University of Southern California Dissertations and Theses

A Rotational Approach To Psychological Invariance

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A Rotational Approach To Psychological Invariance

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Content A ROTATIONAL, A PPR O A C H TO PSYCHOLOGICAL INVARIANCE by W illia m J o sep h D oh erty A D is s e r ta tio n P r e s e n te d to the F A C U L T Y O F TH E G RADUATE SCHOOL UNIVERSITY O F SO UTH ERN CALIFORNIA In P a r tia l F u lfillm e n t of the R e q u ir e m e n ts fo r the D e g r e e DOCTOR O F PHILOSOPHY (P sy c h o lo g y ) A p r il 1973 INFORMATION TO USERS Thii material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependant upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pagas apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the paga in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the matarial. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again - beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pagas you wish reproduced. 5. PLEASE NOTE: Soma pagas may have indistinct print. Filmed as received. Xerox University Microfilms 300 Worth ZMb Rood Ann Arbor, Michigan 401 O S 73-31,337 HEKIT, William Joseph, 1946- A R O T A T IO N A L A P P R O A C H T O P S Y C H O L O G IC A L IN V A R IA N C E . University of Southern C alifornia, Ph.D., 1973 Psychology, general University Microfilms, A X E R O X Company , Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. UNIVERSITY O F S O U T H E R N C A LIFO R N IA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA * 0 0 0 7 This dissertation, written by .H lllia m .-lQ * a p lL .J la h je.rty..................................... under the direction of Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of requirements of the degree of D O C T O R O F P H I L O S O P H Y DISSERTATION COMMITTEE ACKNOW LEDGM ENTS It is v e r y d iffic u lt to fu lly e x p r e s s m y than ks to th o s e p eo p le who h ave m ad e th e c o m p le tio n o f th is d is s e r ta tio n p o s s ib le . H ow ever, I w ould lik e to m ak e an a ttem p t so that th ey know that I r e a liz e and a p p r e c ia te th e ir e ffo r ts and su p p o rt. F ir s t , I w ould lik e to thank m y c h a irm a n . D r . J . P . G u ilford . I b e lie v e that he sp en t m o r e tim e and e ffo r t on m y d is s e r ta tio n than £ d id . N e e d le s s to sa y , its c o m p letio n cou ld not h ave b een p o s s ib le w ithou t h is gu id an ce and a s s is t a n c e . M y a s s o c ia tio n w ith D r . G uilfoxd h a s b een a r a r e h on or and w ill r em a in a s the h ig h lig h t o f m y grad u ate sc h o o l ed u ca tio n . D r. N o rm a n C liff is r e s p o n s ib le in g r e a t p a rt fo r m y c o m p letio n o f grad u ate s c h o o l. He h a s b een an a d v is o r and a fr ie n d who h elp ed m e w ith th e m any p r o b le m s I c r e a te d fo r m y s e lf in the y e a r s le a d in g up to m y d is s e r ta tio n . D r . R alph H oep fn er not on ly p ro v id ed a s s is t a n c e in th e c o m p le tio n of the d is s e r ta tio n , but h e a ls o p ro v id ed a job w h ich a llo w ed m e to con tin u e m y e d u c a tio n . H is fr ie n d sh ip and a d v ic e h a s been of im m e a su r a b le v a lu e to m e . I w ould p a r tic u la r ly lik e to thank D r . F ran k F o x , who w ith th e s m a lle s t p o s s ib le n o tic e took tim e out fr o m h is e x tr e m e ly bu sy sc h e d u le to be on m y d is s e r ta tio n c o m m itte e . W ithout h im , I lit e r a lly cou ld not h ave fin ish e d th is d e g r e e . My s in c e r e thanks a re ii ow ed to h im . L a s tly , I w ould lik e to thank m y fa m ily fo r th e ir m any s a c r i f ic e s and th e ir u n d ersta n d in g . T he m o tiv a tio n fo r c o m p le tio n o f th is d is s e r ta tio n is a r e su lt of th e ir faith in m e . My debt to th em can h ard ly be e x p r e s s e d and n e v e r fu lly rep a id . Hi TA B L E OF CONTENTS P a g e A C K N O W LED M EN TS ......................................................................... ii C h ap ter I. D E V E L O P M E N T O F TH E P R O B L E M ................... 1 F a c to r A n a ly s is D e v elo p m e n t o f F a c to r A n a ly s is F a c to r ia l In v a ria n ce S tru ctu re of I n te lle c t H. P R O C E D U R E S ........................................................................... 26 S e le c tio n of S tu d ies D e sc r ip tio n o f S tu d ies M ethod of T e s t A s sig n m e n t S ta tis tic a l A n a ly s is III. R E SU L T S ................................................................................ 38 T h u rston e; P r im a r y M en tal A b ilitie s T h u rsto n e & t T h u rsto n e: F a c to r ia l S tu d ies o f In te llig e n c e A d k in s & t L y e r ly : F a c to r A n a ly s is of R e a so n in g T e s t s K e lle y : M em o ry A b ilitie s : A F a c to r A n a ly s is T h u rsto n e: E x p e r im e n ta l Study o f S im p le S tru ctu re B ech told t: F a c to r ia l Study o f P e r c e p tu a l S p eed C a r ro ll: A F a c to r A n a ly s is of V erb a l A b ilitie s T a y lo r: A F a c to r ia l Study o f F lu en cy in W ritin g IV. DISCUSSION .............................................................................. 81 C o g n itio n F a c to r s M em o ry F a c to r s D iv e r g e n t P ro d u c tio n F a c to r s C o n v erg en t P ro d u c tio n F a c to r s E v a lu a tio n F a c to r s V. CO NCLUSIO NS A N D IM P L IC A T IO N S ............................. 117 R E F E R E N C E S ................................................................................................. 123 T A B L E S .............................................................................................................. 129 A P P E N D I X .......................................................................................................... 147 iv C H A PT E R I D E V E L O P M E N T O F THE P R O B L E M F a c to r A n a ly s is F a c to r a n a ly s is i s a fo r m a l m o d e l in w h ich h y p o th etica l c o m pon en t v a r ia b le s a ccou n t fo r the lin e a r r e la tio n sh ip s that e x is t am on g a se t o f o b s e r v e d v a r ia b le s . It is a fo r m a l m o d e l b e c a u se it is a p p lied e x ce p t th at the r e la tio n sh ip s b etw een th e v a r ia b le s that a r e to be a cco u n ted fo r a r e lin e a r . T he h y p o th etica l com p on en t v a r ia b le s a r e u su a lly a ss u m e d to h ave th e fo llo w in g p r o p e r tie s : 1) th e c o m ponent v a r ia b le s fo r m a lin e a r ly in d ep en d en t se t o f v a r ia b le s , 2) the h y p o th etica l co m p o n en t v a r ia b le s a r e o f tw o k in ds: a) co m m o n c o m p o n e n ts, co m p o n en ts w h ich a r e sh a re d by m o r e than one o b s e r v e d v a r ia b le , and b) unique c o m p o n e n ts, co m p o n en ts w h ich a r e s p e c ific to ea ch o b s e r v e d v a r ia b le . 3) co m m o n co m p o n e n ts (fa c to r s) a r e a lw a y s a ss u m e d to be u n c o r r e la te d w ith th e unique co m p o n en ts (fa c to r s ). U nique fa c to r s a r e a ls o g e n e r a lly a ss u m e d to be m u tu a lly u n c o r r e la te d , and 4) it is c h a r a c te r is tic a lly a ss u m e d that th e r e a r e fe w e r com m on co m p o n en ts than th e r e a r e o b s e r v e d v a r ia b le s . T h e fu n d am en tal eq u ation o f fa c to r a n a ly s is m a y be e x p r e s s e d a s: *lj ■ *jlx tl +...............+ V x ir + ovil +................+ o v in ( 1 > w h er e is th e sta n d a r d ize d s c o r e o f p e r so n i on v a r ia b le j, and 1 2 a .j is th e w eig h t o r fa c to r lo a d in g o f te a t j on fa c to r 1 and x ^ ia the a c o r e o f p era o n i on fa c to r 1, and VU U the s c o r e o f p era o n i on unique fa c to r 1. U sin g th is fu n d am en tal eq u ation , it b e c o m e s ap p a ren t that the c o r r e la tio n b etw een any two v a r ia b le s m ay be e x p r e s s e d a s: r . = £ £ a ., a r jm jk m n * n 8k (2) o r in m a tr ix notation : R = F C F ’ + U 2 (3) w h er e R i s an m x m c o r r e la tio n m a tr ix w ith m b ein g th e n u m b er of v a r ia b le s , F is an m x r m a tr ix of fa c to r lo a d in g s w ith r b ein g the n u m b er of co m m o n fa c to r s and C is an r x r m a tr ix of c o r r e la tio n s b etw een th e fa c to r s . If the fa c to r s a r e o rth o g o n a l, C b e c o m e s an id en tity m a tr ix . T h e se eq u a tio n s a r e g e n e r a lly h e ld to c o n stitu te the co m m o n fa c to r m o d el and a r e e m p lo y ed m o a t fre q u en tly by so c ia l a c ie n tis ts . F a c to r a n a ly s is is w id ely u sed in t h e s e a r e a s in an a ttem p t to d e c o m p o se la r g e r m a tr ic e s of lin e a r r e la tio n sh ip c o e f f i c ie n ts to a r r iv e at a s m a lle r m a tr ix o f m o r e fu n d am en tal th e o r e tic a l v a r ia b le s . T h e n o tio n that fa c to r a n a ly s is r e s u lts in fu n d am en tal o r m o r e b a s ic v a r ia b le s a te m i fr o m the h is to r ic a l a s p e c ts o f its d e v e l o p m en t. D ev elo p m en t o f F a c to r A n a ly s is T h e fou n d ation s of fa c to r a n a ly s is w e r e b ein g fo r m u la te d in E n glan d around th e tu rn o f th e p r e s e n t c en tu ry . W hile C h a r le s S p earm an is g e n e r a lly r e c o g n is e d a s th e "father" of fa c to r a n a ly is , h e o w e s a g r e a t debt to th e w ork o f K a rl P e a r s o n . P e a r s o n d ev elo p ed 3 the p r o d u c t-m o m e n t c o r r e la tio n c o e ffic ie n t and s u g g e s te d o th e r data red u ctio n te c h n iq u e s u sin g th is c o e ffic ie n t o r o n e s r e la te d to it. U sin g the c o r r e la tio n c o e ffic ie n t a s h is b a s is , and w ork in g in the r e a lm of hum an in te llig e n c e . S p earm an (1904) p r o p o se d h is now fa m o u s tw o -fa c to r th e o r y o f in te llig e n c e . S p earm an fe lt that p e r fo r m a n c e on in te llig e n c e t e s t s r e q u ir e d tw o th in g s, a co m m o n o r g e n e r a l a b ility and an a b ility s p e c ific to e a c h t e s t . He fe lt th at a ll t e s t s of an in te lle c tu a l n atu re sh a red o r m e a s u r e d a sin g le co m m o n com p on en t o r g e n e r a l a b ility , w h ich he c a lle d M g" . In ad d ition , ea ch te s t a ls o m e a s u r e d a s p e c ific o r unique com p on en t that w a s not sh a re d by o th e r t e s t s . T h is m o d el w ould be id e n tic a l to a o n e -fa c to r so lu tio n w ith th e co m m o n fa c to r a n a ly s is m o d e l. In ap p lyin g th is fa c to r a n a ly s is m o d e l to d ata, S p ea r m a n p r o p o se d that th e c o r r e la tio n s b etw een t e s t s o f in te llig e n c e sh ou ld be fu lly e x p la in e d , e x c e p t fo r r e a so n a b le am o u n ts o f e r r o r . S p e c ific a lly , the m eth o d to be u se d , th e m eth od o f d isa p p e a r in g te tr a d s , im p lie d that any two c o lu m n s of a c o r r e la tio n m a tr ix m u st be in a sim p le d ir e c t p r o p o r tio n . U sin g th is p r o p o r tio n a lity , it can be show n that fo r the c o r r e la tio n s b etw een any fo u r t e s t s the fo llo w in g r e la tio n sh ip sh o u ld hold: r r, , - r. r . = 0 (4) a c bd be ad ' ' W hile so m e in te llig e n c e t e s t data did fit th is m o d e l and uphold th e ab ove r e la tio n sh ip , a c o n sid e r a b le am ount o f data did not r e s u lt in d isa p p e a r in g te tr a d s . On the c o n tr a r y , it s e e m e d that so m e t e s t s 4 w e r e c o r r e la te d to & m u ch g r e a te r ex ten t than, co u ld be e x p la in e d by any two fa c to r m o d e l. T h is la c k of c o in c id e n c e b etw een th e data and th e two fa c to r m o d e l le d to a d iv e r g e n c e in the th in k in g of th o se who u s e d fa c to r a n a ly s is . S om e r e s e a r c h e r s , lik e C a tte ll and B u rt c h o se to fo llo w the le a d o f S p ea rm a n and e m p h a s is e d th e im p o r ta n c e o f "g" in th e ir d a ta . O th e r s , u n d er th e in flu e n c e o f T h u rsto n e and H o te llin g , d e v e lo p ed the m o d e ls and m eth o d s o f m u ltip le fa c to r a n a ly s is that a r e so w id ely a c c e p te d and u se d to d a y . M u ltip le fa c to r a n a ly s is is a r e s p o n s e to th e r e a lis a tio n th at the r e la tio n sh ip s b etw een m e a s u r e s o f in te llig e n c e cou ld not be e n tir e ly ex p la in ed by a tw o fa c to r th e o r y . In c o n tr a s t, it p r o p o se d that a ll t e s t s o f I n te llig e n c e sh a red not one s in g le fa c to r but r a th e r g ro u p s o f th e s e t e s t s sh a red s p e c ific co m m o n f a c t o r s . In o th e r w o r d s, fa c to r s e x is te d that w e r e sh a re d by on ly so m e in te llig e n c e t e s t s and not sh a r e d by o th e r in te llig e n c e t e s t s . T e s t s o f v e r b a l r e a so n in g w ould sh a r e a "group" o r co m m o n fa c to r , w h ile t e s t s of n u m e r ic a l co m p u ta tio n w ou ld sh a r e a d iffe r e n t co m m o n fa c to r . In g e o m e tr ic te r m s , th is m o d el p r o p o s e s the e x is te n c e o f a s e t o f v e c to r s ex ten d in g fr o m a co m m o n o r ig in , w ith e a ch v e c to r r e p r e se n tin g a group o r co m m o n fa c to r . W ithin th e sp a c e c r e a te d by th e s e fa c to r v e c to r s a r e o th e r v e c to r s r e p r e se n tin g th e t e s t v a r ia b le s . T h e n e a r e r in sp a c e that a t e s t v e c to r is to a p a r tic u la r fa c to r v e c to r , th e g r e a te r i s the in v o lv e m e n t o f that t e s t w ith th e grou p fa c to r . T h e str u c tu r e o f the fa c to r v e c t o r s is d e te r m in e d fay th e in te r c o r r e la tio n s o f the e x p e r im e n ta l t e s t s . In th e o r y , the 5 m a tr ix (factor p attern m a trix ) co m p o sed of the lo a d in g s (s im ila r to c o r r e la tio n s , in th e orth ogon al c a s e ) of the t e s t s on the fa c to r s should be able to rep rod u ce the c o r r e la tio n m a trix , e x ce p t fo r d if fe r e n c e s due to c h a n c e s or e r r o r . The a lg e b r a ic fo rm u la tio n s o f th is g e o m e tr ic r e p re sen ta tio n o f fa cto r a n a ly s is w e r e p r e se n te d in eq u a tio n s 1 -3 . D e riv in g the fa cto r pattern m a tr ix fro m th e c o r r e la tio n m a trix is the e s s e n c e of m u ltip le fa c to r m eth o d s. T h ere a r e s e v e r a l c o m putational p r o c e d u r e s for a c co m p lish in g th is, the m o st s u c c e s s fu l and popular of th e se b eing H o e te llin g 's p rin cip al com p on en ts m eth od . T h is m ethod w as d evelop ed by H o etellin g (1933) but w as not w id ely u sed b e c a u se o f the com p utational c o m p lex ity w hen the c o r r e la tio n m a tr ix w as not s m a ll. To avoid the p ro b lem ca u sed by th is c o m p le x ity , T h u rston e (1935) d evelop ed the c en tro id m ethod of fa c to r a n a ly s is . T h is m eth od w as com p u tation ally sim p le and r e su lte d in fa c to r s w hich w ere s im ila r to th o se a r r iv e d at by the p rin cip a l com p on en ts p r o c ed u r e. B e sid e s con trib u tin g th e cen tro id m eth od, w hich a llo w ed the u tilisa tio n o f fa c to r a n a ly s is b efore the advent o f the high sp eed e le c tr o n ic com p u ter, T h u rston e b eca m e the shaping fo r c e o f fa cto r a n alytic r e s e a r c h in A m e r ic a . In o r d e r to u n derstand the d ir ec tio n w hich m uch o f the fa c to r a n a ly tic r e s e a r c h took betw een 1930 and the p r e se n t, a s w ell a s the app roach taken to so m e of the c r u c ia l p r o b le m s in volved in th e u se o f fa cto r a n a ly s is , it is n e c e s s a r y to u n derstand T h u rston e, h is m eth od s and h is con cep tion o f fa cto r a n a ly s is . 6 T h u rsto n e e n v isio n e d fa c to r a n a ly s is a s a s c ie n tific to o l w ith w h ich on e cou ld in v e s tig a te th e r e a lm o f hum an b e h a v io r . In p a r tic u la r , one cou ld in v e s tig a te th e in te r n a liz e d str u c tu r e s of in te llig e n c e e v e n though th ey w e r e not d ir e c tly o b s e r v a b le . T h u rsto n e b e lie v e d that by c a r e fu l p r e p a r a tio n and s e le c tio n o f con ten t fo r sta n d a r d ize d in te lle c tu a l t e s t s , one cou ld le a r n and id en tify m u ch about the hum an m en ta l a b ilitie s th rou gh fa c to r a n a ly s is . P u rsu a n t to th is m is s io n fo r fa c to r a n a ly s is , T h u rsto n e (1938, 1941, 1944, 1951) p r o c e d e d to p ro d u ce a n u m b er o f d iffe r e n t fa c to r a n a ly tic s tu d ie s . T h e se stu d ie s em p lo y ed the c e n tr o id m eth od of e x tr a c tio n , fo llo w e d by an o b liq u e r o ta tio n . R otation of a x e s c o n s is t s of ap p lyin g a tr a n sfo r m a tio n to the m a th e m a tic a lly d e r iv e d fa c to r s in an attem p t to a r r iv e at m o r e m ea n in g fu l o r in te r p r e ta b le f a c to r s . F u r th e r d is c u s s io n o f th is su b je c t i s found b elo w . T h e r e s u lt of th e s e a n a ly s e s w a s th e e s t a b lis h m e n t o f s e v e r a l fa c to r s w h ich w e r e g iv en the n a m e s of: S p ace, P e r c e p tu a l S p eed , N u m e r ic a l F a c ility , V erb a l C o m p re h e n sio n , R ote M em o ry , In du ction, W ord F lu e n c y , D ed u ction , G en era l R e a so n in g , and la te r , Sp eed and S tren gth of C lo su r e and F le x ib ility of C lo su r e . * T h e s e fa c to r s w e r e g e n e r a lly c o n sid e r e d by T h u rsto n e to be " p rim a ry m en ta l a b ilitie s " (P M A ). F o llo w in g upon th e w ork o f T h u r sto n e , c a m e stu d ie s by T h u rsto n e*s stu d en ts u su a lly a im ed at v e r ific a tio n of on e o r m o r e o f th e p r e v io u s ly found PM A fa c to r s . A m on g th e s e stu d ie s w e r e th o se ^ T hurston e o r ig in a lly id e n tifie d h is ro ta ted fa c to r s w ith l e t t e r s . L a te r th is w a s ch an ged and th e fa c to r s w e r e id e n tifie d w ith n a m e s . T he n a m e s fo r th e fa c to r s in th is c a s e a r e th o se w h ich w e r e s u b s e q u en tly a p p lied and g e n e r a lly a c c e p te d . o f C oom ba (1941) w h ich fo c u se d on N u m e r ic a l F a c ility , T a y lo r (1947) w h ich fo c u se d on E x p r e s s io n in W ritin g, B ech to ld t (1947) on P e r c e p tual S p eed , B oteu m (1951) on C lo su r e and R ea so n in g a b ilitie s , P em b u rto n (1952) on C lo su r e a b ilitie s and A d k in s and L y e r ly (1951) on R ea so n in g a b ilitie s . T he r e s u lt s of th e s e stu d ie s w e r e g e n e r a lly co n fir m a to r y of T h u r sto n e ’s o r ig in a l fa c to r s . W hen T h u rsto n e d e c id e d that one cou ld s c ie n tific a lly in v e s tig a te th e r e a lm of in te llig e n c e w ith fa c to r a n a ly s is , he w a s im m e d ia te ly fa c e d w ith two d ile m m a s . T h e se d ile m m a s a r e in te r r e la te d and a r e b a sic both to the u s e of fa c to r a n a ly s is and to th e su b seq u en t in te r p r e ta tio n of the r e s u lts ob tain ed fr o m th is m eth od o f a n a ly s is . T he f ir s t d ile m m a is r e fe r r e d to a s r o ta tio n a l in d e te r m in a c y . T he im p o rta n ce o f th is p r o b le m is c r e a te d by th e se co n d d ile m m a , that o f fa c to r ia l in v a r ia n c e . R otation al in d e te r m in a c y i s d e r iv e d fro m the a lg e b r a ic str u c tu r e o f fa c to r a n a ly s is . R e c a llin g the p r io r d i s c u s s io n o f the fa c to r a n a ly tic m o d e l, th e b a sic notion Is to d e r iv e a m a tr ix F w h ich w ill rep ro d u c e a g iv en sa m p le c o r r e la tio n m a tr ix R w ith a c e r ta in d e g r e e of a c c u r a c y . T he d e r iv a tio n of F m a y be found th rou gh th e c en tr o id m eth o d , the p r in c ip a l co m p o n en ts m eth od o r through one of s e v e r a l o th e r m e th o d s. O nce the in itia l m a tr ix F (u su a lly r e fe r r e d to a s fr a m e o f r e fe r e n c e ) h a s b een a r r iv e d at, it i s p o s s ib le to apply tr a n sfo r m a tio n s w h ich w ill r e s u lt in an in fin ite s e t o f o th er fa c to r s w h ich w ill rep ro d u ce th e c o r r e la tio n m a tr ix R to the sa m e d e g r e e o f a c c u r a c y . T he la c k o f a unique s e t o f v a lu e s in th e m a tr ix F is not a p r o b le m if one is u sin g fa c to r a n a ly s is only 8 to s im p lify a g iv e n s e t o f sa m p le data and th e r e is no in te r e s t in id en tify in g th e fa c to r s w ith o th e r c o n str u c ts o r m ak in g g e n e r a liz a tio n s fr o m one study to a n o th er. H o w e v er , a s w a s p r e v io u sly m en tio n ed , the id e n tific a tio n of fa c to r s w ith c o n str u c ts o f hum an in te llig e n c e w as b a s ic to T h u r sto n e 's v is io n of the r o le of fa c to r a n a ly s is . T h e r e fo r e , the p r o b le m o f fa c to r ia l in v a r ia n c e b e c o m e s one o f m a jo r c o n c e r n . F a c to r ia l In varian ce A n e s s e n t ia l in g r e d ie n t to th e s c ie n tific m eth o d , in a d d ition to o b je c tiv e o b s e r v a tio n and c le a r ly d efin ed m e a s u r e m e n t, is r e p lic a b i lit y . T h e p r o c e d u r e s and r e s u lts of any s c ie n tific in v e stig a tio n sh o tid be ca p a b le of b ein g r e p lic a te d and rep ro d u ced w ith in a p r e d e te r m in e d d e g r e e o f e r r o r . In th e n a tu ra l s c ie n c e s and e v e n in so m e c a s e s in th e b e h a v io r a l s c ie n c e s , it is p o s s ib le to con d u ct e x p e r im e n ts w h er e on e in d ep en d en t v a r ia b le i s m a n ip u la ted and th e e ffe c t on on e d ep en dent v a r ia b le o b s e r v e d . In th is c a s e , s im p le s t a t is t ic s w ith known sa m p lin g d istr ib u tio n s a r e u su a lly a v a ila b le . H o w e v er , fa c to r a n a ly s is p r o c e e d s one ste p beyond the r e a lm o f sim p le s t a t is t ic s w ith known stan d ard e r r o r s . T he stan d ard e r r o r s o f the s t a t is t ic s p ro d u ced by fa c to r a n a ly s is a r e th e o r e tic a lly d e te r m in a b le . H o w e v er , the g r e a t v a r ie ty o f in flu e n c e s to be c o n sid e r e d in th e ir d e te r m in a tio n m a k e s th e a ctu a l com p u tation o f th e stan d ard e r r o r s e x tr e m e ly te d io u s and c o m p le x . A n u m b er o f M onte C arlo stu d ie s (C liff it H a m b u rg er, 1967; C liff fc P e n n e ll, 1967) h a v e a ttem p ted to rem ed y the p r o b le m , but the r e s u lts have not b een d e fin itiv e . T h is p r o b le m o f pin n in g down a p r e c is e p r o c e d u r e fo r r e p lic a tin g fa c to r 9 a n a ly tic r e s u lts h a s le a d to a g r e a t v a r ie ty o f a p p r o a c h e s to fa c to r ia l in v a r ia n c e . B e fo r e ex a m in in g the v a r io u s a p p ro a c h e s to in v a r ia n c e , it w ould s e e m th at a c le a r d e lin e a tio n o f w hat In v a ria n ce i s , and w hat ty p e s of in v a r ia n c e e x is t is e s s e n t ia l. F a c to r ia l in v a r ia n c e is th e n otion that fa c to r s d e r iv e d fro m a fa c to r a n a ly s is can be c o n s is te n tly id e n tifie d o v e r s e v e r a l s tu d ie s . In th is c o n te x t, the f ir s t lo g ic a l d istin c tio n that m ay be m ad e is b etw een the m a th e m a tic a l fa c to r s d e r iv e d by the co m p u ta tio n fr o m th e d a ta and the p s y c h o lo g ic a l fa c to r s th at r e s u lt fro m ro ta tio n and in te r p r e ta tio n of th e s e f a c to r s . O b v io u sly th e r e can be at le a s t tw o ty p e s of in v a r ia n c e , m a th e m a tic a l o r p h en o m en a l in v a r ia n c e , and p s y c h o lo g ic a l o r th e o r e tic a l in v a ria n ce, In ad d ition to p s y c h o lo g ic a l-m a th e m a tic a l in v a r ia n c e , a fu r th e r d istin c tio n can be m ad e: co n fig u r a tio n a l v e r s u s n u m e r ic a l. In n u m e r ic a l in v a r ia n c e , the in te r e s t is c e n te r e d on the a ctu a l n u m e r ic a l v a lu e of the p a r tic u la r fa c to r lo a d in g s . In c o n tr a s t th e c o n fig u r a tio n a l in v a r ia n c e is c o n c e r n e d not w ith th e n u m e r ic a l v a lu e s but the co n fig u ra tio n o r p a ttern o f the fa c to r lo a d in g s fr o m on e study to the n e x t. T h u rsto n e d e a lt w ith the p r o b le m o f in v a r ia n c e by a n a ly sin g the data w ith r e g a r d to th e c e n tr a l p u r p o se of fa c to r a n a ly s is , the o b je c t o f w h ich is to d is c o v e r a s e t of sig n ific a n t and m ea n in g fu l p a r a m e te r s fo r d e sc r ib in g a d o m a in . In o r d e r to a r r iv e at th is s e t o f m ea n in g fu l and sig n ific a n t s e t o f p a r a m e te r s , it is n e c e s s a r y to ta k e th e fa c to r s d e r iv e d fr o m the c e n tr o id so lu tio n and ro ta te th e m to a r r iv e at 10 m ea n in g fu l f a c t o r s . T he p r o b le m o f r o ta tio n a l in d e te r m in a n c y a r o s e at th is p o in t, so T h u rsto n e p r o p o sed a c r ite r io n to be u s e d to guid e th e ro ta tio n a l p r o c e s s . T h is c r ite r io n w a s to be a s e t o f o b je c tiv e and e m p ir ic a l stip u la tio n s w h ich , if fo llo w e d , w ou ld r e s u lt in a p a r tic u la r type o f fa c to r ia l so lu tio n . T h is r o ta tio n a l c r it e r ia is c a lle d sim p le str u c tu r e and a s o r ig in a lly p r e s e n te d by T h u rsto n e (1935) c o n s is te d o f th r e e co n d itio n s: 1. E a ch row of a fa c to r str u c tu r e sh ou ld have at le a s t one z e r o , 2. E a ch co lu m n sh ou ld h ave at le a s t m z e r o e s , m b ein g th e to ta l n u m b er of co m m o n f a c t o r s . 3 . F o r e v e r y p a ir o f co lu m n s th e r e sh ou ld be at le a s t m v a r ia b le s w h er e e n tr ie s v a n ish in one co lu m n but not in the o th e r . T he p s y c h o lo g ic a l b a s is for th e u s e o f sim p le s tr u c tu r e a s g iv en by T h u rsto n e (1935): " Ju st a s w e ta k e it fo r gran ted that th e in d ivid u al d iffe r e n c e s in v is u a l a cu ity a r e not in v o lv ed in p itch d is c r im in a tio n , so w e a s s u r e that in in te lle c tu a l ta s k s so m e m en ta l o r c r it ic a l fu n ctio n s a r e not in v o lv ed In e v e r y ta sk . T h is i s the p r in c ip le of 'sim p le str u c tu r e ' o r 's im p le c o n fig u r a tio n ' in the u n d e rly in g o r d e r fo r any g iv en se t o f a ttr ib u te s . " E s s e n tia lly , s im p le str u c tu r e is an attem p t to red u ce th e c o m p le x ity o f the v a r ia b le s . T o e n su r e that sim p le str u c tu r e is a c h ie v a b le and that th e fa c to r h y p e r p la n e s a r e o v e r -d e te r m in e d by th e d ata. T h u rsto n e (1947) la te r added tw o m o r e co n d itio n s to th e o r ig in a l th r e e . T h e se 11 two a r e : 1. F o r e v e r y p a ir o f c o lu m n s o f th e fa c to r m a tr ix , a la r g e p r o p o r tio n o f the v a r ia b le s sh ou ld h a v e v a n ish in g e n t r ie s in both c o lu m n s w hen th e s e a r e fou r o r m o r e fa c to r s . 2 . F o r e v e r y p a ir o f co lu m n s o f the fa c to r m a tr ix th e r e sh ou ld be on ly a s m a ll n u m b er of v a r ia b le s w ith n o n v a n ish in g e n tr ie s in both c o lu m n s. In th e sa m e d is c u s s io n T h u rsto n e sta te d that th e sim p le str u c tu r e p r in c ip le w a s in tro d u ced to so lv e the p r o b le m of in v a r ia n c e . H e sta te d fu r th e r that if su ch r e s t r ic t io n s w e r e p la c e d on a r e fe r e n c e fr a m e , and th at su ch a fr a m e cou ld be found, th en on e cou ld e x p e c t in v a r ia n c e o f the n u m e r ic a l v a lu e s in e a c h row o f the ro ta ted fa c to r m a tr ix , e v en w hen a t e s t i s m o v ed fr o m on e b a ttery to a n oth er w h ich a ls o h a s a d e te r m in a te sim p le str u c tu r e in th e sa m e com m on fa c t o r s . F o llo w in g T h u r sto n e 's p r e se n ta tio n o f th e sim p le str u c tu r e p r in c ip le and its su b seq u en t r e v is io n , m o st fa c to r a n a ly s ts g e n e r a lly a c c e p te d th at it w ou ld g u a ra n tee in v a r ia n c e o f fa c to r s o v e r m e a s u r e s and p o p u la tio n s. R e c e n tly , B u tle r (1 9 6 4 , 1969) h a s c h a lle n g e d the c la im fo r s im p le str u c tu r e and p r o p o se d an a lte r n a tiv e ap p ro a ch . B u tle r (1964) p r e s e n ts e v id e n c e that a n a ly tic so lu tio n s b a sed upon th e s im p le str u c tu r e p r in c ip le do not ex h ib it in v a r ia n c e . F u r th e r , B u tle r (1969) p r o p o s e s th e u s e o f a d iffe r e n t c r ite r io n , that o f the m o s t d istin g u ish a b le f a c to r s . T he m o st d istin g u ish a b le f a c to r s a r e 12 c h o se n on th e b a s is o f the in te r c o r r e la tio n s b etw een th e o r ig in a l se t o f fa c to r s , w ith z e r o c o r r e la tio n s b ein g m o st d is tin g u ish a b le . B u tle r a r g u e s that the r e s u lts g iv en fo llo w in g h is p r o c e d u r e s p e r fo r m b e tte r in a la r g e v a r ie ty o f situ a tio n s than th e s im p le str u c tu r e p r o c e d u r e . G u ilford and Z im m e r m a n (1963) found that the sim p le str u c tu r e p r in c ip le w a s not f r e e o f th e bounds o f m e a s u r e and sa m p le s e le c tio n . In th is stu d y, c o m p a r iso n w a s m ad e b etw een q u a rtim a x , v a r im a x and o rth o g o n a l grap h ic r o ta tio n s. T he a u th o rs co n clu d ed that on ly in the la s t p r o c e d u r e w a s p s y c h o lo g ic a l m e a n in g fu ln e ss p r e s e r v e d . In g e n e r a l, th e n e g a tiv e fin d in g s r eg a r d in g th e in v a r ia n c e of sim p le str u c tu r e have b een o v e r lo o k e d o r d is m is s e d . In d eed , a nu m b er o f a n a ly tic a l ro ta tio n a l p r o c e d u r e s b a sed on s im p le str u c tu r e h a v e b een p ro d u ced . T h e se p r o c e d u r e s a ttem p t to m a x im iz e o r m in i m iz e so m e m a th e m a tic a l fu n ction w h ich is a tr a n sla tio n o f the v e r b a l d e fin itio n o f sim p le s tr u c tu r e . The m o st fa m o u s o f th e s e is the v a r im a x ro ta tio n (K a ise r , 1958). T h is ro ta tio n a tte m p ts to m a x i m iz e th e v a r ia n c e of e a c h s u c c e s s iv e fa c to r , th ereb y hoping to a c h ie v e sim p le str u c tu r e . G u ilford and H oep fn er (1969) c o m p a re d the r e s u lts fr o m the v a r im a x w ith th o s e a c h ie v e d u sin g a ta r g e te d r o ta tio n a l p r o c e d u r e (C liff, 1966), w h ich a ttem p ts to m ak e a le a s t sq u a r e s fit o f the p r in c ip a l a x e s to a h y p o th e tic a l ta r g e t m a tr ix . G u ilford and H oep fn er c o n str u c te d th e ir m a t r ic e s on the b a s is of G u ilfo r d 's (1967) S tr u c tu r e -o f-I n te lle c t m o d e l. T h e se d iffe r e n t m eth o d s w e r e c o m - 13 p a r e d on fo u r c r it e r ia draw n fr o m th e d e fin itio n o f sim p le str u c tu r e : 1) th e fre q u en cy w ith w h ich d iffe r e n t n u m b ers of sig n ific a n t lo a d in g s a p p ea r on fa c to r s (sig n ific a n c e d efin ed a s + .3 0 ) , 2) the c o m p le x itie s o f te s ta , 3) p r o p o r tio n s o f z e r o lo a d in g s and 4) th e d e g r e e to w h ich n e g a tiv e lo a d in g s a r is e fr o m e ith e r m eth o d . In a d d itio n , tw o c r it e r ia r e p r e s e n tin g p s y c h o lo g ic a l m e a n in g fu ln e ss w e r e add ed . In a ll c a s e s the ta r g e te d ro ta tio n p ro v id ed b e tte r r e s u lts than did th e a n a ly tic a l p r o c e d u r e . T h e fa c t th at th e r e a r e s e v e r a l d iffe r e n t a n a ly tic a l p r o c e d u r e s a ll c la im in g to r e su lt in sim p le str u c tu r e , and th e in c r e a s in g ev id en ce that the r e s u lts ob tain ed fr o m th e s e p r o c e d u r e s do not p ro v id e sim p le o r in v a ria n t fa c to r s d e tr a c ts fr o m th e valu e o f sim p le str u c tu r e a s a c r ite r io n fo r a c h ie v in g in v a r ia n c e . B e c a u se of th is d u b io u sn e ss a la r g e n u m b er of in v e s tig a to r s have sou gh t o th e r a p p ro a c h e s to a c h ie v ing o r m e a s u r in g in v a r ia n c e . Out o f th is in v e stig a tio n h a s a r is e n the d e lin e a tio n o f a w id e v a r ie ty o f m e a n in g s o f in v a r ia n c e , a s w e ll a s th e c r e a tio n of a g r e a t a s s o r tm e n t o f in d ic e s to m e a s u r e fa c to r ia l in v a r ia n c e . It w a s m en tio n ed ab ove that in v a r ia n c e cou ld be d e lin e a te d alon g a n u m b er o f d iffe r e n t d im e n s io n s . E x a m p le s o f th is w e r e p h en om en al (m a th e m a tic a l) v e r s u s th e o r e tic a l (p sy c h o lo g ic a l) in v a r ia n c e , and n u m e r ic a l v e r s u s co n fig u r a tio n a l in v a r ia n c e . In a d d ition to th e s e , in v a r ia n c e m ay be c o n c e r n e d w ith fa c to r s that a r e b ein g r e la te d o v e r ch a n g e s in tim e , m e a s u r e s and p o p u la tio n s. F u r th e r d is c u s s io n o f th e su b je ct of in v a r ia n c e w ill be g r e a tly fa c ilita te d if th e r e is a 14 s im p le fr a m e o f r e fe r e n c e a p p lied w ith r e g a r d to th e s e d im e n s io n s . T h e s c h e m a tic b elo w h a s been c o n str u c te d w ith r e s p e c t to v a r ia tio n in th e d im e n sio n s o f p op u lation and m e a s u r e s . T he in te r s e c tio n of e a ch c a te g o r y fo r m e a s u r e s and p op u lation w ill r e s u lt in a se p a r a te typ e of in v a r ia n c e . T he r em a in in g d is c u s s io n of in v a r ia n c e w ill be r e la te d to th is s c h e m a tic and w ill c o n s is t f ir s t o f a g e n e r a l d e fin itio n and r e s e a r c h ex a m p le of e a ch c e ll and th en a r e v ie w o f the in d ic e s or o th e r a tte m p ts to m e a s u r e ea ch of th e s e in v a r ia n c e ty p e s . P o p u la tio n s M e a su r e m e n ts F ix e d D iffe r e n t F ix e d F F FD P a r tly F ix e d P F PD D iffe r e n t DF DD T he f ir s t c e ll u n der c o n sid e r a tio n is the F F c e ll w h ere both th e m e a s u r e s and th e p op u lation a r e u n ch an ged . T h is typ e of in v a r ia n c e is u su a lly found in stu d ie s w h er e th e p r im a r y c o n c e r n is ch an ge o v e r tim e . T h is is the o n ly c a s e w h er e s t r ic t n u m e r ic a l in v a r ia n c e is p o s s ib le . T h is d e sig n m a y be e m p lo y e d in an attem p t to m e a s u r e the r e lia b ility o r sta b ility o f f a c t o r s . In p a r tic u la r , th is d e sig n h a s b een u se d in d e v e lo p m en ta l stu d ie s (O sb o rn e. A n d e rso n and B ash aw , 1967) and in th e study of in te lle c tu a l s tr a te g ie s (D unham , G u ilford and H o ep fn er, 1968) and In the study o f im p r o v e m en t in p sy c h o m o to r s k ills w ith p r a c tic e (F le is h m a n , 1966). T he F F c e ll le n d s i t s e lf to a v a r ie ty o f w a y s of m e a su r in g fa c to r ia l In v a ria n ce . B urt (1948) su g g e ste d the u se of th e c o r r e la tio n 15 b etw een fa c to r m e a s u r e m e n ts in the c a s e of th is d e s ig n . C a tte ll (1949b , 1969) su g g e s te d th e u s e the c o e ffic ie n t o f p a ttern s im ila r ity , fo llo w ed by a c h i-s q u a r e t e s t to ev a lu a te the p r o file s im ila r ity fo r p a ir s of fa c to r s . T h is c o e ffic ie n t o f p attern s im ila r ity c o n s is t s of th e d iffe r e n c e b etw een the fa c to r lo a d in g s fo r tw o fa c to r s a s c o m p a red w ith the d iffe r e n c e s b etw een lo a d in g s o f a p a ir o f fa c to r s that w e r e r e la te d on ly by c h a n c e . P ln n ea u and N ew h o u se (1964) h ave su g g e s te d a c o r r e c tio n in th e p r o c e d u r e p r o p o se d by B u rt. T h ey a r g u e that th e c o e ffic ie n t of co n g r u e n c e con fou n d s c h a n g e s in in d iv i duals' w ith c h a n g e s in fa c t o r s . T o a v o id th is p r o b le m , th ey s u g g e s t u sin g only one o f th e stan d ard s c o r e m a t r ic e s w hen d e r iv in g th e fa c to r s c o r e m a t r ic e s . T hey a ls o s u g g e s t th at if th e c o e ffic ie n t of su b je ct in v a r ia n c e is to be u se d , on ly one fa c to r m a tr ix sh ou ld be u s e d w ith both stan d ard s c o r e m a t r ic e s . F is k e (1948) h a s su g g e s te d th e u se o f the ad ju sted c o r r e la tio n s in an a ttem p t to m e a s u r e in v a r ia n c e . In ad d ition to th e s e m eth o d s, C a tte ll (1949a) h a s su g g e s te d a " s y m m e t r ic a l m a r k e r c r ite r io n " , w h er e the p r o b a b ility that th e m a r k e r v a r ia b le s found in one study w ill be r ep ro d u c ed in the o th e r stu d y. T he c r ite r io n r e q u ir e s stip u la tio n o f w hat v a lu e c o n s titu te s a " m ark er" lo a d in g . H o w e v er , C a tte ll s u g g e s ts its u s e a s a gu id e to d e te r m in e q u ick ly th e g o o d n e ss o f m a tch b etw een p a ir s o f fa c to r s . L ey d en (1953) h a s c o n tr a ste d s ix fa c to r -m a tc h in g c r it e r ia on th e data fr o m n in e s tu d ie s , e a ch u sin g th e sa m e grou p o f p u p ils and a p p ro x im a te ly the sa m e b a ttery o f t e s t s . H is c o m p a r iso n c o n tr a s te d r e s u lt s fr o m B u r t's c o r r e la tio n b etw een fa c to r -m e a s u r e m e n ts , the 16 u n ad ju sted c o r r e la tio n b etw een fa c to r sa tu r a tio n s, a sy m m e tr y c r ite r io n , th e c o r r e la tio n s o f fa c to r m e a s u r e m e n ts w ith e x te r n a l c r it e r ia , F is k e 's a d ju ste d c o r r e la tio n b etw een s a tu r a tio n s , C a tte ll's c o e ffic ie n t of p a tte rn s im ila r ity and s y m m e tr ic a l m a r k e r c r ite r io n . T h e r e s u lts in d ic a te that the v a r io u s c r it e r ia g iv e a w id e ran ge o f v a lu e s . W hile L ey d en r e c o m m e n d s th e u s e o f the u n ad ju sted c o r r e la tio n b etw een fa c to r m e a s u r e m e n ts a s the m o st r e lia b le , th e r e s u lts a r e fa r fr o m c o n c lu s iv e . F r o m the c a s e w h er e the sim p le is fix e d and th e b a ttery of m e a s u r e s is p a rtly (P F ) o r to ta lly d iffe r e n t (D F ), W rig ley and N eu h aas(1955) h ave su g g e s te d th e u s e o f the c o e ffic ie n t o f c o n g r u e n c e . T h is c o e ffic ie n t i s s im ila r to a c o r r e la tio n c o e ffic ie n t and is d e r iv e d u sin g th e fa c to r m e a s u r e m e n ts fr o m th e two b a tte r ie s . P in n ea u and N ew h o u se (1964) su g g e s t th at if the fa c to r s fro m th e two stu d ie s a r e b rought to m a x im u m c o n g r u e n c e , then the c o e ffic ie n ts o f co n g r u e n c e w ou ld be eq u iv a len t to c a n o n ic a l c o r r e la t io n s , and cou ld be ev a lu a ted a s su ch . T u ck er (1958) h as p r e se n te d a m eth od o f fa c to r a n a ly s is w h ich w ou ld s e e m to fit in to th is c a te g o r y . T he in te r -b a tte r y m eth od o f fa c to r a n a ly s e s is u t ilis e d w hen th e sa m e sa m p le is g iv en p a r tia lly d iffe r e n t t e s t b a t te r ie s . In th is m eth od , the c o r r e la tio n m a tr ix is p a r titio n e d into fo u r p a r ts , w ith on e p a r t co n ta in in g c o r r e la tio n s b etw een th e t e s t s co m m o n to both b a tte r ie s . T h is m a tr ix m a y then be fa c to r a n a ly se d and th e su b seq u en t fa c to r s c o r e s c o r r e la te d to g iv e an e s tim a te o f fa c to r r e lia b ility . A c r it ic is m of th is p r o c e d u r e h a s b een p r e s e n te d by G ib son (I9 6 0 ). 