1633 0.1844 0.1406 +28.74 + 2 8 .5 9 + 3 0 .3 8 0 .1 7 0. 1 9 0. 20 60.6 0.2492 +2 2 . 1 9 ± 0 .1 8 62.0 0.23 0.14 0.16 96-129 9 75-132 86-123 16 9 N = 42 m = A v e rag e age sp an = 10 47.5 - 105 A P P E N D IX D G R O W TH C O N S T A N T S --G IR L S : H E IG H T E Q U A T IO N S (y = K ^ r t f i] ± AD) Case M axim am K r Inc i p . iency i A v g. Dev. AD -^-ge Span in M os. No. of M easures Rate IF 2F 3F 5 4 .4 62.1 54.7 0.3856 0.2130 0.4271 + 12.06 +2 6 .2 6 + 9.74 0.20 0.25 0. 0 8 101-122 7/9-124 95-124 5 12 8 4F 5F 6F 5 5 .8 64.1 58.0 0.3783 0.1533 0.2241 + 14.87 + 29.88 + 25.38 0 .1 3 0 .1 6 0 .0 4 85-114 89-113 104-121 8 7 5 8F 1I F 12F 56 .2 55.9 55.7 0.2967 0.5667 0 .3 0 89 + 20.07 - 4.9 3 + 18.95 0.20 0.31 0.2 3 89-125 100-124 91-127 10 7 10 13F 18F 19F 59.1 59.1 58 .2 0.2458 0.2749 0.1830 + 23 .7 7 + 22. 13 + 28.59 0.0 5 0. 3 8 0.1 5 88-112 78-131 90-142 6 10 12 21 F 22 F 24 F 57.0 55.0 54.2 0.2715 0 .3 7 2 1 0.2580 +24. 47 + 18.83 + 26.75 0 .2 2 0.20 0. 1 7 68-121 75-106 71-112 9 8 10 25F 28F 2 9F 57.0 0.2788 60.0 0.2066 0 .1 8 0 .3 7 64.1 0.1366 + 24.30 + 28.20 + 30.42 0.26 85-106 57-114 73-114 5 10 5 31F 32F 35F 54.0 55.0 56 .3 0.3267 0.2546 0.2845 +17.10 +2 4 . 2 9 + 23.32 0. 2 2 0.24 0 .2 8 89-125 79-127 76-117 9 10 8 38F 5 8F 62F 60.0 62.0 60.0 0.1542 0.1735 0.2706 + 30.93 + 28 .02 + 22 .75 0.16 0 .1 3 0 .2 3 55-120 72-127 76-133 11 7 8 63F 64F 65F . 61.0 59.1 58.1 0.2958 0.4383 0.2588 + 22.19 + 4 .0 7 +2 5 . 5 9 0 .2 6 0.30 0.10 75-111 90-126 81-122 5 5 6 106 A P P E N D I X D (C o n tin u ed ) Rate r In c ip iency i A vg . D e v. AD Age Span in Mo s. No. of M ea­ sures Case M ax­ im um K 70F 129F 131F 57.0 55.0 55.0 0.2 0 64 0 .3 1 3 1 0.4194 + 28.14 + 19.22 + 15.52 0.21 0.21 0.22 65-113 87-135 79-U 5 7 13 9 146F 173F 179F 60.0 60.0 62.1 0.1598 0.1598 0.1550 + 29. 42 + 2 7 .6 8 + 2 8. 73 0. 1 9 0.1 8 0.2 6 74-115 85-133 71-124 11 13 14 213F 218F 60.0 61.1 0.2517 0.2133 + 22.7 8 + 2 6.3 8 0 .2 4 0. 1 8 78-114 82-125 10 12 58.2 0.2729 +2 2 .1 7 0.20 N = m = 35 A v e ra g e age sp an = 8.2 40.0 107 A P P E N D IX E G R O W TH C O N S T A N T S --B O Y S : R E A D IN G E Q U A T IO N S (y = K r t - i] ± AD) i ■K> „ Case M ax. im um T, K I n c i•p . lency 1 Avg. 5 Dev. AD A°g e Span in Mo s. T Rate r A No. of M easures 1M 3M 4M 92.0 95.5 85.1 0.5942 0.7 45 0 0.8680 -31.00 -47.38 -60.49 2 .3 2.8 6.3 88-140 106-134 99-127 9 6 6 5M 7M 9M 72.0 57 .5 ' 7 2 .4 0.6613 0.9 81 0 1.254 -46.59 -69.35 -83.26 3.0 4.8 2.2 110-162 100-128 93-121 9 -6 6 10M 11M 12M 95 .5 76.1 75 .9 0.844 0 0.8812 1.391 -47.26 -59.50 -89.44 2 .6 3. 84 2. 2 95-123 100-136 93-122 6 7 6 13M 15M 17M 63.1 60.3 75.9 1.485 1.170 1.148 -110.03 -79:79 -80.36 3.2 3.6 3.1 89-117 92-120 96-124 6 6 6 18M 19M 20M 89.1 75.9 75.9 1.066 0.7 750 1.134 -71.20 -43.09 -85.05 4 .6 4 .4 2.1 99-135 98-134 104-128 7 7 5 21M 22M 2 3M 76.1 79 .4 70.0 0.7217 1.021 0.5179 -46.51 -65.34 -25.89 1.03 3.7 1.14 107-143 89-123 101-145 7 5 8 24M 40 M 41M 57.5 92.0 94.0 1.227 0.9664 0 .7 3 5 0 -108.95 -64.58 -34.72 2 .8 0.98 3.18 119-139 97-133 93-117 4 5 8 42M 44M 45M 107.0 87.1 70.8 0.7769 0.8 54 0 1.349 -52.19 '' - 5 5 . 