17 In v e stig a tio n s o f th e F D c e ll, w h e r e the m e a s u r e s a r e fix e d and th e p o p u la tio n s a r e d iffe r e n t, a r e u su a lly c o n c e r n e d w ith fa c to r s ta b ility . C om m on a n a ly s e s o f th is ty p e a r e c r o s s - c u lt u r a l c o m p a r i so n s and stu d ie s b etw een a g e g r o u p s. P in n ea u and N ew h o u se (1964) h a v e d e v e lo p ed a c o e ffic ie n t o f in v a r ia n c e fo r th is situ a tio n . It is the c o r r e la tio n o f the s c o r e s on on e fa c to r fr o m one study w ith the s c o r e s on a se c o n d fa c to r fo r the o th e r stu d y. It r e f le c t s both th e a n g le w h ich on e w ould n e e d to r o ta te th e seco n d fa c to r in o r d e r fo r the fa c to r to h a v e m a x im u m c o n g r u e n c e and d iffe r e n c e b etw een th e m at that lo c a tio n in fa c to r c o m p o sitio n . T h is c o e ffic ie n t r e f le c t s c o n fig u ra tio n a l in v a r ia n c e , a s it is r e la tiv e ly in s e n s itiv e to d iffe r e n c e s in th e n u m e r ic a l s iz e o f the lo a d in g s . T h e in tr a c la s s c o r r e la tio n co u ld be u s e d if a m e a s u r e o f n u m e r ic a l in v a r ia n c e is d e s ir e d . T u ck er (1951) h a s su g g e s te d th e c o e ffic ie n t of c o n g r u e n c e a s a m e a s u r e o f in v a r ia n c e in th e F D c e l l. T h is c o e ffic ie n t is th e su m o f the c r o s s p r o d u cts of th e lo a d in g s fo r the tw o fa c to r s d iv id ed by the sq u a re r o o t o f th e p rod u ct of the sq u a r ed lo a d in g s . T e s t s o f sig n ific a n c e a r e not a v a ila b le fo r th is c o e ffic ie n t so in te r p r e ta tio n is d iffic u lt. T h e c o e ffic ie n t of s im ila r ity (P in n eau and N e w h o u se, 1964) m a y be e m p lo y e d in th is d e sig n if the fa c to r s fr o m th e tw o stu d ie s h ave b een tr a n sfo r m e d into m a x im u m c o n g r u e n c e . T h is c o e ffic ie n t is s im ila r to a c a n o n ic a l c o r r e la tio n . T h e ro ta tio n o f fa c to r s into a p o s itio n o f m a x im u m co n g r u e n c e h a s b een th e su b je ct o f w ork by G reen (1 9 5 2 ), M ered ith (1964a, 1964b), C liff (1 9 6 6 ), and S chon em an n (1 9 6 6 ). M e r e d ith 's w ork 18 r e su lt* in th e d e v e lo p m en t o f an a lg o r ith m fo r d e r iv in g a fa c to r p a tte rn m a tr ix w h ich ia a " b est fittin g " m a tr ix fo r fa c to r p a ttern m a tr ic e s fr o m d iffe r e n t p o p u la tio n s. T h is b e s t fittin g m a tr ix i s the r o o ts and v e c t o r s of th e a v e r a g e o f th e o r ig in a l fa c to r p a tte rn m a t r ic e s . C liff (1966) p r e s e n ts the p r o c e d u r e s fo r two se p a r a te c a s e s of c o n g r u e n c e . C a se I i s w h er e the m a t r ic e s o f the tw o stu d ie s a r e ro ta ted to a p o s itio n o f m a x im u m c o n g r u e n c e in a le a s t - s q u a r e s s e n s e . In th e se co n d c a s e , th e m a tr ix o f one study is fitte d to a "target" o r h y p o th e tic a l m a tr ix in a le a s t sq u a r e s m eth o d . F u r th e r d is c u s s io n o f th is m eth o d w ill be found in a la te r s e c tio n . R e c e n tly K a is e r , H anka and B ia n ch in i (1971) have s u g g e s te d a m eth o d fo r r e la tin g the fa c to r s fr o m th e stu d ie s o f the F D o r P D c e ll. T h e ap p roach m a x im iz e s th e su m o f the in n er p ro d u ct of th e fa c to r lo a d in g s fo r th e p t e s t s th a t a r e co m m o n to both b a tte r ie s . It is su g g e s te d that th e d e r iv e d c o e ffic ie n ts a r e in te r p r e ta b le a s c o r r e la tio n c o e ff ic ie n ts . J o r e sk o g (1971) h a s p r e s e n te d a m eth od fo r fa c to r a n a ly s is on data d e r iv e d fr o m d iffe r e n t p o p u la tio n s u s in g th e sa m e o r p a r tia lly d iffe r e n t t e s t b a t te r ie s . T h e m eth o d e m p lo y s e s tim a tio n o f the p a r a m e te r s fr o m a s p e c ifie d fa c to r a n a ly s is m o d e l. T he e stim a tio n i s done u sin g m a x im u m lik e lih o o d te c h n iq u e s and a la r g e sa m p le c h i> sq u a re t e s t o f g o o d n e s s o f fit is a v a ila b le . In th e c a s e w h er e th e sa m p le i s fix e d and th e m e a s u r e s a r e a ll d iffe r e n t (D F c e ll) o c c u r s r e la tiv e ly fre q u en tly in th e b e h a v io r a l s c ie n c e s . T he in t e r e s t in stu d ie s o f th is typ e is g e n e r a lly a d em o n 19 str a tio n o f the s a m e d im e n s io n s in to ta lly in d ep en d en t s e t s o f m e a s u r e s . T he m u ltitr a it, m u ltim eth o d m a tr ix w a s o r ig in a lly p r e s e n te d by C a m p b ell and F is k e (1959) fo r a n a ly s is on su b je c ts o th e r than in v a r ia n c e . M eth od s (W er ts, J o r e sk o g , and L in n , 1971; J o r e sk o g , 1970) fo r fa c to r in g th is m a tr ix h ave brought th is w ork into th e r e a lm o f fa c to r ia l in v a r ia n c e . T h e la s t c e ll o f the s c h e m a tic is th e m o st d iffic u lt and demandfc^g a r e a w h er e n e ith e r th e p op u lation n o r the m e a s u r e s a r e the sa m e . Y et th is DD d e s ig n o f f e r s the m o st g e n e r a lity and str en g th to fa c to r s th a t cou ld c o n c e iv a b ly be sh ow n to be in v a r ia n t in th is c a s e . No n u m e r ic a l o r s t a t is t ic a l in d ic e s h ave b een d e v e lo p e d fo r th is c a s e . U n til r e c e n tly the on ly a tte m p ts to d eal w ith data in th is c a te g o r y r e lie d upon in tu itiv e m a tch in g of fa c to r s . T h e c la s s i c e x a m p le of m a tch in g fa c to r s on th is b a s is w a s c o n d u cted by F r e n c h (1 9 5 1 ). F r e n c h took th e ro ta ted fa c to r s fr o m s o m e 69 stu d ie s and a tte m p te d to id e n tify fa c to r s w h ich w e r e co m m o n to m o r e than o n e stu d y . F r e n c h r e p o r te d the e x is te n c e o f at le a s t 59 d iffe r e n t fa c to r s found in on e o r m o r e of th e stu d ie s r e v ie w e d , p lu s m an y m o r e fa c to r s p r e s e n t in th e a n a ly s e s a s s in g le ts o r d o u b le ts. W hile th is w a s a m a m m o th u n d ertak in g, and c e r ta in ly on e w h ich n e e d e d to be don e, th e r e a r e s e v e r a l o b v io u s p r o b le m s . F ir s t of a ll, F r e n c h h im s e lf w a r n s, a s m any a s 20% o f the fa c to r id e n tific a tio n s a r e u n c e r ta in . S e c o n d ly , th e s e Id e n tific a tio n s w e r e m a d e on th e b a s is of th e t e s t s u s e d , the h y p er p la n e count, and th e d e fin itio n o f th e fa c to r by th e a u th o r, not on th e b a s is of e m p ir ic a l r e s u lt s . 20 T h ir d ly , the d e fin itio n a o f th e fa c to r s w h ich w e r e u s e d fo r c r o s s id e n tific a tio n p u r p o se s w e r e b a se d not upon so m e p a r tic u la r th eo ry o f in te lle c tu a l a b ilitie s w h ich g a v e s p e c ific d e fin itio n s to its fa c t o r s , but upon th e in sig h t and p e r h a p s b ia s e s o f th e o r ig in a l a u th o r s. T h e r e fo r e , w h ile F r e n c h 's w ork is o f im m e n se v a lu e a s r e fe r e n c e m a te r ia l and o f v a lu e fo r tr a c in g th e h is to r y o f a t e s t o r a fa c to r , it can n ot o ffe r a u n ifyin g a p p ro a ch o r ablu tion to th e fa c to r a n a ly tic s e a r c h fo r th e n a tu re o f hum an in te llig e n c e , o r d e m o n str a te a d e q u a tely fa c to r ia l in v a r ia n c e . F r o m th is r e v ie w o f th e su b je ct o f fa c to r ia l in v a r ia n c e , it sh ou ld be ap p aren t that th e r e i s no c o r r e c t w ay n o r e v e n a c o n s e n s u s r e g a r d in g th e d e m o n str a tio n o f fa c to r ia l in v a r ia n c e . T h is is p a r ti c u la r ly the c a s e w hen on e e n te r s th e r e a lm w h e r e th e p o p u la tio n s and m e a s u r e s a r e both to ta lly o r p a r tia lly d iffe r e n t. H ow then ca n one u s e the m eth o d o f fa c to r a n a ly s is in an a ttem p t to is o la te the in t e lle c tu a l a b ilitie s o f m an a s T h u rsto n e e n v isio n e d ? T he S tr u c tu r e o f In te lle c t T h e p r o b le m o f in v a r ia n c e a s r e la te d to th e s c ie n tific in v e s t i g ation o f in te llig e n c e h a s b een a d d r e s s e d fr o m a n o th er a n g le . G u ilfo rd and H o ep fn e r (1971) poin t out that in th e in v e stig a tio n o f in te llig e n c e through fa c to r a n a ly s is p r im a r y e m p h a s is is p la c e d not upon th e m a th e m a tic a l fa c to r s but r a th e r on th e r o ta te d o r in te r p r e te d fa c to r s . S in ce th is is th e c a s e , it is im p e r a tiv e to d e m o n str a te p s y c h o lo g ic a l in v a r ia n c e . T h is typ e o f in v a r ia n c e can r e a d ily be d e m o n str a te d th rou gh a h y p o th e s is -te s tin g ap p roach in the a p p lic a tio n 21 o f fa c to r a n a ly s is . S p e c ific a lly , if a m o d el o r theeary o f in te llig e n c e p r e d ic ts a d im e n sio n and th is d im e n sio n m ay be d e m o n str a te d , th en th e d im e n sio n m u st be g iv en a good d eal of c r e d e n c e . If in a se p a r a te stu d y, th e m o d el r e s u lts in th e sa m e d im e n sio n w h ich fits the th e o r e tic a l d e fin itio n o f the e a r lie r a b ility but the m e a s u r e s a n d /o r the p op u lation e m p lo y ed a r e to ta lly o r p a r tia lly ch an ged , th en c e r ta in ly th is is an in d ic a tio n o f fa c to r ia l in v a r ia n c e . G u ilford and H o ep fn er h ave u n d ertak en su ch a d e m o n str a tio n . S p e c ific a lly , th ey u se d the S tr u c tu r e -o f-I n te lle c t m o d el (G u ilford , 1967) to p r e d ic t d im e n sio n s in a s e r ie s of p r e v io u sly con d u cted s tu d ie s . T h e se stu d ie s w e r e then r e a n a ly s e d u tilis in g th e s e p r e d ic tio n s to guide th e r o ta tio n a l p r o c e d u r e s . T he r e s u lts sh ow ed a r em a r k a b le c o n fir m a tio n o f the n otion o f in v a r ia n c e o f S tr u c tu r e -o f-I n te lle c t f a c to r s . T he S tr u c tu r e -o f-I n te lle c t is a m o r p h o lo g ic a l m o d el m u ch lik e the c h e m is t's p e r io d ic ta b le . T he m o d e l i s o r g a n ise d a lon g th r e e d im e n sio n s: o p e r a tio n , w h ich d efin e th e m a jo r k in d s of in te lle c tu a l a c tiv ity un dertaken; co n ten t, w h ich d e fin e s the ty p e of in fo r m a tio n to be p r o c e s s e d ; and a p rod u ct d im e n sio n , w h ich d e fin e s th e r e su lta n t fo r m o f the in fo rm a tio n a fte r p r o c e s s in g by th e in d iv id u a l. E la b o r a tion o f th e co m p o n en ts of e a c h d im e n sio n , a s w e ll a s the sy m b o ls u s e d to r e p r e s e n t e a ch com p en t i s g iv en b elo w . T he o p e r a tio n s d im e n sio n h a s fiv e se p a r a te and d istin g u ish a b le o p e r a tio n s in clu d ed in it . C ogn ition (C) is d efin ed a s im m a d la te d is c o v e r y , a w a r e n e s s , r e d is c o v e r y o r r e c o g n itio n o f in fo rm a tio n in its v a r io u s fo r m s . M em o ry (M) i s d efin ed a s the fix a tio n o f r e c e n tly 22 g ain ed in fo r m a tio n in s to r a g e . D iv e r g e n t P ro d u ctio n (D) is the g e n e r a tio n of lo g ic a l a lte r n a tiv e s fr o m g iv en in fo r m a tio n , w h er e the e m p h a s is is on v a r ie ty , qu an tity and r e le v a n c e of output fr o m the sa m e s o u r c e . C o n v erg en t P ro d u c tio n (N ), on th e o th e r hand, i s c o n c e r n e d w ith g e n e r a tio n o f lo g ic a l c o n c lu sio n s fr o m g iv en in fo r m a tio n , w h e r e the e m p h a s is i s p la c e d upon a c h ie v in g unique o r co n v e n tio n a lly b e s t o u tc o m e . T h e l a s t o p e r a tio n i s E v a lu a tio n (E ), w h ich i s the c o m p a r iso n o f ite m s o f in fo r m a tio n in t e r m s o f v a r ia b le s and m akin g ju d g m en ts c o n c e r n in g c r ite r io n s a tis fa c tio n , su ch a s c o r r e c t n e s s , id e n tity and c o n s is te n c y . T he co n ten t c a te g o r y h a s fou r c o m p o n e n ts, o r d iffe r e n t ty p e s o f p o s s ib le in fo r m a tio n to be p r o c e s s e d . F ig u r a l (F) in fo r m a tio n is d efin ed a s h avin g a c o n c r e te fo r m , a s p e r c e iv e d o r a s r e c a lle d in the fo r m o f im a g e s . T h e S y m b o lic (S) c a te g o r y is c o m p o se d o f a ll in fo r m a tio n w h ich h as th e fo r m of d en o ta tiv e sig n s h avin g no s ig n if i c a n c e in and o f th e m s e lv e s , su ch a s n u m b e r s, le t t e r s , s ig n s , e tc . S e m a n tic (M) in fo r m a tio n p e r ta in s to in fo rm a tio n in th e fo r m of c o n c e p tio n s o r m en ta l c o n s tr u c ts to w h ich w o r d s a r e o ften a p p lie d . T he la s t c a te g o r y is a r e la tiv e ly unique c a te g o r y fo r a m o d el of in te llig e n c e . It is c a lle d B e h a v io r a l (B) and is c o n c e r n e d w ith in fo r m a tio n w h ich is e s s e n t ia lly n o n flg u ra l and n o n v erb a l that is in v o lv ed in hum an in te r a c tio n s , w h e r e the a ttitu d e s, n e e d s , d e s ir e s , m o o d s, in te n tio n s, p e r c e p tio n s and th ou gh ts o f p eo p le a r e in v o lv e d . T h e la s t d im e n sio n o f the S tr u c tu r e -o f-I n te lle c t m o d e l d e a ls w ith i s th e p r o d u cts that r e s u lt fr o m th e a c tio n o f an o p e r a tio n s upon 23 a con ten t. U n its (U) a re r e la tiv e ly se g r e g a te d o r c ir c u m sc r ib e d ite m s o f in fo rm a tio n that s e e m to be an en tity o f th e m s e lv e s . C la s s e s (C) a r e co n cep tio n s u n d erlyin g s e ts o f ite m s o f in form ation grouped by v irtu e o f th e ir com m on p r o p e r tie s . R e la tio n s (R) are co n n ectio n s b etw een ite m s o f in fo rm a tio n b ased upon v a r ia b le s or p o in ts o f co n ta ct th at apply to th em . S y ste m s (S) a r e o rg a n ize d , stru ctu red c o lle c tio n s of ite m s o f in fo rm a tio n . T ra n sfo rm a tio n s (T) a r e r e d e fin itio n s, o r m o d ifica tio n s in e x istin g in fo rm a tio n . T he la s t produ ct ca teg o ry is Im p lica tio n s (1) and i s co n cern ed w ith co n n ectio n s o r e x tra p o la tio n s fro m one bit of in form ation to an oth er. The com b in ation of on e o p era tio n c a te g o ry w ith one content ca teg o ry w ith one p rod u ct c a te g o ry d e fin e s a unique in te lle c tu a l a b ility . T h e se a b ilitie s a re u su a lly d esig n a ted by a tr ig r a m co d e. T he cod e has one le tte r for e a ch d im en sio n in th e fo llo w in g ord er: o p era tio n , con ten t, and p rod u ct. T he le t t e r s to be u sed in the cod e have been given in the d is c u s s io n of each c a te g o r y ab ove. T h u s, for " m em ory for fig u r a l c la s s e s " w ould be d esig n a ted a s M F C . T he S tr u c tu r e -o f-ln te lle c t m od el grew out of fin d in gs fro m r e s e a r c h G uilford condu cted during W orld W ar IE and p o st-w a r r e s e a r c h in the A p titu d es R e se a r c h P r o je c t (A R P) at the U n iv e r sity of Southern C a lifo rn ia . A fter the m od el w as f ir s t p ro p o sed (G uilford. 1956). it guided a sy s te m a tic fa cto r a n a ly tic in v e stig a tio n o f the in te lle c tu a l dom ain . A fter so m e 20 y e a r s . 98 S tr u c tu r e -o f-I n te lle c t a b ilitie s have been id en tified , each in at le a s t one study. A s a fo llo w -u p to A R P . two se p a r a te but r e la te d stu d ie s w e re 24 co n d u cted . T he f ir s t o f th e s e w as r e fe r r e d to p r e v io u s ly . G u ilford and H o ep fn er (1971) p e r fo r m e d a m a s s iv e in v e stig a tio n o f th e fa c to r ia l in v a r ia n c e of S tr u c tu r e -o f-I n te lle c t a b ilit ie s . T h is in v e stig a tio n u tiliz e d th e S tr u c tu r e -o f-I n te lle c t m o d e l a s it w a s know n in 1968. and a p p lied it to a ll the w ork done by A R P fr o m its in c e p tio n . T h is in clu d ed a ll th e stu d ie s done by A R P b e fo r e 1958. a s w e ll a s th o se fo llo w in g th e ad ven t o f C liff's r o ta tio n a l m eth o d . T h e p r o c e d u r e u se d in G u ilfo rd and H o e p fn e r 's in v e stig a tio n c o n s is te d o f r e v ie w in g a ll th e t e s t s e m p lo y e d in th e s e p r e v io u s studies. T h e t e s t s w e r e in d ep en d en tly a s s ig n e d to th e ir h y p o th e siz e d p la c e s w ith in th e S tr u c tu r e -o f-I n te lle c t m o d e l. T he c o r r e la tio n m a tr ic e s w e r e then se p a r a te ly fa c to r e d u sin g the p r in c ip a l fa c to r so lu tio n a s g iv e n by a stan d ard co m p u ter p r o g r a m . T h is p ro v id ed a u n ifo rm b a se a s m an y o f the e a r ly stu d ie s had had on ly a c e n tr o id so lu tio n a v a ila b le. T he n ew ly co m p u ted p r in c ip a l a x e s w e r e then ro ta ted to a th e o r e tic a l ta r g e t u sin g C liff's (1966) p r o c e d u r e , d e s c r ib e d a s C a se II a b o v e. T h e th e o r e tic a l ta r g e t fo r a t e s t w a s c o n str u c te d on th e b a s is of the t e s t 's p r e d ic te d S tr u c tu r e -o f-I n te lle c t fa c to r ia l c o m p o sitio n . The r e s u lt s o f th e s e a n a ly s e s sh ow ed str o n g su p p o rt fo r the e x is te n c e o f the S tr u c tu r e -o f-I n te lle c t a b ilitie s and th e ir in v a r ia n c e o v e r 20 y e a r s o f in v e stig a tio n . T h e se co n d fo llo w -u p study w a s a c o n sid e r a tio n o f fin d in g e v i d e n c e of S tr u c tu r e -o f-I n te lle c t a b ilitie s In s tu d ie s o th e r than th o s e con d u cted by A R P . G u ilfo rd (1972) p r o p o se d that th e S tr u c tu r e -o f- In te lle c t a b ilitie s cou ld be found in P r im a r y M en tal A b ilit ie s (PM A ) 25 o f T h u rsto n e (1 9 3 8 ). H e r e v ie w e d the t e s t s u s e d by T h u rsto n e in the PM A study and id e n tifie d th e ir p la c e s w ith in th e S tr u c tu r e -o f- I n te lle c t. U n lik e th e p r e v io u s in v e s tig a tio n s no a n a ly s e s w e r e c o n d u cted to su p p ort th e s e p r e d ic tio n s . T he sig n ific a n c e of su ch a n a ly s e s w ou ld be su b sta n tia l to th e S tr u c tu r e -o f-I n te lle c t m o d e l and it s f a c to r s . E v id e n c e o f fa c to r ia l in v a r ia n c e o f th is ty p e w ou ld be m o st c o m p e llin g and w ou ld le n d a g r e a t d ea l o f g e n e r a lity to the S tr u c tu r e -o f-I n te lle c t fa c to r s d e m o n str a te d by su ch a n a ly s e s . U n fo rtu n a tely an in v e s tig a tio n o f fa c to r ia l in v e stig a tio n o f T h u r sto n e 's PM A o r s im ila r s tu d ie s w ou ld be o p e r a tin g in th e DD o r at b e s t PD c e lls o f in v a r ia n c e ty p e s . R e c a ll th at fo r th e s e c e l l s , th e ap p roach h a s u su a lly b e e n ta k en is th e in tu itiv e in sp e c tio n m eth od su ch a s in F r e n c h (1951) o r G u ilfo rd (1 9 7 2 ). E m p ir ic a l e v id e n c e o f fa c to r ia l in v a r ia n c e fo r S tr u c tu r e -o f-I n te lle c t a b ilitie s in T h u rsto n ia n stu d ie s can b e s t be o b ta in ed by fo llo w in g a p r o c e d u r e su ch a s th at o f G u ilford and H o ep fn er (1 9 7 1 ). T h e p r e s e n t stu d y u t i l is e s th e p r o c e d u r e s o f the p r e v io u s ly d is c u s s e d stu d y but a p p lie s th em to in v e s tig a tio n s w h ich a r e to ta lly u n r e la te d to A R P o r th e S tr u c tu r e -o f-I n te lle c t. T h e in ten t o f the study is to p r o v id e e m p ir ic a l e v id e n c e fo r the in v a r ia n c e of S tr u c tu r e -o f-I n te lle c t a b ilit ie s . T h is e v id e n c e w ill be in th e fo r m o f th e fit o f the r o ta te d m a t r ic e s to th e th e o r e tic a l ta r g e ts w h ich co n ta in th e h y p o th e sise d S tr u c t u r e -o f -I n te lle c t f a c to r s . T he fo llo w in g s e c tio n p r o v id e s a d e ta ile d d is c u s s io n o f th e e x a c t p r o c e d u r e s e m p lo y e d in th is stu d y. C H A P T E R II PR O C E D U R E S S e le c tio n o f S tu d ies T h e f i r s t a s p e c t of the in v e stig a tio n to be c o n s id e r e d w a s the sc o p e it sh ould have* W hile it s e e m e d fa ir ly c e r ta in that the f ir s t PM A study of T h u rsto n e w ou ld be the c r u x o f the study* it had to be d e c id e d w h eth er th is sh ou ld be th e o n ly on e em p loyed * o r w h eth er a m o r e c o m p r e h e n s iv e study s im ila r to F r e n c h <1951) sh ou ld be u n d e r ta k en . A c o m p r o m is e on th e sid e o f p a r sim o n y w a s ad op ted . It w a s d e c id e d that th e stu d ie s to be in clu d ed fo r in v e s tig a tio n sh ou ld be fr o m T h u r sto n e ’s la b o r a to r y o r co n d u cted in th e T h u rsto n ia n tr a d itio n . T h e r e w e r e tw o r e a s o n s fo r th is d e c is io n . F ir st* th e stu d ie s fr o m T h u rsto n e* s la b o r a to r y w e r e u su a lly b a sed upon th e PM A stu d ie s w h ich w e r e the c ru x o f the p r e s e n t in v e s tig a tio n . Second* stu d ie s that w e r e not fro m th e la b o r a to r y but w e r e in th e T h u rsto n ia n tr a d i tio n w e r e s im ila r in c e r ta in w a y s to stu d ie s co n d u cted by A R P . T h is tr a d itio n h e ld that fa c to r a n a ly s is w a s to be em p lo y ed in a h y p o t h e s is te s tin g r o le . T h erefo re* c a r e fu l s e le c tio n w a s m ad e o f the t e s t s to be u s e d in th e e x p e r im e n ta l b a tte r y . In addition* th e s e t e s t s w e r e c o n str u c te d a c c o r d in g to p r io r h y p o th e se s c o n c er n in g the n a tu re o f th e fa c to r s b ein g in v e stig a te d . T h e s a m p le s w e r e u su a lly h igh sc h o o l o r c o lle g e a g e stu d e n ts. In ad d ition to th e r e s tr ic tio n o f stu d ie s to o n e s in th e T h u r sto - 26 27 n ian tr a d itio n , s e v e r a l o th e r r e s tr ic tio n s w e r e im p o se d . T h e se w e r e : 1) th e study m u st h a v e been p u b lish ed , 2) it had to d ea l w ith on ly in te lle c tu a l fa c to r s , not w ith p e r so n a lity o r p sy c h o m o to r a b ilit ie s , 3) it m u st have b een a r e p r e s e n ta tiv e study done w ithout th e b en efit o f the S tr u c tu r e -o f-I n te lle c t m o d e l, and 4) it had to have a r e a so n a b le sa m p le s iz e and a good fa c to r a n a ly tic a l r e s e a r c h d e sig n . T he a p p lic a tio n o f th e s e c r it e r ia w a s m ad e in an in itia l c o n s i d e r a tio n of 16 s tu d ie s . A t th is p oin t, it w a s d e c id e d that w h ile a ll th e s tu d ie s w ould be r e v ie w e d and p r e d ic tio n s m ad e about th e v a r io u s S tr u c tu r e -o f-ln te lle c t fa c to r s r e p r e se n te d in ea ch , a s m a lle r s e t o f s tu d ie s w ould be s e le c te d fo r a c tu a l a n a ly s e s . T he six te e n stu d ie s in clu d ed fo u r stu d ie s by T h u rsto n e {1938, 1940, 1944, 1951), T h u rsto n e & T h u rsto n e (1941), C oom b s (1 9 4 1 ), T a y lo r (1947), B ech to ld t (1947), R im o ld i (1 9 5 1 ), Botzuxn (1 9 5 1 ), A d kins & L y e r ly (1952), P em b u rto n (1951), K e lle y (1964), W oodrow (1939), C a r r o ll (1941), C h r ista l (1958), and M ooney (1954). T h e d e s c r ip tio n s of the t e s t s u sed in e a c h o f th e s e stu d ie s w e r e e x a m in e d s e p a r a te ly by th e auth or and D r. J . P . G u ilfo rd . On th e b a s is on th e s e d e s c r ip tio n s , e a c h r e v ie w e r in d ep en d en tly a s s ig n e d e a ch t e s t to a p a r tic u la r fa c to r fr o m the S tr u c tu r e -o f-ln te lle c t. T h e s e a s s ig n m e n ts w e r e then su m m a r iz e d to d e te r m in e w h ich fa c to r s w e r e w e ll r e p r e s e n te d in ea ch o f the s tu d ie s . T h e se su m m a r ie s w e r e ad ju d icated to m utu al s a tis fa c tio n . F in a l s e le c tio n o f stu d ie s w a s b a sed upon th e s e fa c to r r e p r e se n ta tio n s u m m a r ie s . In o r d e r to be in clu d ed fo r a n a ly s is , a study m u st h ave: 1) a 28 r e a so n a b le am ount o f o v e r la p w ith th e fa c to r s fr o m th e o th e r s t u d ie s , 2) o ffe r so m e unique co m m o n fa c to r s , and 3) have a r e a so n a b le p r o m ise fo r d e te r m in a tio n of S tr u c tu r e -o f-I n te lle c t a b ilit ie s , i. e . , ea ch fa c to r m u st h ave two o r m o r e t e s t s w h ich a r e u n iv o c a lly p r e d ic te d a s d efin in g it . T h e r e fo r e , stu d ie s w e r e e lim in a te d if they co n ta in ed on ly fa c to r s w h ich w e r e d u p lica te d in a n oth er study that o ffe r e d a ls o so m e unique fa c to r s , o r if th e SI fa c to r s a p p ea red to be p o o r ly d e fin e d . T h e s e c r ite r ia r e s u lte d in th e in c lu sio n o f e ig h t stu d ie s fo r fu r th e r a n a ly s e s . T h e se stu d ie s a r e 1) T h u rsto n e (1938) P M A , 2) T h u rsto n e b T h u rsto n e (1 9 4 1 ), 3) T h u rsto n e (1940), 4) T a y lo r (1947), 5) A d k in s and L y e r ly (1952), 6) K e lle y (1964), 7) B ech to ld t (1947), and 8) C a r r o ll (1941). D e s c r ip tio n of the S tu d ies In 1938 T h u rsto n e rep o rted th e now fa m o u s study on the P r im a r y M en tal A b ilit ie s . In th is study 57 p s y c h o lo g ic a l t e s t s w e r e a d m in is te r e d to 240 c o lle g e stu d e n ts, th e m a jo r ity b ein g fr o m th e U n iv e r sity o f C h ica g o . T he c e n tr o id so lu tio n , w h ich fo llo w ed fr o m a n a ly s is o f the c o r r e la tio n m a tr ix , w a s ro ta ted o r th o g o n a lly to T h u r sto n e 's p r in c ip le o f sim p le s tr u c tu r e . T h is so lu tio n had 13 fa c to r s , nin e o f w h ich w e r e id e n tifie d a s P r im a r y M en tal A b ilit ie s . T he nine in te r p r e te d fa c to r s w e r e nam ed: S p a ce, P e r c e p tio n , N u m b er, V e r b a l, M em o ry , In du ction, D ed u ctio n , W ord F lu e n c y and R e a so n in g . T h e T h u rsto n e and T h u rsto n e (1941) study r e p o r te d two a n a ly s e s o f in te lle c tu a l a b ilitie s . T he a n a ly s is ex a m in ed in the 29 p r e se n t in v e stig a tio n u s e d 60 p s y c h o lo g ic a l t e s t s and th r e e non - in te lle c tu a l v a r ia b le s: a g e , s e x and m en ta l a g e . T he in fo r m a tio n on th e s e v a r ia b le s w e r e c o lle c t e d fr o m 710 s u b je c ts fr o m the eigh th g ra d e in C h ica g o . A n o b liq u e ro ta tio n fo llo w e d a c e n tr o id so lu tio n . A 1 0 -fa c to r so lu tio n r e s u lte d w ith 7 fa c to r s b ein g in te r p r e ta b le . T h e s e w e r e : N u m b er, W ord F lu e n c y , S p a c e , V erb a l C o m p re h e n sio n , M em o ry , Induction and P e r c e p tio n . T h u rsto n e (1940) con d u cted w hat h e c a lle d an e x p e r im e n ta l study o f sim p le s tr u c tu r e . T h is study u s e d a b a tte ry of 36 t e s t s , m any o f w h ich w e r e the sa m e a s th o se in th e o r ig in a l P r im a r y M en tal A b ilitie s stu d y. The te s t b a ttery w a s g iv e n to 266 h igh sc h o o l s e n io r s fr o m the C h icago a r e a . F o llo w in g a c e n tr o id e x tr a c tio n fr o m the c o r r e la tio n m a tr ix , an ob liq u e ro ta tio n w a s p e r fo r m e d . T h e ro ta ted fa cto r m a tr ix had 11 fa c to r s , fr o m w h ich T h u rsto n e c o n fid e n tly id e n tifie d fiv e fa c to r s : N u m b er, V e r b a l, F lu e n c y , S p ace and M em o ry . In ad d ition , th e In d u ctiv e, D ed u ctiv e and P e r c e p tio n fa c to r s w e r e id e n tifie d but w e r e not d efin ed a s w e ll a s the p r e v io u s ly m en tio n ed f a c to r s . B ech to ld t (1947) con d u cted a study a im e d at c la r ify in g th e n atu re o f th e p e r c e p tu a l fa c to r . T h e su b je c ts w e r e 167 v o lu n te e r c o lle g e stu d en ts at th e U n iv e r sity o f C h ic a g o . T he t e s t b a ttery w a s c o m p o se d o f 46 t e s t s w ith a h ea v y c o n c en tr a tio n o f p sy c h o m o to r and p e r ce p tu a l t e s t s . A c e n tr o id so lu tio n fa c to r s w a s o b ta in ed and th ey w e r e r o ta te d to o b liq u e s im p le str u c tu r e . F o u r PM A a b ilitie s w e r e id en tified ; S p a ce, N u m b er, V erb a l and W ord F lu e n c y . B ech to ld t 30 a ls o id e n tifie d s ix p u r e ly p e r c e p tu a l fa c t o r s , but not the p e r c e p tu a l fa c to r o f T h u r sto n e . A d k in s and L y e r ly (1952) con d u cted a c o m p r e h e n s iv e stu d y o f r e a so n in g a b ilit ie s . A b a tte ry o f 65 t e s t s w e r e g iv en to a r e p r e s e n ta tiv e sa m p le of 226 e n lis te d m en o f the U n ited S ta te s A r m y . T h e o r ig in a l sa m p le w a s red u c ed to 200 by e lim in a tin g th o se in d iv id u a ls on w hom in c o m p le te in fo r m a tio n w a s not a v a ila b le . A 66 v a r ia b le (ed u cation w a s in c lu d e d fo r a n a ly s is ) P e a r s o n p r o d u c t-m o m e n t in te r c o r r e la tio n m a tr ix w a s fa c to r a n a ly s e d . A c e n tr o id so lu tio n w a s com p u ted w ith th e c o m m u n a lity e s tim a te s b ein g the la r g e s t en try fo r a v a r ia b le . T h e c e n tr o id so lu tio n had 16 o rth o g o n a l f a c to r s . T h is w a s ro ta ted to ob liq u e sim p le s tr u c tu r e . O f the fin al f a c to r s , eigh t w e r e in te r p r e te d a s b ein g o u ts id e th e r e a lm o f r e a so n in g , fiv e a s b ein g v a r io u s fo r m s o f r ea so n in g and th e r e m a in in g th r e e a s b ein g r e s id u a ls . K e lle y (1964) con d u cted a fa c to r ia l study of m em o r y a b ilitie s . T he t e s t b a ttery had 27 t e s t s d e sig n e d to m e a s u r e v a r io u s h yp o t h e s is e d fo r m s o f m e m o r y , in a d d ition th ir te e n m a r k e r t e s t s fo r r e fe r e n c e w e r e a ls o in c lu d e d . M any o f th e la tte r w e r e o f a p e r c e p tu al o r p sy c h o m o to r n a tu r e . T h is b a tte ry w a s a d m in is te r e d to a sa m p le o f 480 U .S . A ir F o r c e p ilo t c a d e ts . T he fin a l a n a ly s is w as con d u cted u sin g a sa m p le o f 442 m en fe v w h om c o m p le te in fo r m a tio n w a s a v a ila b le . A 4 0 x 4 0 P e a r s o n p r o d u c t-m o m e n t in te r c o r r e la tio n m a tr ix w a s com p u ted and fa c to r a n a ly s e d . A m u ltip le -g r o u p m eth od o f fa c to r in g (T h u rsto n e, 1947) w a s e m p lo y ed and r e su lte d in an 11 31 fa c to r o rth o g o n a l so lu tio n . T h is m a tr ix w a s then r o ta te d to an ob liq u e sim p le s tr u c tu r e . S ix fa c to r s w e r e id e n tifie d a s V erb a l C o m p r e h e n sio n , N u m e r ic a l F a c ility , P e r c e p tu a l S p eed , R ote M em o ry , M ean in gfu l M em o ry and Span M e m o r y . T he r em a in in g fa c to r s w e r e o f an u n c le a r n a tu re . C a r r o ll (1941) co n d u cted a fa c to r a n a ly s is o f v e r b a l a b ilit ie s . In th is study a b a ttery of 42 t e s t s of a v e r b a l n a tu re w e r e u s e d . T h is b a ttery w a s a d m in is te r e d to 170 U n iv e r sity of M in n eso ta u n d e r g r a d u a te s. T he fin a l sa m p le s iz e w a s red u c ed to 119 fo r la c k o f c o m p le te in fo r m a tio n . P r o d u c t-m o m e n t c o r r e la tio n s w e r e co m p u ted , and the r e su ltin g 42 x 42 m a tr ix w a s su b m itted to fa c to r a n a ly s is . A 10 fa c to r c e n tr o id so lu tio n w a s ob tain ed fr o m th is c o r r e la tio n m a tr ix . T h e p r o c e d u r e w a s c o m p le te d in 2 w a y s: 1) so that a v e r b a l fa c to r , d en oted C, w a s c o r r e la te d w ith J, a r e a so n in g fa c to r (s im p le str u c tu r e r e q u ir e s th is b e c a u se th e r e a so n in g t e s t s w e r e a ls o v e r b a l), and 2) so that the v e r b a l fa c to r , d en oted C 1 1 w as o rth o g o n a l to J . E igh t o f the fa c to r s w e r e p o s itiv e ly in te r p r e te d , and in so m e c a s e s id e n tifie d a s b ein g r e la te d to T h u r sto n e 1 s PM A f a c t o r s . T h e la s t study to be In clu ded fo r a n a ly s is in th e p r e s e n t in v e stig a tio n w a s co n d u cted by T a y lo r (1 9 4 7 ). T h is study w a s c o n c e r n e d w ith flu e n c y in w r itin g , and p a r tic u la r ly in id e n tify in g tw o w ord flu e n c y f a c to r s . A t e s t b a tte ry o f 28 t e s t s , in clu d in g ten m a r k e r t e s t s fo r p r im a r y m en ta l a b ilitie s , w e r e a d m in is te r e d to 181 high sc h o o l s e n io r s . T en c e n tr o id fa c to r s w e r e e x tr a c te d fr o m th e p r o d u c t-m o m e n t c o r r e la tio n m a tr ix . An o b liq u e ro ta tio n to 32 s im p le s tr u c tu r e w a s p e r fo r m e d on th is ten fa c to r so lu tio n . F iv e fa c to r s w e r e in te r p r e te d a s PM A a b ilitie s : M em o ry . N u m b er. R e a so n in g . V erb a l C o m p re h e n sio n and P e r c e p tu a l S p ee d . T w o flu e n c y fa c to r s w e r e id e n tifie d a s b ein g W ord F lu e n c y and Id ea tio n a l F lu e n c y . A n a d d itio n a l v e r b a l a b ility w a s te n ta tiv e ly id e n tifie d a s V erb a l V e r s a t ilit y . T h e r e m a in in g fa c to r s w e r e not id e n tifie d . M ethod o f T ea t A s sig n m e n t T he in ten t of th is d is s e r ta tio n is th e d e m o n str a tio n of fa c to r ia l in v a r ia n c e of S tr u c tu r e -o f-I n te lle c t fa c to r s in th e s e le c t e d s tu d ie s . A s w as m en tio n e d p r e v io u s ly , the a p p ro a ch c h o se n to show th is in v a r ia n c e w a s the p r o c e d u r e u tiliz e d by G u ilford and H oep fn er (1 9 7 1 ). E s s e n tia lly th is p r o c e d u r e c o n s is t s o f fou r ste p s: (1) in d ep en d en t ju d gm en t of fa c to r ia l co n ten t o f the t e s t s . (2) a d ju d ica tio n of th e s e ju d g m e n ts. (3) fa c to r a n a ly s is o f the se p a r a te d c o r r e la tio n m a tr ic e s u sin g a p r in c ip a l fa c to r m eth od w ith ite r a te d sq u a red m u ltip le c o r r e la tio n c o e ffic ie n ts a s c o m m u n a lity e s t im a t e s , and (4) ro ta tio n u sin g a ta r g e te d p r o c ed u r e d e v e lo p e d by C liff (1 9 6 6 ). T he ju d g m en ts of the fa c to r ia l c o m p o sitio n o f the t e s t s w e r e th e esssn tial fe a tu r e o f the e n tir e p r o c e d u r e u se d in th is stu d y . T h e se ju d g m en ts w ou ld le a d to th e fa sh io n in g of th e ta r g e t m a tr ix w h ich w ou ld gu id e th e r o ta tio n s. A lso on th e b a s is of th e s e ju d g m en ts the fa c to r s w ou ld be id e n tifie d . In a d d itio n , the d e te r m in a tio n o f th e n u m b er of fa c to r s fo r ro ta tio n w ou ld be th e n u m b er o f fa c t o r s h y p o th e s iz e d by th e s e ju d g m en ts, th is b ein g th e c ru x o f the stu d y . To e n s u r e that th e ju d g m en ts w ould h a v e a g r e a t d ea l of r e lia b ility and a 33 m a x im u m am ount o f e x p e r tis e , th r e e r e v ie w e r s w e r e c h o se n . T h ey w e r e the p r e s e n t au th or. D r . J . P , G u ilfo rd , and D r . R alph H o ep fn er. T he l a s t tw o r e v ie w e r s w e r e c o n sid e r e d the a u th o r itie s on th e S tr u c tu r e -o f-I n te lle c t, both h avin g had a g r e a t d e a l o f e x p e r ie n c e and k n o w led g e of th e e n tir e fie ld of fa c to r a n a ly s is . E ach r e v ie w e r in d ep en d en tly judged th e fa c to r ia l c o m p o sitio n o f the t e s t s fr o m e a ch o f the e ig h t s tu d ie s . T h e se ju d g m en ts w e r e e s s e n t ia lly q u a lita tiv e , althou gh a d is tin c tio n w a s m ad e b etw een p r im a r y and se c o n d a r y fa c to r c o m p o s itio n s . T he p u b lish ed d e s c r ip tio n s o f the t e s t s w e r e u s e d a s th e b a s is fo r th is fa c to r a s s ig n m e n t. A fte r a ll the r e v ie w e r s w e r e fin ish e d w ith th e t e s t a ss ig n m e n t fo r a ll the s tu d ie s , the r e s u lt s w e r e su b m itted fo r a d ju d ica tio n . T he p r o c e s s o f a d ju d ica tio n w a s con d u cted in th e fo llo w in g m a n n e r . T h e d is c r e p a n c ie s in ju d g m en ts w e r e n o ted . T he d e s c r ip tio n s o f t e s t s w e r e r e v ie w e d o n c e a g a in by a ll r e v ie w e r s . T hen a m u tu a lly s a tis fa c to r y ju d gm en t w a s m a d e . T h e s e a d ju d ica ted fa c to r id a s s ig n m e n ts can be found in th e A p p en d ix. T h e a d ju d ica ted ju d g m en ts w e r e u s e d to d e te r m in e w h ich S tr u c t u r e - o f -ln te lle c t fa c to r s w e r e p r e s e n t in ea ch stu d y. In a d d i tio n , fo r e a c h o f th e s e f a c to r s , it w a s n oted how m an y t e s t s w e r e p r e d ic te d to d e fin e it u n iv o c a lly o r in a se co n d a r y fa sh io n . A t th is p oin t a d e c is io n w a s m ad e to e lim in a te a ll t e s t s fr o m s ta t is t ic a l a n a ly s is w h ich f e ll into any o f th e fo llo w in g c a te g o r is : (1) a n o n in te lle c tu a l m e a s u r e , su ch a s w ork in g sp eed o r a g e , (2) fa c to r ia lly c o m p le x in te r m s o f th e S tr u c tu r e - o f- ln te lle c t fa c to r s , and (3) m e a s u r e d a S tr u c tu r e -o f-ln te lle c t fa c to r th at did not have at l e a s t 34 o n e o th e r pu re m e a s u r e p r e d ic te d fo r it, and (4) w a s an a lte r n a tiv e fo r m o f an o th er t e s t in th e battery* T he n o n -in te lle c tu a l m e a s u r e s w e r e e lim in a te d b e c a u se it w as fe lt that th e s e had no p la c e w ith in th e S tr u c tu r e -o f-I n te lle c t m o d e l and w e r e not w ith in th e sc o p e or p u r p o se of th e stu d y . F a c to r la lly c o m p le x t e s t s w e r e e lim in a te d b e c a u se it w a s fe lt that th ey cou ld not len d unique su p p ort to the d e fin itio n o f th e fa c to r s in v o lv ed and th e r e fo r e cou ld on ly s e r v e to c o n fu se the o u tc o m e . T he la s t r e s tr ic t io n w a s ig n o r e d b e c a u se if a t e s t w a s in clu d ed in th e a n a ly s is a s a s in g le t, it cou ld h a r d ly be id e n tifie d a s a S tr u c tu r e - o f- ln t e lle c t fa c to r . T hat i s , if th e t e s t d efin e d a fa c to r by it s e lf In the r e s u lt s , id e n tify in g it a s anyth ing o th e r than a s in g le t w ou ld be m e a n in g le s s . A p p lica tio n of th e s e c r it e r ia to th e e ig h t stu d ie s le d to a s u b sta n tia l red u ctio n in th e n u m b er o f t e s t s to a c tu a lly u n d ergo a n a ly s is . T a b le 1 co n ta in s the n a m e s o f the t e s t s fr o m ea ch study that w e r e r e ta in e d fo r a n a ly s is and th e ir p r e d ic te d fa c to r ia l c o m p o sitio n . T ab le 2 s u m m a r is e s the p r e d ic te d f a c to r s , th e stu d ie s in w h ich th ey w e r e r e p r e se n te d and th e to ta l n u m b er of t e s t s p r e d ic te d fo r e a ch fa c to r . A s show n by th is ta b le , 26 s e p a r a te S t r u c t u r e -o f- ln t e lle c t a b ilitie s w e r e p r e d ic te d to e x is t in th e s e eig h t s tu d ie s . H a lf o f th e s e fa c to r s w e r e found in o n ly on e stu d y. In th e s e c a s e s e v e r y a ttem p t w a s m ad e to h a v e at l e a s t th r e e t e s t s h y p o th e sise d fo r that fa c to r . T h e r e w e r e th r e e e x c e p tio n s to th is r u le and in th is c a s e the a ttem p t w a s d e c id e d to be m ad e b e c a u se th e fa c to r s in v o lv ed w e r e o f an in te r e s tin g n a tu re . 35 S ta tis tic a l A n a ly se a T he p u b lish ed c o r r e la tio n m a tr ic e s fr o m e a ch of the e ig h t stu d ie s w e r e red u ced by e lim in a tio n o f the row and co lu m n o f any t e s t that w a s to be ex clu d ed fr o m the a n a ly s is . T h e se m a t r ic e s a r e r e a d ily a v a ila b le in th e p u b lish ed stu d ie s and a r e th e r e fo r e not in clu d ed in th e body of th is stu d y. In se v e n o f the stu d ie s th e s e m a tr ic e s w e r e c o m p o se d o f P e a r s o n p r o d u ct-m o m e n t c o r r e la tio n c o e ffic ie n ts . T h u rston e*s PM A study w a s the on ly e x c e p tio n to th is . T h e m a tr ix fr o m th is study had a s e n tr ie s th e te tr a c h o r ic c o r r e la tio n c o e ffic ie n t. T h is c o e ffic ie n t w a s u s e d by T h u rsto n e fo r co m p u ta tio n a l c o n v e n ie n c e . H o w ev er, th is c o e ffic ie n t d o e s not n e c e s s a r ily uphold th e G ram m ian p r o p e r tie s o f the c o r r e la tio n m a tr ix r e q u ir e d fo r fa c to r a n a ly s is . T h is poin t w ill b e c o m e im p o rta n t la t e r in th is d i s c u s s io n . E ach c o r r e la tio n m a tr ix w a s su b m itted to a fa c to r a n a ly s is Z co m p u ter p r o g r a m , BMDX7Z (D ixon, 1969). O ne of the fe a tu r e s o f th is p r o g r a m w a s the in te r n a l ite r a tio n of co m m u n a lity e s t im a t e s . In itia l co m m u n a lity e s tim a te s to be u sed by the p r o g r a m w e r e the sq u a red m u ltip le c o r r e la tio n c o e ffic ie n ts . O btained c o m m u n a litie s w e r e ite r a te d u n til th e r e w a s no d iffe r e n c e la r g e r than .0 1 b etw een on e ite r a tio n and th e n e x t, thu s g iv in g a high d e g r e e o f sta b ility . T he p r o g r a m th en p rod u ced the p r in c ip a l a x e s fo llo w in g th e stan d ard r o o ts and v e c to r p r o c e d u r e . T he n u m b er o f fa c to r s to be e x tr a c te d w a s s p e c ifie d by the a u th o r. In a ll c a s e s , th e n u m b er w a s d e te r m in e d by th e n u m b er o f ^ F o r s ta tis tic a l a n a ly s is , co m p u ter a s s is t a n c e w a s ob tain ed fr o m the U n iv e r sity C om puting C en ter at th e U n iv e r sity o f S o . C a lif. 36 h y p o th e sise d f a c t o r s . T h is i s the sa m e p r o c e d u r e a s w a s u s e d by A R P and by G u ilfo rd & H oep fn er (1 9 7 1 ), w h e r e a fu lle r d is c u s s io n m ay be foun d. T h is p r o c e d u r e w a s u s e d h e r e b e c a u se it w a s fe lt that at the p r e s e n t tim e th e r e d o e s not e x is t any to ta lly ad eq u ate m eth o d fo r d e te r m in in g th e n u m b er o f fa c t o r s . T h is b e c a m e e s p e c ia lly a p p a ren t in an u n p u b lish ed study con d u cted by the p r e s e n t au th or (D o h erty , 1971). T h is study p e r fo r m e d a M onte C a r lo c o m p a r iso n o f nin e m eth o d s o f d e ter m in in g th e n u m b er o f f a c to r s . T he r e s u lts sh ow ed that none o f the m eth o d s had a high d e g r e e o f a c c u r a c y o r c o n s is te n c y . T h e r e fo r e , the n u m b er o f fa c to r s w a s the n u m b er o f h y p o th e siz e d fa c to r s in th e stu d y. T h e p r in c ip a l a x e s w e r e su b m itted to a r o ta tio n u tiliz in g a co m p u ter p r o g r a m b a sed upon the ro ta tio n a l m eth od d e v e lo p ed by C liff (1 9 6 6 ). T h is p r o c e d u r e c o n s is t s of an o rth o g o n a l ro ta tio n o f the p r in c ip a l a x e s to a le a s t - s q u a r e s fit w ith th e h y p o th e tic a l ta r g e t m a tr ix . The in itia l ta r g e t m a tr ix fo r e a ch study w a s c o m p o se d o f r o w s (v a r ia b le s) w h ich had on ly one n o n -z e r o lo a d in g . T h is lo a d in g w a s th e sq u a r e ro o t o f the t e s t 's co m m u n a lity , its to ta l v e c to r le n g th , and w a s a s s ig n e d to th e fa c to r foT w h ich th e t e s t w a s h yp o th e s iz e d . C o m p u ta tio n a lly , th is p r o c e d u r e lo o k s fo r a tr a n sfo r m a tio n m a tr ix w ith w h ich to p r e m u ltip ly th e p r in c ip a l fa c to r m a tr ix to m ak e a b e s t e s tim a te o f th e ta r g e t m a tr ix in a le a s t - s q u a r e s s e n s e . T he b e s t e s tim a te is d efin ed a s that m a tr ix w h e r e ro w s a r e m a x im a lly c o llin e a r w ith th o se o f th e ta r g e t. T h is m a x im iz a tio n can be p e r fo r m e d through u s e o f th e E ck h a rt-Y o u n g th e o r e m . S p e c ific a lly , th e 37 d e s ir e d tr a n sfo r m a tio n m a tr ix is the p rod u ct o f th e e ig e n - v e c t o r s of v a r io u s p ro d u cts o f the e m p ir ic a l fa c to r m a tr ix and th e ta r g e t to g e th e r w ith th e ir tr a n s p o s e s . F o llo w in g th e in itia l ro ta tio n of p r in c ip a l fa c to r s to the ta r g e t, d is c r e p a n c ie s w e r e n o ted and a d ju stm e n ts m ad e in th e ta r g e t m a tr ix . T h e p r o c e d u r e of a d ju stm en t w a s con d u cted fo r e a c h o f th e a n a ly s e s u n til a r ea so n a b le fit w a s r ea c h e d b etw een th e ta r g e t and th e p r in c ip a l fa c to r s . At th is p oin t, s m a ll g r a p h ic a l r o ta tio n s w e r e p e r fo r m e d u su a lly in an attem p t to in c r e a s e p o s itiv e m a n ifo ld and sim p le s tr u c tu r e . T h e r e s u lts of th e s e r o ta tio n s a r e the e v id e n c e s fo r p s y c h o lo g ic a l fa c to r ia l in v a r ia n c e and a r e r e p o r te d in th e fo llo w in g s e c tio n . C H A P T E R HI R E SU L T S T h e S tu d ies T h e r e s u lt s o f the ju st d e s c r ib e d r o ta tio n a l p r o c e d u r e s w ill be p r e s e n te d in th is s e c tio n . E a ch of the stu d ie s w ill be p r e se n te d s e p a r a te ly . F o r e a c h stu d y, th e r e s u lts of e a ch h y p o th e sise d fa c to r w ill be p r e se n te d and d is c u s s e d . T h e s e r e s u lts w ill co n ta in th o s e t e s t s w h ich had a sig n ific a n t lo a d in g on th e fa c to r . T r a d itio n a lly , a fa c to r lo a d in g h a s b een c o n sid e r e d to be sig n ific a n t if it w a s . 30 o r g r e a t e r . T h is w ill be fo llo w ed in th e r ep o rtin g o f th e s e r e s u lt s . In p la c e s w h er e th e r e a r e sig n ific a n t lo a d in g s fo r t e s t s that w e r e not h y p o th e siz e d , ex p la n a tio n s w ill be o ffe r e d . B e c a u se o f its p la c e a s a m o tiv a tin g fo r c e fo r th is stu d y, T h u rsto n e* s P r im a r y M en tal A b ilitie s study w ill be p r e s e n te d f ir s t . T h u rsto n e: P r im a r y M en tal A b ilitie s F o llo w in g a p p lic a tio n o f th e t e s t s e le c tio n c r it e r ia , th e o r ig in a l T h u rsto n e (1938) 57 x 57 c o r r e la tio n m a tr ix w a s red u c ed to 30 v a r ia b le s . E ach of th e s e 30 v a r ia b le s w as h y p o th e siz e d to d efin e one o f 11 S tr u c tu r e -o f-I n te lle c t a b ilitie s w h ich w e r e thought to be r e p r e s e n te d in the b a tte r y . The c o r r e la tio n m a tr ix w a s su b m itted to th e sta n d a rd fa c to r a n a ly s is co m p u ter p r o g r a m and 11 p r in c ip a l f a c to r s w e r e e x tr a c te d . Due to th e n o n -G ra m m ia n p r o p e r tie s o f th is c o r r e la tio n m a tr ix , th r e e v a r ia b le s w e r e found to h a v e c o m m u n a litie s 38 39 g r e a te r than u n ity . T he th r e e v a r ia b le e a r e C ode W ords (v a r ia b le 19), N u m b e r -N u m b e r t e s t (v a r ia b le 23) and V o ca b u la ry (v a r ia b le 3 0 ). It is b e lie v e d that th e s e a b n o rm a l c o m m u n a lItie s a r o s e out o f the u s e by T h u rsto n e of the te tr a c h o r ic c o r r e la tio n c o e ffic ie n t w h ich d o e s not g u a ra n tee th e G ram m lan p r o p e r tie s r e q u ir e d fo r the u se o f fa c to r a n a ly s is . B e fo r e ro ta tio n th e p r in c ip a l fa c to r lo a d in g s o f th e s e th r e e v a r ia b le s w e r e r e s c a le d so th a t e a ch c o m m u n a lity w a s u n ity . T h is n ew p r in c ip a l fa c to r m a tr ix w a s su b m itted to a s e r i e s o f ta r g e te d r o ta tio n s w ith th e in itia l ta r g e t m a tr ix h avin g n o n -a e r o lo a d in g s o n ly w h er e th e t e s t w a s h y p o th e sise d to m e a s u r e that fa c to r . T h e se in itia l ta r g e t lo a d in g s w e r e th e sq u a re r o o ts o f the co m m u n a l i t ie s . A fte r th r e e su ch r o ta tio n s, in c o r p o r a tin g m in o r a d ju stm e n ts in th e ta r g e t m a tr ix e a c h tim e , a so lu tio n w a s r e a c h e d w h ich w a s r e a s o n a b le . T h is so lu tio n w a s then su b je c te d to a s e r i e s o f s e v e n g r a p h ic a l r o ta tio n s to in c r e a s e th e p o s itiv e m a n ifo ld and sim p le str u c tu r e . T h is p r o c e d u r e o f g r a p h ic a lly ro ta tin g w a s u s e d in a ll the fo llo w in g stu d ie s and fu r th e r m en tio n o f th is w ill not be m a d e . T he r e su ltin g so lu tio n fo r th e P r im a r y M en tal A b ilit ie s study is p r e s e n te d in T a b le 3. CM U - C o g n itio n o f S e m a n tic U n its 3 0 . V o ca b u la ry (CM U) . 75 .3 4 (DM R) 1. R ea d in g II (CM U) .5 2 .3 1 (EM I) T h e CM U fa c to r i s d efin ed a s th e a b ility to co m p re h e n d th e m e a n in g s o f w o r d s and id e a s . It is ty p ic a lly m a rk ed by v o c a b u la r y t e s t s . Both o f the t e s t s h y p o th e sise d th e m e a s u r e m e n t o f th is 40 fa c to r a r e o f th is ty p e . The v o c a b u la r y te s t waa o b je c tiv e t e s t o f w ord m e a n in g s. R ead in g II req u ire d m a tch in g 2 sta te m e n ts w ith th e m ea n in g o f a g iv en q u otation . T he sig n ific a n t se co n d a r y lo a d in g o f th is t e s t on EM I i s not too s u r p r is in g , EM I i s u su a lly m a rk ed by t e s t s that r e q u ir e ju d gm en t o f ad eq u acy o f a m ea n in g fu l d ed u ction . T he m a tch in g p r o c e s s in th e p r e s e n t t e s t i s o f a s im ila r n a tu re . T he lo a d in g o f th e v o c a b u la r y t e s t on the DM R fa c to r s e e m s to in d ic a te that p e r fo r m a n c e on th is te s t r e q u ir e s the p rod u ction of se m a n tic r e la tio n s . T h is cou ld be b e c a u s e of the high d e g r e e o f d ifficu lty of th e Ite m s o f th is t e s t . T h is t e s t is a ls o one that w a s r e s c a le d and it cou ld be th e r e s u lt o f a sp u r io u sly high c o r r e la tio n . CMC - C ogn ition o f S em a n tic C la s s e s 2. V erb a l C la s s ific a tio n (CM C) .6 7 ,3 1 ( C F T ) 3 . W ord G rou ping (CM C) .6 6 .3 4 (DMR) 2 0 . S y llo g is m s (EM I) .3 3 ,4 7 (C F T ), . 30 (EM I) T h is fa c to r is d efin ed a s th e a b ility to r e c o g n is e co m m o n p r o p e r tie s o f w o r d s, id e a s and o b je c ts . T he two t e s t s that w e r e h y p o th e siz e d fo r th is a b ility do lo a d h ig h ly on th is fa c to r . The V erb a l C la s s ific a tio n t e s t r e q u ir e d tie e x a m in e e to p la c e t e s t w o rd s into one o f 2 c a te g o r ie s . T h is te s t a ls o h a s a sig n ific a n t lo a d in g on th e C F T fa c to r . T he r e a so n fo r th is is not im m e d ia te ly ap p aren t and m a y be due to e r r o r in the c o r r e la tio n s . W ord groupin g in v o lv e s the e x c lu s io n o f w o r d s fr o m c a te g o r ie s . T he lo a d in g o f th is t e s t on DM R is r e a s o n a b le . T he e x a m in e e is in v o lv ed w ith p ro d u cin g r e la tio n s h ip s b etw een th e fiv e w o r d s in o r d e r to fin d th e on e w o rd to e x c lu d e . T he s y llo g is m s te s t r e q u ir e s th e su b je ct to in d ic a te w h eth er 41 o r not a s y llo g is m i s c o r r e c t in its m e a n in g . T h is t e s t should m e a s u r e EM I. but m a y con tain c la s s v a r ia n c e fr o m the c la s s ify in g p r o c e d u r e of jud ging w h eth er o r not th e m ea n in g is c o r r e c t . DM R - D iv e r g e n t P ro d u ctio n o f S em a n tic R e la tio n s 4 . C o n tro lled A s s o c ia tio n s (DMR) .6 3 7. In ven tive S yn on ym s (DMR) . 58 . 36 (DSU) 22. In itia ls (MSI) . 55 .4 7 (MSI) 5. In ven tive O p p o site s (DMR) . 52 .3 5 (CSU) 6 . D isa r r a n g e d W ords (CSU) . 38 .6 3 (CSU) 3. W ord G rouping (CM C) .3 4 . 66 (CM C) 30. V ocab u lary (CMU) . 34 . 75 (CMU) T he a b ility to p ro d u ce m any r e la tio n sh ip s a p p ro p ria te in m ea n in g to a g iv en id ea is c a lle d DM R. In th is b a ttery th r e e t e s t s w e r e h y p o th e siz e d to be DM R m e a s u r e s . A ll th r e e o f th e s e t e s t s had th e ir m a jo r lo a d in g on th is fa c to r . In ven tive S yn onym s and In v en tiv e O p p o site s, w h ile havin g th e ir m a jo r lo a d in g on DM R, had sig n ific a n t se co n d a r y lo a d in g s on the CSU fa c to r . T h is is p rob ab ly due to th e s im ila r ity in str u c tu r e o f th is t e s t w ith th o se w h ich d efin e the CSU fa c to r . T he in itia ls t e s t is a p a ir ed a s s o c ia t e s t e s t w h ich r e q u ir e s the su b je c t to m e m o r iz e n a m e s p a ir e d w ith in itia ls . Its lo a d in g on DMR is so m ew h a t u n c le a r , u n le s s the ta s k w a s so e a s y that it b eca m e e s s e n t ia lly a p ro d u ctio n ta s k . D isa r r a n g e d W ords is a CSU t e s t w h ich h a s an e le m e n t o f flu e n c y in it that cou ld p o s s ib ly have c a u se d the lo a d in g o f th is t e s t on the DM R fa c to r . T h e W ord G roup ing and V o ca b u la ry t e s t s have a lre a d y b een d is c u s s e d . 42 CSU - C ogn ition o f S y m b o lic U n its 6 . D isa r r a n g e d W ords (CSU) .6 3 .3 8 (DM R) 29. S p ellin g (CSU) . 56 5. In ven tive O p p o site s (DM R) .3 6 . 59 (DM R) 7. In ven tive S yn on ym s (DM R) . 35 . 52 (DM R) 8. C u b es (C FS) .3 3 .4 7 (C FS) .5 1 (C F T ) Tw o t e s t s w e r e p r e s e n t in th e PM A b a ttery w h ich fit th e d e fin i tio n o f CSU. T h ey both r e q u ir e d th e su b je ct to r e c o g n iz e g ra p h ic sy m b o lic u n its, su ch a s w o r d s. D isa r r a n g e d W ords r e q u ir e s the su b je ct to c o r r e c tly r e a r r a n g e le t t e r s to fo r m a w ord . Its lo a d in g on DMR h a s b een d is c u s s e d a b o v e. S p ellin g is a t r u e - f a ls e t e s t w h ich r e q u ir e s r e c o g n itio n o f c o r r e c t s p e llin g . T o g e th e r th e s e tw o t e s t s d efin e CSU in th is b a tte r y , a s in tw o stu d ie s r e p o r te d by G u ilford and H oep fn er (1 9 7 1 ). T he p r e s e n c e of In ven tive S yn on ym s and In ven tive O p p o site s on th is fa c to r w a s d is c u s s e d a b o v e. C u b es i s a sp a c e te s t w h ich s p lit it s v a r ia n c e p r im a r ily b etw een C F S and C F T . T h is t e s t r e q u ir e s r e c o g n itio n o f w h eth er two c u b e s a r e the sa m e o r d iffe r e n t fr o m m a r k in g s on th e f a c e s . Its lo a d in g h e r e i s not c le a r and m ay be due to sp u r io u s e r r o r in th e c o r r e la tio n s . C SF - C ogn ition o f F ig u r a l S y ste m s 10. F la g s (C F S, C F T ) . 75 . 59 (C F T ) 26. H ands (C FS) . 55 .3 4 (C F T ) 8. C u b es (C FS) .4 7 .5 1 (C F T ) .3 3 (CSU) 12. L o z e n g e s B (C F T , C FS) .3 4 . 58 (C F T ) 13. S u rfa c e D e v elo p m e n t (C F T ) .3 2 .6 3 (C F T ) O ne o f th e m a jo r e m p h a s e s in th e PM A b a ttery w a s the c o n ce n tr a tio n o f sp a c e t e s t s . T h u rsto n e found one sp a c e fa c to r . L a te r , 43 th e A rm y A ir F o r c e s (G u ilford & L a c e y , 1947) in v e s tig a tio n s s e p a r a te d two sp a c e fa c t o r s . T h e se tw o sp a c e fa c to r s w e r e in c o r - p o r a ted into th e S tr u c tu r e -o f-I n te lle c t a s the C FS and C F T fa c to r s . T h e C FS fa c to r is d efin ed a s the a b ility to co m p re h e n d a r r a n g e m e n ts and p o s itio n s o f v is u a l o b je c ts in sp a c e . T h e C F T fa c to r is d efin ed a s th e a b ility to v is u a liz e how a fig u r e o r o b je c t w ill ap p ea r a fte r g iv en c h a n g e s, su ch a s u n fold in g o r r o ta tio n . T h e se tw o fa c to r s h ave had a h is to r y of sh a rin g t e s t s and c o m p le te se p a r a tio n o f t e s t s fo r th e tw o fa c to r s h a s r a r e ly b een a c h ie v e d . The sp a c e t e s t s in th is study w e r e thought to in clu d e so m e C F S t e s t s , so m e C F T t e s t s , and so m e t e s t s that h ave both. T h e e ffe c ts o f th is sh a r e d v a r ia n c e m ay be s e e n in th e p r e se n te d r e s u lt s . It s e e m s fa ir ly o b v io u s that th e s e fa c to r s a r e ob liq u e at th is p o in t. W hile th is is c o n tr a r y to the p r o c e d u r e s e m p lo y e d , it is not c o n tr a r y to th e o r ig in a l h y p o th e sis of sh a r e d v a r ia n c e . The th r e e t e s t s th at w e r e e ith e r e n tir e ly C F S o r p red o m in a n tly C FS le a d th e fa c to r . T he F la g s t e s t r e q u ir e s th e e x a m in e e to d e te r m in e w h eth er two p ic tu r e s of an A m e r ic a n fla g sh ow th e sa m e o r o p p o site f a c e s o f the fla g . T he H ands te s t a sk e d th e su b je c t to exarrine p ic tu r e s o f han ds and to m ark w h ich r e p r e s e n te d a righ t hand and w h ich a le f t hand. C u b es r e q u ir e s id e n tific a tio n o f w h eth er o r not tw o p ic tu r e s o f a cube a r e th e sa m e cu b e o r n ot. F la g s w e r e h yp o th e s iz e d to h ave C F T v a r ia n c e a ls o and it d o e s . The lo a d in g s o f H ands and C u b es on th e C F T sh ou ld not be too su r p r isin g fo llo w in g th e ab ove d is c u s s io n . T h eir p r e s e n c e m ay a ls o be due to th e o v e r - 44 w h elm in g str e n g th o f th e C F T fa c to r w h ich had fiv e v e r y str o n g m a r k e r s le a d in g on it. L o z e n g e s B and S u rfa ce D e v e lo p m e n t a r e fo r C F T . L o z e n g e s B w as h y p o th e siz e d to h ave so m e C FS v a r ia n c e p r e s e n t. T he r e a s o n fo r S u rfa c e D e v elo p m e n t h avin g a sig n ific a n t lo a d in g h e r e i s unknown but not d istu r b in g . C F T - C o g n itio n o f F ig u r a l T r a n sfo r m a tio n s 14. P u n ch ed H o le s (C F T ) . 82 . 4 0 (CSS) 11. F o r m B oard (C F T ) . 73 13. S u rfa ce D e v elo p m e n t (C F T ) .6 3 .3 2 (C FS) 9. L o z e n g e s (C F T ) .6 0 10. F la g s (C F S, C F T ) . 59 , 75 (C FS) 12. L o z e n g e s B (C P T , C F S) .5 8 . 34 (C FS) 8. C u bes (C FS) .5 1 .4 7 (C F S) 20. S y llo g is m s (EM I) .4 7 .3 3 (CM C) . 30 (EM I) 15. A r e a s (CSS) .4 5 19. C ode W ords (CSS) . 38 . 78 (CSS) 26. H ands (C FS) .3 4 . 55 (C FS) 2 . V erb a l C la s s ific a tio n .3 1 .6 7 ( CMC) T h is fa c to r h a s been d efin ed in th e p r e v io u s s e c tio n . T he r e s u lts sh ow th at th e two fa c to r s m a y be se p a r a te d , althou gh w e a k ly . T he F o r m B oard te s t and L o z e n g e s a r e c le a r and u n iv o c a l m a r k e r s o f th is fa c to r . T h e se c o n d a r y lo a d in g s o f the o th e r C F T t e s t s on C FS h a v e b een d is c u s s e d a s h ave the C FS t e s t s . T h e se co n d a r y lo a d in g o f P u n ch ed H o le s on CSS m ay in d ic a te that th e c o m p le x ity o f th is t e s t i s su ch that sy m b o lic a b ilitie s m a y c o m e in to p la y . T he lo a d in g o f C ode W o rd s, a CSS t e s t , on th is fa c to r m a y be th e r e s u lt o f a str o n g fa c to r d ra g g in g o th e r t e s t s w ith it. A r e a s w a s h y p o th e siz e d a s a CSS t e s t , the ta s k i s to d e te r m in e th e to ta l w h ite a r e a in a b la ck and w h ite ru led sq u a r e . It s e e m s q u ite r e a so n a b le that v is u a liz a tio n m ig h t p la y a p a rt h e r e . 45 V erb a l c la s s if ic a t io n 's lo a d in g on th is fa c to r w a s d is c u s s e d in th e s e c tio n c o n c e r n in g th e CMC fa c to r . T he S y llo g is m s t e s t h a s no r e a l r e a so n fo r b ein g on th is fa c to r . T he lo g ic a l r e a so n fo r its lo a d ing can n ot be e x p la in e d . F r o m the p u b lish ed d e s c r ip tio n o f th is t e s t , it i s a ty p ic a l EM I te s t , y e t it c o r r e la t e s h ig h ly w ith the v is u a liz a tio n t e s t s . It m a y be a s T h u r sto n e s u g g e s ts that so m e p e o p le v is u a liz e d th e ir s y llo g is m s . CSS - C ogn ition o f S y m b o lic S y s te m s T h is fa c to r i s d e fin e d a s the a b ility to u n d e rsta n d th e s y s t e m a tic I n te r r e la te d n e s s o f sy m b o ls w ith in an o r g a n iz e d s e t . C ode W ords r e q u ir e s th e su b je c t to s o lv e a c o d e and m a tch th e c o d ed w o r d s w ith th e ir E n g lish e q u iv a le n ts. It c le a r ly le a d s th e fa c to r , though it h a s a se co n d a r y lo a d in g on the C F T fa c to r . Nv\m h*r S e r ie s r e q u ir e d th e su b je ct to d e te r m in e th e r u le fo r a p r e se n te d n u m b er s e r i e s and to add th e n ex t tw o n u m b e r s in th e s e r i e s . W hile le a v in g it s m a jo r lo a d in g on it s h y p o th e siz e d fa c to r , it h a s a s m a ll s ig n ific a n t lo a d in g on E M I. T he EM I fa c to r is a lo g ic a l r e a so n in g fa c to r and m a y c o m e in to p la y h e r e if the su b je c t t r i e s to d e te r m in e th e a d eq u a cy o f h is c o n c lu sio n is to th e r u le fo r th e s e r i e s . T h e N u m b e r -N u m b e r te s t i s a m e m o r y te a t, w h e r e th e su b je ct le a r n s p a ir s o f two d ig it n u m b e r s . L a te r he m u st p ro d u ce th e c o r r e c t tw o d ig it n u m b er w hen p r e s e n te d w ith the o th e r two d ig it n u m b er. It is p o s s ib le that CSS e n te r s into th e o r g a n iz a tio n a l 19. C ode W ords (CSS) 16. N u m b er S e r ie s (CSS) 14. P u n ch ed H o le s (C F T ) 23. N u m b e r-N u m b e r (MSI) 15. A r e a s (CSS) . 78 .3 8 (C F T ) .4 3 .3 2 (EM I) .4 0 .8 2 (C F T ) .3 5 .9 0 (MSI) .2 1 .4 5 (C F T ) 46 a s p e c ts o f m e m o r iz in g and r e c a llin g th e m a ter ia l* T h e A r e a s t e s t w a s h y p o th e siz e d a s a CSS t e s t , althou gh th is p r e d ic tio n w a s not p o s itiv e . A s th e r e s u lts in d ic a te , th e t e s t lo a d s s o le ly on th e C F T fa c to r . It s e e m s r e a so n a b le in r e tr o s p e c t that the p r im a r y r e q u ir e m e n t in th is t e s t w ould be to v is u a liz e in o r d e r to d e te r m in e the am oun t o f w h ite . EM I - E v a lu a tio n o f S em a n tic Im p lic a tio n s 17. R e a so n in g (EM I) .8 4 18. F a ls e P r e m is e s (EM I) .6 5 16. N u m b er S e r ie s (CSS) .3 2 .4 3 (CSS) 1. R ead in g II (CM U) .3 1 .5 2 (CM U) 20. S y llo g is m s (EM I) .3 0 .4 7 (C F T ) . 33 (CM C) T h is fa c to r is d efin ed a s th e a b ility to d e te r m in e th e ad eq u acy o f a m ea n in g fu l d ed u ctio n . H is to r ic a lly it h a s b een m a rk ed by lo g ic a l r e a so n in g t e s t s . In th is c a s e . R ea so n in g and F a ls e P r e m is e s both c le a r ly and u n iv o c a lly m e a s u r e the fa c to r . B oth o f th e s e t e s t s r e q u ir e th e su b je c t to d e te r m in e w h eth er c o n c lu s io n s a r e c o r r e c t o r w h eth er the r e a so n in g is a d eq u a te. T he se c o n d a r y lo a d in g s o f N u m b er S e r ie s and R ead in g I h ave b een e x p la in ed in th e a p p ro p ria te s e c tio n s fo r th o se t e s t s . T he S y llo g is m s t e s t , w h ile h avin g a sig n ific a n t lo a d in g h e r e , can h a rd ly be r e fe r r e d to a s a m a r k e r fo r EM I. T he fa ilu r e o f th is t e s t h a s b een ta lk e d about p r e v io u s ly in c o n n e c tio n w ith th e C F T fa c to r . M SI - M em o ry fo r S y m b o lic Im p lic a tio n s 2 3 . N u m b e r -N u m b e r (MSI) .9 0 .3 5 (CSS) 2 1 . W ord -N u m b er (MSI) .4 8 2 2 . In itia ls (MSI) .4 7 . 55 (DM R) 47 T h is fa c to r is th e m o s t fre q u en tly o c c u r r in g in the stu d ie s a n a ly z e d in th is in v e s tig a tio n . It o c c u r s s ix t im e s . S p e c ific a lly , it i s the a b ility to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een s y m b o ls . In A R P in v e stig a tio n s it h a s been m a rk ed by t e s t s su ch a s N u m b er- L e tte r w h ich is a p a ir e d a s s o c ia t e s t e s t , p a ir in g n u m b e r s and l e t t e r s . In th e p r e s e n t stu d y , N u m b e r-N u m b e r and W o rd -N u m b er a r e v e r y s im ila r to th at t e s t . Both of th e s e t e s t s c le a r ly in d ic a te th e e x is te n c e o f M SI. T he In itia ls t e s t i s a p a ir e d a s s o c ia t e s t e s t of n a m e s and in it ia ls . W hile h avin g a str o n g lo a d in g on th is fa c to r , it a ls o h a s a s tr o n g e r lo a d in g on DM R. T he ex p la n a tio n o ffe r e d is th at th is ta sk m ay be so e a s y a s to r ed u c e m u ch of the m e m o r y and b e c a m e m o r e of a p ro d u ctio n t e s t . T he se c o n d a r y lo a d in g of the N u m b e r-N u m b e r t e s t h a s a lr e a d y b een d is c u s s e d . MMU - M em ory fo r S e m a n tic U n its 2 4 . W ord R e co g n itio n (MMU) . 80 2 8 . Sound G rouping (N F C ) .3 3 .6 3 (N FC ) 2 5 . P ic tu r e R e c a ll (MMU) . 22 T he M M U fa c to r r e p r e s e n ts th e a b ility to r e m e m b e r is o la te d id e a s o r w o rd m e a n in g s. T h is fa c to r w a s in clu d ed fo r a n a ly s is b e c a u se it w a s th e on ly tim e it a p p ea r e d in any of the eig h t s tu d ie s . U n fo rtu n a tely , the fa c to r did not e m e r g e w ith both m a r k e r t e s t s on it. W ord R e c o g n itio n d e fin e s w hat is e s s e n t ia lly a s in g le t. T h is te s t r e q u ir e s th e su b je c t to m e m o r is e 50 w o r d s and to r e c o g n is e th e m in a l i s t la t e r . T h e P ic tu r e D e ta il t e s t w a s h y p o th e siz e d fo r th is fa c to r . T h is t e s t c o n s is te d o f sh ow in g th e stu d en t a p ic tu r e w h ich w a s to be stu d ied . L a te r , q u e stio n s w e r e a sk e d about fe a tu r e s o f 48 th is p ic tu r e . T he r e s u lts in d ic a te that th is t e s t m u st m e a s u r e a fa c to r o th e r than on e in clu d ed fo r a n a ly s is . It is p o s s ib le that th is i s a M FU te s t . T he Sound G rouping t e s t h a s a sig n ific a n t se co n d a r y lo a d in g on th is fa c to r . E a ch ite m o f th is t e s t c o n s is t s of g rou p s o f fo u r w o r d s. T he e x a m in e e in d ic a te s w h ich w ord sou nd s d iffe r e n tly in rh y m e fr o m th e o th e r th r e e w o r d s. T he lo a d in g on th is fa c to r in d ic a te s the p r e s e n c e o f so m e m e m o r y fu n ctio n . P o s s ib ly , the su b je c t m u s t r e m e m b e r the sound o f the w ord a s he h e a r s th e o th e r w o r d s o f an ite m . N FC - C o n v erg en t P ro d u c tio n of F ig u r a l C la s s e s 2 7 . R hythm (N F C ) . 84 2 8 . Sound G rouping (N F C ) .6 3 .3 5 (MMU) T he e m e r g e n c e o f th is fa c to r i s on e of the p le a sa n t s u r p r is e s o f th is a n a ly s is . T h e N FC a b ility is d efin ed a s the a b ility to c la s s if y u n iq u ely o r c o n v e n tio n a lly ite m s o f fig u r a l in fo r m a tio n . T he two t e s t s h y p o th e siz e d to d e fin e th is fa c to r h a v e so m e unique fe a tu r e s . F ir s t of a ll, both t e s t s u s e w o rd s in th e ir it e m s , y e t th ey a r e h y p o th e s iz e d fo r a fig u r a l fa c to r . T h is i s b e c a u se th e im p o rta n t a s p e c t o f the te s ta is not the w o r d s o r th e ir m ea n in g , but r a th er th e ir so u n d s. G hilford (1967) in d ic a te s that so m e S tr u c tu r e -o f-I n te lle c t fa c to r s w ill have p a r a lle l a u d ito ry , v is u a l and ev en k in e s th e tic f a c t o r s . T he p r e s e n t fa c to r is an e x a m p le of an au d ito ry fig u r a l fa c to r . P r e v io u s ly , C F U -A and C S U -A h ave b een th e on ly a u d ito ry fa c to r s to be id e n tifie d . T h e se r e s u lt s in d ic a te the e x is t e n c e o f a n ew au d ito ry fa c to r , N F C -A . 49 In R hythm , th e su b je c t m u st in d ic a te w h ich o f fo u r d iffe r e n t lin e s o f p o etry had a rh yth m d iffe r e n t fr o m that o f the th r e e o th e r s g iv en w ith it. Sound G rouping r e q u ir e s the su b je c t to in d ic a te w h ich o f fo u r w o rd s sou n d s d iffe r e n tly in rh ym e fr o m th e o th e r th r e e . T h e se co n d a r y lo a d in g o f Sound G rouping h a s a lr e a d y b een d is c u s s e d . T h u rsto n e fc T h u rsto n e: F a c to r ia l S tu d ies o f In te llig e n c e T h e o r ig in a l study co n ta in ed 6 0 v a r ia b le s . A fte r a p p lic a tio n of th e p r e v io u sly m en tio n ed c r it e r ia , 26 t e s t s w e r e le ft fo r s ta tis tic a l a n a ly s is . T he 28 x 28 c o r r e la tio n m a tr ix w a s fa c to r a n a ly z e d and n in e fa c to r s w e r e h y p o th e siz e d and k ep t fo r r o ta tio n . L ik e the o th er stu d ie s th is m a tr ix w ent through a s e r ie s o f ta r g e te d r o ta tio n s fo llo w ed by a n u m b er o f s m a ll g r a p h ic a l r o ta tio n s. T he r e s u lts o f th e s e r o ta tio n s a r e found in T a b le 4 . E ach fa c to r fr o m th is ta b le w ill be p r e se n te d in tu rn . CSU - C ogn ition of S y m b o lic U n its T h is a b ility r e q u ir e s the su b je ct to s e e o r r e c o g n iz e fa m ilia r le t t e r co m b in a tio n s that c o m p r is e fa m ilia r w o r d s, w ith le t t e r s m i s s in g o r r e a r r a n g e d . T h is fa c to r h a s b een d efin e d by a n u m b er o f d iffe r e n t t e s t s . G u ilfo rd (1967) and G u ilford & H oep fn er (1971) p r e se n t a l i s t o f th e s e . F r o m the r e s u lts o f th e p r e s e n t a n a ly s is , it m ay be se e n th at th e r e is so m e co n fu sio n b etw een the CSU fa c to r 2 8 . W ord P u z z le r s (CSU) 14. In co m p le te W ords (CSU) .6 0 .4 4 (DSU) .5 8 2. M ir r o r R ead in g (CSU 2 6 . S u ffix e s (DSU) .4 7 .3 6 .5 4 (DSU) .3 3 . 50 (DSU) . 33 . 