1 6 -100.09 1.38 2.9 1.3 104-124 101-137 99-123 7 5 3 48M 50 M 5 1M 74.1 66.1 83 .2 1.098 1.304 1.390 -83.44 -106.79 -113.90 3.8 2.1 1.9 100-136 107-131 104-136 5 3 4 108 A P P E N D IX E M ax­ im um K Case (C o n tin u ed ) R ate r Inc i p iency i Avg. Dev. AD A ge Span in Mo s. No. of M ea­ sures 52M 55M 94M 72 .4 45.4 80.0 1 .0 94 1.879 0.6608 -76.14 -147.79 -38.93 1.7 0 .1 7 1.11 94-126 97-113 93-129 4 3 7 98M 103M 112M 76.0 76.0 100.0 1.391 0.6075 0.5879 -97.08 -23.88 -31.06 6.89 3.48 3.31 86-122 89-133 88-128 7 8 8 144M 170M 173M 22.9 83.0 56.0 1.9 8 8 0.6508 1.9 6 4 -146.04 -34.40 -143.16 0.15 1.11 0.03 93-109 89-129 93-105 4 8 3 176M 194M 197M 37.1 92.5 58.0 0.4836 1 .2 3 6 1.355 -19.89 -97.57 -97.89 1.05 1.65 1.75 118-154 110-138 92-120 6 6 6 199M 214M 217M 78.0 34.9 78.3 0.8833 2.694 0.7010 -48.11 -204.17 -44.59 1.71 0 4.84 89-129 92-104 95-143 7 3 9 75.2 1.0746 -74.10 . N = 42 m = A v e rag e age span = 6.0 ±2.5 31.4 109 A P P E N D IX F G R O W T H C O N S T A N T S — G IR L S : R E A D IN G E Q U A T IO N S (y = K r t - i] ± AD) i Case M ax­ im um K IF 2F 3F 63.1 91.2 Rate r _ Inciplency 1 69.2 0.8950 1.283 1.022 -■64.90 -80.31 -67.65 4F 5F 6f 58.5 77.6 72.0 2 .4 6 8 1.233 0.6914 8F 1IF 12F 60.3 50.1 1.5 83 0.9510 1. 013 13F 18F 19F 72.4 Avg. Dev. AD Age Span 'in Mo s. No. of M ea­ sures 4 .0 5.0 2 .9 106-134 84-112 100-128 6 6 6 -181.02 - 86.06 -45.17 0.267 4 .3 0 .4 7 90-102 94-122 109-137 3 6 6 -106.85 -73.73 -63.10 1.9 2 .8 5 .3 94-110 105-133 91-119 4 6 5 79.4 1.071 1.249 1.232 -74.64 -89.80 -80.57 1.4 2.4 3.5 100-128 99-134 94-126 6 7 6 21 F 22F 24 F 66.1 77.6 75.9 1.272 1.098 1.343 -85.73 -54.46 -80.44 2.7 3.1 2.6 97-125 79-115 80-116 6 7 7 25F 2 8F 29F 93.3 100.0 56.2 0.8580 0.9720 1.3 03 -47.10 -53.07 -98.11 5.2 6.2 2.2 94-130 86-125 102-118 7 8 •4 31F 32F 35F 66.1 63.1 79.4 1.151 1.187 0.8730 -81.49 -82.73 -52.11 3.2 2.3 3.8 98-134 100-124 93-132 7 5 8 38F 58F 62F 75.0 66.1 72.4 1.478 0.9930 1.322 -110.65 -72.48 -113.69 2.34 3.6 1.8 100-124 100-136 109-133 5 5 4 63F 6 4F 65F 100.0 1.534 1.244 0.7350 -102.26 -102.38 -36.08 2 .8 1.6 3.4 96-120 5 4 5 69.2 69.2 69.2 75.9 106-138 90-126 ' 110 A P P E N D IX F Case M ax­ im um K (C o n tin u ed ) Rate r Inc i p iency i Avg. Dev. AD Age Sp a n in Mo s. No. of M ea­ sures 70F 129F 131F 78.0 46.6 44 .0 1.341 0.8790 1.360 -96.43 -60.95 -86.58 1.63 4.8 0 .3 98-130 96-128 91-103 4 6 3 146F 173F 17 9F 50.0 80.6 7 0 .8 1.438 1.175 1.12 3 -96.56 -88.79 -79.82 0.13 3.83 1.43 91-103 102-138 100-128 3 7 6 213F 218F 81.1 69.0 1.029 2 .1 1 2 -68.22 - 169.26 3.23 1.7 95-131 94-110 7 - 4 71.1 1.2146 N = 35 m = A v e r a g e age s p a n = -83.81 ±2.8 5.5 27.7 T H E R E L A T I O N S H I P B E T W E E N A C H I E V E D G R O W T H IN H E I G H T A N D T H E B E G I N N I N G O F G R O W T H IN R E A D I N G By T h o m a s P o m p h e r t F r a n c i s N ally AN A B S T R A C T S u b m i t t e d to t h e S c h o o l of G r a d u a t e S t u d i e s of M i c h i g a n S t a t e C