52 (DSU) 1. A n a g ra m s (CSU, DSU) 2 3 . R h ym in g W ords (DSU) 50 and th e DSU fa c to r . S om e o f th is co n fu sio n i s p rob ab ly due to the DSU t e s t s r e q u ir in g a c e r ta in am ount o f CSU fo r an ad eq u ate p e r fo r m a n c e . and to DSU h elp in g to a r r iv e at c o r r e c t c o g n itio n s in CSU t e s t s . T h is fa c to r ia l c o m p le x ity can be e lim in a te d by c a r e fu l t e s t c o n str u c tio n , but s in c e th is study w a s con d u cted w ith ou t r e g a r d to th e S tr u c tu r e -o f-I n te lle c t m o d e l, it is not to ta lly u n ex p ec ted to fin d m in o r co n fu sio n su ch a s the p r e s e n t c a s e . In fa c t, it sh ould be n oted that the t e s t A n a g ra m s w a s h y p o th e siz e d to m e a s u r e both f a c to r s , fo r th is r e a s o n . C F T - C ogn ition o f F ig u r a l T r a n sfo r m a tio n s T he C F T fa c to r is on e o f th e c le a r e s t and s tr o n g e s t fa c to r s found in the a n a ly s e s o f T h u rsto n e & T h u r sto n e . T he on ly t e s t s lo a d in g on th is fa c to r a r e o n e s h y p o th e siz e d fo r it, and th e r e is no co n fu sio n w ith o th e r f a c t o r s . T he t e s t s fo r th is fa c to r m e a s u r e d the fa c to r that T h u rsto n e c a lle d S p a ce . The C F T a b ility r e q u ir e s the su b je c t to v is u a liz e c h a n g e s o r r o ta tio n s in fig u r a l m a te r ia l. T h is fa c to r w as f ir s t is o la te d in th e A A F in v e s tig a tio n s (G u ilford fe L a c e y , 1947). It i s o ften found that th is fa c to r w ill be h ard to d iffe r e n tia te fr o m th e C FS fa c to r . T h is i s b e c a u se so m any o f the e a r ly sp a c e t e s t s r e q u ir e s both a b ilit ie s . T h is is e x a c tly w hat h ap pened in th e p r e s e n t in v e stig a tio n o f th e PM A a n a ly s is , a b o v e . It sh ou ld be noted th at th e s e t e s t s sh a r e so m e C FS v a r ia n c e . 3 . C a rd s (C F T ) 7. F ig u r e s (C F T ) 10. F la g s (C F T ) .7 9 .68 . 64 51 NM U - C o n v erg en t P ro d u ctio n o f S e m a n tic U n ite 18. P ic tu r e N am in g (NM U) .7 0 6 . F ig u r e N a m in g (NM U) .4 4 H is to r ic a lly th is fa c to r h a s b een a " la b e lin g 1 ' o r "nam ing" fa c to r . Both o f th e c u r r e n t t e s t s r e q u ir e the stu d en t to n am e p a r tic u la r o b je c ts . It is in te r e s tin g to n ote that w h ile both of th e s e t e s t s u s e fig u r a l s tim u li, th ey m e a s u r e a se m a n tic a b ility . O nce a g a in , w e h ave a c le a r and u n iq u ely d efin ed a b ility . E F U - E v a lu a tio n o f F ig u r a l U n its 5. F a c e s (E F U ) .5 1 13. Id en tica l P ic tu r e s (E F U ) .4 4 .4 2 (C FI) 19. P u r su it (C FI) .3 4 . 53 (C FI) T h is a b ility i s c o m p o se d o f co m p a rin g fig u r a l m a te r ia l w ith r e s p e c t to so m e c r ite r io n su ch a s id e n tity . T h is fa c to r h a s h is t o r i c a lly b een r eg a r d e d a s a sp e e d fa c to r , in fa c t it w a s la b e le d P e r c e p tu a l S p eed . It w a s found in T h u r sto n e 's (193 8) o r ig in a l stu dy and la t e r by C oom b s (1941) and B ech to ld t (1 9 4 7 ). T he d e fin itio n of th is fa c to r in th e S tr u c tu r e -o f-I n te lle c t d o e s not m ak e sp ee d an e s s e n t ia l in g r e d ie n t. A d e m o n str a tio n of E F U w ith o th e r than sp e e d e d t e s t s w a s a c c o m p lish e d in a study (H offm an, G u ilford , H oep fn er & D o h erty , 1968) con d u cted by the A p titu d es R e s e a r c h P r o je c t. In the p r e s e n t in v e stig a tio n th e r e is so m e c o n fu sio n b etw een E F U and C F I. T h is c o n fu sio n m ay be a r e s u lt of th e n a tu re of th is p a r tic u la r E F U fa c to r . T hat i s , a ll th e t e s t s on th is E F U a r e h ig h ly sp e e d e d , and the P u r su it t e s t o f C F I i s a t e s t w h ere sp eed is an im p o rta n t p a r t. 52 DSU - D iv e r g e n t P ro d u c tio n o f S y m b o lic U n its 8. F ir s t end L a st L e tte r s (DSU) 11. F o u r L e tte r W ords (DSU) 26. S u ffix e s (DSU) 2 3 . R h ym in g W ords (DSU) 1. A n a g ra m s (DSU. CSU) 2 8 . W ord P u z z le r s 67 59 54 .3 6 (CSU) 53 .3 3 (CSU) 50 .3 3 (CSU) 44 .6 0 (CSU) T h is fa c to r had fiv e t e s t s h y p o th e siz e d fo r it. A ll of th e s e t e s t s had th e ir p r im a r y lo a d in g s on th is fa c to r . It m a y be se e n that th e r e is so m e c o n fu sio n o f s e v e r a l t e s t s w ith C SU . T he n a tu re of th is c o m p le x ity w a s d is c u s s e d w ith the r e s u lts of that fa c to r . It sh ould be n oted that the top tw o t e s t s fo r th is fa c to r a r e u n iv o ca l t e s t s . By d e fin itio n , th is a b ility r e q u ir e s the p rod u ction o f m any d iffe r e n t sy m b o lic u n its that fit c e r ta in r e q u ir e m e n ts. C h a r a c te r is tic a lly , t e s t s fo r th is fa c to r r e q u ir e p ro d u ctio n o f w o r d s that fit s p e c ific r e q u ir e m e n ts . T h is fa c to r w a s c a lle d "W ord F lu en cy " by T h u r sto n e . M SI - M em o ry fo r S y m b o lic Im p lic a tio n s T h is fa c to r is d efin ed a s th e a b ility to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een s y m b o ls . Both t e s t s h y p o th e siz e d to m e a s u r e th is fa c to r , fit th is d e fin itio n . A s can be se e n fr o m the r e s u lts th is is a c le a r and u n iv o ca l fa c to r , w ith both te a ts lo a d in g on ly on th is fa c to r . W hile th e r e a r e o n ly tw o te s ta fo r th is fa c to r , fr o m th e s iz e and c la r ity o f th e ir lo a d in g s , th is fa c to r s e e m s to be fa ir ly w e ll d e fin e d . 9. F ir s t N a m e s (MSI) 27 . W o rd -N u m b er R e c a ll (MSI) . 57 .4 7 53 C S S- C ogn ition of S y m b o lic S y s te m s 15. L e tte r S e r ie s (CSS) 2 5 . S e c r e t W ritin g (CSS) 17. N u m b er P a tte r n s (CSS) 12. H igh N u m b ers (CSS) . 56 . 52 .4 3 . 37 T h is fa c to r is one o f the s tr o n g e s t and c le a r e s t to e m e r g e in th e a n a ly s is o f the T h u r sto n e & T h u rsto n e stu d y . F o u r t e s t s w e r e h y p o th e siz e d fo r th is fa cto r,w h ich is d efin ed a s th e a b ility to u n d e r stand s y s te m a tic in te r r e la te d n e s s of s y m b o ls w ith in an o r g a n iz e d s e t . T he t e s t s w h ich h a v e d efin ed th is fa c to r in stu d ie s con d u cted by A R P h ave b een o f tw o k in d s, e ith e r s e r i e s t e s t s o r d is c o v e r y - o f - a - s y s t e m t e s t . L e tte r S e r ie s is of the s e r ie s ty p e, w h ile H igh N u m b e rs, N u m b er P a tte r n s and S e c r e t W ritin g a r e of the o th e r ty p e. T h is fa c to r h a s a v e r y good d e fin itio n w ith a w id e range o f t e s t s and u n iv o ca l lo a d in g s . C F I - C ogn ition o f F ig u r a l Im p lic a tio n s T h is fa c to r i s d efin ed a s the a b ility to f o r e s e e the c o n se q u e n c e s in v o lv ed in fig u r a l p r o b le m s . Its h is to r y b e g in s in the A rm y A ir F o r c e stu d ie s w h ere it w a s d efin ed by M o r se typ e of t e s t s w hich r e q u ir e d v is u a l tr a in in g . In a study (H offm an , e t. a l. ) con d u cted by A R P , C FI w a s d efin e d so m ew h a t w ea k ly by t e s t s w h ich r eq u ire d e x tr a p o la tio n o f lin e s . In the p r e se n t stu d y, th e le a d in g t e s t s e e m s to have a slig h t con foun din g w ith on e o f the E F U t e s t s . T h is m a y be due to a sp e e d fa c to r in v o lv e d in both t e s t s . 19. P u r su it (C FI) 13. Id en tica l P ic t u r e s (E F U ) 16. M aze I (C FI) 53 . 34 (E F U ) 42 .4 4 (E F U ) 35 54 W hile th e C FI fa c to r m ay be sa id to e x is t in th is stu d y, not m uch co n fid e n c e can be p la c e d in its id en tity h e r e . CMU - C ogn ition of S em a n tic U n its 20. V ocab u lary (CM U) . 87 21 . S e n te n c e s (CM U) .8 3 24. S am e of O p p osite (CM U) . 75 22. P a r a g r a p h s (CM U) . 72 4 . C o m p letio n (CMU) . 72 O ne cou ld not doubt th e e x is te n c e of th is fa c to r . A ll fiv e t e s t s h y p o th e siz e d fo r it h ave u n iv o ca l lo a d in g s o f o v e r . 70. T h is is not too su r p r isin g a s CMU h a s a lw a y s been a stro n g fa c to r . In the T h u rsto n e a n a ly s e s it is the fa c to r r e fe r r e d to a s " V erb a l" . In te r m s o f the S tr u c tu r e -o f-I n te lle c t, it is d efin ed a s th e a b ility to c o m p r e hend th e m ea n in g s o f w o r d s o r id e a s . A d k in s fc L y e r ly : F a c to r A n a ly s is o f R ea so n in g T e s ts T h is study is a m o r e r e c e n t in v e stig a tio n of the fa c to r ia l a b ili t ie s of r e a so n in g . It fo llo w s th e T h u rsto n ia n tr a d itio n in it s s e le c tio n o f t e s t s , fa c to r s and p r o c e d u r e s . T he study em p lo y ed 66 v a r ia b le s , 65 of w h ich w e r e t e s t s . F o llo w in g a p p lic a tio n o f the p r e s e n t in v e s t i g a tio n 's c r it e r ia , the b a ttery fo r s ta tis tic a l a n a ly s is w a s red u c ed to 28 v a r ia b le s . N in e fa c to r s w e r e e x tr a c te d and r o ta te d . T he r e s u lts o f th is p r o c e s s a r e show n in T ab le 5. C F T - C ogn ition o f F ig u r a l T r a n sfo r m a tio n s 6 . F ig u r e s (C F T ) . 89 1. C a rd s (C F T ) . 72 23. S u rfa ce D e v elo p m e n t (C F T ) . 55 15. P a p e r F o ld in g (C F T ) .4 0 . 39 (C FR ) 20. S e r ie s (C FR ) .3 1 .5 3 (C FR ) 5. F ig u r e S e r ie s (CSS) . 30 .4 7 (CSS) .3 3 (C FR ) .3 1 (E F U ) 14. P a in ted B lo c k s (C F T ) . 16 .3 8 (CSS) .3 4 (DSU) 55 T o m a rk the Sp ace fa c to r of T h u rsto n e, A d k in s and L y e r ly e m p lo y ed m any o f the sa m e v is u a lis a tio n t e s t s . T he T h u rsto n ia n Space fa c to r , w h ich a c tu a lly e m p h a s is e d C FT m o r e than C F S, h as b een id e n tifie d w ith C F T . A s w a s se e n in both o f the p r e v io u sly d i s c u s s e d r e s u lt s , th is fa c to r ten d s to be v e r y stro n g in te r m s of th e num ber o f t e s t s lo a d e d on it. T he f ir s t th r e e t e s t s lo a d str o n g ly and u n iv o ca lly on th is fa c to r . H o w ev er, fr o m that poin t on, the p ic tu r e b e c o m e s m o r e m u d d led . T h is m ay be due to th e o v e r a ll str en g th o f C F T . A " str o n g ” fa c to r s o m e tim e s r o b s w e a k e r fa c to r s of v a r ia n c e . T he S e r ie s te s t w h ich h a s a s m a ll but sig n ific a n t load in g on th is fa c to r is p red o m in a n tly a C F R te s t, but the s e r ie s w h ich the t e s t c o n ta in s r e q u ir e s a c e r ta in am ount of v is u a liz a tio n to c o m p le te th em . T he F ig u r e S e r ie s te s t w a s h y p o th e siz e d a s a CSS t e s t , but the r e s u lts in d ic a te a g r e a t d ea l o f c o m p le x ity in it w ith th r e e sig n ific a n t seco n d a ry lo a d in g s. Why th is te s t lo a d ed on th e C F T fa c to r is not c le a r , althou gh it m ay be due to a sm a ll am ount of v is u a liz a tio n n eed ed fo r ad eq u ate p e r fo r m a n c e in c o m p letin g th e s e r i e s . The P a in ted B lo c k s t e s t w a s h y p o th e siz e d fo r C F T , but it had it s s ig n i fica n t lo a d in g s on CSS and DSU. A s im ila r te s t . B lo ck V isu a liz a tio n , w a s found by A R P and th e A rm y A ir F o r c e to h a v e confoun din g w ith a g e n e r a l-r e a s o n in g a b ility . T he lo a d in g s o f P a in ted B lo c k s m ay in d ica te that so m e p eo p le u se d sy m b o lic a b ilitie s to so lv e the ite m s o f th is t e s t . CSS - C ogn ition of S y m b o lic S y s te m s 2. C ir c le s (CSS) .6 8 5. F ig u r e S e r ie s (CSS) .4 7 . 30 (C F T ) .3 3 (C F R ) .3 1 (E F U ) 9. L e tte r S e r ie s (CSS) .4 6 .3 5 (CM U) 10. M ixed S e r ie s (CSS) .4 6 .4 0 (C F R ) ,3 5 (CM U) 3 . D e co d in g (CSS) .4 5 .3 7 (CM U) 13. N u m b er S e r ie s (CSS) .4 5 .3 1 (C F R ) 14. P a in te d B lo c k s (C F T ) .3 8 .3 4 (DSU) 28. W ord S q u a r es (CMR) . 32 .6 3 (CM R) 8. Id en tica l F o r m s (E F U ) .3 1 .4 8 (E F U ) 26. V erb a l A n a lo g ie s (CM R) .3 1 . 52 (C F R ) .3 5 (CM R) .4 2 (CM U) 17. P r o g r e s s iv e M a tr ic e s (C FR ) . 30 .4 1 (C F R ) A s can be s e e n fr o m the lon g l i s t o f t e s t s lo a d in g on th is fa c to r , it is v e r y str o n g but c o n fu se d . A s w a s p r e v io u s ly m en tio n ed , th is fa c to r d e a ls w ith the a b ility to u n d erstan d th e s y s te m a tic in te r r e la te d n e s s o f s y m b o ls . C ir c le s , F ig u r e s S e r ie s and L e tte r S e r ie s a r e c la s s ic CSS t e s t s and in th e p r e se n t in v e stig a tio n do h a v e th e ir m a jo r lo a d in g s on th is fa c to r . T he F ig u r e S e r ie s te s t is h igh ly c o m p le x and h a s b een found in stu d ie s by A R P to b eh ave in a s im ila r fa sh io n . T he lo a d in g o f L e tte r S e r ie s on CM U, w h ile b ein g u n p r ed icte d , is not d iffic u lt to in te r p r e t. T h is t e s t r e q u ir e s the su b je c t to r e c o g n is e a ru le fo r o r g a n isin g le t t e r s and ex ten d th e s e r i e s . It i s q u ite p o s s ib le that th is w ould r e q u ir e a c e r ta in v o ca b u la ry s k ill. T h e t e s t M ixed S e r ie s w a s o r ig in a lly h y p o th e sise d to m e a s u r e C F R , h o w e v e r , the ite m s c o v e r the gam ut of con ten t and th u s th e lo a d in g on CSS and CMU is not u n r e a so n a b le . D ecod in g i s e s s e n t ia lly a CSS t e s t , but it r e q u ir e s d ecod in g of w o r d s and h en c e th e in v o lv em e n t w ith CM U, 57 N u m b er S e r ie s h a s a m in o r but sig n ific a n t lo a d in g on th e C F R fa c to r w h ich is not to ta lly r e a so n a b le but m ig h t be due to o v e r la p o f o th e r C F R t e s t s w ith th e CSS fa c to r . T he lo a d in g o f P a in ted B lo c k s t e s t h a s a lr e a d y been d is c u s s e d . T he W ord S q u a res te s t and V erb a l A n a lo g ie s t e s t a r e both CMR t e s t s w h ich have s m a ll lo a d in g s on th is fa c to r . T h e ir p r e s e n c e is p rob ab ly due to th e o v e r a ll str e n g th o f th e CSS fa c to r and a p o s s ib le s im ila r ity in fo r m a t. Id en tica l F o r m s h a s c h a r a c te r is tic a lly b een a m a r k e r t e s t fo r E F U . it s lo a d in g on th is fa c to r m ay be due to sh a re d v a r ia n c e w ith th e F ig u r e S e r ie s t e s t . P r o g r e s s iv e M a tr ic e s i s p r im a r ily a C F R t e s t w h o se p r e s e n c e m ay be due to o v e r a ll c o r r e la tio n of the C F R fa c to r w ith CSS. C FR - C ogn ition o f F ig u r a l R e la tio n s 20. S e r ie s (C FR ) . 53 .3 1 (C F T ) 26. V erb a l A n a lo g ie s (CM R) . 52 . 3 1 (CSS) . 35 (CM R) .4 2 (CM U) 4 . F ig u r e A n a lo g ie s (C F R ) .5 1 .4 1 (CM R) 17. P r o g r e s s iv e M a tr ic e s (C F R ) .4 1 . 30 (CSS) 16. P ic tu r e A n a lo g ie s (CMR) .4 1 . 28 (CM R) 10. M ixed S e r ie s (C FR ) .4 0 .4 6 (CSS) .3 5 (CM U) 15. P a p e r F o ld in g (C F T ) .3 9 .4 0 (C F T ) 5. F ig u r e S e r ie s (CSS) . 33 .4 7 (CSS) .3 1 (E F U ) . 30 (C F T ) 13. N u m b er S e r ie s (CSS) .3 1 .4 5 (CSS) C ogn ition of F ig u r a l R e la tio n s i s d efin ed a s the a b ility to r e c o g n iz e fig u r a l r e la tio n s b etw een fo r m s . A s m ay be s e e n fr o m th e s e r e s u lt s , th is fa c to r h a s q u estio n a b le in d ep en d e n c e. E v e r y t e s t that h a s a sig n ific a n t lo a d in g on th is fa c to r h a s a sig n ific a n t lo a d in g on at le a s t one o th e r fa c to r . T h e r e is an a lm o s t to ta l sh a rin g of t e s t s w ith the CMR fa c to r . H o w ev er, th is m ay be due to 58 the n atu re of th e te a ts in v o lv e d . It m ay be sa id that th e r e la so m e su p p ort fo r the e x is te n c e o f th is fa c to r , althou gh its d e fin itio n is an yth ing but c le a r o r su b sta n tia te d . S om e o f the ap p a ren t r e la tio n sh ip s h a v e a lr e a d y b een d is c u s s e d in c o n n e c tio n w ith o th e r fa c to r s . T h e la c k o f in d ep en d en ce o f th e CM R and C FR fa c to r s m ay in d ic a te a c o lla p sin g a c r o s s co n ten t in th is c a s e . DSU - D iv e r g e n t P ro d u c tio n o f S y m b o lic U n its 7. F ir s t and L a s t L e t te r s (DSU) .4 7 2 2 . S u ffix e s (DSU) .4 5 14. P a in ted B lo c k s (C F T ) .3 4 .3 8 (CSS) U n lik e the th r e e p r e v io u sly d is c u s s e d fa c to r s , th is on e is fa ir ly c le a r and w e ll d efin ed . T h e f ir s t tw o t e s t s , w h ile not havin g la r g e lo a d in g s do h ave u n iv o ca l lo a d in g s on th is fa c to r . S u ffix e s h a s b een em p lo y ed In an A R P study (D unham e t. a l. ) and m a rk ed DSU in that stu d y. T h e lo a d in g o f P a in te d B lo c k s on th is fa c to r i s not r e a lly e x p la in a b le , but th e b e h a v io r o f th is t e s t h a s ten d ed to be so m ew h a t e r r a tic in th e p a s t. E v en in th e o r ig in a l A d k in s and L y e r ly a n a ly s is , th is t e s t lo a d e d on th r e e fa c to r s and did not c le a r ly h e lp to d efin e any on e of th e th r e e . E F U - E v a lu a tio n o f F ig u r a l U n its 11. M u tilated P ic t u r e s (E F U ) .6 9 8 . Id en tica l F o r m s (E F U ) .4 8 .3 1 (CSS) 5. F ig u r e S e r ie s (CSS) .3 1 .4 7 (CSS) .3 3 (C FR ) . 3 0 (C F T ) T h is fa c to r is c le a r ly d efin ed by the f ir s t tw o t e s t s . Id en tica l F o r m s h a s b een a m a r k e r fo r th is fa c to r in m any s tu d ie s . T he s m a ll lo a d in g on CSS m ay be due to str en g th o f the CSS fa c to r o r p o s s ib ly 59 b e c a u se of its r e la tio n to th e CSS t e s t F ig u r e S e r ie s . F ig u r e S e r ie s h a s been d is c u s s e d b e fo r e and it s lo a d in g on th is fa c to r is not c le a r , althou gh it m ay have to do w ith a sp e e d e le m e n t. C F U - C ogn ition of F ig u r a l U n its 12. M u tila ted W ords (C F U ) .6 0 2 1 . S tr e e t G e s ta lt C o m p letio n (C F U ). 56 T h e se two t e s t s h ave s e r v e d a s m a r k e r s fo r th e C F U fa c to r sin c e th e in c ep tio n o f th e S tr u c tu r e -o f-I n te lle c t. W hile h avin g on ly tw o s e t s on it, th e fa c to r is c le a r and d is tin c t, se p a r a tin g c le a r ly fr o m both E F U and C F R , it s n e a r e s t fa c to r s in the S tr u c tu r e -o f- In te lle c t m o d e l. T he fa c to r is d efin ed a s th e a b ility to r e c o g n iz e or p e r c e iv e a c o m p le te v isu a l fo r m . It is the sa m e fa c to r a s T h u r sto n e 1 s G e sta lt c lo s u r e fa c to r , C l. CM R - C ogn ition o f S e m a n tic R e la tio n s 28. W ord S q u a res (CM R) .6 3 .3 2 (CSS) 4 . F ig u r e A n a lo g ie s (C FR ) .4 1 .5 1 (C FR ) 2 6 . V erb a l A n a lo g ie s (CM R) . 35 . 52 (C FR ) .4 2 (CM U) .3 1 (CSS) 16. P ic tu r e A n a lo g ie s (CM R) . 28 .4 1 (C FR ) T h is fa c to r is d efin ed a s th e a b ility to r e c o g n iz e o r s e e r e la tio n s b etw een id e a s o r m ea n in g s o f w o r d s. In th e p r e s e n t stu d y, th is fa c to r is h ig h ly s u s p e c t. W hile the W ord S q u a res t e s t h a s a high lo a d in g on th is fa c to r , it s in te r p r e ta tio n is not w e ll su p p orted by o th e r CM R t e s t s . In deed , th e o th e r CM R t e s t s a r e fa c to r ia lly s im ila r to the C F R t e s t s . T h is s e e m s to im p ly a fo r m a t fa c to r , sin c e th e o th e r th r e e t e s t s that w e r e confounded a r e a ll a n a lo g ie s t e s t s . In stu d ie s p e r fo r m e d by A R P , a v e rb a l a n a lo g ie s t e s t h a s b een u s e d to 60 m a rk th is fa c to r , but e v id en tly in th e p r e s e n t study th e t e s t s in v o lv ed a r e not p u re m e a s u r e s . CMU - C ogn ition of S em a n tic U n its 18. R ead in g I (CM U) 2 7 . V ocab u lary (CMU) 19. R ead in g II (CM U) 2 6 . V erb a l A n a lo g ie s (CM R) 3. D eco d in g (CSS) 9 . L e tte r S e r ie s (CSS) 10. M ixed S e r ie s (C FR ) . 83 .68 .6 4 .4 2 . 37 . 35 .3 5 . 52 (C F R ) .3 5 (CM R) .3 1 (CSS) .4 5 (CSS) .4 6 (CSS) .4 6 (CSS) .4 0 (C F R ) T h is fa c to r is u su a lly a stro n g and w e ll m a rk ed fa c to r . In th is c a s e , a ll th r e e h y p o th e siz e d CMU t e s t s lo a d e d str o n g ly and u n iv o c a lly on th is fa c to r . The rem a in in g fou r t e s t s in v o lv e w ord and le t t e r c o m b in a tio n s and th e in v o lv e m e n t of CMU In th e s e t e s t s is not u n r e a s o n a b le . T h e se co n d a r y lo a d in g s o f the o th e r t e s t s have b een d is c u s s e d w ith th e fa c to r s they w e r e h y p o th e siz e d fo r . DMU - D iv e r g e n t P ro d u ctio n o f S em a n tic U n its 2 5 . T o p ic s (DM U) 24. T h in gs Round (DMU) . 73 .6 2 T h is fa c to r is u su a lly r e fe r r e d to a s id e a tio n a l flu e n c y and its t e s t s in v o lv e the p ro d u ctio n o f id e a s and th e s c o r e is c o n c e r n e d w ith th e quantity o f p ro d u ctio n . T h is fa c to r is c le a r ly d efin ed by th e two t e s t s h y p o th e siz e d fo r it. B oth t e s t s r e q u ir e a flu en t p rod u ction o f id e a s , and a r e s im ila r to m any t e s t s u s e d by A R P to d efin e th is fa c to r . Its c le a r se p a r a tio n fr o m the CMU fa c to r is a s a tis fa c to r y fin d in g . 61 K e lle y : M em o ry A b ilitie s : A F a c to r A n a ly s is K e lle y 's In v e stig a tio n w a s c o n c er n e d w ith m e m o r y a b ilit ie s , but h is t e s t b a ttery in clu d ed t e s t s o f o th e r a b ilitie s . T h is b a ttery had 40 t e s t s , m any b ein g o f a p sy c h o m o to r n a tu re . F o llo w in g a p p lic a tio n of the te s t s e le c tio n c r it e r ia , 23 t e s t s r e m a in e d , thought to r e p r e s e n t o u r S tr u c tu r e -o f-I n te lle c t fa c to r s . T h e se 23 t e s t s w e r e fa c to r a n a ly z e d and the fou r fa c to r s e x tr a c te d and r o ta ted . T h e r o ta tio n r e s u lt s a r e found in T ab le 6 . MSI - M em ory fo r S y m b o lic Im p lic a tio n s 4 . M em o ry fo r N u m b ers (MSI) .6 4 23. M em ory fo r W ords II ( R e la te d W ord s) (MSI) . 55 .3 7 (MMI) 5. M em ory fo r W ords I ( U n re la te d W ords) (MSI) . 54 1. R e co g n itio n II (W ord s) (MSI) .5 2 6 . S en ten ce C o m p letio n T e s t (MMI) .4 0 .5 8 (MMI) 3 . M em ory fo r S y lla b le s I (MSI) .3 7 22. M ean in gful M em ory; N u m b er (MSI) .3 1 .3 8 (M FU ) 7. M em o ry fo r R e la tio n s T e s t (M S I). 05 .5 2 (M FU ) T h is fa c to r w a s found in both p r e v io u sly d is c u s s e d T h u rsto n e a n a ly s e s . It is c h a r a c te r is e d a s the a b ility to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een s y m b o ls . In th e p r e s e n t a n a ly s is , it is w ell d efin ed by t e s t s w h ich u s e a v a r ie ty of sy m b o ls; m a r k e r s , w o rd s and s y lla b le s . T he M em o ry fo r W ords II (R ela ted W ords) t e s t h a s a sig n ific a n t se c o n d a r y lo a d in g on th e MMI fa c to r . T h is m ay be due to th e fa c t that th e w o r d s to be r e m e m b e r e d a r e m ea n in g fu lly r e la te d and r e s u lts in a se m a n tic lo a d in g . T h e S en ten ce C o m p letio n t e s t is an MMI t e s t that r e q u ir e s the su b je ct to r e m e m b e r w h ich w ord of a se n te n c e h a s b een d e le te d . T he lo a d in g on MSI d o e s not m ak e a 62 g r e a t d e a l o f s e n s e u n le s s th e su b je c ts tr e a t the s e n te n c e s a s being m e r e ly a c o lle c tio n o f a r b itr a r y w o r d s. The M ean in gfu l M em ory: N u m b er te s t, w h ile b ein g h y p o th e siz e d fo r MSI, h a s a s tr o n g e r lo a d ing on th e M FU fa c to r . T he r e a so n fo r th is lo a d in g is not e x p la in a b le . T he M em ory fo r R e la tio n s te s t w a s h y p o th e siz e d fo r M SI but w a s a llo w ed to go to the M FU fa c to r a s it did not h ave any a p p r e c ia b le lo a d in g on th e MSI fa c to r . T h is t e s t had a p r o g r e s s iv e m a tr ix type o f fo rm a t that req u ire d p rod u ction of th e c e ll of th e m a tr ix . It is p o s s ib le that th is t e s t is e s s e n t ia lly fig u r a l, but it i s im p o s s ib le to d e te r m in e th is fr o m th e b r ie f p u b lish ed d e sc r ip tio n . M FU - M em ory fo r F ig u r a l U n its 16. R ep rod u ction o f V isu a l D e sig n (M FU) . 52 7. M em ory fo r R e la tio n s (MSI) .5 2 19. M ap M em o ry III (M FU) .4 6 17. M ap M em o ry I (M FU ) .4 5 22. M ean in gfu l M em ory: N u m ber (MSI) .3 8 .3 1 (MSI) 2. R eco g n itio n T e s t III (M FU ) . 35 20. M ean in gful M em ory: P ic tu r e s (M FU) .3 0 16. M ap M em o ry II (M FU ) .2 1 T h is fa c to r r e q u ir e s the su b je ct to r e c a ll b a s ic fig u r a l in fo r m a tio n . F iv e of the s ix h y p o th e siz e d M FU t e s t s lo a d e d sig n ific a n tly on th is fa c to r . M ap M em o ry II had no sig n ific a n t lo a d in g s in th e p r e s e n t a n a ly s is , p rob ab ly b e c a u se it r e p r e s e n ts an a b ility not in the a n a ly s is . M em o ry for R e la tio n s t e s t h a s a lr e a d y b een d is c u s s e d a s w e ll a s M ean in gful M em ory: N u m b e rs. 6 3 MMI - M em o ry fo r S em a n tic Im p lic a tio n s 10. M em o ry fo r L im m e r ic k s (MMI) , 82 11. M em o ry fo r Id eas (MMI) .5 9 6 . S e n te n c e C o m p letio n T e s t (M M I). 58 .4 0 (MSI) 9. C o n se q u e n c e s T e s t II (MMI) .5 2 23. M em ory fo r W ords II (R ela ted W ords) (MSI) . 37 . 55 (MSI) 21. M ean in gfu l M em ory: P a ra g ra p h (MMI) .3 3 8. C o n se q u e n c e s T e s t I (MMI) . 32 T he a b ility to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een p a ir s o f m ean in gfu l e le m e n ts of in fo r m a tio n i s c a lle d MMI. S ix t e s t s w e r e h y p o th e siz e d to d e fin e th is fa c to r in th e K e lle y stu d y. T he r e s u lt s sh ow that a ll s ix o f th e s e t e s t s did h ave sig n ific a n t lo a d in g s on the sa m e fa c to r . The fa c to r i s str o n g ly le a d by the L im m e r ic k s t e s t althou gh th r e e o th e r MMI t e s t s h ave r e a so n a b ly stro n g lo a d in g s a s w e ll. It s e e m s that th is fa c to r i s w e ll d efin ed and h a s good b rea th o f c o n ten t. O nly on e te s t , S e n te n c e C o m p letio n t e s t , had a sig n ific a n t se c o n d a r y lo a d in g . T h is h a s p r e v io u sly b een d is c u s s e d . The p r e s e n c e o f the M SI te s t . M em o ry fo r W ords II (R ela ted W ord s) h as a ls o b een ex p la in ed p r e v io u s ly a s b ein g th e r e su lt o f th e m ea n in g fu l r e la tio n s u s e d in that t e s t . T h e se r e s u lts show a stro n g and w e ll d efin ed fa c to r that o ffe r s e v id e n c e fo r in v a r ia n c e . MSS - M em o ry fo r S y m b o lic S y s te m s 15. L e tte r Span T e st II (MSS) . 75 12. N u m b er Span T e s t I (MSS) .7 1 13. N u m b er Span T e s t II (MSS) .6 9 14. L e tte r Span T e s t I (MSS) .6 9 K e lle y in clu d ed fo u r sp an t e s t s in h is m e m o r y b a tte r y . T h is typ e of fa c to r h a s u su a lly b e e n found in th e M SS fa c to r o f th e S tr u c t u r e -o f-I n t e lle c t . T h e p r e s e n t r e s u lt s su p p ort th is . A ll fo u r ty p e s 64 lo a d str o n g ly and u n iv o c a lly on th is fa c to r . U n fo rtu n a tely , a ll o f th e s e t e s t s a r e span t e s t s , w h ile th e M SS fa c to r h a s not b een lim ite d to th is typ e o f t e s t . T h u rsto n e: E x p e r im e n ta l Study of S im p le S tru ctu re T h u rsto n e fo llo w e d h is PM A stu d y w ith th is study w h ich u se d m an y of th e PM A t e s t s . T h is b a ttery had 36 t e s t s and th e o r ig in a l a n a ly s is r e s u lte d in 11 fa c to r s . In th e p r e s e n t in v e stig a tio n , 20 t e s t s w e r e a n a ly se d and u s e d to r e p r e s e n t 6 f a c t o r s . T h e fin a l so lu tio n is p r e s e n te d in T a b le 7. C F T - C ogn ition o f F ig u r a l T r a n sfo r m a tio n s 4 . F ig u r e s (C F T ) . 85 2. C a rd s (C F T ) . 80 18. S q u a r es (C F T ) . 58 .4 5 (CSS) 10. M ec h a n ic a l M o v em en ts (C F T ) .4 3 12. N u m b er P a tte r n s (CSS) . 32 . 58 (CSS) T h e e m e r g e n c e of th e C FT fa c to r in th is study is q u ite c le a r and str o n g . T he le a d in g t e s t s a r e v e r y str o n g and u n iv o ca l and a r e c le a r ly fo r v is u a liz a tio n . H o w ev er, a s in th e A d k in s & L y e r ly stu dy and th e o r ig in a l PM A stu d y , th e r e i s a slig h t sh a rin g by t e s t s of CSS and C F T . T h is m ay in d ic a te that th e r e i s a c r o s s o v e r in a b ilitie s by so m e p e o p le to so lv e p a r tic u la r it e m s . N u m b er P a tte r n h a s a s m a ll and sig n ific a n t lo a d in g on C F T , c o n s is te n t w ith its r e la tio n to th e S q u a res t e s t . CSU - C ogn ition o f S y m b o lic U n its 11. M ir r o r R ead in g (CSU) .7 6 .3 6 (CSS) 3. D isa r r a n g e d W ords (CSU .4 9 17. S p ellin g (CSU) .3 5 .3 0 ICM C) 65 We have s e e n th is fa c to r and th e tw o le a d in g t e s t s on it in the p r e v io u sly d is c u s s e d T h u rsto n e s tu d ie s . T h is fa c to r r e p r e s e n ts th e a b ility to r e c o g n iz e g ra p h ic sy m b o lic u n its , su ch a s w o r d s . M ir r o r R ead in g. D isa r r a n g e d W ords and S p ellin g a ll r e q u ir e the su b je c t to r e c o g n iz e w o r d s that a r e e ith e r d isa r r a n g e d o r r e a r r a n g e d . T h is fa c to r is c le a n and r e p r e s e n ts stro n g e v id e n c e fo r th e in v a r ia n c e o f th is a b ility . T he sid e lo a d in g on CSS fo r M ir r o r R ead in g m a y r e p r e se n t the robbing of a w eak fa c to r by a stro n g o n e . S p e llin g 's lo a d in g on CMC m a y in d ic a te th e p r e s e n c e of se m a n tic v a r ia n c e , in th at t e s t . ESU - E v a lu a tio n o f S y m b o lic U n its 5. Id en tica l N u m b ers (ESU ) .6 8 16. R ep ea ted L e tte r s (ESU ) .5 3 E v a lu a tio n o f S y m b o lic U n its i s the a b ility to m ak e rapid ju d g m en ts r e g a r d in g th e sy m b o lic id e n tity o r a c c u r a c y of w o r d s, le t t e r s e t s and n u m b er s e t s . In Id en tica l N u m b e r s, the su b je c t h a s to m a rk the n u m b er that is th e sa m e a s th e one g iv en at the s ta r t o f a co lu m n . R ep ea ted L e tte r s c a lls fo r rap id id e n tific a tio n o f r e p e a te d l e t t e r s . T he r e s u lt s in d ic a te that th is fa c to r is in d eed p r e s e n t, w ith both h y p o th e siz e d t e s t s lo a d in g u n iv o c a lly on it. M SI - M em o ry fo r S y m b o lic Im p lic a tio n s 19. W ord - N u m b er (MSI) .6 8 6 . In itia ls R e c a ll (MSI) .6 3 A s in p r e v io u s s tu d ie s , th is fa c to r h a s e m e r g e d c le a r ly and s tr o n g ly . Tw o t e s t s w e r e h y p o th e siz e d fo r it and both a r e p r e s e n t to m a rk it. N e ith e r te s t h a s any sig n ific a n t sid e lo a d in g . 66 CSS - C o g n itio n o f S y m b o lic S y s te m s 8. L e tte r S e r ie s (CSS) .6 3 12. N u m b er P a tte r n s (CSS) . 58 .3 2 (C F T ) 13. N u m b er S e r ie s (CSS) . 51 9. M ark s (CSS) .4 9 7. L e tte r G rou ping (CSS) .4 6 18. S q u a r es (C F T ) .4 5 .5 8 (C F T ) 1. A r e a s (CSS) .4 2 14. P a tte r n s (CSS) .4 1 2 0. W ord P a tte r n s (CM C) .4 0 .4 9 (CM C) 11. M ir r o r R ead in g (CSU) .3 6 . 76 (CSU) in p r e v io u sly d is c u s s e d s tu d ie s . CSS is a v e r y str o n g ly r e p r e s e n te d fa c to r . A c c o r d in g to the d e fin itio n of th is fa c to r , m o s t of the t e s t s a r e of a s e r i e s o r se q u e n tia l n a tu r e . The se c o n d a r y lo a d in g s o f S q u a r es. N u m b er P a tte r n s and M ir r o r R ead in g have been d is c u s s e d e ls e w h e r e . T he lo a d in g o f W ord P a tte r n s is not quite c le a r , alth ou gh it i s p o s s ib le that CSS v a r ia n c e w a s in tro d u ced in to t h is t e s t by th e n atu re o f th e r e la tio n s b etw een th e w o r d s in the ite m s o f th is t e s t . T he CSS id e n tific a tio n o f th is fa c to r s e e m s fairly c e r ta in . CM S - C o g n itio n o f S em a n tic C la s s e s 15. P r o v e r b s (CM C) .6 4 20. W ord P a tte r n s (CM C) .4 9 .4 0 (CSS) 17. S p e llin g (CSU) .3 0 . 35 (CSU) T h is fa c to r r e p r e s e n ts the a b ility to r e c o g n is e com m on p r o p e r t ie s of w o r d s, id e a s and o b je c ts . T he P r o v e r b s te s t r e q u ir e s th e s e le c tio n o f a p r o v e r b w ith a d iffe r e n t m ea n in g fr o m fo u r o th er p r o v e r b s o f a c la s s . T h is t e s t is a c le a r m a r k e r fo r CM C. T he W ord P a tte r n s t e s t r e q u ir e s a s im ila r e x c lu s io n o f w o rd s and h a s it s m a jo r lo a d in g on CM C. H o w e v er , so m e CSS v a r ia n c e i s due to th e la c k o f m ea n in g fu l r e la tio n s b etw een th e w ord l i s t s . T he lo a d in g 67 o f S p ellin g on th is fa c to r w a s d e a lt w ith e a r lie r . B ech to ld t; F a c to r ia l Study o f P e r c e p tu a l Sp eed A p p lica tio n o f th e t e s t s e le c tio n c r ite r ia r e s u lte d in a 31 x 31 c o r r e la tio n m a tr ix to be su b m itted fo r a n a ly s is . S even fa c to r s w e r e h y p o th e siz e d fo r th is m a tr ix . A p r in c ip a l fa c to r e x tr a c tio n w a s p e r fo r m e d and se v e n f a c to r s w e r e r e ta in e d and r o ta te d . A fte r the th ir d su ch r o ta tio n , it b e c a m e a p p a ren t th at the ESU fa c to r w h ich w a s m a rk ed by eig h t t e s t s w a s too str o n g fo r the E F U and EM U f a c to r s , w h ich w e r e m a rk ed by fa r fe w e r t e s t s . A c c o r d in gly th e eig h t t e s t s for ESU w e r e red u ced to fo u r . T h is red u ctio n w a s m ad e by k eep in g tw o t e s t s th at had b een ESU m a r k e r s in o th e r stu d ie s a n a ly z ed in th is in v e stig a tio n and by k eep in g tw o t e s t s w h ich w e r e p r e d ic te d to be ESU but not found in any o th e r a n a ly s e s . T he r e s u lt w a s that th e t e s t s C SU Z , F ir s t D ig it C a n c e lla tio n . W ords C on tain in g " s M and L e tte r G rou ps w e r e e lim in a te d . The n ew r ed u ced 27 x 27 c o r r e la tio n m a tr ix w a s su b m itted to e x tr a c tio n and se v e n fa c to r s w e r e r e ta in e d . T h is new p r in c ip a l fa c to r m a tr ix w a s r o ta ted and the r e s u lts a r e found in T a b le 8, C F T - C o g n itio n o f F ig u r a l T r a n sfo r m a tio n s T h is is a fa ir ly fa m ilia r fa c to r by n ow . T h r e e t e s t s u s e d to m a r k th is fa c to r a r e th e sa m e a s u s e d in th e p r e v io u s T h u rsto n ia n a n a ly s e s . The fa c to r e m e r g e s v e r y str o n g ly and c le a r ly . T h e r e a r e no ad d itio n a l lo a d in g s on th e fa c to r , and none o f the th r e e t e s t s 7. C a rd s (C F T ) 1. F la g s (C F T ) 19. F ig u r e s (C F T ) . 78 .66 .66 68 h ave sig n ific a n t se co n d a r y lo a d in g s . It s e e m s fa ir ly c e r ta in that th is fa c to r r e p r e s e n ts th e a b ility to v is u a liz e how a g iv en fig u r e o r o b je c t w ill ap p ea r a fte r g iv en c h a n g e s, su ch a s u n fold in g o r r o ta tio n . F r o m th e r e s u lts of the T h u rsto n e PM A study w h ere t h e s e t e s t s had lo a d in g s on both C FT and C F S , it i s p o s s ib le that th is fa c to r i s a confounding o f C F T w ith C F S. DSU - D iv e r g e n t P ro d u c tio n of S y m b o lic U n its W hile th is fa c to r is m a rk ed by on ly two t e s t s , both o f th e se t e s t s have b een u s e d to m a rk th is fa c to r in s e v e r a l o f th e o th e r a n a ly s e s of th e p r e s e n t in v e stig a tio n . A ls o th e s e t e s t s , o r fo r m s o f th em , h ave b een u sed by the A R P to m ark th e DSU fa c to r . T he id en tity o f th is fa c to r s e e m s fa ir ly c e r ta in th en . T he fa c to r p ic tu r e is not m a r r e d by any n o n -h y p o th e siz e d fin d in g s and both t e s t s a r e r e s t r ic te d to on e fa c to r , ESU - E v a lu a tio n o f S y m b o lic U n its T h is fa c to r is d efin ed a s th e a b ility to m a k e rap id d e c is io n s r e g a r d in g th e sy m b o lic id en tity o r a c c u r a c y o f w o r d s, le tte r s e ts and n u m b er s e t s . T he fo u r t e s t s th at w e r e r e ta in e d fo r the fin a l a n a ly s is le a d th e w ay on th is fa c to r . T h ey a r e a ll u n iv o c a l. A ll of th em r eq u ire ch eck in g in fo r m a tio n a c c o r d in g to th e c r ite r io n 2 . F ir s t and L a s t L e tte r s (DSU) 6 . S u ffix e s (DSU) 56 55 9 . L e tte r A (ESU) 16. 2, 6 , 9 (ESU) 3 . N am e R e co g n itio n (ESU ) 2 0 . L e tte r S q u a r es (ESU) 12. B o y s' F ir s t N a m e s (EM U) 18. V erb a l E n u m era tio n (EM U) . 72 .6 0 . 59 .4 1 .3 8 .6 6 (EM U) .3 0 .7 1 (EM U) 69 o f id e n tity , h en c e th ey fit w e ll w ithin th e g iv en d e fin itio n . In ad d ition , a ll o f th e s e t e s t s have an e le m e n t o f sp e e d . T h e a p p ea r a n c e of B oys' F ir s t N a m e s on ESU m ay be due to sh a r e d sp e e d v a r ia n c e ,o r it is p o s s ib le that so m e e x a m in e e s tr e a te d th is ta s k a s if the b o y s' n a m e s w e r e m e r e ly m e a n in g le s s c o lle c tio n of s y m b o ls , s in c e th ey w e r e fa m ilia r n a m e s. V erb a l E n u m era tio n , w h ich is a ls o an EM U t e s t had a s m a ll but sig n ific a n t lo a d in g h e r e . T he ex p la n a tio n fo r th is is not q u ite c le a r u n le s s the c a te g o r ie s w e r e fe lt to be a r b itr a r y by the e x a m in e e s and th u s tr e a te d a s sy m b o lic m a te r ia l. It is r e a s s u r in g to n o te that non e of th e ESU t e s t s had sig n ific a n t lo a d in g s on e ith e r EM U o r E F U . N F T - C o n v erg en t P ro d u ctio n of F ig u r a l T r a n sfo r m a tio n s T h is i s the f ir s t o c c u r r e n c e of th is fa c to r in any o f th e p r e s e n t a n a ly s e s . In te r m s of th e S tr u c tu r e -o f-I n te lle c t, N F T d efin ed a s th e a b ility to b rea k down g iv en fig u r a l u n its to fo r m new o n e s . T he a b ility h a s b een is o la te d by the A r m y A ir F o r c e stu d ie s and la te r by A R P (H offm an, e t. a l . , 1968) s tu d ie s . It is on e of T h u r sto n e 's o r ig in a l c lo s u r e fa c to r s (C2) and i s e s s e n t ia lly in v o lv ed in b rea k in g down one G e sta lt to fin d a n o th er. G o ttsch o ld t F ig u r e s is the c la s s ic a l t e s t fo r th is fa c to r . It s e e m s fr o m the p r e s e n t r e s u lt s th at th is fa c to r e m e r g e s fa ir ly w e ll. O nly H idden P ic tu r e s h a s a s ig n i fica n t sid e lo a d in g . T h is lo a d in g is on th e C F U fa c to r w h ich is the S tr u c tu r e -o f-I n te lle c t eq u iv a len t o f T h u r sto n e 's o th e r c lo s u r e fa c to r . 4 . G o ttsch a ld t F ig u r e s (N F T ) 22. D e sig n s (N F T ) 8. H idden P ic tu r e (N F T ) . 46 .4 0 .3 9 .3 9 (C FU ) 70 T he sp lit lo a d in g of th is t e s t i s not to ta lly u n r e a so n a b le , a s the fig u r e s h a v e to be r e c o g n is e d a s w e ll. EM U - E v a lu a tio n o f S e m a n tic U n its 18. V erb a l E n u m era tio n (EM U) .7 1 .3 0 (ESU) 5. S iz e C o m p a r iso n (EM U) . 70 10. W ord C h eck in g (EM U) .6 9 12. B o y s' F ir s t N a m e s (EM U) .6 6 .3 8 (ESU) 14. O p p o site s (EM U) .6 5 21. W ords A s s o c ia t e s w ith a H ou se (EM U) .6 1 24. C o n c r e te A s s o c ia tio n s (EM U) .4 8 ,4 7 (E F U ) T h is fa c to r i s the se m a n tic c o u n te rp a rt o f the ESU fa c to r . T he a b ility in th is c a s e is to jud ge th e su ita b ility o r ad eq u acy o f id e a s and o b je c ts in t e r m s o f m e e tin g s p e c ific c r it e r ia . T h is fa c to r is d efin ed by a ll se v e n t e s t s that w e r e h y p o th e siz e d fo r it. T he lo a d in g s o f th e s e t e s t s a r e a ll o f a su b sta n tia l n a tu re . T he se c o n d a r y lo a d in g s o f V erb a l E n u m era tio n and B o y s' F ir s t N a m e s h a s b een d i s c u s s e d in r e la tio n to E SU . T he la r g e se c o n d a r y lo a d in g o f C o n cr ete A s s o c ia tio n s is so m ew h a t o f a p r o b le m . H o w e v er , upon c lo s e e x a m in a tio n of the t e s t s ' d e s c r ip tio n s , it w a s n oted that th is t e s t h a s a r a th er u n u su al fo r m a t. T h is fo rm a t r e q u ir e s th e p r e s s in g o f a righ t o r le ft hand button o n c e th e se m a n tic unit h a s been lo c a te d . T h e s c o r e is th e m ed ia n tim e fo r the f ir s t 19 c o r r e c t r e s p o n s e s . T h is sa m e m od e o f r e s p o n s e i s found In th e t e s t s L e tte r s IV and L e tte r s 1, w h ich c le a r ly m a rk the E F U fa c to r . It s e e m s th en that C o n c r e te A s s o c ia tio n s m a y in d eed have both fa c to r s p r e s e n t in it. 71 C F U - C o g n itio n o f F ig u r a l U n its 2 5 . P ic tu r e C o m p a r iso n (C FU ) . 53 8. H idden P ic t u r e s (N FT ) .3 9 .3 9 (N F T ) 11. M u tila ted W ords (C F U ) .1 8 2 7 , G e o m e tr ic F ig u r e s (C F U ) . 18 17. S tr e e t G e sta lt C o m p letio n (C F U ). 13 A s e v id e n c e d fr o m th e r e s u lt s a b o v e, th is fa c to r can h a rd ly be id e n tifie d a s an yth in g but a d o u b let. T he c la s s i c C FU t e s t s . M u tila ted W ords and S tr e e t G e s ta lt C o m p letio n , fa il to lo a d sig n ific a n tly on th is fa c to r , n or do th ey lo a d on any o th e r fa c to r p r e s e n t. T h is b e h a v io r i s h ig h ly u n u su al, a s th e s e two t e s t s h ave s u c c e s s fu lly In d icated C FU in a n u m b er o f A R P s tu d ie s . E F U - E v a lu a tio n o f F ig u r a l U n its 2 3 . L e tte r s IV (E F U ) .6 1 24. C o n c r e te A s s o c ia tio n s (EM U) *47 .4 8 (EM U) 13. Id en tic a l F o r m s (E F U ) .4 3 15. P ic tu r e S q u a r es (E F U ) .3 6 26. L e tte r s I (E F U ) .3 4 T h is fa c to r is th e fig u r a l co u n terp a rt o f both EM U and E SU . O ne o f the s u c c e s s e s of th is p a r tic u la r study w a s the se p a r a tio n o f th e s e th r e e fa c to r s in data n ot d e sig n e d fo r th e S tr u c tu r e -o f-I n te lle c t. W hile so m e o f the lo a d in g s o f th e h y p o th e siz e d t e s t s a r e not o v e r w h elm in g , th e r e a r e no se c o n d a r y lo a d in g s . T he p r e s e n c e o f C o n c r e te A s s o c ia tio n s on th is fa c to r w a s d is c u s s e d e a r lie r . It w ould s e e m th at th is fa c to r can be sa fe ly id e n tifie d in th is stu d y. C a r r o ll; A F a c to r A n a ly s is o f V erb a l A b ilitie s T h is study w a s in clu d ed in th e p r e s e n t r e s e a r c h b e c a u se o f so m e unique fa c to r s w h ich w e r e thought to be p r e s e n t. T h e o r ig in a l study in clu d ed 42 v e r b a l t e s t s . F o llo w in g a p p ro p ria te s e le c tio n th is 72 w a s red u ced to 15 t e s t s o f fiv e S tr u c tu r e -o f-I n te lle c t c e l ls . The c o r r e la tio n m a tr ix w a s su b m itted to a n a ly s is and fiv e p rin cip a l a x e s w e r e e x tr a c te d . T h e se w e r e then rotated and the r e s u lts a r e shown in T ab le 9. CSU - C ogn ition of S y m b o lic U n its T h is fa cto r h a s o c c u r r e d in a num ber o f the p r e v io u sly d is c u sse d stu d ie s . It should be r e c a lle d that it is d efin ed a s the a b ility to r e c o g n ise grap h ic sy m b o lic u n its, su ch a s w o rd s. In the p r e se n t stu d y, th is fa cto r e m e r g e s , but a ll but one o f the t e s t s have lo a d in g s on o th er fa c to r s . The load in g o f D isa r ra n g ed W ords I on th e NMU fa c to r m ay be a r e su lt of the production req u ired by th is te s t. That i s , th is t e s t r e q u ir e s both r eco g n itio n o f what le t t e r s a r e m is s in g and a lso p rodu ction of the p a r tic u la r w ord in v o lv ed . T h is type of v a r ia n ce h a s c a r e fu lly been elim in a ted from CSU t e s t s d ev elo p ed by A R P . D isa r ra n g ed M orp h em es h a s a sig n ifica n t load in g on the DSU fa c to r . T h is is p robab ly due to the fa ct that in ea ch ite m o f th is t e s t , th e re a r e a num ber o f m o rp h e m es to be rea r ra n g ed into m o r e than one w ord . An e le m e n t o f D isa r ra n g ed W ords II h as a sig n ifica n t r e la tio n sh ip to th e MSI fa c to r . In th is c a s e , th e te s t did not fu rn ish any c lu e s to the m ea n in g s of the w ord s that w e re d isa r r a n g e d . In D isa r ra n g ed W ords 1 a clu e w a s g iv en . T he la ck of 4 , A n a g ra m s (CSU) 6 . D isa r r a n g e d W ords I (CSU) 10. D isa r r a n g e d M orp h em es (CSU) 1. D isa r r a n g e d W ords II (CSU) 2 . W ords S co re (DMU) . 50 .3 2 (NMU) .5 0 .4 4 (DSU) .4 9 .3 4 (MSI) .4 1 .5 8 (DMU) . 53 73 a c lu e a s to th e w ord m ea n in g b r in g s m e m o r y in to p lay and thu s p ro b a b ly r e s u lts in th e s ig n ific a n t lo a d in g on th e o n ly m e m o r y a b ility p r e s e n t in th e b a tte r y , M SI. T h e sig n ific a n t lo a d in g of the W ords S c o r e t e s t , a flu e n c y t e s t , on th is fa c to r is v e r y d iffic u lt to e x p la in . T he s c o r e is d e r iv e d fr o m a th e m e w r itte n by th e su b je c t on a p a r tic u la r to p ic . It is p o s s ib le that the sig n ific a n t CSU lo a d in g r e p r e s e n ts th e p lay of a v o c a b u la r y fa c to r . H o w ev er, CM U, th e n o r m a l v o c a b u la r y fa c to r , is not r e p r e s e n te d h e r e . DM U - D iv e r g e n t P ro d u c tio n o f S e m a n tic U n its 13. P ic tu r e D e s c r ip tio n (DM U) .7 3 2. W ords S c o r e (DM U) .5 8 .4 1 (CSU) Id ea tio n a l F lu e n c y i s th e u su a l v e r b a l la b e l fo r th is fa c to r . T h e a b ility in v o lv ed i s that of p rod u cin g id e a s a p p ro p ria te to g iv en m ea n in g fu l r e q u ir e m e n ts . In P ic tu r e D e sc r ip tio n , th e e x a m in e e m u st d e s c r ib e a p a r tic u la r p ic tu r e and th e s c o r e i s th e n u m b er o f r e le v a n t w o rd s p ro d u ced . A s m en tio n e d e a r lie r , W ords S c o r e is th e n u m b er o f w o r d s w r itte n in a th e m e about a s p e c ific to p ic . T he se c o n d a r y lo a d in g o f th is t e s t h a s a lr e a d y b een d is c u s s e d . T h is fa c to r , w h ile h avin g on ly tw o t e s t s , d o e s c o r r e sp o n d v e r y w e ll to th e the d e fin itio n o f th e DM U a b ility . DSU - D iv e r g e n t P ro d u c tio n o f S y m b o lic U n its 3. S u ffix e s (DSU) . 83 10. D isa r r a n g e d M o rp h e m e s (CSU) .4 4 . 50 (CSU) 5. R h ym in g (DSU) .3 8 74 DSU h a s o c c u r r e d in p r e v io u sly d is c u s s e d s tu d ie s , althou gh it is w e a k e r h e r e . It in v o lv e s th e a b ility to p ro d u ce m any sy m b o lic u n its that c o n fo rm to s im p le s p e c ific a tio n s not in v o lv in g m e a n in g s. T h e S u ffix e s t e s t h a s m a rk ed th is fa c to r in the o th er a n a ly s e s and h a s b een u se d by A R P fo r th is p u r p o se . In th is c a s e , it str o n g ly in d ic a te s th e fa c to r . T he p r e s e n c e o f D isa r r a n g e d M o rp h e m e s w a s d is c u s s e d b e fo r e , and sh ou ld b e c o m e m o r e c le a r fr o m the ab ove d e fin itio n o f DSU and th e d e s c r ip tio n o f the ta sk in v o lv ed in th e t e s t . R h ym in g lo a d s sig n ific a n tly a s p r e d ic te d , but not a s str o n g ly a s e x p e c te d . N e ith e r o f the two h y p o th e siz e d DSU t e s t s h a s se co n d a r y lo a d in g s . M SI - M em o ry fo r S y m b o lic Im p lic a tio n s 7. P a ir e d A s s o c ia t e s T -E (MSI) .9 0 8. P a ir e d A s s o c ia t e s E -T (MSI) .9 0 9. M em o ry I (MSI) . 50 1. D isa r r a n g e d W ords II (CSU) .3 5 .4 9 (CSU) T he e x is te n c e of th is fa c to r i s r a th e r h ard to d isp u te . It sh ou ld be r e c a lle d fr o m p r e v io u s d is c u s s io n s o f th is fa c to r that it is th e a b ility to r e m e m b e r a r b itr a r y a s s o c ia t io n s b etw een s y m b o ls . In the f ir s t tw o t e s t s , P a ir e d A s s o c ia t e s T -E and P a ir e d A s s o c ia te d E -T , th e su b je c t is r e q u ir e d to r e m e m b e r th e E n g lish m e a n in g s of T u rk ish w o r d s , and then to p ro d u ce the a p p ro p ria te p a r t upon r e c a ll. In M em o ry I, the su b je c t is to r e c a ll n u m b e rs that h a v e b een a s s o c ia te d w ith w o r d s . T h e se th r e e t e s t s c le a r ly a r e a p p ro p ria te fo r th e d e fin i tio n and u n iv o c a lly m a rk th e fa c to r . The p r e s e n c e o f D isa r r a n g e d 75 W ords II h a s b een d is c u s s e d w ith the r e s u lts o f th e CSU fa c to r . NM U - C o n v erg en t P ro d u ctio n of S em a n tic U n its 14. F o r m N am in g (NMU) . 75 15. C o lo r N a m in g (NMU) . 72 12. G ivin g F ir s t N a m e s (NM U) .4 2 11. N am in g S ta te s o f the U nion (NMU) .3 4 6. D isa r r a n g e d W ords I (CSU) . 32 T he NM U a b ility i s d efin ed a s th e a b ility to c o n v e r g e upon an a p p ro p ria te n am e o r su m m a r iz in g w ord fo r any g iv en inform ation ,. T h e fo u r h y p o th e siz e d t e s t s o f th is a b ility a ll r e q u ir e th e e x a m in e e to p ro d u ce th e w ord w h ich d e s c r ib e s o r la b e ls a fo r m , c o lo r , sta te o r p e r s o n . T hey c le a r ly fit the d e fin itio n and th e r e s u lts in d ic a te a p u re fa c to r . T he lo a d in g o f D isa r r a n g e d W ords I on th is fa c to r h as a lr e a d y b een p r e se n te d and d o e s not h in d er the id e n tific a tio n o f th is fa c to r a s NM U. T a y lo r ; A F a c to r ia l Study of F lu en cy in W riting T h is study w a s a ls o in clu d ed b e c a u se o f so m e v e r b a l a b ilitie s it w a s d e sig n e d to in v e s tig a te . T he o r ig in a l b a ttery had 28 t e s t s . F o llo w in g s e le c tio n . 19 of th e s e t e s t s w e r e a n a ly z e d . T he c o r r e la tio n m a tr ix w a s su b m itted to fa c to r e x tr a c tio n and s ix fa c to r s w e r e r e ta in e d . T h e se w e r e th en ro ta ted and th e r e s u lt s can be found in T a b le 10. M SI - M em o ry fo r S y m b o lic Im p lic a tio n s 2 . W o rd -N u m b er (MSI) .6 1 1. F ir s t N a m e s (MSI) .5 0 T h is fa c to r a p p ea red in s e v e r a l o f the stu d ie s u se d in th is in v e stig a tio n . In e a c h c a s e it h a s a p p ea red q u ite c le a r ly . T h is tim e 76 Is no e x c e p tio n . O nly th e tw o t e s t s h y p o th e siz e d to m e a s u r e the fa c to r h a v e sig n ific a n t lo a d in g s on it. W o rd -N u m b er is a t e s t fr o m the T h u rsto n e and T h u rsto n e study w h er e it a ls o m e a s u r e d M SI. It r e q u ir e s the su b je ct to r e c a ll n u m b e rs th at w e r e a s s o c ia te d w ith w o r d s. F ir s t N a m e s i s a ls o a T h u rsto n e and T h u rsto n e t e s t and r e q u ir e s r e c a ll o f f ir s t n a m e s w hen a s s o c ia t e d la s t n a m e s a r e p r e se n te d to h im . CSU - C ogn ition of S y m b o lic U n its 3 . M ir r o r R ead in g (CSU) .4 4 8. A n a g ra m s (CSU, DSU) .4 4 .4 9 (DSU) T h is fa c to r h a s a p p ea red in fo u r o f the p r e v io u s s tu d ie s . In fa c t, both of th e s e t e s t s a r e fr o m the T h u rsto n e and T h u rsto n e t e s t b a tte r y . A s in that c a s e th ey m a rk the CSU fa c to r . T h e lo a d in g o f A n a g ra m s on DSU in d ic a te s the p r e s e n c e o f both fa c to r s in the t e s t . T he r e s u lts of th is study c le a r ly show th is to be the c a s e . DSU - D iv e r g e n t P ro d u ctio n of S y m b o lic U n its 5. S u ffix e s (DSU) .7 1 7. F ir s t L e tte r s (DSU) .7 1 4 . F ir s t and L a s t L e tte r s (DSU) . 63 13. N u m b er of L e tte r s (DSU) .6 1 15. G iven L e tte r s (DSU) .6 1 8. A n a g ra m s (CSU, DSU) .4 9 .4 4 (CSU) 6 . S yn on ym s (DM R) .3 9 .4 6 (DM R) T h e a b ility to p ro d u ce m any sy m b o lic u n its th a t c o n fo rm to s im p le s p e llin g s p e c ific a tio n s is c a lle d D SU . T h is fa c to r h a s b een id e n tifie d in f u r o th e r stu d ie s u n der in v e stig a tio n h e r e . T h is a n a ly s is p r e s e n ts th e s tr o n g e s t DSU fa c to r w ith a ll s ix h y p o th e sise d t e s t s lo a d in g sig n ific a n tly on it. O f th e s e s ix t e s t s , on ly A n a g r a m s h as 77 a n o th er a ig n ifle a n t lo a d in g , and that a ls o w a s p r e d ic te d . T h e o th e r fiv e t e s t s h ave a ll b een se e n in on e o f the o th e r a n a ly s e s and w ill n ot be d is c u s s e d h e r e . T he lo a d in g o f S yn on ym s on th is fa c to r is d iffic u lt to e x p la in . It m a y be that S yn on ym s w a s p u lled to th is fa c to r by the o v e r a ll stren g th o f th e DSU fa c to r by r e a so n o f ch a n ce in fla ted c o r r e la tio n s o f that t e s t w ith so m e DSU t e s t s . DM R - D iv e r g e n t P ro d u c tio n o f S em a n tic R e la tio n s T h is fa c to r is d e fin e d a s the a b ility to p ro d u ce m an y r e la tio n sh ip s a p p ro p ria te in m ea n in g to a g iv en id e a . P a ir e d O p p o site s in v o lv e s th e p ro d u ctio n o f p a ir s o f w o rd s th at a r e o p p o site in m ea n in g . It h a s a c le a r and u n iv o ca l p la c e on th is fa c to r . T he S yn on ym s t e s t r e q u ir e s the p ro d u ctio n of th r e e w o r d s w ith th e sa m e m ea n in g a s a g iv en w o rd . W hile h avin g its m a jo r lo a d in g in the a p p ro p ria te p la c e , th is t e s t h a s a d istu r b in g se c o n d a r y lo a d in g on the DSU fa c to r . T h is m ay be due to th e w e a k n e s s in th e DM R fa c to r , a s w e ll a s the o v e r a ll str en g th of th e DSU fa c to r . DMS - D iv e r g e n t P ro d u c tio n o f S e m a n tic S y s te m s T h e a b ility to o r g a n iz e w o r d s in v a r io u s m ea n in g fu l c o m p le x id e a s i s c a lle d DM S. S im ile s r e q u ir e s the e x a m in e e to p ro d u ce th r e e w a y s in w h ich e a c h g iv en in c o m p le te s im ile can be c o m p le te d . 11. P a ir e d O p p o site s (DM R) 6 . S yn on ym s (DM R) . 72 1 46 .3 9 (DSU) 10. S im ile s (DM S) 16. S en ten ce F lu en cy (DMS 12. L e tte r S ta r s (DM S) 14. T o p ic s (DM U) . 71 .6 0 .4 3 (DM U) . 59 .4 5 .5 7 (DM U) 78 S en ten ce F lu en cy te s t e d th e a b ility to p ro d u ce a v a r ie ty o f d iffe r e n t s e n te n c e s e a ch w ith the sa m e g e n e r a l id e a . T h is t e s t a ls o had a sig n ific a n t se co n d a r y lo a d in g on DM U, It is p o s s ib le that so m e e x a m in e e s tr e a te d ea ch se n te n c e a s a u n it and th u s th is t e s t b e c a m e lik e a DMU t e s t , r a th er than a to ta l DMS te s t . C o n v e r se ly , the T o p ic s t e s t , w h ich is h y p o th e siz e d fo r DM U, h a s so m e DMS v a r ia n c e . In th is c a s e , th e e x a m in e e i s r e q u ir e d to w r ite m any id e a s fo r on e to p ic . It i s p o s s ib le that e v e n though the p rod u ced id e a s a r e s e p a r a te u n its, th ey a r e c o n n e c te d in to a s y s te m by the c o n tro l fe a tu r e of a sin g le to p ic . DMU - D iv e r g e n t P ro d u ctio n of S em a n tic U n its T he DMU a b ility i s co m m o n ly r e fe r r e d to a s Id eation al F lu e n c y . S p e c ific a lly it is th e a b ility to p ro d u ce m any e le m e n ta r y id e a s a p p ro p ria te to g iv en r e q u ir e m e n ts . T he n atu re o f the sid e lo a d in g of T o p ic s and S en ten ce F lu e n c y t e s t s w a s d is c u s s e d a b o v e. T h in g s to E a t and T h in g s Round r e q u ir e the su b je ct to p ro d u ce the n a m e s o f th in g s that fit in to th o se c a te g o r ie s* In th e A d je c tiv e s t e s t th e su b je c t had to p ro d u ce a s m any a d je c tiv e s a s p o s s ib le to d e s c r ib e a h o u se . T he T h em e te s t w a s sim p ly a count o f th e n u m b er o f w o rd s w r itte n about a p a r tic u la r to p ic in a th e m e style* 14. T o p ic s (DM U) 18. T h in gs to E a t (DMU) 9. A d je c tiv e s (DM U) 19. T h em e (DM U) 16. S e n te n c e F lu e n c y (DM S) 17. T h in g s Round (DM U) .4 3 .6 0 (DM S) .4 1 .4 9 .4 8 .4 7 .5 7 .4 5 (DMS) 79 A t th is poin t th e r e s u lt s fr o m the eigh t se p a r a te a n a ly s e s h ave been p r e se n te d and it s e e m s a p p ro p ria te to s u m m a r iz e th em b r ie fly at th is p oin t. In g e n e r a l th e a n a ly s e s sh ow ed su p p ort fo r the o r ig in a l h y p o th e se s. O nly two fa c to r s fa ile d to e m e r g e at a ll and th e s e fa c to r s w e r e C FU in th e B ech to ld t study and MMU in T h u r sto n e 's PM A stu d y . E x p la n a tio n s fo r th e s e tw o p r o b le m s w e r e o ffe r e d . In the c a s e of th e C FU fa c to r , it w a s p oin ted ou t that th is fa c to r h a s b een Id en tifie d in s e v e r a l o c c a s io n s w ith th e M u tilated W ords and S tr e e t G e s ta lt C o m p letio n t e s t s , and that th e ir fa ilu r e h e r e m u st be due to so m e q u e stio n a b le o c c u r r e n c e . T h e se two t e s t s e v en d e fin e d th e C FU fa c to r in th e A d kins and L y e r ly study u n der c u r r e n t a n a ly sis* T he MMU fa c to r w a s h y p o th e siz e d to be d efin ed by tw o t e s t s , w h ich w a s not su ffic ie n t in n u m b er o r p u rity to r e s u lt in a so lid fa c to r . A n oth er p r o b le m in th e r e s u lts i s th e o c c u r r e n c e o f s e v e r a l d ou b let fa c to r s, i . e . . w h er e a fa c to r w a s h y p o th e siz e d and found to be m e a s u r e d by on ly two t e s t s . W hile p a in s w e r e taken to e lim in a te su ch fa c to r s b e fo r e a n a ly s is , so m e fa c to r s still had su ch an a p p e a r a n ce in in d ivid u al s tu d ie s . D o u b lets a r e a p r o b le m fo r in te r p r e ta tio n , but the p u rp o se o f the study m u st be tak en into a c co u n t. M any of th e s e d o u b lets o c c u r r e d in o th e r stu d ie s u n d er c o n sid e r a tio n h e r e , in m an y c a s e s w ith m o r e than tw o t e s t s . It i s the b e lie f of th e au th or that th is r e p e titio n o f su ch h y p o th e siz e d fa c to r s , w h ich o n ly h ave tw o t e s t s , p r o v id e s enough e v id e n c e o f th e ir e x is te n c e to e n a b le th e m to a c t a s su p p ort fo r th e in v a r ia n c e of th e s e fa c to r s . 80 T h e la s t p r o b le m th at can be se e n in th e s e r e s u lt s h a s to do w ith th e PM A stu d y . T h is study had th e p o o r e s t r e s u lt s in te r m s o f c le a r cu t and in d ep en d en t fa c to r s , and in te r m s of se co n d a r y lo a d in g * Som e o f th e c o n fu sio n in th e s e r e s u lt s a r e p o s s ib ly due to th e la c k o f G ra m m la n p r o p e r tie s o f th e a n a ly se d c o r r e la tio n m a tr ix . It is u n fortu n ate that a m a tr ix w ith p ro d u ct m o m en t c o r r e la tio n c o e ffic ie n ts w a s not a v a ila b le . In the fo llo w in g d is c u s s io n ch a p ter, p oor r e s u lts fr o m th is stu dy w ill th e r e fo r e be e x a m in e d c a r e fu lly . On th e w h o le , it can be sa id th at th e r e s u lt s a r e g e n e r a lly su p p o rtiv e o f the S tr u c tu r e -o f-I n te lle c t m o d e l. T he h y p o th e siz e d fa c to r s w e r e u su a lly id e n tifia b le and m a rk ed by the p r e d ic te d t e s t s . T he im p o r ta n c e o f th e s e r e s u lt s a s e v id e n c e fo r fa c to r ia l in v a r ia n c e o f th e s e fa c to r s i s e x a m in e d in th e su b seq u en t c h a p te r . C H A P T E R IV DISCUSSION T he p r e v io u s s e c tio n r e p o r te d th e r e s u lt s o f th e r o ta tio n s fo r e a c h o f th e e ig h t stu d ie s u n d er in v e stig a tio n h e r e . T he fa c to r s o b ta in e d in e a ch study w e r e ex a m in ed and th e r e s u lt s e x p la in e d . T h is se c tio n fo llo w s a d iffe r e n t ap p roach to th e r o ta tio n a l r e s u lt s . In th is se c tio n , e a ch o f the unique S tr u c tu r e -o f-I n te lle c t fa c to r s th at w a s h y p o th e sise d to e x is t In th e data o f th e s e stu d ie s w ill be e x a m in e d . T he in ten t of th is e x a m in a tio n w ill be to d e te r m in e th e d e g r e e o f c o n fid e n c e one can p la c e in th e e x is te n c e o f e a c h fa c to r , that i s , w h eth er th e r e s u lts in d ic a te that fa c to r ia l in v a r ia n c e d o e s e x is t in th e s e d ata. T he fa c to r s w ill be p r e s e n te d in th e sa m e o r d e r a s in T a b le 2, w h ere e a ch fa c to r h a s b een lis t e d a s w e ll a s the n u m b er of stu d ie s it a p p e a r s in and th e n u m b er o f t e s t s that w e r e h y p o th e siz e d to m e a s u r e it . F o r e a c h fa c to r th e r o ta tio n a l r e s u lts fr o m a ll th e stu d ie s in w h ich it o c c u r r e d w ill be p r e s e n te d . T he a b b r e v ia tio n o f th e study of w h ich a t e s t is p a rt fo llo w s th e n a m e of the t e s t . An a s t e r is k w ill in d ic a te a sig n ific a n t lo a d in g o f a t e s t w h ich w a s not h y p o th e siz e d fo r the fa c to r u n d er d is c u s s io n . C o g n itio n F a c to r s T h e fa c to r s to be d is c u s s e d in th is f ir s t s e c tio n a r e a ll in v o lv e d 81 82 w ith w hat the S tr u c tu r e -o f-I n te lle c t m o d e l c a lls th e c o g n itio n o p e r a tio n . T h is o p e r a tio n is g e n e r a lly d efin ed a s a w a r e n e s s , im m e d ia te d is c o v e r y o r r e d is c o v e r y , o r r e c o g n itio n of in fo rm a tio n in v a r io u s fo r m s : c o m p r e h e n sio n o r u n d ersta n d in g . S om e of th e fa c to r s of th is se c tio n a r e the o ld e s t and m o st w e ll-k n o w n of the in te lle c tu a l a b ili t i e s . S p e c ific d e fin itio n s w ill be g iv en w ith e a ch fa c to r . CMU - C ogn ition of S em a n tic U n its 3 0 . V ocab u la ry (PM A) . 75 . 34 (DMR) 1. R ead in g H (PM A ) . 52 .3 1 (EMI) 20. V ocab u lary (T&T) . 87 21. S e n te n c es (T& T) . 83 2 4 . Sam e o r O p p o site (T&T) . 75 2 2 . P a ra g r a p h s (T&T) . 73 4. C om p letion (T&T) . 72 18. R ead in g I (A&L) . 83 27. V ocab u lary (A&L) .6 8 19. R eading II (A&L) .6 4 * 2 6 . V erb al A n a lo g ie s (A&L .4 2 .5 2 (C FR ) .3 5 (CMR) .3 1 (CSS) * 3. D ecod in g (A&L) . 37 .4 5 (CSS) The CM U a b ility i s d efin ed a s th e a b ility to co m p reh en d the m ea n in g s o f w o rd s o r id e a s . T h is fa c to r is p rob ab ly the b e st know n and m o st w id ely d e m o n str a te d o f a ll th e in te lle c tu a l fa c to r s . Its h is to r y can be tr a c e d back to C y r il B u rt at the turn o f the c e n tu r y . C h a r a c te r is tic a lly , th is fa c to r Is m e a s u r e d by so m e fo r m o f a v o ca b u la ry t e s t . In p a r tic u la r , t e s t s w h ich r e q u ir e the e x a m in e e to p r o v id e d e fin itio n s o r o th e r r e s p o n s e s w h ich in d ic a te a fa m ilia r ity w ith th e w ord w ork q u ite w e ll. G u ilfo rd (1967) in d ic a te s that th e CM U a b ility d e m o n s tr a te s not on ly th e sc o p e o f a p e r s o n 's v o ca b u la ry and read in g a b ility , but a ls o can be d efin ed by t e s t s w h ich r e q u ir e a p r e c is e k n ow led ge o f the m ea n in g s o f fa m ilia r w o r d s. T hat i s , a 83 p e r so n m u st be ab le to d is tin g u ish b etw een fin e sh a d in g s in m ea n in g o f fa m ilia r w o r d s, a s w e ll a s be a b le to know th e m e a n in g s of l e s s fa m ilia r w o r d s. T h e CM U fa c to r w a s h y p o th e siz e d to e x is t in th r e e stu d ie s u n d er a n a ly s is h e r e . T hey w e r e T h u r sto n e 's P M A , th e T h u rsto n e and T h u rsto n e study and A d kins and L y e r ly . In g e n e r a l, a read in g c o m p r e h e n sio n and v o c a b u la r y te a t w e r e u s e d in e a ch study to m a rk th e CMU fa c to r . T h e T h u rsto n e & T h u rsto n e study a ls o had t e s t s o f a slig h tly d iffe r e n t n a tu r e . T h e C o m p letio n t e s t r e q u ir e s th e su b je ct to f ill in th e w ord w hen g iv en th e d e fin itio n . T he ta sk in S am e o r O p p o site w a s to c h o o se the on e w o rd in fo u r w h ich w a s the sa m e or o p p o site in m ea n in g to a g iv en w o rd . T he S e n te n c e s t e s t c o n ta in s s e n te n c e s w h ich th e su b je ct m u st c o m p le te and k e e p th e m ea n in g o f th e s e n te n c e s in ta c t. T h e P a r a g r a p h s t e s t is a read in g c o m p r e h e n sio n te a t. A s can be se e n fr o m th e r e s u lt s , a ll th e t e s t s h y p o th e siz e d fo r the CMU fa c to r in a ll th r e e s tu d ie s , had la r g e sig n ific a n t lo a d in g s on th e a p p ro p ria te fa c to r . O nly in the PM A stu d y, did CMU t e s t s h ave sig n ific a n t se co n d a r y lo a d in g s . T h e se w e r e e x p la in ed in the p r e v io u s s e c tio n . In th e A d k in s & L y e r ly stu d y, tw o non-C M U t e s t s had sig n ific a n t lo a d in g s on the CM U fa c to r . T h e se o u tc o m e s p rob ab ly in d ic a te that the t e s t s n e ed ed th e v o ca b u la ry a b ility fo r ad eq u ate p e r fo r m a n c e . T h e se lo a d in g s a r e not th at s u r p r isin g o r u n r e a so n a b le . G u ilford (1967) m e n tio n s that c a r e fu l c o n tr o l m u st be fo llo w ed in c o n str u c tio n o f v e r b a l t e s t s o r the CMU a b ility m igh t 84 c o m e into p la y . It w ou ld s e e m that if it is p o s s ib le to d e m o n str a te p s y c h o lo g ic a l in v a r ia n c e , th is fa c to r i s that c a s e . A ll the t e s t s in the th r e e stu d ie s c le a r ly fit the CMU d e fin itio n in th e S tr u c tu r e -o f-I n te lle c t. In e a ch stu d y, th e CMU fa c to r e m e r g e d c le a r ly w ith the h y p o th e siz e d t e s t s lo a d in g h e a v ily on it. T he c o n c lu sio n s e e m s so m ew h a t o b v io u s that th e CM U fa c to r can be sa id to e x is t in th e data o f th e s e s tu d ie s , and th at th e s e t e s t s d e fin e it. CMC - C ogn ition of S e m a n tic C la s s e s 2 . V erb a l C la s s ific a tio n (PM A ) .6 7 .3 1 (C F T ) 3 . W ord G rou ping (PM A) .6 6 .3 4 * 2 0 . S y llo g is m s (PM A) .3 3 .4 7 (C F T ) . 30 (EM I) 15. P r o v e r b s (S. S) .6 4 20. W ord P a tte r n s (S. S) .4 9 .4 0 (CSS) * 1 7 . S p ellin g (S. S) .3 0 .3 5 (CSU) T h is a b ility is d efin ed a s the a b ility to r e c o g n iz e com m on p r o p e r tie s of w o r d s, id e a s and o b je c ts . T he CM C fa c to r w a s p r e d ic te d to e m e r g e in T h u r sto n e 's PM A study and in h is la te r study on S im p le S tr u c tu r e . T he t e s t s u se d in th e s e stu d ie s a r e d iffe r e n t. V erb a l c la s s if ic a t io n h a s the su b je ct in d ic a te in w h ich o f two c a t e g o r ie s e a c h o f s ix t e s t w o r d s sh ou ld be p la c e d . T h e W ord G rouping t e s t w a s an e x c lu s io n t e s t w h er e th e su b je c t w a s to in d ic a te w h ich o f fiv e w o rd s did not b elo n g w ith th e o th e r fo u r . T h e s e t e s t s fit w e ll w ith th e d e fin itio n of the S tr u c tu r e -o f- In te lle c t a b ility o f C M C . In fa c t, th e V erb a l C la s s ific a tio n t e s t o f the PM A h a s b een u s e d in stu d ie s by A R P and h a s b een found to m a rk CMC in th o se s tu d ie s . T he o th e r PM A t e s t . W ord G rou ping, i s v e r y 85 s im ila r to th e W ord C la s s ific a tio n t e s t o f A R P . T h is t e s t a ls o h a s b een u se d by A R P to m e a s u r e CM C. G u ilford (1967) in d ic a te s that th e CMC t e s t s h a v e su ffe r e d fr o m se c o n d a r y v a r ia n c e s . T h is s e e m s to a g r e e w ith th e r e s u lt s p r e s e n te d h e r e , a s th r e e o f th e fo u r h yp o th e s iz e d t e s t s h a v e sm a ll se c o n d a r y lo a d in g s on o th e r f a c t o r s . T he p r e s e n c e o f the S y llo g is m s te s t and S p ellin g t e s t on th is fa c to r h a s a lr e a d y b een d is c u s s e d and is not g e rm a n e to th e p r e s e n t d is c o u r s e . It w ou ld s e e m that th e r o ta tio n a l r e s u lt s do c o n fir m th e e x is te n c e o f CMC in th e p r e d ic te d p la c e s . T he fa c t that t h e s e t e s t s h ave se c o n d a r y lo a d in g s , w h ile b ein g d is tr a c tin g i s not out of lin e w ith the r e s u lt s found by G u ilfo r d 's p r o je c t. O nce a gain th e fa c to r h as e m e r g e d w h ere p r e d ic te d and d efin ed by th e t e s t s h y p o th e siz e d to m e a s u r e it. It s e e m s that th e s e r e s u lts do o ffe r su p p o rt to th e in v a r ia n c e o f the CM C fa c to r , CM R - C ogn ition o f S em a n tic R e la tio n s 28. W ord S q u a r es (A b L ) .6 3 . 32 (CSS) * 4 . F ig u r e A n a lo g ie s (A&L) .4 1 .5 1 (C F R ) 26. V erb a l A n a lo g ie s (A&L) .3 5 . 52 (C F R ) .4 2 (CM U) .5 1 (CSS) 16. P ic tu r e A n a lo g ie s (A&L) . 28 .4 1 (C F R ) T he a b ility to s e e r e la tio n s b etw een id e a s o r m e a n in g s o f w o r d s is c a lle d CM R. O nly one study had enough t e s t s th at w e r e h y p o th e s iz e d to m e a s u r e CMR fo r it to be in v e stig a te d . T he A d k in s & L y e r ly study had th r e e t e s t s p r e d ic te d to m e a s u r e C M R . W ord S q u a r es is a m a tr ix t e s t w h er e the su b ject m u st w r ite the f i r s t le t t e r o f the m is s in g w o rd . It c le a r ly le a d s th is fa c to r . T h e se c o n d a r y 86 lo a d in g on CSS i s p rob ab ly fr o m th e m eth o d o f r e s p o n s e , i. e ., w r itin g th e f ir s t le t t e r . T he o th e r two t e s t s fo r th is fa c to r a r e V erb a l A n a lo g ie s and P ic tu r e A n a lo g ie s . V erb a l A n a lo g ie s i s a sim p le a n a lo g ie s t e s t that r e q u ir e s th e su b je c t to c h o o se w h ich w ord c o r r e c tly c o m p le te s th e a n a lo g y . P ic tu r e A n a lo g ie s is a s im ila r te s t , but w ith a fig u r a l fo r m a t. T h e r e s u lts fo r therfe two t e s t s a r e not v e r y su p p o rtiv e o f th e CMR fa c to r . In fa c t, th e r e s e e m s to b e a g r e a t d eal o f confoun din g w ith the o th e r r e la tio n s fa c to r that e x is t s in th e b a tte r y , n a m e ly C F R . It s e e m s that th is fa c to r can h a rd ly be o ffe r e d a s e v id e n c e o f fa c to r ia l in v a r ia n c e fo r the CM R fa c to r of th e A R P in v e s tig a tio n s . Its fa ilu r e to e m e r g e m ay be due to th e la c k o f enough p u re m e a s u r e s fo r both CM R and C F R in th e b a tte r y . C FU - C o g n itio n of F ig u r a l U n its 12. M u tilia ted W ords (A&L) .6 0 2 1 . S tr e e t G e s ta lt C o m p letio n (A& L). 56 2 5 . P ic tu r e C o m p a riso n (B e) . 53 * 8. H idden P ic tu r e s (B e) .3 9 11, M u tilia ted W ords (B e) . 18 27 . G e o m e tr ic F ig u r e s (B e) . 18 17. S tr e e t G e sta lt C o m p letio n (B e) .1 3 T h is fa c to r w a s f ir s t is o la te d by T h u rsto n e (1 944) and c a lle d " sp eed of p e r c e p tio n " . It w a s la te r id e n tifie d by F r e n c h (1951) a s " g e sta lt p e r c e p tio n " . In th e S tr u c tu r e -o f-I n te lle c t it is c a lle d C FU and is d e fin e d a s th e a b ility to " c lo se " fig u r a l in fo r m a tio n to p e r c e iv e a c o m p le te v is u a l fo r m . In th e p r e s e n t in v e s tig a tio n , it w a s p r e d ic te d to e m e r g e in tw o stu d ie s: A d k in s & L y e r ly and B e ch to ld t. T he A d k in s & L y e r ly study co n ta in ed th e tw o t e s t s w h ich h a v e b een 87 u s e d r e p e a te d ly by A R P to d e fin e th is fa c to r . B oth M u tila ted W ords and S tr e e t G e sta lt C o m p letio n a r e th e c la s s i c C FU t e s t s . In th e A d k in s & L y e r ly stu d y , th e s e t e s t s c le a r ly and u n iv o c a lly m a r k the C FU fa c to r . T h e r e s u lt s fr o m th e B ech to ld t study a r e a to ta l c o n tr a d ic tio n to th o se found in a ll o th e r c a s e s . T he n o r m a l m a r k e r s o f M u tila ted W ords and S tr e e t G e sta lt C o m p letio n did not h ave any sig n ific a n t lo a d in g s on any fa c to r s a n a ly z ed in th e B ech to ld t stu d y. In a d d itio n , the G e o m e tr ic a l F ig u r e s t e s t w h ich w a s h y p o th e siz e d a s a C F U did not lo a d sig n ific a n tly on any fa c to r . In stea d , a d ou b let fa c to r e m e r g e d w ith P ic tu r e C o m p a riso n and H idden P ic t u r e s . A s sta te d e a r lie r , th is fa c to r can n ot be id e n tifie d a s C F U . T he r e s u lts o f th e C FU fa c to r fo r in v a r ia n c e a r e a lit t le c o n fu sin g . In A d k in s & L y e r ly , the fa c to r e m e r g e d a s p r e d ic te d and w ith on ly th e h y p o th e siz e d t e s t s lo a d in g on it. T h is w ou ld s e e m to su p p ort in v a r ia n c e fo r the C FU fa c to r . T he la c k o f e m e r g e n c e o f the C F U fa c to r in the B e ch to ld t b a ttery d o e s not h e lp the c a s e fo r in v a r ia n c e o f th is fa c to r . T he c o r r e la tio n b etw een M u tila ted W ords and S tr e e t G e sta lt C o m p letio n i s on ly . 11, w h ich i s to ta lly at o d d s w ith th e c o r r e la tio n s b etw een th e s e t e s t s in A R P stu d ie s and in A d k in s & L y e r ly . T he fa c t th at the C F U t e s t s did not lo a d on a n o th er fa c to r i s c o m fo r tin g e v id e n c e that th ey w e r e not m is c la s s if ie d . A t th is p oin t it s e e m s the s a f e s t c o n c lu sio n to m ak e w ith r e g a r d to C F U is that it d o e s e x is t and that so m e u n u su al co n d itio n i s p r e v en tin g s o lid su p p ort fro m th e B e ch to ld t stu d y. 88 C F R - C ogn ition o f F ig u r a l R e la tio n s 2 0 . S e r ie s (A&L) .5 3 .3 1 (C F T ) * 2 6 . V erb a l A n a lo g ie s (A&L) . 52 .3 1 (CSS) . 