o l l e g e of A g r i c u l t u r e a n d A p p l i e d S c i e n c e i n p a r t i a l f u l f i l l m e n t of th e r e q u i r e m e n t s f o r t h e d e g r e e of DOCTOR OF PHILOSOPHY D e p a r t m e n t of E l e m e n t a r y E d u c a t i o n Y e a r 1953 Approved 1 THOMAS N A L L Y ABSTRACT T h e p u r p o s e of t h i s s t u d y i s to a t t e m p t to d e t e r m i n e w i t h p r e c i s i o n t h e r e l a t i o n s h i p b e t w e e n a c h i e v e d g r o w t h i n h e i g h t a n d the b e g i n n i n g of g r o w t h i n r e a d i n g , i n t h e b e l i e f t h a t s u c h a r e l a t i o n s h i p w i l l e n a b l e t h e u s e r , u n d e r c o n s t a n t c o n d i t i o n s , to p r e d i c t w i t h i n f a i r l y n a r r o w l i m i t s t h e t i m e a t w h i c h a s p e c i f i c i n d i v i d u a l s h o u l d be r e a d y to r e a d . T h e d a t a f o r t h i s r e s e a r c h , c o n s i s t i n g of 77 c a s e s - - 4 2 b o y s a n d 35 g i r l s - - w e r e s e l e c t e d f r o m t h e m o r e t h a n 300 c a s e s w h i c h constitute the ''D e a r b o r n D a t a . ' 1 T h ese data a r e longitudinal in n a t u r e a n d a r e th e r e s u l t of a p p r o x i m a t e l y t e n y e a r s of m e a s u r e m e n t d u r i n g th e p e r i o d f r o m k i n d e r g a r t e n t h r o u g h th e n i n t h g r a d e . T h o s e c a s e s w h i c h w e r e c o m p l e t e a n d w h i c h w e r e f o u n d to c o n t a i n t h r e e o r m o r e m e a s u r e m e n t s i n th e p r e a d o l e s c e n t c y c l e of g ro w th in both re a d in g and heig h t w e re s e le c te d fo r th is study. The G o m p e r z function, w h ere y = achieved growth, 2 a s a p p l i e d by C o u r t i s , y = k ^ r t ± i], k = m a x i m u m , r =* 'rate, i = i n c i p i e n c y , C o l l e c t e d b y C. V. ' M i l l a r d a t t h e H e n r y F o r d S c ho ol , D e a r b o r n , M ich ig an , and a v a ila b le a t the Child D e v elo p m e n t L a b o r a ­ to r i e s , M ichigan State C ollege, E a s t L a n sin g , Michigan. 2 THOM AS N A L L Y * ABSTRACT t = v a r i a b l e t i m e , a n d =£ ] =' i s o c h r o n i c v a l u e , w a s u t i l i z e d in t h i s r e ­ search. This function ad equately d e s c r i b e s grow th p h en o m en a when m a t u r a t i o n i s a f a c t o r w i t h i n a n a v e r a g e e r r o r of ± 2 p e r c e n t . 3 E q u a t i o n s w e r e f o r m u l a t e d f o r the p r e a d o l e s c e n t c y c l e of m a t u r a t i o n i n r e a d i n g a n d i n h e i g h t f o r e a c h of t h e 77 c a s e s . The r e a d i n g e q u a t i o n s w e r e s o l v e d f o r 0,1 p e r c e n t of d e v e l o p m e n t i n o r d e r to d e t e r m i n e th eo retically begins. Mt , " i . e . , c h r o n o l o g i c a l a g e a t w h i c h r e a d i n g This ch ronological age, " t , " was then su b sti­ t u t e d i n t o th e e q u a t i o n s of h e i g h t a n d t h e s e e q u a t i o n s w e r e s o l v e d to d e t e r m i n e t h e p e r c e n t of d e