35 (CM R) .4 2 (CM U) 4. F ig u r e A n a lo g ie s (A&L) .5 1 .4 1 (CM R) 17. P r o g r e s s iv e M a tr ic e s (A&L) .4 1 .3 0 (CSS) * 1 6 . P ic tu r e A n a lo g ie s (A&L) .4 1 10. M ixed S e r ie s (A&L) .4 0 .4 6 (CSS) .3 5 (CM U) *1 5 . P a p e r F o ld in g (A&L) .3 9 .4 0 (C F T ) T he a b ility to r e c o g n is e fig u r a l r e la tio n s b etw een fo r m s is c a lle d C F R , T h is a b ility w as p r e d ic te d to emergp in on ly th e A d k in s & L y e r ly stu d y. F ou r t e s t s w e r e h y p o th e siz e d to m e a s u r e th is fa c to r . A ll of th e s e t e s t s did h a v e sig n ific a n t lo a d in g s on a C F R fa c to r . H o w e v e r , th r e e n o n -C F R t e s t s a ls o had sig n ific a n t lo a d in g s on th is fa c to r , and a ll th e C FR te s ta had sig n ific a n t se c o n d a r y lo a d in g s . In r e s e a r c h con d u cted by A R P , C FR h a s b een d e fin e d by t e s t s o f fig u r a l a n a lo g ie s o r m a tr ix typ e t e s t s . T he a n a lo g ie s ty p e o f te s t is r e p r e s e n te d by F ig u r e A n a lo g ie s. T he m a tr ix typ e is show n by th e P r o g r e s s iv e M a tr ic e s t e s t . S e r ie s and M ixed S e r ie s a r e fig u r a l t e s t s that w e r e u s e d in th is stu d y. In the p a st, s e r i e s t e s t s h a v e had se c o n d a r y lo a d in g s , u su a lly on a s y s t e m s fa c to r . T he se c o n d a r y lo a d in g s and a n o n -p r e d ic te d lo a d in g have been e x p la in ed in th e p r e v io u s s e c tio n . W hen ex a m in in g th is fa c to r fo r p u r p o se s o f in v a r ia n c e , it i s im p o rta n t to n o te that th e t e s t s w h ich d e fin e th e fa c to r h e r e a r e v e r y s im ila r to th o se u se d by A R P to m a rk th is fa c to r . A ls o , th is fa c to r a s d efin ed by th e s e t e s t s fits the d e fin itio n o f C F R . S ec o n d a r y lo a d in g s o f th e C FR t e s t s a r e not u n r e a so n a b le and can be e x p la in e d . T he 89 p r e s e n c e o f n o n -h y p o th e siz e d t e s t s i s so m ew h a t d is c o m fo r tin g . T he V erb a l A n a lo g ies te s t h a s a str o n g lo a d in g on th is fa c to r , and y e t it a p p e a r s fr o m the ite m s to be a p u rely se m a n tic t e s t . A s e v id e n c e o f in v a r ia n c e , th is fa c to r s e e m s to be of a p r o m isin g n a tu re , but d e fin ite ly not c o n c lu s iv e . C FS - C ogn ition o f F ig u r a l S y s te m s 10. F la g s (PM A ) . 75 . 59 (C F T ) 2 6 . H ands (PM A ) .5 5 .3 4 (C F T ) 8. C u b es (PM A ) .4 7 .5 1 (CFT .3 3 (CSU) *12. L o z e n g e s B (PM A ) .3 4 . 58 (C F T ) * 1 3 . S u rfa c e D e v elo p m e n t (PM A ) .3 2 .6 3 (C F T ) Sp atial fa c to r s h ave a lo n g h is to r y . T h u rsto n e (1938) is o la te d on e sp a ce fa c to r in h is PM A b a tte r y . T he A r m y A ir F o r c e in v e s t i g a tio n s la te r se p a r a te d tw o sp a c e f a c to r s . T h e se w e r e in c o r p o r a te d Into the S tr u c tu r e -o f-I n te lle c t a s C F S and C F T . T h e C FS fa c to r is th e a b ility to ap p reh en d v is u a lly th e sp a tia l a r r a n g e m e n ts o f th in g s in o n e 's p s y c h o lo g ic a l fie ld . A p a r tic u la r ly good m a r k e r t e s t o f th is fa c t is S p atial O rien ta tio n , P a r t V o f the G u ilfo r d -Z im m e r m a n A p titu de S u rv ey . W hile th is t e s t g e n e r a lly d e fin e s C F S c le a r ly , th e r e h a s b een a p r o b le m o f to ta lly se p a r a tin g th e C FT and C FS f a c t o r s , ev en in A R P s tu d ie s . E ven under the m o s t c o n tr o lle d t e s t c o n str u c tio n p r o c e d u r e s , it h a s b een found to be v e r y d iffic u lt to e lim in a te th e CFT v a r ia n c e fr o m C FS t e s t s . T he T h u rsto n e PM A b a ttery h a s a la r g e c o n c e n tr a tio n of sp a tia l t e s t s in it, m o s t o f w h ich a r e C F T t e s t s . H o w e v e r , so m e o f the sp a tia l t e s t s w e r e p r e d ic te d to be e ith e r p u re C FS t e s t s o r at le a s t p red o m in a n tly C FS t e s t s . It w a s d e c id e d to try and is o la te 90 th is fa c to r , e v e n though it w a s e x p e c te d to find th e p r e d ic te d C FS t e s t s to h ave lo a d in g s on the C FT fa c to r . H ands and C u b es w e r e p r e d ic te d a s b ein g a lm o s t p u re m e a s u r e s of C FS and F la g s w a s p r e d ic te d to be p red o m in a n tly C F S , but w ith a d e fin ite am ount of C F T v a r ia n c e p r e s e n t. S u rfa ce D e v elo p m e n t w as p r e d ic te d a s b ein g a C F T t e s t . T h e r e s u lts o f th e a n a ly s is w e r e a s e x p e c te d . T he p r e d ic te d CFS t e s t s did in d eed d e fin e a fa c to r , but they a ls o had sig n ific a n t lo a d in g s on the C F T fa c to r . L o z e n g e s B sh ow ed it s C F S v a r ia n c e by h avin g a sig n ific a n t se c o n d a r y lo a d in g th e r e . T h e s m a ll lo a d in g o f S u rfa ce D e v elo p m e n t i s not too s u r p r is in g , though u n e x p ec ted . T h is lo a d in g cou ld e a s ily a r is e fr o m the c o r r e la tio n b etw een th e C FS and C F T fa c to r s . It sh ou ld be n oted at th is poin t that fin d in g th e C F S fa c to r w a s a ttem p ted on ly in th e PM A stu d y . In the o th e r s tu d ie s , sp a tia l t e s t s su ch a s F ig u r e s undoubtedly have C FS v a r ia n c e in th em , but w e r e a llo w e d to go to C F T . T h is i s b e c a u se only in the PM A study w e r e th e r e enough t e s t s that w e r e c o n sid e r e d to be p u re o r p red o m in a n tly C FS t e s t s to a ttem p t to is o la te the C FS fa c to r fr o m th e C F T fa c to r . T h e r e fo r e , in th e o th e r s tu d ie s , th e C FT fa c to r , w h ile b ein g e s s e n t ia lly C F T , w ill a lm o s t c e r t airly r e p r e s e n t a m ix tu r e o f C F T and so m e C F S v a r ia n c e . W hile the C F S fa c to r h e r e is n ot to ta lly c le a r , it d o e s s e e m to r e s e m b le that found by A R P a s C F S . E v en it s con foun din g w ith C F T c o r r e s p o n d s to that found by A R P . The e m e r g e n c e o f th e fa c to r in th e p r e d ic te d m a n n er g iv e s su p p ort to the p s y c h o lo g ic a l in v a r ia n c e 91 h e r e . C F T - C ogn ition o f F ig u r a l T r a n sfo r m a tio n s 14. P u n ch ed H o le s (PM A) . 82 .4 0 (CSS) 11. F o r m B oard (PM A ) . 73 13. S u rfa c e D e v elo p m e n t (PM A ) .6 3 . 32 (C FS) 9. L o z e n g e s (PM A ) .6 0 * 1 0 . F la g s (PM A ) . 59 . 75 12. L o z e n g e s B (PM A ) .5 8 . 34 (C FS) * 8 . C u b es (PM A ) .5 1 .4 7 (C FS) * 2 0 . S y llo g is m s (PM A ) .4 7 .3 3 (CM C) . 30 (EM I) * 1 5 . A r e a s (PM A ) .4 5 * 1 9 . C ode W ords (PM A) . 38 . 78 (CSS) * 2 6 . H ands (PM A ) .3 4 . 55 (C FS) * 2. V erb a l C la s s ific a tio n (PM A ) .3 1 .6 7 (CM C) 3. C a r d s (T&T) .7 9 7. F ig u r e s (T&T) .6 8 10. F la g s (T& T) .6 4 6. F ig u r e s (A&L) .8 9 1. C a rd s (A&L) . 72 23. S u rfa ce D e v e lo p m e n t (A&L) . 55 15. P a p e r F o ld in g (A&L) .4 0 . 39 (C FR ) * 2 0 . S e r ie s (A&L) .3 1 . 53 (C FR ) * 5. F ig u r e S e r ie s (A&L) . 30 .4 7 (CSS) . 33 (C F R ) .3 1 (E F U ) 14. P a in ted B lo c k s (A&L) . 16 .3 8 (CSS) . 34 (DSU) 4 . F ig u r e s (S. S) . 85 2. C a rd s (S .S ) . 80 18. S q u a r es (S .S ) . 58 . 45 (CSS) 10. M ec h a n ic a l M o v em en ts (S. S) .4 3 * 1 2 . N u m b er P a tte r n s (S .S ) .3 2 . 58 (CSS) 7. C a rd s (B e) . 78 1. F la g s (B e) .6 6 19. F ig u r e s (B e) .6 6 A s e v id e n c e d fr o m th e lo n g l i s t o f t e s t s lo a d in g on th is fa c to r , it w a s w e ll r e p r e s e n te d in th e stu d ie s u n d er in v e s tig a tio n . T h is fa c to r w a s p r e d ic te d to e m e r g e In fiv e stu d ie s and to be m a rk ed by a to ta l o f 20 t e s t s . In so m e c a s e s , the sa m e t e s t s w e r e u sed in m o r e than on e stu d y. F o r e x a m p le , the F ig u r e s , C a rd s and F la g s t e s t s o c c u r r e d in s e v e r a l s tu d ie s . 92 T h e C F T fa c to r i s d efin ed a s th e a b ility to v is u a liz e how a g iv en fig u r e o r o b je ct w ill a p p ea r a fte r g iv en c h a n g e s, su ch a s u n fold in g o r r o ta tio n . It w ill be r e c a lle d fr o m the p r e v io u s d is c u s s io n o f C FS th at th e tw o fa c to r s h ave lo n g b een d iffic u lt to s e p a r a te , u s u a lly b e c a u se th e t e s t s in v o lv ed h a v e both c o m p o n e n ts. G u ilford (1967) l i s t s F o r m B o a r d s, P u n ch ed H o le s , S u rfa ce D e v elo p m e n t and M ec h a n ic a l P r in c ip le s a s b ein g c le a r m e a s u r e s o f th is fa c to r . T h e se t e s t s a r e in c lu d e d in the PM A study and a s the r e s u lts in d ic a te do in d eed m a rk the v is u a liz a tio n fa c to r . In one o f th e s tu d ie s , A d k in s & L y e r ly , so m e o f th e C F T t e s t s h ave te n d e n c ie s to h ave s ig n ific a n t se c o n d a r y lo a d in g s . T he s p e c ific e x p la n a tio n s o f th e s e h ave b een g iv en in th e p r e v io u s s e c tio n , but a g e n e r a l ex p la n a tio n is that fo r lo a d in g s in CSS t h is is u su a lly an in d ic a tio n o f sy m b o lic r ea so n in g v a r ia n c e . In th e PM A stu d y, the C F T fa c to r h a s m any t e s t s w h ich w e r e h y p o th e siz e d fo r o th e r fa c to r s lo a d in g on it. In s o m e c a s e s th is m ay be due to th e o v e r a ll str e n g th o f the C FT fa c to r . T he C F T fa c to r e m e r g e d in e a ch o f th e fiv e stu d ie s it w a s p r e d ic te d fo r . In a ll c a s e s it w a s d efin ed by the t e s t s h y p o th e siz e d fo r it. In s o m e in s ta n c e s th e r e w e r e so m e se c o n d a r y lo a d in g s , but th e s e a r e e a s ily e x p la in a b le and h a v e a lr e a d y b een d is c u s s e d . T he id e n tific a tio n o f th is fa c to r i s m ad e e a s y by th e u s e o f th e sa m e t e s t s in d iffe r e n t s tu d ie s . T he e v id e n c e fo r the in v a r ia n c e o f th is fa c to r is v e r y str o n g . C F I - C ogn ition o f F ig u r a l Im p lic a tio n s 19. P u r s u it (T& T) . 53 .3 4 (E F U ) * 1 3 , Id en tica l P ic tu r e s (T&T) .4 2 .4 4 (E F U ) 16. M a ze I (T& T) .3 5 93 T he a b ility to f o r e s e e the c o n se q u e n c e s in v o lv e d in fig u r a l p r o b le m s i s la b e le d C F I. T h is a b ility w a s f ir s t sou gh t in th e A rm y A ir F o r c e in v e s tig a tio n s , w h er e e m p h a s is on fo r e s ig h t and p lan n in g in fig u r a l a r e a s w a s c o n s id e r e d im p o rta n t fo r p ilo t s . R oute P la n n in g and M aze T r a cin g w e r e d e v e lo p e d in th is m od e and a s C o m p e titiv e P la n n in g and P la n n in g a C ir c u it w e r e d e v e lo p ed la t e r . T h e se t e s t s a r e of a m a z e v a r ie ty and r e q u ir e the su b je ct to f o r e s e e th e b e s t str a te g y to ta k e o r to d e te r m in e th e b e st path to fo llo w . T h e C F I fa c to r w a s m o r e r e c e n tly d efin e d (H offm an, e t. a l . , 1968) by te a ts w h ich r e q u ir e s e x tr a p o la tio n o f in c o m p le te lin e s o r fig u r e s . T he C F I fa c to r w a s p r e d ic te d to e m e r g e on ly in th e T h u r sto n e and T h u rsto n e study and to be d efin ed by two t e s t s . Both o f th e s e t e s t s have th e ir m a jo r lo a d in g on th is fa c to r . H o w e v er , an E F U t e s t a ls o h a s a la r g e lo a d in g on th is fa c to r . W hile it s e e m s lik e ly that th is fa c to r r e p r e s e n ts C F I, no r e a l p r o o f can be o ffe r e d . It is u n fortu n ate that th is fa c to r o c c u r r e d in on ly one stu d y , o r it m ig h t be p o s s ib le to put m o r e fa ith in th e e x is te n c e o f th is fa c to r fo r in v a r ia n c e te r m s . CSU - C ogn ition o f S y m b o lic U n its 6. D isa r r a n g e d W ords (PM A ) .6 3 . 38 (DM R) 29. S p ellin g (PM A ) .5 6 * 5. In ven tive O p p o site s (PM A) . 36 . 58 (DM R) * 7. In ven tive S yn on ym s (PM A ) .3 5 . 52 (DM R) * 8. C u b es (PM A ) . 33 .4 7 (C F S) . 51 (C F T ) 28. W ord P u z z le s (T&T) .6 0 . 44 (DSU) 14. In co m p le te W ords (T&T) . 58 2. M ir r o r R ead in g (T&T) .4 7 *2 6 . S u ffix e s (T& T) . 36 . 54 (DSU) 1. A n a g r a m s (T&T) . 33 . 50 (DSU) *2 3 . R h ym in g W ords (T&T) .3 3 . 53 (DSU) 94 11. M ir r o r R ead in g (S. S) .7 6 . 36 (CSS) 3 . D isa r r a n g e d W ords (S. S) .4 9 17. S p e llin g (S. S) .3 5 .3 0 (CM C) 4 . A n a g r a m s (C a r. ) .5 3 6 . D isa r r a n g e d W ords I ( C a r .) .5 0 .3 2 (NM U) 10. D isa r r a n g e d M o rp h e m e s (C ar. ) . 50 . 44 (DSU) 1. D isa r r a n g e d W ords II (C a r. ) .4 9 . 3 5 (MSI) * 2. W ords S c o r e (C a r. ) .4 1 . 58 (DM U) 3. M ir r o r R ead in g (T a y lo r) .4 4 8. A n a g r a m s (T a y lo r ) .4 4 . 4 9 (DSU) T he C F I fa c to r i» d efin e d a s th e a b ility to r e c o g n is e g ra p h ic sy m b o lic u n its, su ch a s w o r d s . In r e s e a r c h con d u cted by A R P , th e unit in v o lv ed in t e s t s o f th is fa c to r h a s u su a lly b een th e w o rd . T h e se t e s t s a r e c o n c e r n e d w ith th e a b ility to r e c o g n is e fa m ilia r le t te r c o m b in a tio n s a s w o r d s . In p a r tic u la r , the t e s t s u s e d to m a rk CSU h ave b e e n of th e D ise m v o w e le d W ords T e s t, w h ere w o rd s a r e p r e se n te d w ith b lan k s w h er e v o w e ls n o r m a lly a p p ea r , o r the C o r r e c t S p ellin g t e s t , w hen th e e x a m in e e m u st d e te r m in e w h eth er a w ord i s sp e lle d c o r r e c tly o r n ot, o r the W ord C om b in ation t e s t , w h e r e the su b je ct m u st g e n e r a te n ew w o r d s fr o m th e en d s and b e g in n in g s o f p r e se n te d w o r d s . G u ilfo rd (1967) a ls o r e c o m m e n d s a t e s t by M ooney (1954) a s a m e a s u r e o f C SU . The R e v e r s e d R ead in g t e s t fr o m M ooney p r e s e n ts s ta te m e n ts w ith w o r d s s p e lle d b a c k w a rd s. T he su b ject m u st e x tr a c t th e m ea n in g and a n sw e r w h eth er the sta te m e n t is tr u e o r f a ls e . In th e p r e s e n t in v e s tig a tio n , th e t e s t s D isa r r a n g e d W ords I, D isa r r a n g e d W ords II, A n a g r a m s, In co m p lete W o rd s, and D isa r r a n g e d W ords a r e a ll w ord r e a r r a n g e m e n t t e s t a . In th e PM A and S im p le S tr u c tu r e stu d y, a S p ellin g t e s t su ch a s C o r r e c t S p ellin g is in c lu d e d . T he M ir r o r R ead in g i s v e r y s im ila r to th e p r e v io u s ly 95 m en tio n e d R e v e r s e d R ead in g o f M oon ey. T h e se t e s t s c h a r a c t e r is tic a lly lo a d ed on the CSU fa c to r . H o w e v e r , th e r e w a s u su a lly a fa ir n u m b er o f se co n d a r y lo a d in g s . In so m e c a s e s th e s e lo a d in g s w e r e on th e DSU fa c to r . The A n a g ra m s t e s t that a p p ea r s in th r e e o f the fo u r stu d ie s w a s h y p o th e siz e d to sp lit its v a r ia n c e b etw een DSU and CSU. T h e r e fo r e , its se co n d a r y lo a d in g s w e r e e n c o u r a g ed . In so m e c a s e s it is b e lie v e d that th is m a y h a v e le d to o th e r CSU t e s t s havin g s m a ll se co n d a r y lo a d in g s on th e DSU fa c to r . T h e CSU fa c to r a ls o s e e m s to h a v e p ic k e d up a n u m b er o f lo a d in g s fr o m t e s t s not h yp o th e s iz e d fo r it. T he s p e c ific e x p la n a tio n s fo r e a ch of th e s e lo a d in g s h a v e b een p r e se n te d b e fo r e . H o w e v er , it sh ou ld be n oted that th e s e lo a d in g s a r e u su a lly fr o m t e s t s w h ich p rob ab ly in clu d e th e CSU com p on en t in ad d ition to th e ir m a jo r fa c to r ia l c o m p o n e n ts. T h e CSU fa c to r e m e r g e d in a ll fo u r stu d ie s fo r w h ich it w a s p r e d ic te d . W hile the n u m e r ic a l r e s u lts a r e som ew h at m u d d led , th is i s p rob ab ly due to th e la c k o f fa c to r ia l p u rity o f th e t e s t s that w e r e p r e d ic te d to m e a s u r e CSU and it s c lo s e n eig h b o r, D SU . The p r e d ic te d t e s t s did a lw a y s lo a d on th e p r o p e r fa c to r fo r e a ch o f th e fo u r s tu d ie s . It s e e m s that th is is good e v id e n c e o f p s y c h o lo g ic a l in v a r ia n c e . CSS - C ogn ition o f S y m b o lic S y s te m s 19. C od e W ords (PM A ) . 78 . 38 (C F T ) 16. N u m b er S e r ie s (PM A) .4 3 . 32 (EM I) * 1 4 . P u n ch ed H o le s (PM A) .4 0 . 82 (C F T ) * 2 3 . N u m b e r-N u m b e r (PM A ) .3 5 . 90 (MSI) 15. A r e a s (PM A) .2 1 .4 5 (C F T ) 15. L e tte r S e r ie s (T&T) . 56 25. S e c r e t W ritin g (TfeT) . 52 17. N u m b er P a tte r n s (T& T) .4 3 12. H igh N u m b ers (TfcT) . 37 96 2. C ir c le s (A&L) .6 8 5. F ig u r e S e r ie s (A&L) .4 7 . 30 . 33 .3 1 (C F T ) (C F R ) (E F U ) 9. L e tte r S e r ie s (A&L) . 46 .3 5 (CMU) * 1 0 . M ixed S e r ie s (A&L) .4 6 .4 0 .3 5 (C FR ) (CM U) 3. D eco d in g (A&L) .4 5 . 37 (CMU) 13. N u m b er S e r ie s (A&L) .4 5 .3 1 (C F R ) * 1 4 . P a in te d B lo c k s (A&L) .3 8 .3 4 (DSU) * 2 8 . W ord S q u a r e s (A&L) .3 2 .6 3 (CM R) * 8. Id en tica l F o r m s (A&L) .3 1 .4 8 (E F U ) * 2 6 . V erb a l A n a lo g ie s (A&L) .3 1 . 52 . 35 .4 2 (C F R ) (CM R) (CMU) *1 7 . P r o g r e s s iv e M a tr ic e s (A&L) . 30 .4 1 (C FR ) 8. L e tte r S e r ie s (S. S) .6 3 12. N u m b er P a tte r n s (S. S) . 58 .3 2 (C F T ) 13. N u m b er S e r ie s (S. S) .5 1 9. M ark s (S. S) .4 9 7. L e tte r G rouping (S .S ) .4 6 *1 8 . S q u a res (S. S) .4 5 . 58 (C F T ) 1. A r e a s (S. S) .4 2 14. P a tte r n s (S .S ) .4 1 * 2 0 . W ord P a tte r n s (S .S ) .4 0 .4 9 (CMC) * 1 1 . M ir r o r R ead in g (S. S) . 36 . 76 (CSU) F o u r stu d ie s w e r e p r e d ic te d to con tain t e s t s w h ich m e a s u r e the CSS fa c to r . T he S tr u c tu r e -o f-I n te lle c t d e fin itio n o f th is fa c to r is th e a b ility to u n d ersta n d th e s y s te m a tic in te r r e la te d n e s s o f sy m b o ls w ith in an o r g a n ise d s e t. A sy m b o lic s y s te m is an o r g a n ise d o r str u c tu r a l p a ttern o r " g e s ta lt1 1 of le t t e r s o r n u m b e rs o r o th er sig n m a te r ia l. G u ilford (1967) sta ted th a t T h u r sto n e 's Induction fa c to r is in p a r t the CSS a b ility . In p a r tic u la r . T h u r sto n e 's t e s t L e tte r S e r ie s h a s b een found to be a m e a s u r e o f CSS a b ility in stu d ie s con d u cted by A R P . T he e s s e n c e o f CSS t e s t s i s the e x tr a c tio n o f the r u le fo r o r g a n isa tio n o f th e c o m p le x sy m b o lic s y s t e m . A fter e x tr a c tio n o f the r u le , th e t e s t s u su a lly r e q u ir e con tin u in g o r adding to the s y s te m o r a d e sc r ip tio n o f the ru le a s e v id e n c e o f the e x a m in e e 's 97 k n o w led g e o f the r u le . A R P h a s u s e d fo u r t e s t s to m e a s u r e th is a b ility : C ir c le R e a so n in g , L e tte r T r ia n g le , N u m b er S e r ie s , and L e tte r S e r ie s . E a ch o f th e s e h a s e ith e r d ir e c t o r v e r y s im ila r c o u n te r p a r ts in th e t e s t s fr o m th e fo u r stu d ie s that w e r e to in clu d e CSS. A L e tte r S e r ie s te s t w a s in clu d ed In th r e e of the fouT stu d ie s . A N u m b er S e r ie s te a t w a s a ls o in clu d ed in th r e e s tu d ie s . The r o ta tio n al r e s u lts fr o m the fo u r stu d ie s sh ow that the CSS fa c to r d o e s in d eed e m e r g e . In the PM A stu d y, th is fa c to r p ick ed up so m e a d d itio n a l t e s t s , a s w e ll a s having sig n ific a n t se co n d a r y lo a d in g s fo r the h y p o th e s iz e d CSS t e s t s . T h e s p e c ific e x p la n a tio n s fo r th e s e w e r e g iv en in the p r e v io u s c h a p te r . H o w e v e r , th is auth or b e lie v e s that so m e o f th is c o n fu sio n of th e fa c to r ia l c o m p o sitio n is due to th e n o n -G ra m m ia n p r o p e r tie s o f the c o r r e la tio n c o e ffic ie n ts u s e d by that stu d y. A v e r y stro n g and c le a r CSS fa c to r e m e r g e d in th e T h u rsto n e & T h u rsto n e stu d y. A ll fou r h y p o th e siz e d t e s t s had sig n ific a n t and u n iv o c a l lo a d in g s on the CSS fa c to r . T h is g iv e s a good d eal of su p p ort to the in d ep en d en t e x is te n c e of th is fa c to r . The CSS fa c to r in th e A d k in s & L y e r ly study is an e x tr e m e ly str o n g fa c to r . F iv e t e s t s w e r e p r e d ic te d to be CSS m e a s u r e s h e r e . A ll fiv e had s ig n ific a n t lo a d in g s on th is fa c to r , le d by the C ir c le s t e s t w h ich i s e s s e n t ia lly th e sa m e a s the C ir c le R ea so n in g t e s t o f A R P . In th is study th e r e is a g r e a t d ea l of se c o n d a r y lo a d in g ta k in g p la c e . T h is i s p rob ab ly due to th e fa c to r ia l c o m p le x ity of the m e a s u r e s in v o lv ed in te r m s o f th e S tr u c tu r e -o f- I n te lle c t. In th e S im p le S tru ctu re stu dy, th e r e w e r e se v e n CSS t e s t s . 98 M any of th e m w e r e the sa m e a s t e s t s fr o m th e o th e r th r e e s tu d ie s . O nce a g a in , a str o n g fa c to r e m e r g e d . A s in th e PM A and A d k in s & L y e r ly stu d y, the CSS fa c to r p ic k e d up lo a d in g s fr o m n on -C S S t e s t s . T he a u th o r 's op in ion is that th is i s due to g e n e r a l r e a so n in g c o m p o n en ts in the o th e r t e s t s . In t e r m s of th e S tr u c tu r e -o f-I n te lle c t g e n e r a l r e a so n in g a b ility is u su a lly d e s c r ib e d a s C M S. H o w e v er , in none of th e s e stu d ie s w a s the CM S a b ility r e p r e s e n te d . It is p o s s ib le then that th e r e a so n in g com p on en t of th e s e t e s t s took the fo r m of lo a d in g s on th e CSS fa c to r w h ich r e p r e s e n ts a sy m b o lic r e a so n in g fa c to r . M em o ry F a c to r s T h e m e m o r y a b ilitie s h a v e a h is to r y dating b ack to th e " fath er of fa c to r a n a ly s is " , C h a r le s S p ea rm a n . S p earm an (1927) co n clu d ed that th e r e a r e se p a r a te v e r b a l and n o n v erb a l m e m o r ie s , ev en s e p a ra te m e m o r ie s fo r v isu a l and au d ito ry in fo r m a tio n . H e co n clu d ed that th e r e w a s no se p a r a tio n o f a b ilit ie s fo r im m e d ia te v e r s u s d ela y ed m e m o r y , o r fo r r e c o g n itio n v e r s u s r e c a ll m e m o r y . T h is p o sitio n h a s b een su p p orted by the w ork con d u cted in r e la tio n to the S tr u c tu r e - o f- I n te lle c t th e o r y . T he M em o ry o p e r a tio n i s d efin ed a s the r e te n tio n o r s to r a g e , w ith so m e d e g r e e o f a v a ila b ility o f in fo r m a tio n in th e sa m e fo r m it w a s c o m m itte d to sto r a g e and in r e s p o n s e to th e sa m e c u e s in c o n n ectio n w ith w h ich it w a s le a r n e d , G u ilfo rd (1 9 6 7 , p . 1 1 0 -1 1 1 ) m a k e s so m e s p e c ific h y p o th e se s r e g a r d in g the fa c to r ia l co n ten t o f th e m e m o r y t e s t s in th e PM A b a tte ry an a s s o c ia t iv e m e m o r y fa c to r r ep o rted by F r e n c h . T he r e s u lts in th is se c tio n w ill in d ic a te the v a lid ity o f th e s e h y p o th e se s. F iv e m e m o r y a b ilitie s w e r e p r e d ic te d to 99 e m e r g e In th e a n a ly s e s of th e r ig h t s tu d ie s . MMU - M em o ry fo r S em a n tic U n its 24, W ord R eco g n itio n (PM A) . 80 * 2 8 . Sound G rouping (P M A ) .3 3 .6 3 (N FC ) 28. P ic tu r e R e c a ll (PM A) . 22 T he M MU fa c to r w a s p r e d ic te d to e m e r g e on ly in th e PM A stu d y. It is d efin ed a s th e a b ility to r e m e m b e r is o la te d id e a s o r w ord m ean * in g s . Tw o t e s t s w a re h y p o th e siz e d to m e a s u r e th is a b ility . W ord R e co g n itio n and P ic tu r e R e c a ll. T he r e s u lt s sh ow a stro n g s in g le t d efin ed by W ord R e co g n itio n , w h er e the e x a m in e e m u st in d ic a te r e c o g n itio n o f p r e v io u sly r e m e m b e r e d w o r d s. T h is t e s t is c le a r ly an MMU t e s t . T he s m a ll s ig n ific a n t lo a d in g of S o c ia l G rou ping, an N F C t e s t , is u n c le a r . T he P ic tu r e R e c a ll t e s t , w h ile b ein g h y p o th e s iz e d a s an MMU te s t , is p rob ab ly an M FU t e s t o r a m e a s u r e o f both f a c t o r s . It sh ou ld be n o ted that it did not h ave a sig n ific a n t lo a d in g on th is fa c to r . W hile the r e s u lt s a r e not su p p o rtiv e o f the in v a r ia n c e of th e MMU fa c to r , th ey do a g r e e w ith th e c o m p le x ity o f the T h u rsto n ia n ro te m e m o r y fa c to r a s su g g e s te d by G u ilford (1 9 7 2 ). MM I - M em o ry fo r S em a n tic Im p lic a tio n s 10. M em o ry fo r L im e r ic k s (K elley), 82 11. M em o ry fo r Id eas (K elle y ) .5 9 6 . S e n te n c e C o m p letio n T est(K d ley)i 58 .4 0 (MSI) 9. C o n se q u e n c e s T e s t II (K elley ) . 52 * 2 3 . M em o ry fo r W ords T e s t II (r e la te d w o r d s) (K elle y ) .3 7 .5 5 (MSI) 2 1 . M ean in gfu l M em o ry : P a ra g r a p h (K e lle y ) .3 3 8. C o n se q u e n c e s T e s t I (K elley ) . 32 100 T h is fa c to r w a s p r e d ic te d to e x is t on ly in on e stu d y, n a m ely on e o f K e lle y 's . W hile r e p lic a tio n o f fa c to r s w a s d e s ir e d in th is in v e stig a tio n , a c o m p e n sa tin g fe a tu r e in th is c a s e w a s th e la r g e n u m b er o f t e s t s h y p o th e siz e d to m e a s u r e th e factor* S ix t e s t s w e r e thought to fit th e d e fin itio n o f the M MI fa c to r . T he M MI a b ility is b ein g ab le to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een p a ir s o f m ea n in g fu l e le m e n ts o f in fo r m a tio n . T h is a b ility h a s on ly o n c e been is o la te d s u c c e s s fu lly in an A R P in v e s tig a tio n . T he r e s u lts p r e se n te d h e r e sh ow a se c o n d o c c u r r e n c e . T h is is a str o n g fa c to r w ith a lm o st a ll u n iv o ca l lo a d in g s . The se co n d a r y lo a d in g o f th e S en ten ce C o m p le tio n te s t on the M S Ifa c to r h a s a lr e a d y b een e x p la in e d . T he p r e s e n c e of the M SI t e s t , M em o ry fo r W ords T e s t II (R ela ted W ord s) is due to the m ea n in g fu l r e la tio n s b etw een th e w o rd s w h ich c a u s e s th is t e s t to h a v e se m a n tic a s w e ll a s sy m b o lic v a r ia n c e . A s e v id e n c e fo r p s y c h o lo g ic a l in v a r ia n c e , it w ou ld s e e m that th is fa c to r c e r ta in ly q u a lifie s . A ll p r e d ic te d t e s t s b eh aved a s in d ic a ted and in an a lm o s t c o m p le te ly u n iv o ca l m a n n er . T he t e s t s h a v e a fa ir v a r ie ty o f fo r m and add b rea d th to th e fa c to r a s found in th e A R P in v e stig a tio n , M F U - M em o ry fo r F ig u r a l U n its 16. R ep ro d u ctio n of V isu a l D e sig n T e s t (K elle y ) .5 2 * 7. M em o ry fo r R e la tio n s (K elley) . 52 19. M ap M em o ry III (K elle y ) .4 6 17. M ap M em o ry I (K elle y ) .4 5 * 2 2 . M ean in gfu l M em ory: N u m b er (K elle y ) .3 8 .3 1 (MSI) 2. R e co g n itio n T e s t III (K e lle y ) .3 5 2 0 . M ean in gfu l M em ory: P ic tu r e s (K e lle y ) .3 0 18. M ap M em o ry II (K elley ) , 21 101 T h is fa c to r i s d e s c r ib e d in th e St r u c tu r e -o f - In te lle c t m o d e l and is the a b ility to r e c a ll b a s ic fig u r a l in fo r m a tio n . S ix t e s t s w e r e h y p o th e siz e d to m e a s u r e th is fa c to r in the a n a ly s is o f the K e lle y t e s t b a tte r y . F iv e of th e s e s ix t e s t s had th e ir sig n ific a n t lo a d in g s on th is fa c to r . A ll of the t e s t s req u ire d m e m o r iz a tio n of fig u r a l m a te r ia l w ith su b seq u en t r e c a ll in v a r io u s fo r m s . F o r M ap M em o ry II the r e c a ll m od e w a s v e r b a l r e s p o n s e . It is p o s s ib le th a t th is is the r e a so n fo r its fa ilu r e to lo a d sig n ific a n tly on th e M FU fa c to r . R ep rod u ction of V isu a l D e sig n s t e s t r e q u ir e s the su b je c t to rep ro d u ce a r e c a lle d g e o m e tr ic d e sig n . T h is t e s t is c le a r ly M FU and le a d s the fa c to r . T he M em o ry for R e la tio n s t e s t w a s h y p o th e siz e d a s on an M SI t e s t . H o w e v e r , so m e of the it e m s of th is t e s t w e r e g e o m e tr ic a l fig u r e s and a ll ite m s w e r e in th e fo r m of p r o g r e s s iv e m a t r ic e s . It i s p o s s ib le that th is c a u se d th e sig n ific a n t M FU lo a d in g . W hile b ein g so m ew h a t u n c le a r , th is fa c to r s e e m s to r e p r e s e n t an M FU fa c to r a s d efin e d by th e S tr u c tu r e -o f-I n te lle c t. W hile not b ein g o v e r w h e lm in g e v id e n c e o f in v a r ia n c e , it d o e s s e e m to sh ow su p p ort fo r the in v a r ia n c e o f an M FU fa c to r . MSS - M em o ry fo r S y m b o lic S y ste m s 15. L e tte r Span T e s t II (K elley ) . 75 12. N u m b er Span T e s t I (K elle y ) . 71 13. N u m b er Span T e s t II (K elle y ) .6 9 14. L e tte r Span T e s t I (K elle y ) .6 9 T h e MSS fa c to r is d efin ed a s the a b ility to r e m e m b e r the o r d e r o f sy m b o lic in fo r m a tio n . G u ilford (1967) s ta te s that span m e m o r y t e s t s should d efin e th e MSS a b ility . In fa c t, a t e s t c a lle d C on son an t. D ig it, and N o n se n se W ord Span h a s b een u s e d by A R P to m ark th is 102 factor* In th e p r e s e n t a n a ly sis* fo u r sp an t e s t s w e r e in clu d ed in the K e lle y b a tte r y . T h ey d e fin e a s tr o n g and u n iv o ca l fa c to r . T h is fa c to r is b e lie v e d to r e p r e s e n t M SS, H ow ever* it w ould be a s tr o n g e r d e fin itio n if at le a s t one n o n -sp a n t e s t w a s in clu d ed in the a n a ly s is . U nfortunately* th is w a s not the c a s e . N otin g th e p o s s ib le d etraction * th e e v id en ce i s s till in fa v o r o f c o n sid e r in g th is fa c to r a s M SS. T h u s, su p p ort o f the in v a r ia n c e p o s i tion is a g a in g iv en by th e ro ta tio n a l r e s u lt s . MSI - M em o ry fo r S y m b o lic Im p lic a tio n s 23. N u m b e r-N u m b e r (PM A ) . 90 .3 5 (CSS) 21. W ord -N u m b er (PM A ) .4 8 22. In itia ls (PM A) .4 7 . 55 (DMR) 9. F ir s t N a m e s (TfcT) . 57 27. W ord -N u m b er R e c a ll (TfeT) .4 7 4 . M em ory fo r N u m b ers (K elley ) .6 4 23. M em o ry fo r W ords II (R ela ted W ords ) (K elley ) . 55 .3 7 (MMI) 5. M em ory fo r W ords I (U n rela ted W ords) (K elle y ) . 54 1. R eco g n itio n III (W ords) (K elley) . 52 * 6. S en ten ce C o m p letio n T e s t (K elley ) .4 0 . 58 (MMI) 3 . M em o ry fo r S y lla b le s I (K elley) .3 7 22 . M ean in gfu l M em ory: N u m b er (K elley ) .3 1 .3 8 (M FU) 7. M em o ry fo r R e la tio n s T e s t (K elley ) .0 5 . 52 (M FU) 19. W ord -N u m b er (S .S ) .6 8 6 . In itia ls R e c a ll (S .S ) .6 3 7. P a ir e d A s s o c ia t e s T -E (C ar. ) . 90 8. P a ir e d A s s o c ia t e s E -T (C ar. ) . 90 9. M em o ry I (C ar. ) . 50 * 1. D isa r r a n g e d W ords II ( C a r .) . 35 . 49 (CSU) 2. W ord -N u m b er (T a y lo r) .6 1 1. F ir s t N a m e s (T a y lo r) .5 0 103 T h is fa c to r o c c u r r e d in m o r e stu d ie s (six ) than any o th e r S tr u c tu r e -o f-I n te lle c t fa c to r . T he fa c to r is d efin ed a s the a b ility to r e m e m b e r a r b itr a r y c o n n e c tio n s b etw een s y m b o ls . In r e s e a r c h c o n ducted by A R P , the M SI fa c to r w a s p r im a r ily m e a s u r e d by n u m e r ic a l o p e r a tio n s t e s t s . G u ilford (1967) p o in ts out that the n u m e r ic a l o p e r a tio n s fa c to r found in p r e v io u s stu d ie s is e s s e n t ia lly M SI w ith a slig h t confounding w ith the N SI fa c to r . In ad d ition to th e o p e r a tio n s te s ta , A R P a ls o u sed a N u m b e r -L e tte r A s s o c ia tio n T e s t to d efin e M SI. In th e p r e se n t in v e stig a tio n , m o s t of the t e s t s of MSI a r e of the la tte r ty p e. A ls o , the te s ta in clu d e m e m o r y te s ta o f in it ia ls , o r n a m e s a s in th e In itia ls te a t, F ir s t N a m e s, and In itia ls R e c a ll. G u ilford (1967, p . Ill) s u g g e s ts that th e p a ir ed a s s o c ia t e s t e s t s o f the T u r k ish - E n g lish v a r ie ty r e p r e s e n t the MSI a b ility . T he r e s u lt s o f the r o ta tio n s in the s ix stu d ie s sh ow the e m e r g e n c e o f th is fa c to r in e a ch c a s e . In the m a jo r ity of c a s e s , the fa c to r w as c le a r and u n iv o c a l. In the PM A stu d y , one o f the M SI t e s t s . In itia ls, h a s a str o n g se co n d a r y lo a d in g on a DMR fa c to r . T h is h a s a lr e a d y b een e x p la in ed a s r e p r e se n tin g flu e n c y v a r ia n c e b e c a u se th e ta sk w as so e a s y . T h e K e lle y study had a str o n g MSI fa c to r w ith one h y p o th e s iz e d te s t lo a d in g sig n ific a n tly on th e M FU fa c to r . T h e s u c c e s s fu l e m e r g e n c e of th is fa c to r on s ix p r e d ic te d o c c a s io n s a r g u e s str o n g ly fo r the e x is te n c e of th is fa c to r . G en era lly sp ea k in g , th is fa c to r w a s found e a s ily and c le a r ly . It s e e m s that th is is good e v id e n c e of in v a r ia n c e . 104 D iv e rg e n t P ro d u c tio n F a c to r * T he D iv e rg e n t P ro d u c tio n a b ilitie s r e p r e s e n t th e c r e a tiv e a b ilitie s in the S tr u c tu r e -o f-I n te lle c t. T hey a r e the flu e n c y and fle x ib ility fa c to r s . T he se m a n tic p ro d u ctio n a b ilitie s can tr a c e th e ir h is to r y to T h u r sto n e 's PM A study w h er e a w ord flu e n c y fa c to r w a s id e n tifie d . T he d iv e r g e n t p ro d u ctio n o p e r a tio n is c o n c e r n e d w ith th e g e n e r a tio n of in fo r m a tio n fr o m g iv en in fo r m a tio n , w h er e the e m p h a s is is on the v a r ie ty and quantity o f output fr o m th e sa m e s o u r c e . In the p r e se n t a n a ly s is , fou r d iffe r e n t d iv e r g e n t p rod u ction a b ilitie s w e r e h y p o th e siz e d to e x is t. DM U - D iv e r g e n t P ro d u ctio n o f S em a n tic U n its 25. T o p ic s (A&L) . 73 24. T h in g s R ound (A&L) .6 2 13. P ic tu r e D e sc r ip tio n (C ar. ) . 73 2. W ords S c o r e ( C a r .) . 58 . 4 1 (CSU) 14. T o p ic s (T a y lo r) . 57 . 45 (DM S) 18. T h in g s to E at (T a y lo r) .4 9 9. A d je c tiv e s (T a y lo r) .4 8 19. T h em e (T a y lo r) .4 7 16. S en ten ce F lu en cy (T a y lo r) . 43 . 60 (DM S) 17. T h in g s Round (T a y lo r) .4 1 T he DMU fa c to r is the a b ility to p rod u ce m any e le m e n ta r y id e a s a p p ro p ria te to g iv en r e q u ir e m e n ts . In th e p a s t, th is fa c to r h a s b een c a lle d id e a tio n a l flu e n c y . T he lon g h is to r y o f study in the v e r b a l a r e a h a s m ad e th is fa c to r one o f the m o r e w e ll e s ta b lis h e d f a c t o r s . G u ilford & H oep fn er (1966) l i s t s e v e n d iffe r e n t t e s t s that m ark th is a b ility . M any o f th e s e t e s t s a r e the sa m e a s o n e s found in th e p r e s e n t in v e stig a tio n . The T h e m e , T o p ic s , T h in g s to E a t, T h in g s Round and A d je c tiv e s te s ta h a v e a ll b e e n u sed in A R P in v e s t i g a tio n s and h a v e been found to id en tify DM U. The W ords S c o r e t e s t 105 s im ila r to T o p ic s , o r T h e m e , w h er e th e s c o r e i s the n u m b er o f w o rd s w r itte n about a p a r tic u la r su b je c t. T h e r e is lit t le doubt that th is is th e DMU fa c to r , w ith so m any t e s t s th e sa m e a s th o se In A R P in v e s tig a tio n s . In the th r e e stu d ie s w h er e th e fa c to r w a s p r e d ic te d , it w a s found. T he m in o r se c o n d a r y lo a d in g s of so m e o f the DM U t e s t s h a v e b een e x p la in ed and a r e r e a s o n a b le . O nce a g a in , it s e e m s that th e r e is a m p le e v id e n c e o f p s y c h o lo g ic a l in v a r ia n c e . DM R - D iv e r g e n t P ro d u ctio n of S e m a n tic R e la tio n s 4 . C o n tro lled A s s o c ia tio n s (PM A ) .6 3 7. In v en tiv e S yn on ym s (PM A ) . 58 .3 6 (CSU) * 22. In itia ls (PM A ) . 55 .4 7 (MSI) 5. In v en tiv e O p p o site s (PM A ) . 52 .3 5 (CSU) * 6 . D isa r r a n g e d W ords (PM A) .3 8 .6 3 (CSU) * 3 . W ord G rouping (PM A ) .3 4 .6 6 (CM C) * 3 0 . V o ca b u la ry (PM A ) .3 4 ,7 5 (CM U) 11. P a ir e d O p p o site s (T a y lo r) .7 2 6. S yn on ym s (T a y lo r) .4 6 .3 9 (DSU) G u ilford (1 9 6 7 , p . 