v e l o p m e n t i n h e i g h t f o r t h e p r e a d o l e s c e n t c y c l e of g r o w t h e a c h i n d i v i d u a l h a d a c h i e v e d . D istributions w ere m a d e f o r t h e c h r o n o l o g i c a l a g e of r e a d i n g i n c i p i e n c y a n d p e r c e n t a g e of d e v e l o p m e n t i n h e i g h t . T h e s e d a t a c o n c u r w i t h t h e g e n e r a l l i t e r a t u r e i n tw o a s p e c t s : (1) A b e g i n n i n g r e a d i n g a g e of 7 7 ,7 ± 2 .9 m o n t h s f o r b o y s a n d 77.5 ± 3.3 m o n t h s f o r g i r l s w a s o b t a i n e d . m o n t h s r e p o r t e d i n th e l i t e r a t u r e . T h i s c o n c u r s w i t h t h e 78 (2) T h e r a t e of g r o w t h of g i r l s e x c e e d e d t h a t of t h e b o y s a t t h e 10 p e r c e n t l e v e l of c o n f i d e n c e . . 3 M ichigan: C o u r t i s , S. A. T h e M e a s u r e m e n t of G r o w t h . B r u m f i e l d a n d B r u m f i e l d , 1932. Ann A r b o r , 3 THOMAS N A L L Y ABSTRACT T h e 42 boy c a s e s w e r e f o u n d to b e g i n c e n t of 7 2 . 4 ± 1.2 reading at a m e a n per p e r c e n t of d e v e l o p m e n t i n h e i g h t . S i m i l a r l y , the 35 g i r l c a s e s w e r e f o u n d to b e g i n r e a d i n g a t a m e a n p e r c e n t of 76 .3 ± 1.2 p e r c e n t of d e v e l o p m e n t i n h e i g h t . L ittle w a s f o u n d b e t w e e n p e r c e n t of d e v e l o p m e n t i n height and ch ro n o lo g i­ c al age at which re a d in g began. relationship P e a r s o n P ro d u c t M om ent C oeffi­ c i e n t s w e r e 0. 1 6 f o r t h e g i r l s a n d 0.27 f o r t h e b o y s , r e s p e c t i v e l y . T h e r a n g e of p e r c e n t of d e v e l o p m e n t i n h e i g h t , 10.6 p e r c e n t fo r the bo y s and 8.7 p e r cen t f o r the g i r l s , when changed to equated u n i t s ( m o n t h s ) is m u c h s m a l l e r t h a n t h a t of c h r o n o l o g i c a l a g e of reading incipiency. T h i s e q u a t e d r a n g e w a s 18 .4 m o n t h s f o r th e b o y s a n d 15.5 m o n t h s f o r the g i r l s a s c o m p a r e d to 2 9 .2 m o n t h s and 3 1 .5 m o n t h s , respectively. S i n c e d e v e l o p m e n t in h e i g h t a p p e a r s to b e a r a p r e d i c t i v e r e ­ l a t i o n s h i p to r e a d i n g i n c i p i e n c y , i t w o u ld s e e m d e s i r a b l e to f u r t h e r t e s t i t s u s e f u l n e s s in p l a n n i n g t h e r e a d i n g c u r r i c u l u m a n d a l s o a s a possible m ean s of a l l e v i a t i n g f a i l u r e i n r e a d i n g t h r o u g h i n d i v i d u a l analysis. T h e v a l u e of t h e G o m p e r z f u n c t i o n , a s a p p l i e d by C o u r t i s , f o r d e s c r i b i n g r e l a t i o n s h i p s in both ed u ca tio n a l and p h y s ic a l data, 4 T H O M A S NALLY sh .o u .ld be i n v e s t ig a te d and m u s t be tio n a l ABSTRACT fu rth er. co n sid ered research. T h i s m e t h o d of a p p r o a c h a m a j o r c o n tr ib u tio n of t h i s is study unique to ed u ca­