147) s ta te s th at a fa c to r known a s a s s o c ia tio n a l flu e n c y w a s la ten t in T h u r sto n e 's PM A study, but did not e m e r g e . T h is fa c to r is d efin ed a s th e a b ility to p ro d u ce m any r e la tio n sh ip s a p p r o p r ia te in m ea n in g to a g iv en id e a . G u ilfo rd h y p o th e sise d that C o n tr o lle d A s s o c ia tio n s and In ven tive O p p o site s w ou ld m a rk th is fa c to r in that stu d y . C o n tr o lle d A s s o c ia tio n s h a s b een u s e d in A R P stu d ie s to d efin e th is fa c to r . T h e r e s u lts of the a n a ly s is o f the DM R fa c to r in th e PM A stu dy sh ow th at G u ilford w a s c o r r e c t. C o n tro lled A s s o c ia t io n s and In v en tiv e O p p o site s do in d eed m a rk the DMR fa c to r . T h er e is so m e p r o b le m in that study w ith se c o n d a r y lo a d in g s, but non e o f th e s e a r e d am agin g to 106 th e id e n tific a tio n of th is fa c to r . A DM R fa c to r a ls o e m e r g e d in T a y lo r 's stu d y. W hile b ein g in d ic a ted by tw o t e s t s , it n e v e r t h e le s s a p p e a r s to be a r e a so n a b le DMR fa c to r . T he p r o b le m of the se c o n d a r y lo a d in g s fo r c e s on e to r ed u c e th e o v e r a ll c o n fid e n c e in th is fa c to r a s su b sta n tia l e v id e n c e fo r in v a r ia n c e . H o w e v e r , it d o e s o ffe r so m e su p p ort to the n otion o f in v a r ia n c e . DM S - D iv e r g e n t P ro d u c tio n o f S e m a n tic S y s te m s 10. S im ile s (T a y lo r ) . 71 16. S en ten ce F lu en cy (T a y lo r) .6 0 .4 3 (DM U) 12. L e tte r S ta r s (T a y lo r) . 59 * 14. T o p ic s (T a y lo r) .4 5 . 57 (DM U) T h e a b ility to o r g a n iz e w o rd s in v a r io u s m ea n in g fu l c o m p le x id e a s w a s p r e d ic te d to e m e r g e on ly in the T a y lo r stu d y . T h is fa c to r had th r e e t e s t s h y p o th e siz e d fo r it. T he r e s u lts in d ic a te that the fa c to r is w e ll d efin ed by th r e e t e s t s . T he p r e s e n c e of T o p ic s is due to the fa c t that th is t e s t r e q u ir e d th e su b je c t to w r ite an in te g r a te d th e m e about a to p ic . T h is in tro d u ced th e DMS v a r ia n c e in to an o th e r w is e DM U t e s t. A te s t v e r y s im ila r to th e S im ile s t e s t h a s been u se d by A R P to in d ic a te th is fa c to r . W hile it i s un fortu n ate th is fa c to r did not o c cu r in m o r e than on e stu d y, th e e v id e n c e is s t ill in fa v o r o f th e p s y c h o lo g ic a l in v a r ia n c e o f th is fa c to r . - D iv e r g e n t P ro d u c tio n of S y m b o lic U n its 8. F ir s t and L a s t L e tte r s (T&T) .6 7 11. F o u r L e tte r W ords (T&T) .5 9 26. S u ffix e s (T& T) .5 4 .3 6 (CSU) 23. R h ym in g W ords (T&T) . 53 .3 3 (CSU) 1. A n a g ra m s (T&T) . 50 .3 3 (CSU) * 2 8 . W ord P u z z le r s (T&T) .4 4 . 60 (CSU) 7. F ir s t and L a s t L e tte r s (A&L) .4 7 22. S u ffix e s (A&L) .4 5 * 1 4 . P a in ted B lo c k s (A&L) .3 4 . 38 (CSS) 107 2. F ir s t and L a st L e t te r s (B e) . 56 6 . S u ffix e s (B e) .5 5 3 . S u ffix e s ( C a r .) . 83 * 1 0 . D isa r r a n g e d M o rp h em es (C a r .) .4 4 .5 0 (CSU) 5. R h ym in g (C ar. ) .3 8 5. S u ffix e s (T a y lo r) .7 1 7. F ir s t L e tte r s (T a y lo r) ,7 1 4 . F ir s t and L a st L e tte r s (T a y lo r) .6 3 13. N u m b er o f L e t te r s (T a y lo r) .6 1 15. G iven L e tte r s (T a y lo r) .6 1 8. A n a g ra m s (T a y lo r) .4 9 .4 4 (CSU) * 6 . S yn on ym s (T a y lo r) .3 9 .4 6 (DM R) T h is fa c to r h a s p rob ab ly b een in v e stig a te d m o r e than any o th e r d iv e r g e n t p ro d u ctio n a b ility . T h u rsto n e c a lle d th is fa c to r W ord F lu e n c y . G u ilford (1967) s ta te s that th is fa c to r i s one of the e a s ie s t to t e s t u n iv o ca lly and h a s a w id e ran ge o f t e s t s . T h e s p e c ific d e fin i tio n o f DSU i s the a b ility to g e n e r a te m an y sy m b o lic u n its, lik e w o r d s, that c o n fo rm to sim p le s p e c ific a tio n s that do not in v o lv e m e a n in g s. A m on g th e t e s t s u sed by A R P to m a rk DSU a r e S u ffix e s , W ord B eg in n in g s T e s t and WoTd B e g in n in g s and E n d in gs t e s t . T he S u ffix e s t e s t is the sa m e a s th at u s e d in th e stu d ie s b ein g in v e stig a te d h e r e . F ir s t L e tte r s and F ir s t and L a st L e tte r s a r e th e sa m e a s the o th e r two A R P t e s t s . It sh ou ld be a p p aren t that id e n tific a tio n o f the DSU fa c to r in th e fiv e stu d ie s w a s r e la tiv e ly s im p le . T he fa c to r u su a lly e m e r g e d a s a u n iv o ca l str o n g fa c to r w ith t e s t s th a t w e r e know n to m a rk DSU. In so m e c a s e s , th e r e is v a r ia n c e of DSU t e s t s on th e CSU fa c to r . T h is w a s e x p e c te d a s th e t e s t s do con tain CSU v a r ia n c e In th e ir fa c to r ia l c o m p o sitio n . In fa c t, th e A n a g ra m s te s t w a s p r e d ic te d to s p lit its v a r ia n c e in that fa sh io n . 108 T he r e s u lts p r e se n te d h e r e c le a r ly in d ic a te th e p r e s e n c e of DSU in th e stu d ie s b ein g in v e stig a te d . O n ce a g a in , str o n g su p p ort is g iv en to th e S tr u c tu r e -o f-I n te lle c t m o d e l. C o n v erg en t P ro d u c tio n F a c to r s T he fa c to r s to be d is c u s s e d in th is s e c tio n a r e s im ila r to th o s e of the p r e c e d in g s e c tio n . T h ey r e q u ir e th e su b je ct to p ro d u ce o r g e n e r a te in fo r m a tio n . U n lik e th o se a b ilit ie s , th e s e fa c to r s a r e not c o n c er n e d w ith v a r ie ty and qu an tity, but r a th er on a r r iv in g at unique o r co n v e n tio n a lly a c c e p te d o u tc o m e s . T h e se fa c to r s a r e s o m e tim e s r eg a r d e d a s d e d u ctiv e o r lo g ic a l r ea so n in g fa c to r s . In the p r e s e n t in v e stig a tio n , th r e e su ch fa cto r s w e r e h y p o th e siz e d to e m e r g e . NM U - C o n v erg en t P ro d u c tio n of S e m a n tic U n its 18. P ic tu r e N am in g (T& T) . 70 6 . F ig u r e N am in g (T& T) .4 4 14. F o r m N am in g (C a r. ) . 78 15. C o lo r N am in g (C ar. ) . 72 12, G iving F ir s t N a m e s ( C a r .) ,4 2 11. N am in g S ta te s of the U n ion fC arJ. 34 * 6 . D isa r r a n g e d W ords I (C ar. ) .3 2 . 50 (CSU) T h is fa c to r is g e n e r a lly r eg a r d e d a s a n am in g o r la b e lin g fa c to r . It i s d efin ed a s th e a b ility to c o n v e r g e upon an a p p ro p ria te n am e o r su m m a r iz in g w o rd fo r any g iv en in fo r m a tio n . NM U w a s p r e d ic te d to e m e r g e in the T h u rsto n e & T h u rsto n e study and m o r e str o n g ly in th e C a r r o ll study w h er e s ix t e s t s w e r e h y p o th e siz e d a s NM U te s ta . T h e r e s u lts in d ic a te that th e p r e d ic tio n s w e r e c o r r e c t. T he fa c to r s w e r e found and in v o lv ed te a ts th at r e q u ir e d the su b je c ts to p ro d u ce la b e ls o r n a m e s. O nly on e non -N M U t e s t had a sm a ll but 109 s ig n ific a n t lo a d in g on the NM U fa c to r . It is in te r e s tin g to n ote that N am in g S ta te s of th e U nion t e s t did lo a d on th is fa c to r . Its sm a ll lo a d in g is p rob ab ly due to p erh a p s la r g e r m e m o r y v a r ia n c e . T he o th e r NM U t e s t s a r e s im ila r to th o se r ec o m m e n d ed a s NM U m a r k e r s by G u ilford and H o ep fn er (1966) and G u ilford (1 9 6 7 ). It s e e m s sa fe to con clu d e that the r e s u lts sh ow so m e e v id e n c e o f in v a r ia n c e o f th is fa c to r . N F C - A C o n v erg en t P ro d u ctio n o f F ig u r a l C la s s e s - A u d itory 27. R hythm (PM A ) .8 4 2 8 . Sound G rouping (PM A ) .6 3 .3 5 (NMU) T h is fa c to r h a s n e v e r b een is o la te d b e fo r e in A R P r e s e a r c h . T h e N F C a b ility i s th e a b ility to c la s s if y u n iq u ely o r c o n v en tio n a lly ite m s of fig u r a l In fo rm a tio n . G u ilford (1967) p o in ts out that so m e o f the S tr u c tu r e -o f-I n te lle c t a b ilitie s h ave c o u n te r p a r ts in v a r io u s s e n s o r y m o d a litie s , su ch a s v is u a l, a u d ito ry and k in e s th e tic . T h is is th e c a s e o f an au d ito ry a b ility . The a b ility in v o lv ed h e r e is N FC b e c a u se both t e s t s r e q u ir e c la s s ific a tio n and it i s au d itory b e c a u se th e c la s s if ic a tio n is b a sed upon sound. T he r e s u lt s sh ow a fa ir ly stro n g fa c to r h e r e . It is un fortu n ate that th e r e w e r e not m o r e N FC t e s t s in the PM A b a tte ry , o r that the N F C a b ility did not o c c u r in any of the o th e r s tu d ie s . It d o e s s e e m th at the fa c t that the a b ility w a s p r e d ic te d and w a s su b seq u en tly is o la te d g iv e s su p p ort fo r in v a r ia n c e . N F T - C o n v erg en t P ro d u ctio n o f F ig u r a l T r a n sfo r m a tio n s 4 . G o ttsch a ld t F ig u r e s (B e) .4 6 2 2 . D e s ig n s (B e) .4 0 8. H idden P ic tu r e s (B e) .3 9 .3 9 (C FU ) no T he N F T fa c to r b e g in s it s h is to r y w ith th e T h u rsto n e (1944) in v e stig a tio n o f p e r c e p tio n . H e c a lle d th e fa c to r " g e sta lt f le x ib ilit y 1 and it w a s m a rk ed by a G ottsch ald t F ig u r e s te s t and H idden P ic tu r e s t e s t . S u b seq u en tly , th is fa c to r w a s p la c e d into the S tr u c tu r e -o f- I n te lle c t, w h er e it is d efin ed a s the a b ility to b reak down g iv en fig u r a l u n its to fo r m new o n e s . G u ilford (1967, p . 178) s ta te s that th is fa c to r w ill o c c u r w h en ev er a G o ttsch a ld t F ig u r e s t e s t and a H idden P ic tu r e s o r H idden F a c e s te s t h ave ap p ea red to g e th e r . T he B ech to ld t study w a s the only one u n der in v e stig a tio n h e r e in w h ich th is w as th e c a s e . T he r e s u lts in d ica te th at G u ilford w a s c o r r e c t in h is p r e d ic tio n that N F T d o e s e m e r g e . T he H idden P ic tu r e s te s t s h a r e s its v a r ia n c e w ith an ill-d e fin e d C F U fa c to r th at is r e a lly a s in g le t. Support i s g iv en to th e e x is te n c e o f the N F T fa c to r by th e s e r e s u lt s . E v a lu a tio n F a c to r s T he la s t o p e r a tio n in th e S tr u c tu r e -o f-I n te lle c t m o d el is e v a lu a tio n . A s an o p e r a tio n th is a b ility h a s b een r e la tiv e ly n e g le c te d by r e s e a r c h e r s o th e r than A R P in v e s tig a to r s . T h is w a s one of the r e a s o n s it w a s im p o rta n t to d e m o n str a te the e x is te n c e o f su ch fa c to r s in o th e r d ata. E v a lu a tio n is c o n sid e r e d to be a ch eck in g , v e r ify in g o r jud ging p r o c e s s w h ere a s p e c ific c r ite r ia su ch a s id e n tity is e m p lo y e d . F o u r ev a lu a tio n a b ilitie s w e r e p r e d ic te d to e m e r g e . EM U - E v a lu a tio n o f S em a n tic U n its 111 18. V erb a l E n u m era tio n (B e) . 71 . 30 (ESU) 5. S iz e C o m p a riso n (B e) .7 0 10. W ord C h eck in g (B e) B o y s' F ir s t N a m e s (B e) .6 9 12. .6 6 . 3 8 (ESU ) 14. O p p o site s (B e) .6 5 21. W ords A s s o c ia te d w ith a H ou se (B e) .6 1 24. C o n c r e te A s s o c ia tio n s (B e) .4 8 .4 7 (E F U ) T he EM U a b ility in v o lv e s the c a p a c ity to jud ge the s u ita b ility o r ad eq u acy of id e a s and o b je c ts in te r m s o f m e e tin g c e r ta in c r it e r ia . T h is a b ility w a s to e m e r g e on ly in th e B ech to ld t stu d y . W hile it w ould be p r e fe r a b le to h a v e the fa c to r p r e se n t in m o r e s tu d ie s , th e r e w e r e s e v e r a l p o s itiv e a s p e c ts in th e p r e se n t situ a tio n . F ir s t ly , se v e n t e s t s o f a w id e ran ge o r co n ten t w e r e h y p o th e siz e d to m e a s u r e th e fa c to r . S eco n d ly , E F U and ESU a b ilitie s , th e c lo s e s t n e ig h b o r s to EM U, w e r e p r e d ic te d to e x is t in the B ech to ld t b a tte r y . If the fa c to r w ould e m e r g e c le a r ly in th is b a ttery it w ould p r o v id e a str o n g e v id e n c e of it s in d ep en d en t sta tu s. T he te s ta u se d by A R P to d efin e EM U h ave b een o f a w ord c h eck in g v a r ie ty . T h is ty p e of te s t is w e ll r e p r e s e n te d in th is stu d y. V e rb a l E n u m era tio n , W ord C h eck in g, and W ords A s s o c ia te d w ith a H o u se a ll r e q u ir e th e su b je ct to d e te r m in e w h eth er the w ord b e lo n g s in a p a r tic u la r c a te g o r y . T he o th e r t e s t s a ll r e q u ir e c h e c k ing of w o r d s w ith a s p e c ific c r ite r io n su ch a s s iz e o r w h eth er it is a b o y 's n a m e . It m ay be s e e n fr o m th e r e s u lts that th is fa c to r e m e r g e d q u ite c le a r ly . A ll se v e n h y p o th e siz e d t e s t s h a v e sig n ific a n t lo a d in g s on th is fa c to r . T he e x is te n c e of the m in o r se c o n d a r y lo a d in g s on th e ESU 112 fa c to r h a v e a lr e a d y b een d is c u s s e d In th e p r e c e d in g section * T he e x is t e n c e o f EM U in an o th er stu dy w ould h a v e fo r tifie d the c la im o f in v a r ia n c e o f th is fa c to r . It d o e s seem * though* that w ith se v e n t e s t s d efin in g it* th e r e is a m p le e v id e n c e fo r so m e c la im to p sy ch o lo g ic a l in v a r ia n c e . EM I - E v a lu a tio n o f S em a n tic Im p lic a tio n s T he EM I fa c to r h a s had an u n u su al h is to r y w ith in th e S tr u c tu r e - o f-I n te lle c t th e o r y . A t f ir s t EM I w a s fe lt to be a fa c to r id e n tifie d p r e v io u s ly a s ''s e n s itiv ity to p r o b le m s" . T h is fa c to r w a s la t e r a s s ig n e d to th e CMI fa c to r and EM I w as d e sig n a te d a s a " lo g ic a l evaluation" fa c to r . G u ilford (1967) p o in ts out that th is fa c to r f ir s t o c c u r r e d in T h u r sto n e 's PM A stu d y . It is th is fa c to r w h ich w a s in v e s tig a te d in the p r e s e n t a n a ly s is . A fte r EM I had b een d efin ed a s lo g ic a l ev a lu a tio n , it w a s is o la te d in a study con d u cted by A R P . T he t e s t s u se d to m a rk th is f a c t o r a ll e s s e n t ia lly r e q u ir e d th e su b je ct to d e te r m in e the ad eq u acy o f r e a so n in g . T he R eason in g* F a ls e P r e m is e s and S y llo g is m s t e s t s in th is in v e stig a tio n a ll c o n fo rm to th is ta s k d e s c r ip tio n . U n fortu n ately th e r e s u lts a r e not v e r y s p e c ta c u la r . F a ls e P r e m is e s and R e a so n in g c le a r ly and u n iq u ely d e fin e the fa c to r . S y llo g ism s* w h ich w a s the th ir d h y p o th e sise d m e a s u r e , h a s two o th e r l a r g e r sig n ific a n t lo a d in g s . B e c a u se of th e b eh a v io r of th is t e s t , it can a lw a y s be sa id 17. R e a so n in g (PM A ) 18. F a ls e P r e m is e s (PM A ) * 1 6 . N u m b er S e r ie s (PM A) .8 4 .6 5 * 1. R ead in g II (PM A ) 2 0 . S y llo g is m s (PM A ) .3 2 .4 3 (CSS) .3 1 ,5 2 (CM U) ,3 0 .4 7 (C F T ) .3 3 (CM C) 113 that th is fa c to r Is nothing m o r e than a d o u b let. The e v id e n c e of in v a r ia n c e of th is fa c to r is du biou s due to th is la c k o f c o n fo rm ity of S y llo g is m s . O n ce a g a in , if th e fa c to r had b een p r e s e n t in an o th er stu d y, it w ould h a v e added im m e n s e ly to the p o sitio n o f th is fa c to r in te r m s of in v a r ia n c e . E F U - E v a lu a tio n o f F ig u r a l U n its 5. F a c e s (T& T) .5 1 13. Id en tic a l P ic tu r e s (T& T) .4 4 * 19. P u r s u it (T& T) .3 4 11. M u ltila ted P ic tu r e s (A&L) .6 9 8. Id en tic a l F o r m s (A&L) .4 8 * 5. F ig u r e S e r ie s (A&L) .3 1 2 3 . L e t te r s IV .6 1 24 . C o n c r e te A s s o c ia tio n s .4 7 13. Id en tica l F o r m s .4 3 15. P ic tu r e S q u a r es .3 6 26 . L e tte r s I . 34 T h is fa c to r is d e fin e d a s the a b ility to ju d ge q u ick ly and a c c u r a te ly u n its o f fig u r a l in fo rm a tio n a s b ein g s im ila r o r d iffe r e n t, b a se d upon m in o r a s p e c ts of in fo r m a tio n . H is to r ic a lly , th e E F U fa c to r h a s b een r e fe r r e d to a s P e r c e p tu a l S p eed , In a r e c e n t A R P study (H offm an, e t. a l . , 1968) the co n c ep tio n of E F U w a s expand ed to tak e into a cco u n t n o n -sp e e d e d t e s t s . U n til that tim e , th e c la s s ic t e s t s w e r e the Id e n tic a l F o r m s te s t and a t e s t c a lle d P e r c e p tu a l S p eed . T he Id en tica l P ic t u r e s t e s t and th e Id en tic a l F o r m s t e s t o c c u r s in th e stu d ie s u n d er a n a ly s is h e r e . T h e r e s u lt s in d ic a te th at in the T h u rsto n e & T h u rsto n e study and th e A d k in s and L y e r ly stu d y, th is fa c to r e m e r g e d , but in an u n c le a r fa sh io n . T h is w a s p rob ab ly due to th e s m a ll n u m b er (2) of .4 2 (C FI) .5 3 (CFI) . 3 1 (CSS) .4 7 (CSS) .3 3 (C FR ) . 50 (C F T ) .4 8 (EM U) 114 E F U t e s t s p r e s e n t in th o se b a t te r ie s . In th e c r u c ia l study o f B ech to ld t. E F U e m e r g e s m u ch m o r e str o n g ly and c le a r ly . T he B ech to ld t study w a s c r u c ia l to th e E F U fa c to r fo r two r e a s o n s . F ir s t ly , it w a s th e on ly study w h e r e th e r e w e r e a r e a so n a b le n u m b er (4) o f E F U t e s t s p r e s e n t. S e c o n d ly , th is study co n ta in ed th e v e r y s im ila r EM U and ESU f a c t o r s , and it w ou ld b e v ita l to d e m o n str a te the in d ep en d en ce o f the E F U fa c to r fr o m th e s e . T h is au th or b e lie v e s th at th e r e s u lt s sh ow th is in d ep en d e n c e. A ls o , it s e e m s r e a so n a b le to co n clu d e that E F U h a s b een d e m o n str a te d in th r e e se p a r a te a n a ly s e s , and that i s good e v id e n c e o f fa c to r ia l in v a r ia n c e . ESU - E v a lu a tio n of S y m b o lic U n its 5. Id en tica l N u m b e rs (S .S ) .6 8 16. R e p e a ted L e tte r s (S. S) .5 3 9. L e tte r A (B e) . 72 16. 2, 6 , 9 (B e) .6 0 3. N a m e R e co g n itio n (B e) .5 9 20. L e tte r S q u a res (B e) .4 1 * 1 2 . B o y s 1 F ir s t N a m e s (B e) .3 8 .6 6 (EM U) * 1 8 . V erb a l E n u m era tio n (B e) .3 0 .7 1 (EM U) T h e la s t fa c to r to be p r e d ic te d in th e a n a ly s e s w a s th e ESU fa c to r . T h is fa c to r is d efin ed a s the a b ility to m ak e rap id d e c is io n s r e g a r d in g th e sy m b o lic id e n tity o r a c c u r a c y of w o r d s, le t t e r s e ts , and n u m b er s e t s . In e a r ly a n a ly s e s w o rd and le t t e r t e s t s w e r e o ften found to lo a d on th e sa m e fa c to r a s m a r k e r t e s t s fo r E F U . L a te r th is w a s d e te r m in e d to be a r e s u lt o f a confoun din g o f E F U and ESU t e s t s on th e sa m e fa c to r . T h e s e t e s t s a r e u s e d by A R P to In d icate th e e x is te n c e o f E S U . T h ey a r e Sym b ol Id e n titie s , L e tte r "U" and F ir s t D ig it C a n c e lla tio n . In th e f ir s t t e s t , th e e x a m in e e s a r e r eq u ire d to jud ge w h eth er both m e m b e r s o f p a ir s o f w o r d s and of n u m b e rs a r e 115 th e sa m e . T h e L e tte r "U M te a t c o n ta in s lon g l i s t s o f w o rd s and the su b je c t m u st ch e ck th o se w o rd s that have th e le t t e r "u" p r e s e n t. T h is e sse n tia lly is th e sa m e a s th e ta sk in L e tte r A and 2, 6, 9. T he th ir d A R P t e s t i s F ir s t D ig it C a n c e lla tio n , w h er e the ta sk i s to c r o s s out the n u m b er w h ich is th e sa m e a s th e f ir s t d ig it in th e co lu m n . T he sa m e ty p e o f ta sk is p r e s e n t in Id en tica l N u m b e r s, R ep ea ted L e t te r s , N am e R e co g n itio n and L e tte r S q u a r e s. T h e ESU fa c to r w a s p r e d ic te d to e m e r g e in tw o s tu d ie s , T h u r sto n e 's <1940) study of sim p le str u c tu r e and B e c h to ld t's stu d y. T he ESU fa c to r w a s found in both c a s e s . T he r e s u lts show a fa ir ly stro n g and c le a r fa c to r to be p r e s e n t in both c a s e s . In th e B ech to ld t stu d y th e r e is a sm a ll b it of confounding w ith the EM U fa c to r , but t h e s e h a v e b een e x p la in e d . E v en w ith the p r e s e n c e o f th e s e sm a ll se co n d a r y lo a d in g s of EM U t e s t s , th e e v id e n c e is str o n g ly in fa v o r o f p o s itiv e id e n tific a tio n o f th e fa c to r s a s ESU and that th e s e in s ta n c e s c o n stitu te e v id e n c e of fa c to r ia l in v a r ia n c e . T he r e s u lts of the a n a ly s e s o f th e eig h t stu d ie s h ave been p r e s e n te d and d is c u s s e d f ir s t study by stu d y, and then by ea ch in d iv id u a l fa c to r . In the f ir s t c a s e w e w e r e c o n c e r n e d w ith a c c u r a c y o f p r e d ic tio n w ith in a stu d y. In th e se c o n d c a s e , th e c o n c e r n is w ith r e p e a te d d e m o n str a tio n o f a th e o r e tic a lly d efin ed fa c to r . H aving p r e s e n te d the r e s u lt s in th e s e w a y s the n ex t and fin a l ch a p ter w ill tu rn to th e to p ic s o f 1) the v a lid ity of th e s e fin d in g s, and 2) w hat c o n c lu s io n s can be draw n fr o m th e s e r e s u lt s , and 3) w hat th e im p li c a tio n s can be fo r e s e e n . 116 It can be se e n fr o m th e s e r e s u lts that th e S t r u c tu r e -o f-ln te lle c t m o d e l p r o v id e s a v e r y u s e fu l r e fe r e n c e fr a m e w ith in w h ich on e can lo c a te fa c to r s fr o m m any d iffe r e n t s o u r c e s . T h e se r e s u lts show that s o m e o f th e fa c to r s w h ich w e r e w eak o r u n c le a r in on e in d ivid u al a n a ly s is to be s tr o n g o r c le a r w hen co m b in ed w ith th e r e s u lts fr o m d iffe r e n t a n a ly s e s . T h is r e p e titio n o f a fa c to r in m o r e than on e study sh ou ld c o m p e n sa te fo r the s m a ll n u m b er o f t e s t s m a rk in g a fa c to r in s o m e s p e c ific a n a ly s e s . C H A P T E R V CONCLUSIONS AND IM PLICA TIO NS F a c to r ia l in v a r ia n c e is the d e m o n str a tio n that a fa c to r that e x is te d in th e fa c to r ia l a n a ly s is o f on e b a ttery can be found by the sa m e m eth o d s in a b a ttery w h ich d iffe r s in th e p op u lation o f su b je c ts that w e r e g iv en th e b a ttery o r in th e v a r ia b le s w h ich w e r e u s e d in the b a ttery o r in both r e s p e c t s . In v a ria n ce b e c o m e s a c o n c e r n on ly w hen the r e s u lts o f a fa c to r a n a ly s is a r e to be u sed fo r o th e r than a d e s c r ip tio n of a s e t o f sa m p le c o r r e la tio n c o e f fic ie n ts . Any th e o ry or m o d el w h ich u t iliz e s fa c to r a n a ly s is a s its b a s is m u st, in th e fin a l a n a ly s is , d eal w ith the q u estio n o f in v a r ia n c e . T h is is p a r tic u la r ly tru e o f th e o r ie s o f in te llig e n c e w h ich e ith e r im p ly o r sp e c ify that th e fa c to r ia l a b ilitie s in v o lv ed a r e not bounded by a t e s t sa m p le o r by a te s t b a tte r y . T h e p u rp o se o f th is d is s e r ta tio n is the d e m o n str a tio n o f the in v a r ia n c e of fa c to r ia l a b ilitie s sp e c ifie d by th e S tr u c tu r e -o f-I n te lle c t m o d e l o f in te llig e n c e . T he s p e c ific typ e o f in v a r ia n c e that w a s d e a lt w ith can be c a lle d p s y c h o lo g ic a l in v a r ia n c e a s d is tin c t fr o m m a th e m a tic a l in v a r ia n c e . In the f ir s t c a s e , c o n c e r n i s on the r ep ea ted e x is te n c e o f fa c to r s w h ich co n fo rm to th e p r in c ip le o f p sy c h o lo g ic a l m e a n in g fu ln e s s. T h is u su a lly m e a n s th at th e fa c to r s that a r e u n d er sc ru tin y have b een ro ta ted to a c h ie v e th is m e a n in g fu ln e s s. T he se co n d typ e o f in v a r ia n c e d e a ls w ith the fa c to r s a s th ey a r e d e r iv e d 117 118 fr o m th e m a th e m a tic s o f th e fa c to r -a n a ly tic m o d e l and the e m p h a s is is not on in te r p r e ta tio n . T he ap p roach ta k en in th is in v e stig a tio n is so m ew h a t u n u su a l. In stea d of c o n str u c tin g new b a tte r ie s of t e s t s and a d m in is te r in g th e m to d iffe r e n t sa m p le s fr o m d iffe r e n t p o p u la tio n s of su b je c ts , th is d is s e r ta tio n u s e d th e data g a th e re d fr o m p r e v io u s ly con d u cted stu d ie s . T he in ten t w a s to d e m o n str a te th e e x is te n c e o f th e S tr u c tu r e -o f- I n te lle c t a b ilitie s in b a tte r ie s that w e r e n ot c o n str u c te d fo r th is p u r p o s e . T h is w ould e lim in a te e x p e r im e n te r b ia s and o ffe r str o n g e r e v id e n c e fo r the g e n e r a lity of th e s e a b ilit ie s . S e c o n d ly , sin c e the data c a m e fr o m p a s t s tu d ie s , the r e s u lts w ould o ffe r a b rid g e o f u n ific a tio n b etw een the w ork don e on th e S tr u c tu r e -o f-I n te lle c t and th is o ld e r fa c to r a n a ly tic w ork . O p e r a tio n a lly , th e stu d ie s w e r e s e le c te d fo r a v a r ie ty o f s p e c ific c r it e r ia that w e r e en u m era ted in an e a r lie r s e c tio n o f th is r e p o r t. B r ie fly , th e data c a m e fr o m p u b lish ed stu d ie s that w e r e c o n d u cted e ith e r by T h u rsto n e o r in h is tr a d itio n . T he fa c to r ia l c o m p o s i tio n o f ea ch te s t fr o m th e eig h t stu d ie s c h o se n fo r in v e stig a tio n w a s h y p o th e sise d fr o m the p u b lish ed d e s c r ip tio n . On the b a s is o f th is d e te r m in a tio n th e o r ig in a l b a tte r ie s o f v a r ia b le s w e r e red u ced to in clu d e on ly t e s t s w h ich w e r e in te lle c tu a l in n atu re and not fa c to r ia lly c o m p le x and r e p r e se n te d a fa c to r that had at le a s t on e o th e r p u re m e a s u r e in the b a tte r y . T h e se red u ced s e t s of v a r ia b le s w e r e fa c to r a n a ly se d u sin g a p r in c ip a l fa c to r m eth o d . The r e su ltin g fa c to r s w e r e ro ta ted to a ta r g e t m a tr ix c o n str u c te d on the b a s is o f the h y p o th e sise d 119 fa c to r s fo r e a ch b a tte r y . T h ea e ro ta ted r e s u lt s a r e th e e v id e n c e s o f in v a r ia n c e . A s m en tio n ed in th e f ir s t p a ragrap h of th is c h a p te r , in v a r ia n c e i s the d e m o n str a tio n of th e e x is te n c e o f a fa c to r on m o r e than one o c c a s io n . S e co n d ly , s e v e r a l fa c to r s u n d er in v e stig a tio n w e r e p r e d ic te d to o c c u r and w e r e found in m o r e than on e study in clu d ed fo r a n a ly s is . T h is ad d s e v en g r e a te r str e n g th to th e e v id e n c e o f in v a r ia n c e fo r th e s e p a r tic u la r f a c to r s . F o llo w in g the d e s c r ib e d p r o c e d u r e le d to th e h y p o th e sis that 26 S tr u c tu r e -o f-I n te lle c t fa c to r s sh ou ld be found in on e o r m o r e of the e ig h t s tu d ie s . T he r e s u lt s in d ic a te th at on ly in tw o c a s e s w e r e the f a c to r s not found. T h e se fa c to r s w e r e th e MMU fa c to r in the PM A study and the C F U fa c to r in the B ech to ld t stu d y. In th e f ir s t c a s e o n ly tw o t e s t s w e r e p r e d ic te d to m a r k th e fa c to r and one fa ile d to do s o . T h is m a y be th e r e s u lt o f the s m a ll n u m b er o f t e s t s in th e b a ttery fo r th is fa c to r . E v id e n c e c o n c er n in g th e C FU fa c to r is m o r e c o m p le x . T h e C F U fa c to r w a s p r e d ic te d fo r tw o s tu d ie s , th e A d k in s and L y e r ly study and th e B ech to ld t stu d y. In th e f ir s t o f th e s e , th e fa c to r e m e r g e d and w a s d efin ed by th e tw o t e s t s h y p o th e sise d fo r it. T h e s e t e s t s h ave b een the m a r k e r s fo r th is fa c to r through out th e h is to r y o f the S tr u c tu r e -o f-I n te lle c t. T he fa c to r to ta lly fa ile d to a p p ea r in the B e ch to ld t stu d y, e v en though th e s e sa m e tw o t e s t s w e r e in the a n a ly s is . T h is r e s u lt had le d th e au th or to co n clu d e that th e e v id e n c e fo r in v a r ia n c e o f the C F U fa c to r is n ot su ffic ie n t to m ak e a p o s itiv e fin d in g in that c a s e . H o w ev er, the bulk of e v id e n c e on th is fa c to r 120 and it s r e la tio n to th e tw o m a r k e r t e s t s , th is le a d s to th e c o n c lu sio n th at the B ech to ld t data w e r e the r e s u lt of so m e q u e stio n a b le o c c u r - r e n c e . T h e p o s itiv e e v id e n c e fo r in v a r ia n c e in 22 out o f 26 fa c to r s is str o n g su p p ort fo r th e s e a b ilit ie s . P a r tic u la r ly w hen on e c o n s id e r s th at h a lf o f th e s e fa c to r s w e r e found on m o r e than o n e o c c a s io n in th is in v e stig a tio n , it w ou ld s e e m that th e r e s u lt s in d ic a te that th e S tr u c tu r e -o f-I n te lle c t i s an e x tr e m e ly u se fu l m o d el to fo llo w in the a r e a o f in te lle c tu a l r e s e a r c h . T h e e v id e n c e found h e r e c o in c id e s w e ll w ith that found by G u ilford and H oep fn er (1971) w hen th ey fo llo w e d a s im ila r p r o c e d u r e , A fin a l im p lic a tio n th at m ay be draw n fr o m th is w ork is the p la c e m e n t o f T h u rsto n ia n t e s t s w ith in th e S t r u c tu r e -o f-ln te lle c t m o d e l. G u ilford (1972) h y p o th e sise d th is , but th is in v e stig a tio n p r o v id e s c o n c r e te e v id e n c e w ith r e g a r d to th is m a tte r . O ne n ote o f ca u tio n sh ou ld be o ffe r e d w ith r e g a r d to th e s e r e s u lts and th e c o n c lu s io n s draw n fr o m th e m . C r itic is m h a s r e c e n tly b een m ad e of th e r o ta tio n a l p r o c e d u r e e m p lo y ed in th is stu d y. H orn (1973) h a s b een th e m o s t v o c a l w ith r e s p e c t to th is a r e a . T he m a in c r it ic is m i s that th e ta r g e te d a p p ro a ch a llo w s the in v e s tig a to r to c o n str u c t h is ow n r o ta tio n a l c r it e r ia and th is p r e su m a b ly m ea n s s u b je c tiv ity . H orn m a in ta in s th at a n a ly tic p r o c e d u r e s o f r o ta tio n a r e o b je c tiv e and sh ou ld b e u se d and th at th e ta r g e te d r o ta tio n s m ay c a p ita lis e on ch an ce to m ak e th e r e s u lt s m o r e fa v o r a b le to the in v e s tig a to r s ' h y p o th e se s. T he notion that the a n a ly tic ro ta tio n 121 p r o c e d u r e s a r e o b je c tiv e is a d iffic u lt p o sitio n to d efen d . W hile it is tru e th at th e s e p r o c e d u r e s do not a llo w the in v e s tig a to r to d e te r m in e h is own h y p o th e se s w ith r eg a r d to th e str u c tu r e of the data, it is tru e that th e s e m eth o d s a r e nothing m o r e than an em b o d im en t o f the sim p le str u c tu r e p r in c ip le . T h is p r in c ip le , w h ile not b ein g p a r t o f the in v e s tig a to r 's h y p o th e se s, is the h y p o th e sis of on e m an w ith r e s p e c t to the n a tu re o f the d a ta . T h u rsto n e p r o p o sed sim p le str u c tu r e a s h is e s tim a tio n o f th e w ay fa c to r s sh ould be found, not the w ay th ey m u st be found. The fa c t that the a n a ly tic p r o c e d u r e s h a v e tr a n sfo r m e d th is c r ite r io n into a s e t of c o m p le x m a th e m a tic a l fu n ctio n s d o e s not r e m o v e the o r ig in a l su b je c tiv ity fr o m the c r ite r io n . In ad d ition , th is c r ite r io n is not c le a n ly and n e a tly s p e c ifie d by T h u rsto n e and th is h a s le d to a v a r ie ty of in te r p r e ta tio n s and m a th e m a tic a l fo r m u la tio n s. A s a lr e a d y m en tio n ed th e r e h a s b een o b je c tio n s to th e u s e o f th is c r ite r io n , p a r tic u la r ly in the a r e a of in v a r ia n c e . It w ou ld s e e m that H o rn 's co n ten tio n o f th e o b je c tiv ity o f the a n a ly tic p r o c e d u r e s is not w e ll foun ded. The co n ten tio n that the m eth o d c a p ita liz e s on ch a n ce h a s y e t to be p ro v en and can p rob ab ly be show n to e x is t fo r the a n a ly tic p r o c e d u r e s , ea ch o f w h ich m a x im iz e s ap p roach to it s own c r ite r io n . T he ab ove d is c u s s io n w a s added to in su r e that a fu ll and c o m p r e h e n siv e c o v e r a g e w a s m ad e o f the fie ld o f in v a r ia n c e and the ap p roach taken by th is in v e stig a tio n . W hile the ab ove c h a r g e s a r e w orthy o f c o n sid e r a tio n , th ey have y e t to be fu lly p ro v en and do not le s s e n the im p o r ta n c e o f th is in v e s tig a tio n 's fin d in g s. It is sa fe then 122 to in s is t that th e r e s u lts p r e s e n te d in th is d is s e r ta tio n a r e e v id e n c e of the p s y c h o lo g ic a l in v a r ia n c e of S tr u c tu r e - o f -ln te lle c t fa c to r s . R E F E R E N C E S 123 REFERENCES 124 A d k in s, D . C . & L y e r ly , S. B. F a c to r a n a ly s is of r ea so n in g t e s t s . C h apel H ill: U n iv e r sity o f N o rth C a r o lin a , D ep a rtm en t of P s y c h o lo g y , 1951. B e ch to ld t, H. P . F a c to r ia l In v e stig a tio n of th e p e r c e p tu a l sp eed fa c to r . A m e r ic a n P s y c h o lo g is t, 1947, 2, 3 0 4 -3 0 5 . B o tzu m , W. A . A fa c to r ia l study of th e r e a so n in g and c lo s u r e fa c to r s . P s y c h o m e tr lk a , 1951, 1_6, 3 6 1 -3 8 6 . B u rt, C. F a cto r a n a ly s is and c a n o n ic a l c o r r e la tio n s . B r itis h J ou rn al of P s y c h o lo g y , 1948, 1 _ , 9 5 -1 0 6 . B u tle r , J . S im p le s t data fa c to r s and s im p le str u c tu r e in fa c to r a n a ly s is . E d u ca tio n a l and P s y c h o lo g ic a l M e a su r e m e n t, 1964, 24, 7 5 5 -7 6 3 . B u tle r , J . M . S im p le str u c tu r e r e c o n sid e r e d : d is tin g u ish a b ility and in v a r ia n c e in fa c to r a n a ly s is . M u ltiv a r ia te B e h a v o r ia l R e s e a r c h , 1969, 4} 6 -2 8 . C a m p b e ll, D. T . & F is k e , D . W. C o n w rg en t and d is c r im in a tio n v a lid a tio n by th e m u ltitr a it-m u ltim e th o d m a tr ix . P s y c h o lo g ic a l B u lle tin . 1959, 56j 8 1 -1 0 5 . C a r r o ll, J . D . A fa c to r a n a ly s is of v e r b a l a b ilitie s . P sy c h o m e tr ik a , 1941, 6 , 2 7 9 -3 0 7 . C a tte ll, R. B. A note on fa c to r in v a r ia n c e and th e id e n tific a tio n of fa c to r s . B r itis h J o u rn a l of P s y c h o lo g y . 1949a, 2 , 1 3 4 -1 3 8 . C a tte ll, R. B, r— and o th er c o e ffic ie n ts of p a ttern s im ila r ity . P sy c h o m e tr ik a . 1949b, 14, 2 7 9 -2 9 8 . C a tte ll, R. B . , B a lc o r , K . R. , H orn , J. L . , & N e s s e lr o e d e , J . R. F a c to r m a tch in g p r o c e d u r e s: an im p r o v em e n t of th e s ind ex; w ith ta b le s . E d u ca tio n a l and P s y c h o lo g ic a l M e a su r e m e n t. 1969, 2 9 . 7 8 1 -7 9 2 . C h r ista l, R. E . F a c to r a n a ly tic study o f v is u a l m e m o r y . P s y c h o lo g ic a l M o n o g ra p h s, 1958, 72 (13, W hole N o. 4 6 6 ). C liff, N . O rth ogon al ro ta tio n to c o n g r u e n c e . P s y c h o m e tr ik a , 1 9 66. 31_. 3 3 -4 2 . C liff, N. & H a m b u rg er, C . D . The stu d y o f sa m p lin g e r r o r s in fa cto r a n a ly s is by m ea n s of a r tific ia l e x p e r im e n ts . P s y c h o lo g ic a l B u lletin , 1967, 6 8 , 4 3 0 -4 4 5 . 125 C liff N . & P e n n e ll, R. T he in flu e n c e of c o m m u n a lity , fa c to r stren g th and lo a d in g s iz e on th e sa m p lin g c h a r a c t e r is tic s of fa c to r lo a d in g s. P s y c h o m e tr ik a . 1967, 32, 3 0 9 -3 2 6 . C o o m b s, C. H . A fa c to r ia l study of n u m b er a b ility . P s y c h o m e tr ik a , 1941, 6 , 1 6 1 -1 8 9 . D ix o n , W. J . B io m e d ic a l co m p u ter p r o g r a m s , X - s e r ie s . L o s A n g e le s: H ealth S c ie n c e C om puting F a c ility , U. C .L . A . , 1969. D o h e r ty , W. J . A c o m p a r iso n of n in e m eth o d s fo r d e te r m in in g th e n u m b er of fa c to r s u sin g a M onte C a r lo tec h n iq u e. U n p u b lish ed m a s t e r 's t h e s is . U n iv e r s ity of Southern C a lifo r n ia , 1971. D unham , J . L . , G u ilfo rd , J . P . , S i H o ep fn er, R. M u ltiv a r ia te a p p ro a ch es to d is c o v e r in g th e in te lle c tu a l co m p o n en ts of co n cep t le a r n in g . P s y c h o lo g ic a l R e v ie w . 1968, 75> 2 0 6 -2 2 1 . F is k e , D . W. C o n siste n c y of th e fa c to r ia l str u c tu r e of p e r so n a lity r a tin g s fr o m d iffe r e n t s o u r c e s . A m e r ic a n P s y c h o lo g is t , 1948, 3, 360. F le is h m a n , E . A . H um an a b ilitie s and the a c q u isitio n of s k ills . W ash ington, D . C. : A m e r ic a n In stitu te s fo r R e s e a r c h , 1966. F r e n c h , J. W. The d e sc r ip tio n of ap titu d e and a c h ie v e m e n t t e s t s in te r m s of ro ta ted f a c to r s . P s y c h o m e tr ic M o n o g ra p h s, 1951, N o. 5. G ib son , W. A . R em a rk s on T u c k e r 's in te r -b a tte r y m eth od o f fa c to r a n a ly s is . P s y c h o m e tr ik a , I9 6 0 , 2 5j 1 9 -2 5 . G reen , B . F . T he o rto g o n a l a p p ro x im a tio n of an ob liq u e str u c tu r e in fa c to r a n a ly s is . P sy c h o m e tr ik a . 1952, J_7, 4 2 9 -4 4 0 . G u ilfo rd , J . P . T he str u c tu r e of in te lle c t. P s y c h o lo g ic a l B u lle tin , 1956, 53, 2 7 6 -2 9 3 . G u ilfo rd , J. P . T he n a tu re of hum an in te llig e n c e . N ew Y ork: M cG ra w -H ill, 1 9 ^ G u ilfo rd , J . P . T h u r sto n e 's P r im a r y M en tal A b ilitie s and S tr u c tu r e - o f - ln t e lle c t A b ilitie s . P s y c h o lo g ic a l B u lle tin , 1972, 77, 1 2 9 -1 4 3 . G u ilifo rd , J . P . & H o ep fn er, R. S tr u c tu r e -o f-in te lle c t fa c to r s and th e ir t e s t s . R e p o r ts fr o m th e P s y c h o lo g ic a l L a b o ra to r y , N<k 3&, L o s A n g e le s: U n iv e r sity of Southern C a lifo r n ia , 1966* G u ilfo rd , J. P . fa H o ep fn e r, R. C o m p a riso n s of v a r im a x r o ta tio n s w i th r o ta tio n s to th e o r e tic a l ta r g e ts . E d u ca tio n a l and P s y c h o lo g i c a l M e a su r e m e n t, 1969, 29, 3 -2 2 . G u ilford , J . P . fa H oep fn er, R. The a n a ly s is of in t e llig e n c e . N ew York: M c G r a w -H ill, 1971. 126 G u ilford , J . P , , & L a c e y , J . I. ( E d s .) P r in te d c la s s if ic a t io n t e s t s . A rm y A ir F o r c e s A v ia tio n P sy c h o lo g y R e s e a r c h P r o g r a m R e p o r ts. N o. 5, W ash in gton , D , C. : G FO , 1947. G u ilford , J . P . , 8t Z im m e r m a n , W. S. S om e v a r ia b le -s a m p lin g p r o b le m s in the r o ta tio n o f a x e s in fa c to r a n a ly s is . P s y c h o lo g ic a l B u lle tin , 1963, 60, 2 8 9 -3 0 1 . H o e te llin g , H . A n a ly s is o f a c o m p le x of s ta tis tic a l v a r ia b le s into p r in c ip a l c o m p o n e n ts. J o u rn a l of E d u ca tio n a l P s y c h o lo g y , 1933. 24, 4 1 7 -4 4 1 , 4 9 8 -5 2 0 . H offm an , K . , G u ilford , J . P . , H o ep fn er, R . , & D o h erty , W. A fa c to r a n a ly s is o f th e fig u r a l-c o g n itio n and fig u r a l-e v a lu a tio n a b ilitie s . R e p o r ts fr o m the P s y c h o lo g ic a l L a b o r a to r y . L o s A n g e le s: U n iv e r sity o f S ou thern C a lifo r n ia , 1968, H orn , J. & K nano, J , On th e su b je c tiv e c h a r a c te r o f the e m p ir ic a l b a se o f G u ilfo r d 's s t r u c t u r e - o f - in t e lle c t m o d e l. P s y c h o lo g ic a l B u lletin (in p r e s s ) . J o r e sk o g , K . G. A g e n e r a l m eth od fo r a n a ly s is o f c o v a r ia n c e s tr u c tu r e s . B lo m e tr ik a . 1970, j>7, 2 3 9 -2 5 1 . J o r e sk o g , K . G . S im u lta n eo u s fa c to r a n a ly s is in s e v e r a l p o p u la tio n s. P sy c h o m e tr ik a , 1971, 3(>, 4 0 9 -4 2 6 . K a is e r , H . F . T he v a r im a x c r ite r io n fo r a n a ly tic ro ta tio n in fa c to r a n a ly s is . P s y c h o m e tr ik a . 1958, 2 3 , 1 8 7 -2 0 0 . K a is e r , H. F , , H anka, S . , & B ia n ch in i, J . C . R e la tin g fa c to r s b etw een stu d ie s b a sed upon d iffe r e n t in d iv id u a ls. M u ltiv a r ia te B e h a v o r ia l R e s e a r c h . 1971, 6 , 4 0 9 -4 2 2 . K e lle y , H . P . M em o ry a b ilitie s : a fa c to r a n a ly s is . P s y c h o m e tr ic M on ograp h s, 1964, N o . 11. L e y d e n , F . T he id e n tific a tio n and in v a r ia n c e o f fa c t o r s . B r itish Jo u rn a l o f P s y c h o lo g y . 1953, 119. M ered ith , W. N o te s on fa c to r ia l in v a r ia n c e . P s y c h o m e tr ik a , 1964, 29, 1 7 7 -1 8 5 (a). M ered ith , W. R otation to a c h ie v e fa c to r ia l in v a r ia n c e . P s y c h o m e tr ik a . 1964b, 29. 1 8 7 -2 0 6 . M oon ey, C. M . A fa c to r ia l study of c lo s u r e . C anadian Jou rn al o f P s y c h o lo g y . 1954, ji, 5 1 -6 0 . O sb o rn e, R . T . , A n d e rso n , H . E . , & B a sh a w , W . L . T he sta b ility of the WISC fa c to r str u c tu r e at th r e e a g e le v e ls . M u ltiv a r ia te B e h a v io ra l R e s e a r c h . 1967, 4 4 3 -4 5 1 . 127 P e m b e r to n , C . T he c lo s u r e fa c to r s r e la te d to o th e r c o g n itiv e p r o c e s s e s . P sy c h o m e tr ik a , 1952, _1_7, 2 6 7 -2 8 8 , P in n ea u , S. R . & N e w h o u se, A . M e a s u r e s of in v a r ia n c e and c o m p a r a b ility in fa c to r a n a ly s is fo r fix e d v a r ia b le s . P sy c h o - m e tr ik a , 1964, 29, 2 7 1 -2 8 1 . R im o ld i, H . J . A , T he g e n e r a l in te llig e n c e fa c to r . P sy c h o m e tr ik a , 1951, _16^ 7 5 -1 0 1 . S ch on em an n , P . H. A g e n e r a liz e d so lu tio n o f the o rth o g o n a l p r o c r u s te s p r o b le m . P sy c h o m e tr ik a , 1966. 31, 1 -1 0 , S p ea rm a n , C . " G en eral In te llig e n c e " o b je c tiv e ly d e te r m in e d and m e a s u r e d . A m e r ic a n Jou rn al o f P s y c h o lo g y , 1904, _15, 2 0 1 -2 9 3 . S p ea rm a n , C . A b ilitie s o f m a n . N ew Y ork: M a c m illa n , 1927. T a y lo r , C . W. A fa c to r ia l study o f flu e n c y in w r itin g . P s y c h o m e tr ik a , 1947, 12, 2 3 9 -2 6 2 . T h u r sto n e , L , L , T he v e c to r s of m in d . C h icago: U n iv e r sity of C h ica g o P r e s s , 1935. T h u r sto n e , L . L . P r im a r y m en ta l a b ilitie s . P s y c h o m e tr ic M ono g r a p h s, 1938, N o . 1. T h u r sto n e , L . L . E x p e r im e n ta l study of s im p le str u c tu r e . P sy c h o m e tr ik a . 1940, ji, 1 5 3 -1 6 8 , T h u r sto n e , L . L . A fa c to r a n a ly s is study o f p e r c e p tio n . P s y c h o m e tr ic M on ograp h s, 1944, N o, 4, T h u r sto n e , L . L . M u ltip le fa c to r a n a ly s is . C h icago: U n iv e r sity of C h icago P r e s s ' 1 9 i7 . T h u r sto n e , L . L . A n a n a ly s is o f m e c h a n ic a l ap titu d e. T he P s y c h o m e tr ic L a b o ra to r y , R ep o rt N o. 6 2 . C h icago: U n iv e r sity of C h icago P r e s s , 1951. T h u r sto n e , L . L . & T h u rsto n e, T . G. F a c to r ia l stu d ie s o f in te llig e n c e . P s y c h o m e tr ic M on ograp h s, 1941, N o . 2. T u ck er , L . R . A m eth o d fo r s y n th e s is o f fa c to r a n a ly s is stu d ie s . P e r s o n n e l R e s e a r c h S e c tio n R e p o r t, N o. 984. W ash ington, D . C . : D ep a rtm en t of th e A r m y , 1951. T u c k e r , L . R . A n in te r -b a tte r y m eth od o f fa c to r a n a ly s is , P s y c h o m e tr ik a . 1958, 23, 1 1 1 -1 3 6 . 128 W e r ts, C . E , , J o r e sk o g , K . G . , & L in n , R. L . A m u ltitr a it- m u ltim eth o d m o d e l fo r stu d yin g g ro w th . R e s e a r c h B u lletin R B -7 1 -1 3 . P r in c e to n , N . J . : E d u ca tio n a l T e stin g S e r v ic e , 1971, W oodrow , H. T h e co m m o n fa c to r s In fifty -tw o m en ta l t e s t s . P s y c h o m e tr ik a . 1939, 4 , 9 9 -1 0 8 . W r ig le y , C . S. & N ew h au s, J . O . T he m a tch in g of two s e ts o f f a c t o r s . A m e r ic a n P s y c h o lo g is t, 1955, 10. 4 1 8 -4 1 9 . TABLES 1Z9 130 Table 1 T e s ts and th e ir h y p o th e siz e d fa c to r s fo r a ll e ig h t s tu d ie s . T h u rston e: P r im a r y M en tal A b ilitie i T e s t N am e F a c to r 1. R eading 11 CMU 2. V erb a l C la s s ific a tio n CMU 3. Word G rouping CMC 4. C o n tro lled A s s o c ia tio n s DMR 5. In v en tiv e O p p o sites DMR 6 . D isa r r a n g e d W ords CSU 7. In v en tiv e Synonym s DMR 8. C u b es C FS 9. L o z e n g e s C F T 10. F la g s C F S , C F T 11. F o r m B oard C F T 12. L o z e n g e s B C F T , C F S 13. S u rfa ce D e v elo p m e n t C F T 14. P u n ch ed H o les C F T 1 5. A r e a s CSS 16. N u m b er S e r ie s CSS 17. R ea so n in g EMI 18. F a ls e P r e m is e s EMI 19. C ode W ords CSS 20. S y llo g is m s EMI 21. W ord- N um be r MSI 22. In itia ls MSI 23, Num b e r - N um be r MSI 24. Word R eco g n itio n MMU 25. P ic tu r e R e c a ll MMU 26. H ands C FS 27. R hythm NFC 28. Sound G rouping N FC 29. S p ellin g CSU 30. V ocab u lary CMU Table 1 (con t'd .) 131 T h u rsto n e & T h u rston e: F a c to r ia l S tu d ies of I n te llig e n c e . T e s t N am e F a c to r 1. A n a g ra m s CSU, DSU 2. M ir r o r R ead in g CSU 3. C a rd s C FT 4 . C o m p letio n CMU 5. F a c e s EFU 6 . F ig u r e N am in g NMU 7. F ig u r e s C F T 8. F ir s t and E a st L e tte r s DSU 9. F ir s t N a m e s MSI 10. F la g s C FT 11. F o u r L e tte r W ords DSU 12. H igh N u m b ers CSS 13. Id en tica l P ic tu r e s E FU 14. In co m p le te W ords CSU 1 5. L e tte r S e r ie s CSS 16. M a ze I C FI 17. N u m b er P a tte r n s CSS 18. P ic tu r e N am in g NMU 19. P u r s u it C FI 20. V o ca b u la ry CMU 21. S e n te n c e s CMU 22. P a r a g r a p h s CMU 23. R hym ing W ords DSU 24. S am e or O p p o site CMU 25. S e c r e t W riting CSS 26. S u ffix e s DSU 27. W ord -N u m b er R e c a ll M SI 28. W ord P u z z le s CSU Table 1 (cont'd.) 132 A d kins & L y e rly : F a c to r A n a ly s is of R e a so n in g T e s ts T e s t N am e F a c to r 1. C ard s C F T 2. C ir c le s CSS 3. D ecod in g CSS 4 . F ig u r e A n a lo g ie s C FR 5. F ig u r e S e r ie s CSS 6 . F ig u r e s C F T 7. F ir s t and L a st L e tte r s DSU 8. Id en tica l F o r m s E F U 9* L e tte r S e r ie s CSS 10. M ixed S e r ie s CFR 11. M u tilated P ic tu r e s EFU 12. M u tilated W ords C FU 13. N u m b er S e r ie s CSS 14. P a in ted B lo c k s C F T 15. P a p e r F o ld in g C F T 16. P ic tu r e A n a lo g ie s CMR 17. P r o g r e s s iv e M a tr ic e s C FR 18. R eading I CMU 19. R eading II CMU 20. S e r ie s CFR 21. S tr e e t G e sta lt C o m p letio n CFU 22. S u ffix es DSU 23. S u rfa ce D e v elo p m e n t C F T 24. T h in gs Round DMU 25. T o p ic s DM U 26. V e rb a l A n a lo g ie s CM R 27. V o ca b u la ry CMU 28. Word S q u ares CM R Table 1 (cont'd.) 133 K e lle y : M em o ry A b ilitie s : A fa c to r A n a ly s is T e s t N a m e F a c to r 1. R e co g n itio n T e s t 11 MSI 2. R eco g n itio n T e s t III M FU 3. M em o ry fo r S y lla b le s 1 MSI 4. M em o ry fo r N u m b ers T e s t M SI 5. M em o ry fo r W ords T e s t I M SI 6. S en ten ce C o m p letio n T e s t MMI 7. M em o ry fo r R e la tio n s T e s t MSI 8. C o n se q u e n c e s T e s t 1 MMI 9. C o n se q u e n c e s T e s t U M MI 10. M em o ry fo r L im e r ic k s MMI 11. M em o ry for Id ea s MMI 12. N u m ber Span I M SS 13. N u m b er Span II M SS 14. L e tte r Span I M SS 15. L e tte r Span II M SS 16. R ep rod u ction of V isu a l D e sig n M FU 17. M ap M em o ry I M FU 18. M ap M em o r y II M FU 19. M ap M em o ry III M FU 20. M ean in gfu l M em o ry , P ic t u r e s M FU 21. M ean in gfu l M e m o r y , P a ra g r a p h M MI 22. M ean in gfu l M e m o r y , N u m b er M SI 23. M em o ry fo r W ords T e s t II M MI 134 T a b le 1 (c o n t'd .) T aylor: F lu en cy in W riting. T e st N am e F a cto r 1. F ir s t N a m es MSI 2. W ord-N um ber MSI 3. M ir r o r Reading CSU 4. F ir s t and L a st L e tte r s DSU 5. Su ffixes DSU 6. Synonym s DMR 7. F ir s t L e tte r s DSU 8. A n agram s DSU. CSU 9. A d jec tiv e s DMU 10. S im ile s DMR 11. P a ir e d O p p osites DMR 12. L e tte r S tares DMS 13. N um ber of L e tte r s DSU 14. T o p ics DMU 1 5. G iven L e tte r s DSU 16. Sentence F lu en cy DMS 17. Things Round DMU 18. Things to E at DMU 19. T h em e DMU T a b le 1 (c o n t'd .) 135 C arroll: Study of v erb a l T e s t N am e F a cto r 1. D isa r ra n g ed W ords II CSU 2. Words Score DMU 3. Su ffixes DSU 4. A n a g ra m s DSU. CSU 5. R hym ing DSU 6. D isa r ra n g ed W ords I CSU 7. P a ir e d A s s o c ia te s T -E MSI 8. P a ir e d A s s o c ia te s E -T MSI 9. M em o ry I MSI 10. D isa r ra n g ed M orp h em es CSU 11. N am ing States of the Union NMU 12. Giving F ir s t N a m e s NMU 1 3. P ic tu r e D e sc r ip tio n DMU 14. F o r m N am ing NMU 15. C olor N am ing NMU T a b le 1 (c o n t'd .) B echtoldt: Study of P er ce p tu a l Speed T e st N am e F actor 1. F lags CFT 2. F ir s t and L a st L e tte r s DSU 3. N am e R ecognition ESU 4. G ottschaldt F ig u r e s N FT 5. Size C om p arison EMU 6. Suffixes DSU 7. C ards CFT 8. Hidden P ic tu r e s N FT 9. L etter A ESU 10. Word Checking EMU 11. M utilated W ords CFU 12. B oy's F ir s t N a m es EMU 13. Identical F o r m s EFU 14. O p p osites EMU 15. P ic tu r e Squares EFU 16. 2 . 6 , 9 ESU 17. S treet G estalt C om pletion CFU 18. V erban E num eration EMU 19. F ig u re s C FT 20. L etter Squares ESU 21. Words A sso c ia te d with a H ouse EMU 22. D e sig n s N FT 23. L e tte r s IV EFU 24. C on crete A s so c ia tio n s EMU 25. P ic tu r e C om pletion CFU 26. L e tte r s I EFU 27. G eo m e trica l F ig u r e s CFU 137 T ab le 1 (c o n t'd ,) T hurstone: E xp erim en tal Study of Sim ple Structure T e s t N am e F a cto r 1. A r e a s CSS 2. C ards CFT 3. D isarran ged W ords CSU 4. F ig u r e s CFT 5. Identical N u m b ers ESU 6. In itials R eca ll MSI 7. L etter Grouping CSS 8. L etter S e r ie s CSS 9. M arks CSS 10. M ech an ical M ovem en ts C F T 11. M irro r R eading CSU 12. N um ber P a ttern s CSS 13. N um ber S e r ie s CSS 14. P a ttern s CSS 15. P r o v e rb s CMC 16. R epeated L e tte r s ESU 17. Spelling CSU 18. Squares CFT 19. W ord-N um ber MSI 20. Word P a ttern s CMC Table 2 Number of T ests for Each Hypothesized Factor by Study S. L Thurstone Adkins Simple Total No. Factor PMA Thurstone L yerly K elley Structure Bechtoldt Carroll Taylor of Studies CMU 2 5 3 3 CMC 2 2 2 CMR 3 1 CFU 2 4 1 CFR 4 1 CFS 3 1 CFT 5 3 5 4 3 5 CFI 2 1 CSU 2 4 3 4 2 5 CSS 3 4 5 7 4 MMU 2 1 MMI 6 1 MFU 6 1 MSS 4 1 MSI 3 2 6 2 3 2 6 DMU 2 2 5 3 DMR 3 2 2 DMS 3 1 DSU 5 2 2 3 6 5 NMU 2 4 2 NFC 2 1 NFT 3 1 EMU 7 1 EMI 3 1 EFU 2 2 4 3 ESU 2 4(8)* 2 No. of factors II 9 9 4 6 7 5 6 per study * Eight te sts w ere hypothesized for this factor, only four w ere analyzed. 138 1 2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 T able 3 Rotated F actor M atrix - T h urstone's P rim ary M ental A b ilitie s CMU CMC DMR CSU CFS CFT CSS EMI MSI MMU 0. 52 0.22 0 .2 8 0. 15 - 0. 10 0.21 0.25 0.31 0.23 0.2 4 0.09 0.67 0.21 0 .0 8 0. 11 0.31 0.21 0. 18 0. 17 0.28 0. 22 0.66 0 .3 4 0. 15 0.06 0. 11 0.25 0.21 - 0 .0 4 0.23 0. 17 0.27 0.63 - 0 .0 3 - 0 . 15 0.01 - 0 . 12 - 0. 02 0.25 - 0 .0 2 0.28 0.22 0.52 0.35 0.04 0. 11 0. 16 0. 09 0.22 0. 11 - 0 . 02 - 0 .0 9 0 .3 8 0.63 0. 11 0 .2 7 0.29 - 0 .0 1 - 0.00 0.26 0. 16 0. 06 0.58 0.36 0.04 - 0 . 02 0.29 0.23 0. 10 0.23 - 0 . 14 0.27 - 0.07 0.33 0.47 0.51 0. 13 0.07 0.03 0.C4 0. 28 - 0 .0 4 - 0. 12 0.13 0.26 0 .6 0 0. 26 0.22 - 0 .0 9 0. 18 0.13 0. 03 - 0. 02 - 0 .0 7 0.75 0 .5 9 0.13 0. 13 - 0 . 09 0.02 0. 15 0.16 0.21 0. 18 0. 17 0. 73 0.08 0. 09 0. 11 0. 27 -0 .0 6 0. 20 - 0 . 09 0.04 0.34 0 .5 8 0. 17 0. 19 0. 16 0.2 7 0.05 0.11 0. 16 0.08 0.32 0.63 0.08 0. 10 0.19 - 0 .0 1 0 .0 4 0. 03 0.06 - 0 .0 6 - 0 .0 9 0. 82 0 .4 0 0. 18 0.03 0. 17 - 0 . 13 0. 06 0. 04 0.04 0.08 0.45 0.21 0. 22 0 .2 4 0.22 - 0 .0 2 0.21 0. 02 0.23 - 0 .0 2 0.26 0.43 0.32 0.25 - 0 .0 3 0. 15 0 .0 0.28 0. 17 0.01 0.23 0.24 0 .8 4 0. 10 0.03 0 .0 9 0. 19 0. 17 0.22 - 0 .0 1 0.11 0. 22 0.65 0. 25 0. 12 0.16 0.22 0.29 - 0 .0 1 0. 17 0 .3 8 0.78 0. 11 0. 10 0. 18 0.03 0.33 0. 22 0.01 0. 17 0.47 0. 20 0.30 0. 10 0. 14 - 0 .0 3 0. 10 0. 17 0. 17 - 0 .0 7 0.21 - 0.07 0. 11 0.48 0.23 0.12 - 0 . 09 0. 55 0.01 - 0 . 18 0. 15 0. 17 0.21 0.47 0.21 0. 07 0.06 - 0 . 12 - 0 .0 0 0. 19 0.01 0.35 0. 05 0. 90 0.01 0. 07 - 0 . 07 0. 11 0. 16 - 0. 11 0 .1 8 - 0.02 0. 20 0. 22 0.80 - 0 .0 0 0.21 0. 12 0. 17 0. 10 0 .0 0 0.21 - 0.30 0. 15 0.22 - 0 . 27 - 0 .0 4 0.09 - 0 . 15 0.55 0 .3 4 0. 11 0. 06 0. 12 0.20 - 0 .0 8 - 0.06 0. 18 0. 11 - 0 .0 5 0. 27 0.05 - 0 . 05 0. 08 - 0 .0 5 0. 10 0.29 0. 22 0. 10 0.29 0. 10 0.29 0. 11 - 0 .0 6 0.33 0. 20 0.27 0.25 0.56 - 0.03 - 0 .0 0 - 0.06 0.27 0. 14 0.09 0. 75 0. 14 0. 34 0.29 - 0 .1 9 0 .2 7 - 0. 10 - 0 . 07 - 0 .0 3 0.02 Rotated Factor Matrix CSU CFT NMU EFU 1 0.33 0.01 0.11 0.22 2 0.47 0.15 0. 19 0. 24 3 0 .0 0 0 .7 9 0.12 0. 22 4 0.1 0 0 .0 7 0.25 0.05 5 0 .2 4 0.25 0 .1 9 0.51 6 0 .2 4 - 0 . 0 8 0 .4 4 0.25 7 0. 02 0 .6 8 0.01 0 .2 0 8 0.21 0.02 0 .0 4 0 .0 9 9 0.26 - 0 . 09 0.13 0.01 10 0.01 0 .6 4 0 .0 7 0.07 11 0.22 0. 09 0. 07 0 .0 8 12 0.08 0 .2 9 0.21 0 .2 9 13 0 .1 8 0 .1 2 0 .0 9 0 .4 4 14 0.58 - 0 . 00 0 .2 7 0. 08 15 0 .2 7 0.12 - 0 .0 4 - 0 .0 1 16 - 0 .1 7 0 .1 9 0.2 7 0 .2 7 17 0.16 0. 05 0. 15 0. 14 18 0.21 - 0 .1 1 0. 70 0.01 19 - 0 . 08 0. 18 0. 10 0.34 20 0.07 0. 07 0 .0 6 - 0 .0 3 21 0.08 0. 12 0 .0 8 0. 06 22 0. 15 0 .0 8 0. 00 - 0 . 00 23 0.33 0. 02 0 .2 4 - 0 .1 5 24 0 .1 4 0.03 0. 14 0.01 25 0. 16 0.21 0.07 0.21 26 0.36 0. 02 0,05 0.05 27 - 0 . 02 0.01 0. 08 0. 06 28 0 .6 0 0 .0 0 0 .1 4 0.05 Thurstone & Thurstone DSU MSI CSS CFI CMU 0 .5 0 0 .0 7 0. 24 0.07 0. 14 0. 26 0. 08 0. 22 0. 23 0 .0 8 0. 04 - 0 . 02 0. 19 0. 08 0 .0 7 0.25 0.03 0.25 0 .0 9 0 .7 2 0. 14 0.06 0. 23 0. 29 0.05 0.01 0. 16 0. 12 0. 08 0.03 0 .0 7 - 0 . 03 0. 13 - 0. 00 0. 17 0 .6 7 0 .0 0. 11 0 .0 8 0 .0 9 0, 11 0.57 0. 18 - 0 .0 2 0.23 0. 13 - 0 . 04 0.28 0.16 0.13 0 .5 9 0.05 0.11 - 0 .0 7 0.21 0. 10 0 .0 0.37 0.08 0. 14 0.01 - 0 . 03 0.27 0.42 0.02 0.29 0.03 0 .0 7 0.06 0. 17 0. 14 0. 12 0. 56 0. 18 0 .2 8 0. 17 - 0 . 08 0 .1 8 0 .3 5 - 0 .0 7 0. 10 0. 04 0.43 0. 13 - 0 . 02 0. 11 0.03 0. 06 0.25 - 0 .0 2 0. 11 - 0 .0 4 0 .1 9 0.53 - 0 .0 3 0. 17 0. 04 0.03 0. 13 0 .8 7 0. 11 - 0 .0 1 0.11 0.02 0. 83 0. 11 0 .0 5 0 .0 4 0.03 0. 73 0.53 0.01 0 .0 7 0. 17 0. 29 0. 13 0 .0 4 0 .0 8 0 .1 4 0. 75 0.05 0. 15 0.52 0. 11 0.16 0 .5 4 0. 14 - 0 .0 7 0.15 0 .1 8 0. 10 0 .4 7 0. 16 - 0 .0 4 - 0 . 11 0 .4 4 0.06 0 .2 0 0.05 0. 19 o Table 5 Rotated F a cto r M atrix - Adkins & L yerly CFT CSS CFP DSU EFU CFU CMR CMR DMU 1 0. 72 0. 18 0, 17 0. 10 0.01 0 .0 5 0. 16 0. 04 - 0.03 2 0.26 0 .6 8 0. 13 - 0 .0 6 - 0 .0 8 0. 05 0.21 0. 09 0. 13 3 0. 22 0 .4 5 0. 29 - 0 .0 8 0.05 0. 10 0. 29 0 .3 7 0. 09 4 0.29 0 .2 4 0.51 0.11 0 .0 8 - 0 .0 2 0.41 0. 20 - 0. 03 5 0.30 0 .4 7 0.33 - 0 .0 7 0.31 0. 02 0.15 0.21 0 .0 4 6 0. 89 0,05 0. 19 - 0 . 14 - 0 .0 9 0.01 - 0 . 04 0 .2 7 0. 13 7 0.06 0 .1 2 0.21 0 .4 7 - 0 .0 2 0.01 0 .1 0 0 .2 9 0.21 8 0 .2 4 0.31 - 0 .0 8 0.06 0 .4 8 0 .2 8 0. 25 0. 14 0. 05 9 0 .2 4 0.46 0 .2 7 0.06 0. 14 0 .0 0.16 0.35 0. 11 10 0.26 0.45 0 .4 0 0. 18 0. 15 0. 19 0.21 0.35 0.07 11 0 .1 9 0.06 0.27 - 0 .0 8 0 .6 9 0. 13 0. 05 0. 10 0. 13 12 0.11 0 .0 9 0.03 0.27 0 .1 7 0 .6 0 - 0 .0 6 0. 19 - 0 . 09 13 0 .2 7 0.45 0.31 0. 12 0.02 - 0 .0 1 0. 17 0 .2 0 0 .0 0 14 0.16 0 .3 8 0. 10 0 .3 4 0. 15 - 0 . 06 0. 13 0 .2 7 0 .0 7 IS 0 .4 0 0 .2 7 0 .3 9 0 ,0 9 0. 13 0. 12 0 .2 8 0. 03 -0 .0 5 16 0.16 0 .1 9 0.41 0 .0 8 0. 03 0. 06 0 .2 8 0. 19 0.05 17 0 .2 4 0 .3 0 0.41 0 .0 2 0 .0 6 - 0 .0 5 0 .1 4 0. 15 0.01 18 0.21 0.16 0.12 0.05 - 0 .0 1 0. 18 0. 16 0. 83 0. 11 19 0 .0 9 0 .1 8 0.21 0.05 0. 11 - 0 .0 8 0 .2 8 0 .6 4 0. 12 20 0.31 0,25 0.53 0.02 - 0 . 10 0.03 0 .2 8 0 .1 8 0 .0 8 21 0.13 0.01 0. 15 - 0 .1 0 0 .2 7 0. 56 0. 05 0. 22 0 .2 2 22 0.11 - 0 . 05 0.21 0 .4 5 - 0 .0 1 0. 16 0. 15 0 .2 7 0 .2 7 23 0.55 0 .2 9 0 .2 7 0 .0 8 0.25 0. 12 0. 14 - 0. 05 - 0 .0 6 24 . 0 . 0 4 0.15 - 0 .0 2 0 .0 7 0. 04 0 .2 0 0 .2 7 0. 18 0 .6 2 25 0.05 0 .1 2 0.05 0 .2 7 0. 11 - 0 . 06 - 0 . 15 0. 14 0.73 26 0. 13 0.31 0.52 0 .0 8 0 .0 2 - 0 .0 2 0.35 0. 42 0 .1 2 27 0. 07 0 .1 9 0 .2 8 0 .2 8 0 .0 7 0.22 0.26 0 .6 8 0 .0 7 28 0 .2 9 0 .3 2 0. 15 0.06 0. 22 - 0 .0 1 0.63 0. 29 0. 19 Table 6 Rotated F actor M atrix MSI MFU 1 0.52 0.01 2 0.2 0 0,35 3 0 .3 7 0.0 4 4 0 .6 4 0. 12 5 0 .5 4 0.03 6 0 .4 0 0 .1 2 7 0.05 0.52 8 - 0 . 00 0 .2 7 9 0.16 0.02 10 - 0 .0 8 0 .0 4 11 - 0 . 00 0 .0 8 12 0. 03 - 0.03 13 0 .0 9 0 .0 0 14 0.03 0 .0 0 15 0.11 - 0 .0 8 16 0.05 0.52 17 0.26 0.45 18 0. 16 0.21 19 0.15 0.46 20 0. 09 0 .3 0 21 0. 17 0. 17 22 0.31 0 .3 8 23 0.55 0 .1 4 - K elley MMI MSS 0 .1 8 0 .1 0 0 .2 7 0 .0 9 0.2 2 0 .2 8 0.2 2 0 .2 0 0 .2 9 0.21 0 .5 8 0 .0 9 0.11 0 .2 4 0.32 0. 12 0.52 0 .0 8 0 .8 2 0. 18 0 .5 9 0. 12 0 .0 7 0.71 0.13 0 .6 9 0 .1 4 0 .6 9 0 .1 7 0.75 0.05 0 .2 4 0. 13 0. 14 0 .1 2 0.15 0 .1 2 0.23 0.25 0 .2 4 0.33 0. 15 0. 03 0. 23 0 .3 7 0. 13 142 1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 16 17 18 19 20 Table 7 R otated F a cto r M atrix - E xperim ental Study of Sim ple Structure CFT CSU ESU MSI CSS CMC 0.24 0 .2 8 0. 10 0.21 0.42 - 0 .0 6 0.8 0 0. 13 - 0 . 03 0. 12 0. 17 - 0 .0 5 0. 14 0 .4 9 0. 29 0.23 0 .2 7 0. 14 0. 85 0. 10 0. 17 0. 11 0.0 9 0.01 - 0 .0 4 0.16 0.68 0.23 0.15 - 0 . 03 - 0 .0 1 0 .0 8 - 0. 07 0.63 0. 15 0.01 0. 19 0 .2 0 0. 25 0. 12 0 .4 6 0 .2 7 0.20 0.25 0. 13 0.21 0.63 0. 19 0.21 0 .0 9 0. 00 0, 17 0 .4 9 0. 03 0.43 0 .2 2 - 0 . 18 0.04 0.23 - 0 . 00 0.28 0 .7 6 - 0. 05 0. 23 0 .3 6 - 0 . 06 0.32 0 .1 2 0. 14 0. 12 0 .5 8 - 0 . 06 0.29 0.21 0. 12 0. 06 0.51 0.15 0.27 0 .1 9 0.05 0. 13 0.41 - 0 . 03 0.16 0 .2 0 0.01 0. 23 0. 26 0 .6 4 0. 16 0 .2 2 0. 53 0.21 0. 24 - 0 .0 5 - 0.06 0 .3 5 0. 19 0. 22 0. 12 0 .3 0 0.58 0.03 0. 17 0. 11 0 .4 5 - 0. 11 0.01 - 0 .0 5 0. 04 0.68 0. 14 - 0 . 04 0.14 0.25 0. 03 0. 22 0 .4 0 0 .4 9 143 T able 8 R otated F a cto r M atrix - Bechtoldt CFT DSU ESU NFT 1 0.66 0.26 0 .0 7 0 .2 9 z - 0 .0 4 0. 56 0 .2 9 0.11 3 0.03 0 .0 2 0.59 - 0 .0 5 4 0 .2 7 0 .2 0 - 0.12 0.46 5 0.03 0 .0 7 0.25 - 0 .2 9 6 0 .0 8 0.55 0.05 - 0 .0 7 7 0.78 0. 13 0 .0 7 0 .2 8 8 - 0.02 - 0 .0 9 0.06 0 .3 9 9 - 0 .1 0 0 .0 0 0.72 0. 13 10 0. 10 - 0 . 12 0.21 - 0.03 11 0.16 0 .1 8 0.22 0.2 8 12 - 0 .0 9 0 .0 9 0 .3 8 0 .0 8 13 0.26 - 0.25 0 .2 8 0.23 14 0.07 0. 19 0 .2 4 0 .0 0 15 0 .0 7 - 0 .0 6 0.25 - 0 .0 6 16 - 0 .0 1 0.0 5 0.6 0 - 0 .0 7 17 0.0 0 - 0 .0 8 - 0 .0 9 0.27 18 - 0 . 10 - 0 .0 4 0.30 0. 24 19 0.66 - 0.06 - 0.04 0. 18 20 0.18 0. 24 0.41 - 0 . 09 21 - 0 . 11 - 0 .0 4 0.21 0.23 22 0.29 - 0 .0 3 0. 11 0.40 23 0.07 0. 12 0.21 0. 11 24 - 0 .2 2 0.28 - 0.06 0. 10 25 0 .0 4 - 0 . 02 - 0.08 - 0 .0 4 26 - 0.02 0.26 - 0.05 0. 10 27 0.1 0 - 0 .0 5 0.28 - 0 . 11 EMU CFU EFU 0. 13 0. 14 0. 10 0.25 0.01 0.0 5 0 .1 8 0.06 0. 17 0 .2 0 0. 13 0.29 0 .7 0 - 0 .0 5 0. 03 0. 19 0.01 - 0 . 10 0 .0 4 0. 18 0. 14 0.04 0 .3 9 - 0.01 0 .0 4 - 0, 10 0.26 0 .6 9 - 0. 15 0.13 - 0 .0 4 0. 18 0. 05 0.66 0. 19 0. 02 0 .2 8 0. 13 0.43 0.65 0 .0 8 0 .0 4 0. 17 0 .2 9 0.36 0.29 0. 10 0.05 0.24 0. 13 0. 10 0.71 0. 16 0. 04 0. 15 0,01 0.19 0. 18 0. 17 0.08 0.61 - 0. 12 - 0. 05 0. 26 0.04 0. 10 0.09 0. 07 0.61 0.48 0.20 0.47 0 .2 0 0. 53 0. 12 0.28 -0 .0 1 0 .3 4 0.02 0. 18 0 .2 8 144 T able 9 Rotated F actor M atrix CSU DMU DSU 1 0 .4 9 0 .0 8 0 .2 9 2 0.41 0.58 0. 06 3 0 .0 9 - 0 .0 8 0. 83 4 0,53 0.08 0 .2 9 5 0 .2 9 0. 14 0.38 6 0 .5 0 - 0.02 0.2? 7 0. 12 0.06 - 0. 08 8 0 .2 4 - 0.11 - 0 . 07 9 - 0 .0 8 0 .0 0.29 10 0 .5 0 0. 14 0 .4 4 11 0 .0 6 0 .0 4 0. 18 12 0.02 0.19 0.01 13 - 0 .1 6 0.73 0.02 14 0 .0 9 0.08 0.07 15 0.23 0 .0 9 0. 03 Carroll MSI NMU 0.35 0 .0 2 - 0 . 14 0 .2 0 0. 16 0 .2 7 0 .2 4 0 .0 9 0.16 0.05 0. 23 0 .3 2 0. 90 - 0 .0 3 0 .9 0 - 0 .0 3 0 .5 0 0. 16 0 .2 7 0. 11 0. 14 0 .3 4 - 0 .0 1 0.42 0 .0 7 0. 14 0. 24 0. 75 0. 18 0. 72 Table 10 R otated F actor M atrix - MSI c s u DSU 1 0.50 0.06 0. 12 2 0.61 0.12 0. 14 3 0.17 0.44 0. 13 4 0.09 0.06 0.63 5 0.18 -0.11 0.71 6 0.06 0.13 0.39 7 0.13 0.18 0.71 8 0.19 0.44 0.49 9 0.13 -0.19 0.23 10 0.09 - 0. 02 0. 14 11 0. 18 0.01 0.29 12 0. 03 0.10 0.28 13 0. 17 0.29 0.61 14 0.27 -0.01 0.20 15 0.19 0.08 0.61 16 0. 09 - 0.01 0.18 17 0.21 0.04 0. 12 18 - 0. 12 0.29 0.28 19 0.01 0.05 0. 25 Taylor DMR 0.09 0.08 0. 14 0.00 0.07 0.46 0.25 0. 23 0.25 0.29 0. 72 0.20 0.26 0. 24 0.23 0.18 0.19 0.29 0. 18 DMS -0. 14 - 0.01 0. 14 -0 . 07 0.03 0. 23 0. 19 0. 05 0.29 0.71 0. 26 0. 59 0.20 0.45 0. 12 0.60 0. 29 0. 12 0.09 DMU 0. 12 0. 00 0. 00 0. 08 0. 20 0. 14 - 0. 02 0. 10 0.48 0.28 -0.03 0. 22 - 0. 12 0.57 0. 19 0.43 0.41 0.49 0.47 A PPE N D IX 147 T hurstone: P r im a r y m en tal a b ilitie s. T e st F actor 148 R eason for E x clu sio n I. Reading I CMU a ltern a te fo rm 2. Reading 11 CMU 3. V erb al C la ssific a tio n CMU 4. Word Grouping CMU 5. F ig u re C la ssific a tio n CFC sin g let factor 6. C ontrolled A sso c ia tio n s DMR 7. Inventive O p p osites DMR 8. C om pletion C M U .N M U co m p lex 9. D isa r ra n g ed W ords csu 10. F ir s t and L a st L e tte r s DSU sin g le t factor 11, D isa rra n g ed S en ten ces CMS. NMS co m p lex 12. A n agram s CSU, DSU com p lex 1 3. Inventive Synonym s DMR 14. B lock Counting EFI, C FI, CFT com p lex 15. Cubes CSF 16. L o z en g es C F T 17. F la g s CFS, CFT 18. F o rm Board C F T 19. L o z en g es B C F T , CFS 20. Surface D evelop m en t CFT 21. P unched H oles CFT 22. M ech an ical M ovem en ts • * • co m p lex 23. Identical F o rm s EFU sin g let factor 24. P u rsu it C FI, CFU sin g let fa cto r 25. Copying C F U ,E F U com p lex 26. A r e a s CSS 27. N um ber Code NSI.M SI com p lex 28. Addition MSI, NSI com p lex 29. Subtraction MSI, NSI com p lex 30. M ultip lication MSI, NSI com p lex 31. D iv isio n MSI, NSI com p lex 32. T abular C om pletion CSS, MSI, NSI com p lex 33. E stim a tin g CMS, CSI com p lex 34. N um ber S e r ie s CSS 35. N u m e r ic a l Judgm ent CMS, NSI com p lex 36. A r ith m etica l Judgm ent CMS, MSI, NSI com p lex 37. R easoning EMI 38. V erb al A n a lo g ies CMR sin g let fa cto r 39. F a ls e P r e m is e s EMI 40. Code Words CSS 41. P a ttern A n a lo g ies CFR sin g le t factor 42. S y llo g ism s EMI 43. W ord-N um ber MSI 44. In itials MSI 45. N u m b er-N u m b er MSI 46. Word R ecognition MMU 47. F igu re R ecognition M FU sin g let fa cto r 48. P ic tu r e R ecall MMU 49. Hands CFS T hurstone: P r im a r y m en tal a b ilitie s, (cont'd. ) T eat F a cto r R eason for E xclu sion 50. Rhythm 51. Sound Grouping 52. Spelling 53. G ram m ar 54. V ocabula ry 55. F r e e Writing 56. Word K now ledge 57. T hem e N FC N FC csu EMU CMU D M U .O M S CMU DM U, DMS sin g let factor co m p lex a ltern ate fo rm co m p lex T hurstone & Thur stone: F a cto r ia l stu d ies of in te llig e n c e . 150 T e s t F actor R eason for E xclu sion 1. ABC 2. A b su rd ities 3. Addition 4. A n agram s 5. A rith m etic 6. A sso c ia tio n 7. M ir ro r Reading 8* Cards 9. C la ssific a tio n 10. C om pl etion 11. D igit Span 12. D ir ec tio n s 13. D isa rra n g ed Sentences 14. Dot Counting I 15. Dot Counting 11 16. Dot Counting 111 17. Dot P a ttern s 18. F a c e s 19. F igu re Grouping 20. F igu re Nam ing 21. F igu re R ecognition 22. F ig u res 23. F ir s t and L a st L ette rs 24. F ir s t L e tte r s 25. F ir s t N a m es 26. F la g s 27. Four L etter Words 28. G eo m e trica l F o rm s 29. H igh N um bers 30. Identical N um bers 31. Identical P ic tu r e s 32. Incom plete Words 33. L e tte r Grouping 34. L e tte r S eries 35. M aze I 36. M aze II 37. M ultip lication 38. N um ber P a ttern s 39. P aragrap h R eca ll 40. P e d ig r e e s 41. P ic tu r e N am ing 42. P r e fix e s 43. P r o v e r b s 44. P u rsu it 45. V ocabulary 46. Sentences 47. P aragraph s 48. P aragrap h s 49. R easoning NSI EMU MSI, NSI CSU.DSU CMS, MSI, NSI DMU csu CFT NSC CMU MSS NMS, CMS C F C , NFC EFU CFC NMU MFU CFT DSU DSU MSI CFT DSU NFU CSS ESU EFU CSU CSU, CSS CSS CFI CFI MSI, NSI CSS MMU MMI NMU DSU CM C.NM C CFI CMU CMU CMU SMU NMI sin g let fa cto r sin g let factor co m p lex co m p lex sin g let fa cto r sin g let factor sin g let fa cto r n o n -in tellectu a l com p lex n o n -in tellectu a l altern ate form altern ate fo rm com p lex sin g let factor sin g le t factor sin g let fa cto r sin g let factor com p lex altern ate fo rm co m p lex sin g le t factor sin g let factor a lter n a te fo rm co m p lex a ltern a te fo rm sin g let factor 151 T hurstone & Thur stone: F a cto r ia l stu d ies of in te llig e n c e , (cont'd. ) T e st F a cto r R eason for E x clu sio n 50. Rhym ing Words DSU 51. Sam e or O pposite 52. S cattered X's CMU e s s non - inte llectu a l 53. S ecret Writing CSS 54. Suffixes DSU 55. Synonym s DMR sin g le t fa cto r 56. T h re e-H ig h er NSR sin g le t fa cto r 57. V erb al Enum eration EMU doublet factor 58. Word Checking EMU doublet fa cto r 59. W ord-N um ber R ecall MSI 60. Word P u z z le s CSU Adkins & L yerly: F a cto r a n a ly sis of reason in g t e s t s . I®* T e st F a cto r R eason for E x clu sio n 1. A b su rd ities EMU sin g let fa cto r 2. A rith m etic CMS. MSI. NSI co m p lex 3. B lock Counting C FI. E F I, CFT co m p lex 4. C am ouflaged O utlines N FT doublet fa cto r 5. C ards C FT 6. C ir c le s CSS 7. C on clu sion s EMI, EMR com p lex 8. D ecoding CSS 9. D e sig n s N FT doublet factor 10. F a ls e P r e m is e s EM R, EMI com p lex 11. F igu re A n a lo g ies CFR 12. F igu re C la ssific a tio n 1 CFC sin g le t factor 13. F igu re C la ssific a tio n 11 CFC a ltern ate form 14. F igu re C la ssific a tio n 111 CFC altern ate form 15. F ig u re S e r ie s CSS 16. F ig u re s C FT 17. F ir s t and C ast L ette rs DSU 18. F o rm s NSI sin g let factor 19. G eo m etrica l P u z z le s N F S, DFS sin g le t fa cto r 20. Identical F o r m s EFU 21. In com p lete O utlines NM S, CMS com p lex 22. L e tte r S e r ie s CSS 23. L o g ica l P u z z le s NMI sin g le t factor 24. Map Planning EFI sin g let factor 2 5. M a tr ic e s VI NFS sin g le t fa cto r 26. M ech an ical Inform ation s e e n o n -in tellectu a l 27. M ech an ical M ovem en ts C F T , MK non- in tellectu a l 28. M ixed S e r ie s CFR 29. M utilated P ic tu r e s EFU 30. M utilated Words CFU 31. N im CSI sin g let factor 32. N um ber S e r ie s CSS 33. N u m er ic a l O perations I MSI, NSI, ESI com p lex 34. N u m er ic a l O perations II MSI, NSI, ESI altern a te fo rm 35. N u m er ic a l P u z z le s CMS sin g le t factor 36. O verlapping C ir c le s E FR sin g le t factor 37. P ain ted B lock s FCT 38. P a p er Folding CFT 39. P ic tu r e A n a lo g ies CMR 40. P ic tu r e A rran gem en t NM S, N F S com p lex 41. P ic tu r e C la ssific a tio n CMC, NMC co m p lex 42. P ictu re-G ro u p N am ing NMU sin g let fa cto r 43. P lanning a C ircu it CFI sin g le t fa cto r 44. P r a c tic a l Situations « a a com p lex 45. P r o g r e s s iv e M a trices CFR 46. P r o g r e s s iv e M a tr ice s CFR altern ate form 47. P r o g r e s s iv e M a tr ice s CFR a ltern a te form 48. P r o g r e s s iv e M a tr ice s CFR altern ate fo rm 49. Reading I CMU 153 Adkins & L yerly: F a cto r a n a ly sis of rea so n in g t e s t s , (con t’d . ) T e st__________________________ F a cto r R eason for E x clu sio n 50. R eading 11 CMU 51. R ea so n s DM1 sin g let fa cto r 52. Sentence O rder NMS sin g let factor 53. S e r ie s CFR 54. S treet G estalt C om pletion CFU 55. Suffixes DSU 56. Surface D evelop m en t C F T 57, Things Round DMU 58. T op ics DMU 59. V erb al A n a lo g ies CMR 60. V erb al C la ssific a tio n 1 CMC, NMC com p lex 61. V erb al C la ssific a tio n 11 CMC, NMC altern a te form 62. V ocabulary CMU 63. W ord-G roup N am ing NMU doublet factor 6 4 . Word S election EMI sin g le t fa cto r 6 5 . Word Squares CMR 154 T aylor: A fa cto ria l study of fluency in w ritin g. T e st F a cto r R eason for e x clu sio n 1. F ir s t N a m es MSI 2. W ord-N um ber MSI 3. Identical N u m b ers ESU sin g le t factor 4. M irro r Reading CSU 5. L etter S e r ie s CSS sin g le t fa cto r 6. L etter Grouping CSC sin g le t fa cto r 7, Addition MSI, NSI co m p lex 8. M ultiplication MSI, NSI co m p lex 9* Sam e or O pposite CMU sin g let fa cto r 10. C om pletion NMU, CMU sin g let fa cto r 11. F ir s t and L ast L e tte r s DSU 12. Suffixes DSU 13. Synonym s DMR 14. F ir s t L e tte r s DSU 15. A n agram s CSU, DSU 16. D isa rra n g ed Sentences NM S, CMS sin g le t fa cto r 17. A d jectiv es DMU 18. S im ile s DMR 19. P a ried O pp osites DMR 20. L etter Stars DMS 21. U nfinished S tories DM1 22. N um ber of L e tte r s DSU 23. T op ics DMU 24. G iven L e tte r s DSU 25. Sentence F luency DMS 26. T hings Round DMU 27. Things to Eat DMU 28. T hem e DMU C arroll: A factor an alysis of verbal a b ilities. T e st F actor___ ______R eason for E xclu sion 1. D isarran ged Words 1 CSU 2. Words Score DMU 3. V erbal A nalogies CMR sin glet factor 4. Spelling MSS sin glet factor 5. Suffixes DSU 6. A nagram s CSU. DSU 7. Rhyming DSU 8. D isarran ged Words 11 CSU 9. Inventive O pposites NM R.DM R sin glet factor 10. P h ra se Com pletion DM1 sin glet factor 11. L etter-Star T est DMS sin glet factor 12. P a ired A s so c ia te s T -E MSI 13. P aired A sso c ia te s E -T MSI 14. V ocabulary CMU sin g let factor 15. W ord-Choice EM U. CMU sin glet factor 16. M em ory I MSI 17. D isarran ged M orphem es CSU 18. S im iles DMR sin glet factor 19. N am ing States of the Union NMU 20. Giving F ir st N am es NMU 21. P ictu re D escription DMU 22. F orm Nam ing NMU 23. C olor-N am ing NMU 24. P aragraph M em ory MMU sin glet factor K elley: M em ory A b ilities: A fa cto r a n a ly s is . 156 T e st________________________________ F a cto r R eason for E x clu sio n 1. R ecogn ition T e s t 1 MSU 2. R ecognition T e st 11 MSI 3. R ecogn ition T e s t 111 MFU 4. M em o ry fo r S yllab les 1 MSI 5. M em ory for S yllab les 11 MSI 6. M em ory for N u m bers T e s t MSI 7. M em ory for W ords T e s t I MSI 8. M em o ry for Words T e st II MMI 9. Sentence C om pletion T e st MM I 10. M em o ry for R elation s T e st MSI 11. C on seq u en ces T e st I MMI 12. C on seq u en ces T e st II MMI 13. M em ory for L im e r ic k s MMI 14. M em ory for Ideas MMI 15. N um ber Span I MSS 16. N um ber Span U MSS 17. L e tte r Span I MSS 18. L e tte r Span II MSS 19. Sentence Span T e st MMU, MMS 20. M em ory for In struction s MMU, MMS 21. R eproduction of V isu al D e sig n s MFU 22. Map M em ory I MFU 23. M ap M em ory 11 MFU 24. Map M em ory III M FU 25. M eaningful M em ory: P ic tu r e s MFU 26. M eaningful M em ory: P aragrap h MMI 27. M eaningful M em ory: N um ber MSI sin g let factor altern ate fo rm com p lex doublet com p lex doublet Thurstone: E x p erim en ta l study of sim p le stru ctu re. T e s t___________________ F a cto r R eason for E xclu sion 1. Addition MSI. NSI co m p lex 2. A rea s CSS 3. A rith m etic CMS, MSI, NSI com p lex 4. C ards CFT 5. C om pletion NMU, CMU sin g let fa cto r 6. D ir e c tio n s • • • non - inte He ctual 7. D isa rran ged Words CSU 8. F ig u re Grouping C F C , N FC sin g let factor 9. F ig u re s CFT 10. Identical F o rm s EFU sin g let fa cto r 11. Identical N u m bers ESU 12. Initials R eca ll MSI 13. L etter Grouping CSS 14. L etter S e r ie s CSS 15. M arks CSS 16. M ech an ical M ovem en ts CFT 17. M irro r Reading CSU 18. M ultiplication MSI, NSI co m p lex 19. N um ber P a tte rn s CSS 20. N um ber S e r ie s CSS 21. P a tte rn s CSS 22. P r o v e rb s CMC 23. P u rsu it CFI, CFU sin g let fa cto r 24. R eason in g I EMI, EMR sin g le t fa cto r 25. R easoning II EMI, EMR a ltern ate fo rm 26. R eason in g III EMI, EMR a ltern a te fo rm 27. R epeated L e tte r s ESU 28. Sam e O pposite S cattered X 's CMU sin g le t factor 29. CFU sin g le t fa cto r 30. Spelling CSU 31. Squares CFT 32. V erb al A n a lo g ies CMR sin g let factor 33. V erb al Sum m ation EMU sin g le t fa cto r 34. W ord-N um ber MSI 35. Word P a tte rn s CMC 36. Sam e O pposite CMU altern ate fo rm 158 B echtold: A fa cto r ia l in v estig a tio n of the p ercep tu al speed fa cto r. T e st F a cto r R eason for E x clu sio n 1. V ocabulary 2. T w o-d ig it Addition 3. F la g s 4. F ir s t and L a st L e tte r s 5. N am e R ecognition 6 . G ottschaldt F ig u r e s 7. Size C om p arison 8. T o p ics-W o rd s 9. M ultip lication 10. C om pletion 11. Suffixes 12. C ards 13. Hidden P ic tu r e s 14. L e tte r A 15. D is c u s s io n 16. Word C hecking 1 7. M utilated Words 18. L e tte r s CSVZ 19. B oy's F ir s t N am es 20. Dot P a ttern s 21. Identifal F o r m s 22. O pp osites 23. F ir s t D igit C an cellation 24. F iv e -L e tte r Words containing S 25. P ic tu r e Squares 26. W riting W ords 27. W riting X's 28. 2,6,9 29* Street G estalt C om pletion 30. V erb al E num eration 31. L e tte r Groups 32. F ig u re s 33. F o u r -L e tte r W ords 34. L e tte r Squares 35. W ords A sso c ia te d with a H ouse 36. D e sig n s 37. Tw o-hand coordination 38. L e tte r s IV 39. C on crete A sso c ia tio n s 40. P ic tu r e C om pletion 41. L e tte r s I 42. G eo m e tr ic a l F ig u res 43. Shape C onstancy 44. P e r ip h e r a l Span 45. T o p ics 46. Two -hand Coordination CMU MSI, NSI C F T DSU ESU N F T EMU DMU MSI, NSI NM U, CMU DSU C F T N F T ESU DMS EMU CFU ESU EMU m 9 9 EFU EMU ESU ESU EFU ESU CFU EMU ESU CFT CSU ESU EMU N FT 9 9 0 EFU EMU CFU EFU CFU sin g let factor com p lex sin g let factor com p lex sin glet fa cto r sin g let fa cto r p ercep tu al n o n -in tellectu a l non - in tell e ctual n o n -in tellec tu a l DMU non- inte lie ctual non- in tellectu a l a ltern ate fo rm n o n -in tellec tu a l

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Creator Doherty, William Joseph (author)

Core Title A Rotational Approach To Psychological Invariance

Degree Doctor of Philosophy

Degree Program Psychology

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,psychology, general

Format dissertations (aat)

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Guilford, Joy P. (committee chair), Cliff, Norman (committee member), Fox, Frank (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-887116

Unique identifier UC11363291

Identifier 7331337.pdf (filename),usctheses-c18-887116 (legacy record id)

Legacy Identifier 7331337

Dmrecord 887116

Document Type Dissertation

Format dissertations (aat)

Rights Doherty, William Joseph

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA