University of Southern California Dissertations and Theses

The Discriminant Function As A Model For Diagnostic Problem-Solving

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The Discriminant Function As A Model For Diagnostic Problem-Solving

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Content This dissertation has been microfilmed exactly as received 69-5076 WONG, Wilson, 1927- THE DISCRIMINANT FUNCTION AS A MODEL FOR DIAGNOSTIC PROBLEM SOLVING. U n iversity of Southern C afifom ia, Ph.D., 1968 Psychology, experim ental University Microfilms, Inc., Ann Arbor, Michigan THE DISCRIMINANT FUNCTION AS A MODEL FOR DIAGNOSTIC PROBLEM SOLVING by W ilson Wong A D i s s e r t a t i o n P r e s e n te d to th e FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In P a r t i a l F u l f i l l m e n t o f th e R e q u ire m e n ts f o r th e Degree DOCTOR OF PHILOSOPHY (P sycho log y) A ugust 1 9 6 8 UNIVERSITY O F S O U T H E R N CA LIFORNIA TH E GRADUATE SC H O O L UNIVERSITY PARK LOS ANGELES. CA LIFO RN IA 9 0 0 0 7 This dissertation, written by W ilso n Wong under the direction of h.i_a„ Dissertation Com mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R OF P H I L O S O P H Y Dean Date......... DISSERTATION COMMITTEE _ ACKNOW LEDGMENT T h is s tu d y was s u p p o r t e d "by an IBM G ra d u a te F e llo w s h i p i n th e D e p a rtm e n t o f P sy c h o lo g y a t th e U n i v e r s i t y o f S o u th e rn C a l i f o r n i a f o r 1 9 6 6 - 1 9 6 7 . The a u t h o r g r a t e f u l l y ack n o w le d g es t h e I n t e r n a t i o n a l B u s in e s s M achines C o r p o r a t i o n f o r making t h i s r e s e a r c h p o s s i b l e . i i TABLE OP CONTENTS C h a p te r Page I . INTRODUCTION ............................................................................. 1 Background D e s c r ip t i o n o f th e Study I I . RELATED STUDIES ................................................................... 8 I I I . THE EXPERIMENT.............................................. 17 E x p e rim e n ta l P ro ced u re A d m in is tr a tio n o f E x perim ent by Computer IV. EFFICIENCY A N A L Y S IS ......................................................... 36 A n a ly s is 1 A n a ly s is 2 V. THE DISCRIMINANT MODEL.................................................... 52 D is c r im in a to r y A n a ly s is The Model E v a lu a tin g th e Model VI. DISCUSSION AND SUMMARY.................................... 71 C o n c lu sio n s D is c u s s io n Summary LIST OF REFERENCES................................................................................. 84 APPENDICES..................................................................................................... 87 APPENDIX I.A S a t e l l i t e 1: T y p ic a l S tim u lu s M a t r i x ........................................ . 88 I .B S a t e l l i t e 2: T y p ic a l S tim u lu s M a trix .............................................. 89 I.C S a t e l l i t e 3= T y p ic a l S tim u lu s M atrix .............................................. 90 I I .A Computer Program f o r A dm inis t r a t i o n o f th e E x p e r i m e n t ..................... 91 I I . B Computer Program to D erive S tim u lu s V a r ia b le V alu es .......................... 95 i i i Page APPENDIX I I I . A S tim u lu s D ata and S tim u lu s P r e s e n t a t i o n .................................................... 98 I I I . B S a t e l l i t e 1. S tim u lu s Data . . . 101 I I I . C S a t e l l i t e 2. S tim u lu s D ata . . . 102 I I I . D S a t e l l i t e 3 . S tim u lu s Data . . . 103 IV.A S u b je c t 1 R esp o n ses on SATl* SAT2 and SAT3 .............................................. 105 IV.B S u b je c t 2 R esp o n ses on SATlj SAT2 and S A T 3 .............................................. 110 IV.C S u b je c t 3 R esp o n ses on SAT1, SAT2 and S A T 3 .............................................. 115 IV.D S u b je c t 4 R esp o n se s on SAT1, SAT2 and SAT3 .............................................. 120 IV .E S u b je c t 5 R esp o n ses on SAT1, SAT2 and S A T 3 .............................................. 125 V.A S a t e l l i t e 1 C o e f f i c i e n t s . . . . . 130 V.B S a t e l l i t e 2 C o e f f i c i e n t s ................... 131 V.C S a t e l l i t e 3 C o e f f i c i e n t s ................... 132 VI.A Means and S ta n d a rd D e v ia tio n s f o r S te p 1 ......................................................... 133 V I.B Means and S ta n d a rd D e v ia tio n s f o r S te p 2 ......................................................... 134 VI.C Means and S ta n d a rd D e v ia tio n s f o r S te p 3 ......................................................... 135 V I.D Means and S ta n d a rd D e v ia tio n s f o r S a t e l l i t e 3 ......................................... 136 V I I . Rank O rder o f C o e f f i c i e n t s . . . . 138 V I II .A Agreem ent o f S s TC h o ice s on SAT3 w ith D e riv e d D is c r im in a n t F u n c tio n (SAT3 ) ......................................... 139 V I I I .B Agreem ent o f S s ' C h o ices on SAT3 w ith A ssig n ed D is c r i m i n a n t F u n c tio n ( f rom SAT1-SAT2) . . . . 140 i v LIST OP TABLES T a b le Page 1. A n a ly s is o f V a r ia n c e D esign A n a l y s i s 1 ................................................................................... 39 2. Summary o f A n a l y s i s , SAT1, AV l a ................................ 40 3. Summary o f A n a l y s i s , SAT2, AV l b ................................. 4 l 4 . A n a ly s is o f V a r ia n c e D esign A n a l y s i s 2 ................................................................................... 45 5. Summary o f A n a l y s i s , SAT1, AV 2 a ................................ 46 6 . Summary o f A n a l y s i s , SAT2, AV 2 b ................................ 47 7. Agreem ent o f D i s c r i m i n a n t F u n c tio n s o v e r S u b j e c t s ......................................................................................... 62 8 . Agreem ent o f D i s c r i m i n a n t F u n c tio n s o v e r S t e p s .............................................................................................. 64 9. Agreem ent o f S s ' R e sp o n se s Kith D e riv e d D i s c r i m i n a n t F u n c tio n P r e d i c t i o n s ................... 66 10. Agreem ent o f S s 1 R e sp o n se s w ith D i s c r i m i n a n t F u n c tio n P r e d i c t i o n s on SAT3 D a t a ..................... 6 8 11. R e l a t i o n o f S tim u lu s I n f o r m a t io n . ........................... 100 v LIST OF ILLUSTRATIONS F ig u re Page 1. Sample S tim u lu s M atrix ........................................................ 22 2. Flow Diagram f o r C om puter-A dm inistered E x p e rim e n ta l Sequence .................................................. 30 3- Flow Diagram o f Com putation o f S tim ulu s V a r ia b l e s V alues ........................................ 3^ 4. E f f i c i e n c y a s a F u n c tio n o f I n c r e a s in g F a i l u r e - P r o b a b i l i t y D i s t r i b u t i o n S k e w n e s s ...................................................................... 43 5- E f f i c i e n c y a s a F u n ctio n o f S u cc essiv e S te p s in Response Sequence ................................... 48 6. D ecisio n Axis f o r 2-Space Case I l l u s t r a t i n g L in e a r D is c r im in a n t F u n ctio n Concept . . . . 56 7. Comparison o f P r e d i c t io n A b i l i t y on SAT3 D ata betw een a SAT3 D isc rim in a n t F u n ctio n and an A ssigned (SAT1-SAT2) D is c rim in a n t F u n ctio n .................................................. 70 v i CHAPTER I INTRODUCTION Background P r o b le m -s o lv in g can be c h a r a c t e r i z e d a s th e p r o c e s s in v o lv e d i n a t t a i n i n g a d e s i r e d r e s u l t from a g iv e n i n i t i a l s i t u a t i o n u s in g c e r t a i n r u l e s i n a sequ en ce o f d i s c r e t e s t e p s . In a b ro a d s e n s e , t h i s t a k e s i n a l l human b e h a v io r . In a more l i m i t e d s e n s e , th e p r o c e s s can be view ed as a con s i d e r a t i o n and c h o ic e betw een a l t e r n a t i v e s w ith u n c e r t a i n o utcom es. What do p e o p le do when th e y choose betw een a l t e r n a t i v e s w hich i n v o lv e u n c e r t a i n outcom es? In a n sw erin g t h i s q u e s tio n f o r a s p e c i f i c s i t u a t i o n , one lo o k s f o r common a p p ro a c h e s i n d e c is io n -m a k in g and p ro b le m - s o lv in g b e h a v i o r s , even a c r o s s such d i v e r s e t a s k s i t u a t i o n s a s e l e c t r o n i c s t r o u b l e s h o o t i n g , c l i n i c a l d i a g n o s i s , and c o n c e p t f o r m a tio n . I t Is ' g e n e r a l l y a c c e p te d t h a t , w h a te v e r p e o p le do, t h e y a re n o t m axim ally e f f i c i e n t i n u s in g th e in f o r m a tio n a v a i l a b l e i n th e t a s k e n v iro n m e n t. In d e e d , th e g e n e r a l c r i t i c i s m o f fo rm al t h e o r i e s o f d e c is io n -m a k in g i s t h a t th e model does n o t a g re e w ith th e e m p i r i c a l d a t a (Edwards, 1961; B ecker & M cC lin to ck , 1 9 6 7 ) . Simon (1956) a l s o c o n te n d s 2 t h a t b e h a v i o r does n o t m atch th e models s t a t i n g t h a t s u b j e c t s do n o t b eh av e so a s to m axim ize e x p e c te d u t i l i t y . T h is i s no more th a n sa y in g t h a t t h e r e i s g e n e r a l l y a d i f f e r e n c e b etw een optimum b e h a v i o r and o b s e r v e d b e h a v i o r . S e v e r a l i n v e s t i g a t o r s a p p ro a c h t h i s d i f f e r e n c e by f o c u s s i n g on th e s t i m u l u s s i t u a t i o n s to d e s c r i b e a c t u a l b e h a v i o r . In t h i s a p p ro a c h , i t i s a s s e r t e d t h a t what p e o p le do i s to cho ose a l t e r n a t i v e s w hich r e f l e c t th e s t i m u l u s s t r u c t u r e (D a v is , 1967; B ru n e r, e t a l . , 1 9 5 6 ). G a rn e r ( 1 9 6 6 ) d e m o n s tr a te d t h i s i n a c l a s s i f i c a t i o n t a s k , and e l a b o r a t e d : "a s i n g l e s t i m u l u s can h ave no r e a l m eaning w i t h o u t r e f e r e n c e to a s e t o f s t i m u l i , b e c a u s e th e a t t r i b u t e s w hich d e f i n e i t c a n n o t be s p e c i f i e d w i t h o u t knowing w hat t h e a l t e r n a t i v e s a r e . " I t i s c l e a r t h a t any m odel d e s c r i b i n g p r o b le m - s o lv in g m ust ta k e i n t o a c c o u n t th e s u b j e c t ' s s t r u c t u r i n g o f th e e n v iro n m e n t. A n o th e r a p p ro a c h to d e s c r i b i n g human p r o b l e m - s o l v in g i n v o l v e s a t h i n k i n g - a l o u d p r o c e d u r e by Ss d u r in g th e d a ta c o l l e c t i o n p r o c e s s . T h is p ro c e d u re p r o v i d e s a ru n n in g a c c o u n t o f Ss' t h o u g h ts and c o n s i d e r a t i o n s accom panying each s t e p o r d e c i s i o n i n t h i s s o l u t i o n se q u e n c e . On th e b a s i s o f t h e s e d a t a , v e r b a l i z e d and v a r i e d i n c o n t e n t and d e t a i l , th e b u i l d e r s o f i n f o r m a t i o n - p r o c e s s i n g m odels f o r m u la te h y p o t h e s e s a b o u t b o th c o g n i t i v e and b e h a v i o r a l phenomena, and d e s c r i b e th e p r o c e s s i n th e form o f a com puter p ro g ram . To e v a l u a t e th e t h e o r y embodied i n th e m odel, th e program o u t p u t i s compared w ith o b se rv ed b e h a v io r o f th e S. P robably because o f th e in c r e a s in g a v a i l a b i l i t y and f l e x i b i l i t y o f com puters, th e number o f s t u d i e s o f t h i s type i s i n c r e a s i n g . The p r e s e n t stu d y , l i k e th e in f o rm a tio n p ro c e s s in g ap p roach, em phasizes developm ent o f a d e s c r i p t i v e model f o r th e i n d i v i d u a l r a t h e r than a norm ative model f o r a group. T h is stu d y , however, a v o id s th e s u b j e c t iv e i n t e r p r e t a t i o n s a s s o c i a t e d w ith a n a ly z in g p r o t o c o l d a ta f o r c o n s t r u c t io n o f th e model by n o t r e l y i n g on v e r b a l r e p o r t s f o r i t s d a ta . I n s t e a d , i t a d o p ts th e app roach which fo c u s e s on th e stim u lu s s t r u c t u r e . R a th e r than u s in g a com puter s im u la tio n te c h n iq u e to fo rm a liz e and t e s t th e model, i t u s e s a m u l t i v a r i a t e s t a t i s t i c to p ro v id e d i r e c t e s t im a t e s o f model p a ra m e te rs . These model p a ra m e te rs a re r e l a t e d to the s tim u lu s v a r i a b l e s as w e ig h tin g c o e f f i c i e n t s so t h a t an i n d i v i d u a l 's re s p o n s e s a re d i r e c t l y r e f l e c t e d and q u a n t i f i e d in term s o f the stim u lu s s t r u c t u r e . The s p e c i f i c pu rpo se and approach o f th e p r e s e n t study a re d e s c r ib e d n e x t. D e s c r ip tio n o f th e Study The purpose o f t h i s stu d y was to t e s t th e l i n e a r d is c r im i n a n t f u n c t i o n ’* ' as a model f o r d i a g n o s ti c problem - "*'Discriminant a n a l y s i s i s a m u l t i v a r i a t e s t a t i s t i c a l method in which a s e t o f m u lt i p le m easurem ents i s u se d to p ro v id e a l i n e a r f u n c tio n t h a t w i l l d i s c r im i n a t e between o r s e p a r a te two s e l e c t e d c a t e g o r i e s . I t I s d is c u s s e d in Chap t e r V. s o lv in g . I t was h y p o th e s iz e d t h a t o b se rv e d p ro b le m -s o lv in g r e s p o n s e s o f i n d i v i d u a l s c o u ld be a d e q u a te ly a cc o u n te d f o r by model p r e d i c t i o n s . A tr o u b le s h o o t i n g t a s k was con s t r u c t e d as t h e d i a g n o s t i c p ro b le m -s o lv in g t a s k s i t u a t i o n and a~ c o m p u te r -a d m in is te r e d e x p erim e n t was d e sig n e d to c o l l e c t b e h a v i o r a l d a ta . Models d e s c r i b i n g th e perform ance o f each i n d i v i d u a l were d e r iv e d and m atched to d a ta from one s e t o f problems., and v a l i d a t e d on a n o th e r s e t o f p ro b lem s. In a d d i t i o n , th e e f f e c t s o f e x p e r im e n ta l c o n d it i o n s on p r o b le m -s o lv in g perfo rm an ce were e v a lu a te d b o th by comparing m odels d e riv e d u n d e r d i f f e r e n t c o n d i t i o n s and by a n a l y s i s o f v a r i a n c e . Human p r o b le m -s o lv in g was d e f in e d e a r l i e r a s a p r o c e s s which b e g in s w ith a g iv e n i n i t i a l s i t u a t i o n and in v o lv e s a sequence o f d i s c r e t e s t e p s , u s in g c e r t a i n r u l e s , to a t t a i n a s p e c i f i e d g o a l. D ia g n o s tic p ro b le m -s o lv in g i s con s i d e r e d one k in d o f p r o b le m - s o lv in g , d i f f e r i n g from i t s ■ p a r e n t p r i m a r i l y i n term s o f i t s t a s k en v iro n m en t. Major c h a r a c t e r i s t i c s o f th e d i a g n o s t i c p ro b le m -s o lv in g t a s k in t h i s stu d y a re : 1. A sequence o f i n f o r m a t i o n - a c q u i s i t i o n s t e p s i s r e q u i r e d . In o t h e r k in d s o f problem s th e s o l u t i o n may be re a c h e d i n a s i n g l e s t e p . The sudden i n s i g h t ("ah a phenome non") and th e s i n g l e c h o ic e in some d e c isio n -m a k in g s t u d i e s a re two exam ples. In th e d i a g n o s ti c s i t u a t i o n , t h e r e i s i n v a r i a b l y i n s u f f i c i e n t in f o r m a tio n g iv e n a t th e i n i t i a l sam- 5 p l i n g to y i e l d a o n e - s t e p s o l u t i o n . A s e r i e s o f in f o r m a t i o n - a c q u i r i n g s t e p s i s e s s e n t i a l . 2. The t a s k i s w e l l s t r u c t u r e d . P o s s i b l e r e s p o n s e a l t e r n a t i v e s a r e c o m p le te ly s p e c i f i e d . Ss s e l e c t from a g iv e n s e t o f r e s p o n s e s i n s t e a d o f b e in g f r e e to p r o v id e t h e i r own. 3- The d a t a a re o b j e c t i v e . The r e l a t i o n betw een s tim u lu s and re s p o n s e does n o t r e l y upon s u b j e c t i v e i n t e r p r e t a t i o n o f i n t r o s p e c t i v e r e p o r t s . The re s p o n s e a l t e r n a t i v e s a re d e f in e d i n term s o f th e v a lu e s o f th e in d e p e n d e n t v a r i a b l e s . The a p p ro a c h i n t h i s s tu d y i s t o 'd e s c r i b e th e b e h a v io r in v o lv e d i n s o l v i n g d i a g n o s t i c p ro b le m s. In d e e d , u n t i l th e p r o c e s s e s r e l a t e d to s p e c i f i c t a s k s i t u a t i o n s a re more d e f i n i t i v e l y s t a t e d , t h e r e w i l l be l i t t l e b a s i s f o r d e s c r i b i n g th e g e n e r a l i z e d c a s e , n o r f o r com paring th e r e s u l t s o f d i f f e r e n t s t u d i e s . A t r o u b l e s h o o t i n g t a s k was c o n s t r u c t e d i n which Ss i s o l a t e d a m a l f u n c tio n in g e le m e n t from an a g g r e g a tio n o f n _ f u n c t i o n a l l y - r e l a t e d e le m e n ts . The t r o u b l e s h o o t i n g t a s k was r e p r e s e n t e d as one i n w hich Ss p e rfo rm e d a s members o f a team r e s p o n s i b l e f o r c o r r e c t i v e m a in te n a n c e on a s a t e l l i t e . The team was a s s i s t e d by a d i g i t a l c o m p u ter, and Ss commu n i c a t e d w ith th e com puter and w ith team members by means o f a t e l e t y p e c o n s o le . The p r o c e d u r e s f o r c o n d u c tin g th e e x p e rim e n t, and f o r c o l l e c t i n g and p r o c e s s in g S s 1 r e s p o n s e s 6 ( s t e p by ste p ) were hand led by a computer program . Not o n ly d id the computer en ab le I d e n t i c a l , o b j e c t i v e , and e r r o r l e s s p r e s e n t a t i o n o f th e e x p e rim e n t, p ro v id in g th e s e quence o f s t i m u l i which were a fu n c tio n o f Ss p r e v io u s r e sp o n ses, b u t i t made long p e r io d s o f t e s t i n g f o r i n d i v i d u a l Ss f e a s i b l e , w hile m a in ta in in g m o tiv a tio n o f Ss in a r e a l i s t i c t e s t s e t t i n g . The d a ta a t each s te p o f th e m a lfu n c tio n i s o l a t i o n p ro c e s s c o n s i s t e d o f each S 's d a t a - a c q u i s i t i o n re s p o n se : one o f s e v e r a l a l t e r n a t i v e s t h a t would, p ro v id e in fo rm a tio n about th e s t a t u s o f e le m e n ts. Each a l t e r n a t i v e was d e fin e d by a s e t o f in d ep e n d en t v a r i a b l e s . These v a r i a b l e s were e v a lu a te d a t each s te p by th e method o f d i s c r im i n a t o r y a n a l y s i s to d e term in e the c o n t r i b u t i o n o f each v a r i a b l e in d i s c r i m i n a t i n g o r s e p a r a tin g th e a l t e r n a t i v e s e l e c t e d by S from th e n o n s e le c te d a l t e r n a t i v e s . The d i s c r im in a n t fu n c t i o n computed by t h i s method was used a s a model o f i n d i v i d u a l S s' b e h a v io r . The p a ra m e te rs o f th e model were th e r e l a t i v e w e ig h ts o f th e stim u lu s v a r i a b l e s t h a t com prised th e stim u lu s s e t d e f in in g each a l t e r n a t i v e . These w e ig h ts, o r c o e f f i c i e n t s o f th e d is c r im i n a n t f u n c tio n , were i n t e r p r e t e d as th e r e l a t i v e im p ortance a t t r i b u t e d to each v a r i a b le by th e i n d i v i d u a l p ro b le m -s o lv e r in choosing between a l t e r n a t i v e s . In a d d i t i o n , th e e f f i c i e n c y o f S s 1 re s p o n s e s was a n a ly z e d f o r e f f e c t s o f l e a r n in g d u rin g the e x p erim en t, e f f e c t s o f f a i l u r e - p r o b a b i l i t i e s a s s o c i a t e d w ith th e e l e m ents, th e c o n f i g u r a t i o n o f th e a g g re g a tio n o f e le m e n ts, and th e e f f e c t o f s t e p s in a s o l u t i o n se q u en c e. R e la te d s t u d i e s a re rev iew ed i n th e n e x t c h a p t e r to p ro v id e th e s e t t i n g f o r th e ap p ro ach in t h i s s tu d y . Chap t e r I I I d e s c r i b e s th e e x p e rim e n ta l p ro c e d u re and a d m in is t r a t i o n o f th e e x p e rim e n t by com puter. C h a p te r IV d e s c r i b e s th e group a n a l y s e s o f th e d a ta . C h a p te r V d i s c u s s e s th e d i s c r i m i n a n t m odel, in c l u d i n g th e d i s c r i m i n a t o r y a n a l y s i s method, th e a ssu m p tio n s o f th e m odel, and t e s t s p e rfo rm ed to e v a l u a t e th e m odel. C h a p te r VI p r e s e n t s th e summary and c o n c l u s i o n s . CHAPTER I I RELATED STUDIES I t h a s "been s t a t e d t h a t a model b a s e d on th e assum p t i o n t h a t p e o p le a re i d e a l d e c is io n - m a k e r s i s n o t g e n e r a l l y c o n firm e d by th e e m p i r i c a l d a t a . Agreem ent can be sou ght betw een t h e o r y and f a c t by w eakening th e l o g i c a l assum p t i o n s o f th e m odel: by d e g ra d in g th e model to a p p ro x im a te human b e h a v i o r . R a th e r th a n s t a r t i n g w ith th e i d e a l and d e g ra d in g to th e a c t u a l , a n o th e r a p p ro a c h f o c u s e s on d i r e c t m ethods o f r e p r e s e n t i n g and d e s c r i b i n g th e b e h a v i o r a l p r o c e s s . T h is d i s t i n c t i o n in a p p ro a c h p o i n t s to th e fu n d am e n ta l d i f f e r e n c e o f th e n o rm a tiv e and d e s c r i p t i v e a p p ro a c h e s i n th e a r e a o f d e c is io n - m a k in g ; th e fo rm e r i s c o n ce rn e d w ith b e h a v io r p e o p le ou ght to h a v e , w h ile th e l a t t e r i s co n c e rn e d w ith d e s c r i b i n g a c t u a l b e h a v i o r . The e x p e rim e n ts m en tio n ed l a t e r in t h i s c h a p t e r , a re exam ples o f s t u d i e s w hich a r e p r i m a r i l y c o n c e rn e d w ith th e d e s c r i p t i o n o f th e p ro b le m - s o lv in g p r o c e s s . ^ R ig n ey , e t a l . ( 1 9 6 6 ) , d e s c r i b e d a B a y esia n ap p ro ach f o r a n a ly z in g th e c o g n i t i v e lo a d in g s in v o lv e d in e l e c t r o n i c s t r o u b l e s h o o t i n g t a s k s . The a c q u i s i t i o n o f in f o r m a tio n ..by Navy e l e c t r o n i c t e c h n ic i a n s was compared s te p by s te p w ith p o t e n t i a l u n c e r t a i n t y re d u c tio n * computed a c c o rd in g to B ayes' theorem* tak en a s th e c r i t e r i o n m easure o f t r o u b l e s h o o tin g a b i l i t y . The_model was about th r e e tim es as e f f i c i e n t in t r o u b le s h o o t i n g th e same c i r c u i t as were th e t e c h n i c i a n s . One f e a t u r e o f t h e i r e x p erim en t was the i n t r o d u c t i o n o f a sym ptom -m alfunction m a trix which showed i n t e r r e l a t i o n s h i p s between th e p o s s i b l e m a lfu n c tio n s and t h e i r c o r re sp o n d in g s e t o f symptoms. T h is m a trix con cep t was ad ap ted f o r p r e s e n t a t i o n o f the p ro b le m -so lv in g t a s k in t h i s e x p e r i ment* and i s d is c u s s e d i n C h ap ter I I I * p. 23. D avis ( 1 9 6 7) o b se rv e d s u b j e c t s i n a d i a g n o s ti c ta s k s i t u a t i o n where th ey asked q u e s tio n s to o b ta in in f o r m a tio n . He showed t h a t Ss ten d ed to group o r s t r u c t u r e s i m i l a r e l e m ents to g e th e r* even when such g ro u p in g s would make the p r o c e s s o f i s o l a t i n g th e " c o r r e c t " elem en t i n e f f i c i e n t by i n c r e a s i n g th e av erag e number o f s te p s to s o l u t i o n . In t r o u b le s h o o tin g a p p lic a tio n s * th e h a l f - s p l i t p r i n c i p l e i s an example o f an e x p e c te d v a lu e m ax im ization th e o r y . Davis d e m o n stra te d t h a t Ss do n o t fo llo w t h i s model* b u t i n s t e a d , ask q u e s tio n s b ased on a s e l e c t i v e s t r u c t u r i n g o f elem en ts in th e t a s k s i t u a t i o n . The well-known con cep t fo rm a tio n e x p e rim e n ts o f Bruner* e t a l . (195^) and Hunt ( 1 9 6 2) and Hunt* e t a l . ( 1 9 6 6) showed t h a t th e v a r io u s s t r a t e g i e s employed by Ss a re d e term in ed by th e p a r t i c u l a r a t t r i b u t e dim ensions to which a s u b j e c t cho oses to a t t e n d . S t r a t e g i e s were d i f f e r e n t i a t e d i n term s o f which a t t r i b u t e s o f th e s tim u lu s were n o t ic e d and w h e th er th e y were u se d singly., c o n j u n c t i v e l y , o r d i s j u n c t i v e l y . Consider., f o r exam ple, a s e t o f e le m e n ts t h a t can be d e s c r i b e d alon g a number o f a t t r i b u t e dimen s io n s (su c h a s shape, c o l o r , s i z e , n u m e ro s ity , e t c . ) . A s u b s e t o f th e e le m e n ts can be d e s c r i b e d by a p a r t i c u l a r com b ination o f a t t r i b u t e d im e n sio n s and a t t r i b u t e v a lu e s a lo n g each d im e n sio n . T h is co m b in atio n i s th e c o n ce p t d e f i n i n g th e s u b s e t o f i n t e r e s t . The t a s k f o r th e S i s to d is c o v e r th e c o n c e p t, g iv e n th e in f o r m a tio n t h a t a s p e c i f i c elem en t i s o r i s n o t an i n s t a n c e o f th e c o n c e p t. The su b j e c t may te n d to fo c u s on one o f th e s e dim en sio n s s i n g l y , r a t h e r th an u se two o r more o f them s im u lta n e o u s ly to d i s c o v er th e c o n c e p t. He may ask q u e s t io n s r e g a r d in g e le m e n ts d i f f e r i n g i n shape o n ly , u n t i l t h a t dim ension i s co nfirm ed o r r e j e c t e d , and th en t u r n to c o l o r , s u c c e s s i v e l y c o n s i d e r in g and e l i m i n a t i n g o r in c l u d i n g each d im en sion . B runer c a l l s t h i s s t r a t e g y o f fo c u s in g on one dim ension a t a tim e a s i m p l i f i c a t i o n which r e d u c e s c o g n it i v e s t r a i n b u t a t a c o s t o f e f f i c i e n c y . S i m i l a r l y , in s e l e c t i n g t e s t s to t r o u b l e s h o o t a complex e l e c t r o n i c system , i t i s assumed t h a t th e t e c h n i c ia n w i l l i n t r o d u c e a form o f s i m p l i f i c a t i o n by fo c u s in g on a s p e c i f i c a t t r i b u t e d im en sion from th e s e t o f p o s s i b l e d i m ensions. I t i s f u r t h e r a s s e r t e d t h a t t e s t s e l e c t i o n i s 11 b a se d on th e t e c h n i c i a n ' s e x p e r ie n c e w ith th e s t r u c t u r e o f th e c i r c u i t and h i s s u b j e c t i v e p r o b a b i l i t i e s o f component f a i l u r e . O th e r s t u d i e s , u s in g an i n f o r m a t i o n - p r o c e s s i n g a p p ro a c h , a l s o make th e b e h a v i o r a l p r o c e s s th e c e n t e r o f i n t e r e s t . In th e s e s t u d i e s , th e s t i m u l u s f a c t o r s a t t e n d e d to by an i n d i v i d u a l a r e i n f e r r e d from th e c o n te n t o f h i s i n f o rm a tio n - g a t h e r i n g r e s p o n s e s and i n th e sequence o f t h e s e r e s p o n s e s . B e h a v io r i s d e s c r i b e d p r i n c i p a l l y by means o f a n a ly z in g v e r b a l d a t a . For exam ple, K leinm untz ( 1 9 6 5 ) ob s e rv e d n e u r o l o g i s t s i n d i a g n o s t i c s i t u a t i o n s to s i m u l a t e 't h e p r o c e s s e s u n d e r ly in g t h e i r i n f o r m a t i o n - g a t h e r i n g b e h a v io r . The g o a l was to d i s c o v e r as much a s p o s s i b l e a b o u t th e d i a g n o s t i c i a n ' s c o g n i t i v e a c t i v i t i e s : to d e s c r i b e how he .s t o r e s o r r e p r e s e n t s i n f o r m a ti o n in h i s memory, and how he p r o c e s s e s t h i s in f o r m a ti o n d u rin g h i s p r o b le m - s o lv in g . He i s c o n c e rn e d w ith fo rm a l d i a g n o s i s , c o n s i d e r i n g d i a g n o s i s to be a s p e c i a l i n s t a n c e o f p r o b l e m - s o l v in g i n w hich th e c l i n i c i a n i s c o n f r o n te d by an a r r a y o f d a t a , and in w hich he s e a r c h e s and s i f t s th ro u g h t h i s a r r a y , r e j e c t i n g some a s p e c t s o f th e a v a i l a b l e i n f o r m a ti o n and c a l l i n g f o r more i n f o r m a t i o n ■to su p p lem en t e x i s t i n g d a t a . The p ro b lem to be s o lv e d by th e d i a g n o s t i c i a n i s u s u a l l y i n th e form o f a p a t i e n t a b o u t whom c e r t a i n b i o g r a p h i c a l d a t a , symptoms, s i g n s , l a b o r a t o r y t e s t r e s u l t s , and o t h e r o b s e r v a b le and e l i c i t e d cu es a re a v a i l a b l e . The s o l u t i o n to th e p r o b lem c o n s i s t s o f an e t i o l o g i c f o r m u la ti o n , a c l a s s i f i c a t i o n o f th e p a t i e n t i n t o a taxonom ic c a t e g o r y , and th e p r e s c r i p t i o n o f some t r e a t m e n t recom m en dation s. The f a c t t h a t d i f f e r e n t c l i n i c i a n s may a d o p t h i g h l y id o s y n - c r a t i c b e h a v i o r , d e a l i n g w ith d i f f e r e n t s e t s o r i n s t a n c e s 12 o f the a v a i l a b l e in fo rm a tio n , does n o t a l t e r th e f a c t t h a t s i m i l a r p ro b le m -so lv in g p r o c e s s e s may u n d e rly them a l l . To d is c o v e r the d i a g n o s t i c i a n 's se a rc h s t r a t e g y , i t was r e q u i r e d t h a t the d i a g n o s ti c i a n " th in k aloud " d u rin g th e p ro b le m -so lv in g s e s s io n s . The t a s k e n t a i l e d q u e s tio n in g th e p re s e n c e o f c e r t a i n symptoms, s ig n s , b i o g r a p h i c a l d a ta , o r l a b o r a to r y r e s u l t s . These re s p o n s e s were c a s t in th e form o f a t r e e s t r u c t u r e , o r d i s c r i m i n a t i o n n e t , r e p r e s e n t in g the d i a g n o s t i c i a n 's s o l u t i o n p a th from a s e t o f a p r i o r i c o n d itio n s to c o r r e c t i d e n t i f i c a t i o n o f th e se a rc h o b j e c t . The s iz e and s t r u c t u r e o f each d i a g n o s t i c i a n 's d i s c r im i n a t i o n n e t p ro v id e th e b a s ic in fo r m a tio n f o r s p e c ify in g a com puter program . The program r e p r e s e n t s th e d i a g n o s ti c p ro c e s s and c a r r i e s i t th ro u g h s te p by s t e p . I t in c o r p o r a t e s n o t o n ly th e in fo rm a tio n a v a i l a b l e i n th e a r r a y o f d a ta b u t employs p r o b a b i l i t y n o tio n s and w e ig h tin g schemes to ta k e i n t o c o n s id e r a tio n th e r e l a t i v e fre q u e n c y o f symp toms o r syndromes o f a p a r t i c u l a r d i s e a s e . T his work has been c o n tin u e d by Wertman ( 1 9 6 6), w ith p r e l i m i n a r y r e s u l t s i n d i c a t i n g t h a t th e d i a g n o s ti c p ro c e s s o f a n e u r o l o g i s t can be c h a r a c t e r i z e d by two s t r a t e g i e s : e i t h e r an involv em ent w ith th e e t i o l o g i c a l (cause) compo n e n t o r th e a n a to m ic a l ( p l a c e ) ' com ponent. The b a s i c assum ption o f th e above work i s t h a t " c l i n i c a l i n t u i t i o n " i s s u s c e p t i b l e to s c i e n t i f i c stu d y . T h e re fo re , fo c u s in g on th e p ro b le m -so lv in g m ethods, and 13 n o tin g th e s t r a t e g y (i n c o n s i s t e n c i e s and e r r o r s as w e ll as c o n s i s t e n c i e s ) , should p ro v id e answ ers t h a t h e lp in th e e d u c a t io n and t r a i n i n g o f f u t u r e c l i n i c i a n s (o r in g e n e r a l , f u t u r e p r o b l e m - s o l v e r s ) ; and i t should p ro v id e a b a s i s f o r m odifying and im proving th e d i a g n o s ti c se a rc h s t r a t e g y . A i r c r a f t a c c id e n t i n v e s t i g a t i o n may be c o n s id e re d one ty p e o f p ro b le m -s o lv in g t a s k which r e q u i r e s i n v e s t i g a t o r s to have much e x p e rie n c e and e x p e r t i s e . T his e x p e r t i s e , however, i s d i f f i c u l t to d e s c r i b e . B ra u n s te in and Coleman ( 1 9 6 6) a tte m p te d to d e fin e th e a c t i o n s o f a c c id e n t i n v e s t i g a t o r s , w ith an u l t i m a t e g o a l to i n c r e a s e u n d e rs ta n d in g o f p ro b le m -so lv in g t a s k s i n g e n e r a l . V e rb al r e p o r t s were e l i c i t e d from i n v e s t i g a t o r s as th e y perform ed t h e i r i n v e s t i g a t i o n s . These d a ta , supplem ented by m otion p i c t u r e s , were a n a ly z e d to d e te rm in e th o se f e a t u r e s o f a i r c r a f t dam age and t e r r a i n d i s t u r b a n c e s th e i n v e s t i g a t o r u s e s , and t h e i r sequence, to e s t a b l i s h the c ra s h k in e m a tic s o f th e a c c id e n t. An i n f o r m a tio n - p r o c e s s in g model was c o n s tr u c te d to develop such k in e m a tic s h y p o th e s e s (e . g ., a i r c r a f t speed, a l t i t u d e , a t t i t u d e p r i o r to th e a c c id e n t) b ased upon th e f e a t u r e s and p r i o r i t i e s o f th o se f e a t u r e s o b ta in e d from a n a l y s i s o f i n v e s t i g a t o r s ' r e p o r t s . One b a s i c c o n c lu sio n was t h a t th e i n v e s t i g a t o r s c o n t i n u a l l y engage in h y p o th e s is - t e s t i n g : form ing h y p o th e s e s e a r l y in th e i n v e s t i g a t i o n and th en seek in g evid en ce to t e s t th e h y p o th e s e s . I t was found t h a t one n e g a tiv e in s t a n c e i s f r e q u e n t ly s u f f i c i e n t to 14 r e j e c t th e h y p o t h e s i s . The p o i n t i s t h a t th e i n v e s t i g a t o r fo c u s e s on some s p e c i f i c a s p e c t s early., and h i s p ro b lem s o lv in g b e h a v io r i s c e n te r e d aro und a c q u ir in g in f o r m a tio n to t e s t t h a t s p e c i f i c h y p o t h e s i s . T his i s c o n tr a r y to the p ro c e d u re o f g a th e r in g a l l e v id e n ce and th en form ing a con c l u s i o n — a p ro c e d u re ta u g h t i n most t r a i n i n g c o u rs e s . How e v e r , i t i s c o n s i s t e n t w ith f i n d i n g s in c o n c e p t fo rm a tio n t a s k s (pages 9 “ 1 0 ).* Johnson (1 9 6 4 ), in a c o n c e p t- fo r m a tio n t a s k , a ls o viewed th e p r o b le m - s o lv e r as an i n f o r m a t i o n - p r o c e s s o r . He u se d a t h i n k i n g - a l o u d p ro c e d u re to o b t a i n d a ta from h i s Ss to shed l i g h t on th e n a tu r e o f t h e i r in f o r m a tio n - h a n d lin g p r o c e s s e s . H is purpose was to c o n s t r u c t an i n f o r m a ti o n - p r o c e s s in g model t h a t d e s c r i b e d how th e s u b j e c t s produ ced h y p o th e s e s and t e s t e d them. The t a s k was to d e f in e th e p r i n c i p l e by which g iv e n p a t t e r n s o f d o ts were c l a s s i f i e d i n t o one o f two c a t e g o r i e s . He found t h a t th e s t r a t e g y o f s u b j e c t s i s to e s t a b l i s h h y p o th e s e s by s e a r c h in g f o r " a l l o r none" p r o p e r t i e s among th e s e t o f o b j e c t s . Simple h y p o th e s e s c o n s id e r e d one p r o p e r t y a t a time,- when th e s e f a i l e d , complex h y p o th e s e s were c o n s id e r e d , in v o lv in g co n j u n c t i v e and d i s j u n c t i v e c o m b in a tio n s o f th e o b se rv e d p ro p e r t i e s . The model was c o n s t r u c t e d to r e p r e s e n t th e human p r o b le m - s o lv e r , com plete w ith h i s sh o rtc o m in g s, o r " p e r fo rm a n c e -re d u c in g d e v ic e s " : f a i l u r e to p e rc e iv e c e r t a i n a t t r i b u t e s o r c l a s s e s o f a t t r i b u t e s , u s e o f i n v a l i d h y p o th e - 15 s e s , p e r s i s t e n c e in r e p a i r i n g r e f u t e d h y p o th e s e s i n s t e a d o f r e j e c t i n g them, and e i t h e r e x c e s s u se o r a v o id a n c e o f com p l e x h y p o t h e s e s . The im p o r ta n t p o i n t in c o n s i d e r i n g th e above e x p e r i m ents i s t h e i r i n t e r e s t and c o n c e rn w ith d e s c r i p t i o n . T h e ir a p p ro a c h i s th e d e r i v a t i o n o f d e s c r i p t i v e m o d e ls— m od els o f an I n d i v i d u a l p r o b l e m - s o l v e r . The p r e s e n t stu d y s h a r e s t h i s p o i n t w ith th e i n f o r m a t i o n - p r o c e s s i n g a p p ro a c h ; how ever,. i n s t e a d o f making i n f e r e n c e s from v e r b a l , p r o t o c o l d a t a , t h i s stu d y c o l l e c t s n o n v e rb a l d a t a . And, i n s t e a d o f e s t a b l i s h i n g model p a r a m e te r s by s i m u l a t i o n , t h i s stu d y a p p l i e s m u l t i v a r i a t e s t a t i s t i c a l t e c h n iq u e s w hich p ro v id e a d i r e c t e s t i m a t e o f th e model p a r a m e te r s from o b j e c t i v e d a ta . M u l t i v a r i a t e te c h n iq u e s were u s e d in a s tu d y o f p e r c e p t u a l p r o c e s s e s r e p o r t e d by Rodwan & Hake (1 9 6 4 ). T h e ir e x p e rim e n t in v o lv e d c l a s s i f i c a t i o n o f f a c e s by th e 0 ( o b s e r v e r ) a s i n t e l l i g e n t o r n o n i n t e l l i g e n t . F or th e p u r p o s e s o f a n a l y s i s th e f a c e s were d e s c r i b e d by m ea su re s on f o u r p h y s i c a l d im e n s io n s . The d i s c r i m i n a n t f u n c t i o n was h y p o t h e s iz e d a s an a d e q u a te model f o r p e r c e p t i o n . S p e c i f i c a l l y , th e q u e s t i o n s were w h e th e r th e two c o n c e p ts ( i n t e l l i g e n t o r n o n i n t e l l i g e n t ) were d i s c r i m i n a b l y d i f f e r e n t , w h e th e r th e d i s c r i m i n a n t f u n c t i o n a g r e e s w ith th e 0 i n h i s c l a s s i f i c a t i o n , and w h e th e r th e d i s c r i m i n a n t w i l l be th e same f o r d i f f e r e n t e x p e r im e n ta l c o n d i t i o n s . T h e ir c o n c lu s i o n s were a l l p o s i t i v e . 16 I n d e s c r i b i n g t h e i r m odel, Rodwan & Hake p r e s e n t t h r e e a s s u m p tio n s f o r th e l i n e a r d i s c r i m i n a n t f u n c t i o n w hich a r e r e l e v a n t to t h i s s tu d y : "A co n cept- i s d e f in e d a s a r e g i o n i n n_-space i f i t h a s i n - a t t r i b u t e s . " T h is means t h a t i f th e p h y s i c a l d im e n s io n s o f a s t i m u l u s o b j e c t have a p s y c h o l o g i c a l c o r r e l a t e , th e n th e o b j e c t c o u ld be d i s t i n g u i s h e d on t h a t d im e n s io n . "An 0 u s e s a l i n e a r c o m b in a tio n o f th e n _ - a t t r i b u t e s to form th e LDF" [ l i n e a r d i s c r i m i n a n t f u n c t i o n ] . T h is means th e 0 does n o t a t t e n d s e p a r a t e l y to a l l th e v a r i a b l e s , b u t a c t s a s i f he u s e s a w e ig h te d l i n e a r c o m b in a tio n o f them . "The LDF i s so o r i e n t e d t h a t i t w i l l m axim ize th e d i s t a n c e i n th e n - s p a c e b etw een any two c o n c e p t s ( r e g i o n s ) . " T h is means t h a t 0 can r e l i a b l y d i s c r i m i n a t e b etw een two c o n c e p ts when he a s s i g n s a n_-dim ensional a l t e r n a t i v e to a p a r t i c u l a r c a t e g o r y (when he s e l e c t s an a l t e r n a t i v e ) . The w e i g h ts a t t a c h e d to eac h v a r i a b l e r e p r e s e n t s t h e v a lu e , o r r e l a t i v e im p o r ta n c e , t h a t 0 a t t r i b u t e s to t h a t v a r i a b l e . The d i s c r i m i n a n t f u n c t i o n i s i n t e r p r e t e d s i m i l a r l y i n th e p r e s e n t s tu d y , w hich e x te n d s t h i s a p p ro a c h from t h e a r e a o f p e r c e p t i o n to th e s tu d y o f p r o b l e m - s o l v in g p r o c e s s e s . CHAPTER I I I THE EXPERIMENT E x p e rim e n ta l Procedure The e x p erim en t c o n s i s t e d o f a d ia g n o s tic problem so lv in g ta s k p r e s e n te d u n d er th r e e d i f f e r e n t problem s i t u a t i o n s . These s i t u a t i o n s were p r e s e n te d as a s tim u lu s -m a tr ix f o r each o f t h r e e S a t e l l i t e s . In each S a t e l l i t e , th e p ro b lem was r e p r e s e n te d a s a m a lfu n c tio n in g System, com prised o f n_ subsystem s, each w ith a s p e c i f i e d p r o b a b i l i t y o f f a i l u r e . The S 's ta s k was to i s o l a t e th e m a lfu n c tio n in g subsystem . Ss o b ta in e d in f o r m a tio n by s e l e c t i n g a " c h a n n e l” from a number o f a l t e r n a t i v e s . The Problem S i t u a t i o n The com plete t e x t o f th e i n s t r u c t i o n s to th e Ss i s p re s e n te d h e re to d e s c r ib e th e problem s i t u a t i o n . ^ ■^The a u th o r i s in d e b te d to M ichael D. H art f o r h i s a s s i s t a n c e in c o n d u ctin g many o f th e e x p e rim e n ta l s e s s io n s . 17 INSTRUCTIONS Many o f o u r comp]ex d e fe n s e and sp ace sy stem s now o p e r a t e a s a u to m a tic o r unmanned sy ste m s; f o r example* s u r v e i l l a n c e r a d a r n e tw o rk s i n th e A rc tic * o r b i t i n g co m m unicatio ns s a t e l l i t e s * and unmanned s p a c e c r a f t on th e l u n a r s u r f a c e . When t h i s equipm ent m a lfu n c tio n s * i t i s im p o r t a n t t h a t c o r r e c t i v e a c t i o n be ta k e n a s q u ic k ly as p o s s i b l e . B ecause t h i s eq uipm ent i s rem ote and h i g h l y i n a c c e s s i b l e , t r o u b l e s h o o t i n g m ust be done on th e b a s i s o f s t a t u s i n f o r m a ti o n s e n t b ack from th e System . The Space A d m in is tr a tio n i s d e v e lo p in g means f o r d e t e c t i n g and c o r r e c t i n g t r o u b l e s i n S a t e l l i t e S ystem s. A team h a s been o r g a n iz e d to do th e f o llo w in g : Group 1 - D e te c t m a lf u n c t i o n s Group 2 - I s o l a t e m a l f u n c t i o n s Group 3 - R e p a ir m a lf u n c tio n s Your job w i l l be w ith Group 2* to i s o l a t e m a l f u n c t i o n s i n th e S a t e l l i t e . Once Group 1 h a s d e t e c t e d som ething wrong* th e y c a l l on you to i s o l a t e th e f a u l t to a p a r t i c u l a r equipm ent sub system o f th e S a t e l l i t e . You w i l l p a s s th e i n f o r m a tio n - o n to th e R e p a ir Group 3 j who w i l l i n i t i a t e p r o c e d u r e s to r e p a i r th e f a u l t y su b sy stem . T h is t e l e t y p e i s y o u r means f o r r e c e i v i n g and se n d in g i n f o r m a t i o n . You u s e i t to communi c a t e w ith th e o t h e r team members. I t I s a ls o c o n n e c te d to a com puter to h e lp you to f i n d th e equipm ent m a lf u n c tio n . I w i l l now show you how to o p e r a t e th e t e l e ty p e and g iv e you a sam ple t a s k to demon s t r a t e w hat you have to d o . The fo llo w in g t a s k w i l l be e x p la in e d * s t e p by step* a s you o p e r a t e th e t e l e t y p e . Read i t q u i c k l y now. Group 1 w i l l in fo rm you by t e l e t y p e when t h e r e i s a m a l f u n c t i o n .I n a S a t e l l i t e S ys tem. Each System w i l l be i d e n t i f i e d by a System number. The System d e s c r i p t i o n w i l l a p p e a r a s a t a b l e i n t h i s book, a s f o llo w s : SYSTEM NUMBER 1 Subsystem C hannel P r o b a b i l i t y 00 1 2 3 4 5 SS 1 1 1 0 0 1 50 SS 2 1 0 1 0 0 30 SS 3 0 1 0 1 0 15 SS 4 0 0 1 1 0 05 System 1 c o n t a i n s 4 subsystem s* r e p r e s e n t e d by th e rows a s SS 1 to SS 4 . C hannels ( c o l umns) 1 to 5 m easure f i v e f u n c t i o n s o f th e System . The " I ” i n Channel 5 I n d i c a t e s t h a t eq u ip m en t SS 1 i s r e q u i r e d to p e rfo rm f u n c t i o n 5 j and t h a t Channel 5 t h e r e f o r e m easures th e c o n d i t i o n o f SS 1. The "0" means t h a t a SS i s n o t c o n n e c te d w ith a f u n c tio n * and n o t m easu red by th e c h a n n e l. The two " l " s i n C hannel 1 i n d i c a t e t h a t b o th SS 1 and 2 a r e c o n n e c te d w ith f u n c t i o n 1. The com puter c o n ti n u o u s l y s e n s e s th e s t a t u s o f th e c h a n n e ls . You can o b t a i n two k in d s o f i n f o r m a ti o n a b o u t a System f u n c t i o n by ta k i n g a c h a n n e l r e a d i n g : a NORMAL r e a d in g o r an ABNORMAL r e a d i n g . I f you s e l e c t Chan n e l 1 and r e c e i v e a NORMAL re a d in g * i t wp.uld mean t h a t a l l su b sy stem s c o n n e c te d to i t (SS 1 and 2) a r e o p e r a t i n g n o r m a lly . An AB NORMAL r e a d i n g would t e l l you t h a t e i t h e r SS 1 o r SS 2 i s f a u l t y . Thus* d ep en d in g on th e r e a d i n g , you can e l i m i n a t e as p o s s i b l e f a u l t s e i t h e r th e su b sy stem s w ith "1" o r M 0" i n t h a t column. The Subsystem column (Column 00) c o n n e c ts you to th e R e p a ir Group so t h a t you can t e l l them w hich su b sy stem you want f i x e d . When you t h i n k you have i s o l a t e d th e m a l f u n c t i o n in g su b sy ste m --y o u sh o u ld s e l e c t Column 00 to t e l l Group 3 w hich su bsy stem to r e p a i r . The P r o b a b i l i t y column l i s t s th e f r e q u e n c i e s o f f a i l u r e s f o r eac h sub system o v e r th e p a s t 100 f a i l u r e s . T h is in f o r m a tio n g i v e s you th e p r o b a b i l i t y o f a- sub sy stem m a lfu n c tio n * g iv e n t h a t a m a lf u n c tio n h a s o c c u r r e d i n th e System . 20 To summarize th e i n s t r u c t i o n s : 1. Your o b j e c t i v e in Group 2 i s to i s o l a t e a m a lfu n c tio n w ith o u t e r r o r as q u ic k ly as p o s s i b l e . The perform ance o f the Team i s dependent on how w e ll and how q u ic k ly each Group perfo rm s i t s . jo b . 2. Taking a s e r i e s o f chan n el r e a d in g s i s th e q u i c k e s t and e a s i e s t way to i s o l a t e th e f a u l t . Since a c h an n el re a d in g m easures more th an one subsystem., you w i l l n o t g e t a d i r e c t i n d i c a t i o n o f th e m a lfu n c tio n in g subsystem . But th e i n fo rm a tio n you r e c e i v e w i l l p e rm it you to red u ce th e number o f subsystem s which are p o s s i b l y f a u l t y . 3. S e l e c ti n g Column 00 c o n n e c ts you to th e R e p a ir Group so t h a t you can t e l l them which subsystem i s to be f i x e d . The R e p a ir Group w i l l th en i n i t i a t e p r o c e d u re s to r e p a i r and v e r i f y th e c o n d i t i o n o f th e subsystem . They w i l l be a b le to t e l l you d i r e c t l y i f th e su b s y s tem was f a u l t y o r n o t. T his c o u ld save you a number o f s t e p s . But i f you made a m ista k e and chose th e wrong subsystem,, i t would p rove c o s t l y and a w aste o f tim e . The d e la y i n - s e n d in g Group 3 on a "w ild goose chase" could je o p a rd iz e th e m is s io n . 4. Only one subsystem w i l l m a lfu n c tio n each tim e . Each s e s s io n w i l l l a s t 2 h o u rs . You w i l l be p a id f o r your tim e. A bonus, depending on o v e r a l l p e rfo rm a n ce, w i l l be added., Are t h e r e any q u e s tio n s b e fo r e you s t a r t ? The S was th en s e a te d a t the t e l e t y p e and g iven the sample problem s. Q u e stio n s r e l a t i n g to th e ta s k and to th e o p e r a tio n o f th e t e l e t y p e were answered as he worked th e sample problem . When S d e m o n stra te d u n d e rs ta n d in g o f th e t a s k , the e x p e rim e n te r i n i t i a t e d th e com puter f o r th e f i r s t 21 S a t e l l i t e and the exp erim en t was condu cted by th e com puter. S u b je c ts Five male s t u d e n ts , p a id v o l u n te e r s from th e U n iv e r s i t y o f S outhern C a l i f o r n i a , se rv ed as Ss. None had p r e v i ous e x p e rie n c e on t h i s type o f e x p erim e n t. The Ss were 18 to 22 y e a r s o f age, w ith m ajors in E n g lis h , Fine A r ts , I n d u s t r i a l Management, P re -M e d ic al, and Oceanography. P roblem -S olving T r i a l s The t a s k was p r e s e n te d i n t h r e e p ro b le m -so lv in g s i t u a t i o n s . Three S a t e l l i t e s , each w ith d i f f e r e n t Systems and a d i f f e r e n t number o f su bsy stem s, r e p r e s e n te d th e p ro b le m -so lv in g s i t u a t i o n s . They were i d e n t i f i e d as S a t e l l i t e 1 (SATl) w ith 12 system s composed o f 16 subsystem s each; S a t e l l i t e 2 (SAT2), 12 system s composed o f 24 subsystem s each; and S a t e l l i t e 3 (SAT3), 12 system s composed o f 20 su b s y s tems each. A p ro b le m -s o lv in g t r i a l began when a m a lfu n c tio n in g system (a problem) was r e p o r t e d to S. A problem s i t u a t i o n i s i l l u s t r a t e d in F ig u re 1, which i s System 12 o f SAT3. One o f th e e i g h t re s p o n se a l t e r n a t i v e s (columns 1-8) was s e l e c t e d by S a t each s te p o f th e p ro b le m -so lv in g t r i a l . The t r i a l ended when S c o r r e c t l y I s o l a t e d th e m a lfu n c tio n in g subsystem . A f te r each s te p , th e m a trix w as-reduced by th e com puter. The subsystem s l o g i c a l l y e lim in a te d from c o n s id e r a t i o n by th e re sp o n se a t each s te p were d e le te d and th e 22 re m a in in g s t i m u l u s - m a tr i x was a u t o m a t i c a l l y d is p l a y e d f o r th e n e x t s t e p . SYSTEM NUMBER 12 S u b sy st 00 1 2 Channel 3 ^ 5 6 7 8 P r o b a b i l i t y SS 1 1 0 1 1 1 1 0 0 5 SS 2 1 0 0 0 0 1 0 0 5 SS 3 0 0 0 1 1 1 1 1 5 SS 4 1 0 1 1 0 1 1 1 5 SS 5 0 0 1 0 1 0 1 1 5 SS 6 1 0 1 1 0 0 0 1 5 SS 7 0 0 0 1 0 0 0 1 5 SS 8 1 1 0 1 0 0 1 0 5 SS 9 0 0 0 1 0 0 0 1 5 SS 10 0 1 0 0 1 0 0 1 5 ss 11 1 1 0 0 1 0 0 1 5 ss 12 0 0 0 1 0 1 1 1 5 ss 13 0 0 0 1 0 1 1 0 5 ss 14 0 1 0 0 0 1 1 0 5 ss 15 1 0 0 1 0 1 0 1 5 ss ' 16 0 1 0 1 1 1 1 0 5 ss 17 0 0 0 0 0 1 1 0 5 ss 18 0 0 0 1 1 1 1 0 5 ss 19 1 0 0 1 0 1 1 0 5 ss 20 1 1 0 0 1 0 0 0 5 F ig . 1 . --Sam ple S tim u lu s M atrix The 12 Systems o f each S a t e l l i t e com prised a b lo c k o f t r i a l s p r e s e n t e d in random o r d e r . S ucceeding t r i a l s were r e p l i c a t i o n s o f th e 12 System s, b u t were p r e s e n t e d i n a d i f f e r e n t random o r d e r w ith in b lo c k s . The b lo c k o r d e r was g e n e r a te d i n ad vance, and a l l Ss r e c e iv e d th e same o r d e r o f p r e s e n t a t i o n . A System problem was caused by one and o n ly one sub sy stem . The m a lf u n c tio n in g subsystem s were p r e s e l e c t e d # 23 random ly b u t p r o p o r t i o n a l to th e f a i l u r e - p r o b a b i l i t i e s a s s o c i a t e d w ith each subsystem . E x p e rim e n ta l S e ss io n s A s e s s io n was a tw o-hour p ro b le m -s o lv in g p e r i o d . In a s e s s i o n , Ss worked one h o u r on SAT1 p ro b lem s, and one h our on SAT2 p ro b lem s. Ss were t e s t e d on as many s e s s io n s a s r e q u i r e d to com plete a t l e a s t 60 p ro b le m -s o lv in g t r i a l s on each SAT1 and SAT2. SAT3 pro b lem s were th e n p r e s e n t e d f o r a f i n a l s e s s i o n . Data o b t a i n e d from SAT3 . were u se d to v a l i d a t e th e model d e riv e d from the f i r s t two S a t e l l i t e s . T o ta l t e s t i n g f o r Ss v a r i e d from 14 to 18 h o u rs (7 to 9 s e s s i o n s ) , b e cau se o f i n d i v i d u a l d i f f e r e n c e s in speed and b e ca u se o f v a r i a b l e tim e d e la y s cau sed by lo a d on th e tim e - sh a re d com puter. In S s' f i r s t s e s s io n , an h o u r was u se d f o r i n s t r u c - . t i o n s and d e m o n s tra tio n on sample p ro b lem s. S tim u lu s M a tric e s A m a trix was u se d to p r e s e n t th e p r o b le m - s o lv in g s i t u a t i o n , each m a tr ix r e p r e s e n t i n g one o f th e S a t e l l i t e System s. The m a trix i s s i m i l a r to th e "sym ptom -m alfunc- 2 t i o n " m a tr ix d e s c r ib e d by R igney, e t a l . T h e ir m a trix 2 The m a trix c o n ce p t c o u ld be im plem ented in a v a r i e t y o f ways. M a lfu n c tio n s could be e n te r e d f o r any l e v e l o f hard w are t h a t co u ld be c o n s id e re d a p o t e n t i a l l y f a l l i b l e u n i t . The symptom in f o r m a tio n co u ld lik e w is e be a t d i f f e r e n t l e v e l s : v o l t a g e , r e s i s t a n c e , o r waveform r e a d i n g s a t 24 showed th e i n t e r r e l a t i o n s h i p s betw een p o s s i b l e m a l f u n c t i o n s i n a c i r c u i t and th e s e t o f symptoms w hich e a c h m a l f u n c t i o n c o u ld c a u s e . F o r th e p r e s e n t s tu d y , th e m a t r ix was s i m p l i f i e d to show th e " c o n n e c tio n " r e l a t i o n s h i p betw een s u b s y s tem s and c h a n n e ls and th e p r o b a b i l i t y o f f a i l u r e o f eac h s u b s y s te m . A ppendix I p r e s e n t s a t y p i c a l ' s t i m u l u s m a tr ix f o r e a c h S a t e l l i t e . These m a t r i c e s w ere e s t a b l i s h e d i n th e f o l lo w in g way: 1. C o n f i g u r a t i o n . S ubsystem s a r e d i s p l a y e d a s “ ro w s, and c h a n n e ls a s colum ns, o f th e s t i m u l u s m a t r i x . S in c e th e System s w ere h y p o t h e t i c a l , a t a b l e o f random num b e r s was u s e d to s e l e c t a 1 o r 0 w ith e q u a l p r o b a b i l i t y f o r e a c h c e l l . The p r o p o r t i o n o f 1 ' s i n a c h a n n e l o b t a i n e d by t h i s p r o c e d u r e v a r i e d such t h a t th e minimum and maximum number o f su b s y ste m s c o n n e c te d to a c h a n n e l w ere 3 -1 2 , 7 - 1 6 , and 4-13 f o r th e System s w ith 16, 24, and 20 s u b s y s te m s, r e s p e c t i v e l y . T h is p r o v id e d a s i m i l a r ra n g e o f v a r i a t i o n f o r e a c h S a t e l l i t e . Two c o n f i g u r a t i o n s o f l r s and 0 ' s were g e n e r a t e d f o r e a c h S a t e l l i t e . 2. D i s t r i b u t i o n . The c o n d i t i o n a l p r o b a b i l i t y o f f a i l u r e a s s o c i a t e d w ith e a c h su b sy stem was p r i n t e d i n an a d d i t i o n a l column o f th e m a t r i x . The number c o u ld ta k e a t e s t p o i n t s ; d i s p l a y r e a d i n g s from a f r o n t p a n e l d i s p l a y o r c o n s o l e ; s e n s o r y i n f o r m a t i o n such a s smoke, a b n o rm al n o i s e l e v e l , o r s p a r k s . The m a t r ix c o n c e p t h a s b een u s e d in o t h e r d i a g n o s t i c a p p l i c a t i o n s to d e s c r i b e "sy m p to m -d ise a se com p lexes" i n t h e f i e l d o f m e d ic in e . 25 v a lu e from- 0 to 100* and th e sum o f a l l subsystem f a i l u r e p r o b a b i l i t i e s t o t a l l e d 100. Three l e v e l s o f f a i l u r e - p r o b a b i l i t y spread* o r v a r i a b i l i t y * among th e subsystem s were employed a s e x p e rim e n ta l c o n d it i o n s . These l e v e l s were d e f i n e d a s th r e e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n s : uniform* m o d e ra te ly skewed* and skewed. In th e u n ifo rm d i s t r i b u tio n * th e v a lu e s were i d e n t i c a l f o r a l l subsystem s* e . g .* a "5" f o r each subsystem i n th e 20 subsystem m a trix as in F ig u re 1. A m o d e ra te ly skewed d i s t r i b u t i o n was a r b i t r a r i l y e s t a b l i s h e d such t h a t th e c u m u lativ e freq u e n cy o f f a i l u r e p r o b a b i l i t i e s e q u a lle d 50 f o r th e f i r s t q u a r t e r o f the sub system s and 70 f o r h a l f o f th e subsystem s (see Appendix I.C ). S im ila rly * th e cu m u lativ e f r e q u e n c i e s f o r a skewed d i s t r i b u t i o n app rox im ated 75 f o r th e f i r s t q u a r t e r o f th e su b sy s tems* and 90 f o r h a l f . Each S a t e l l i t e in c lu d e d d i s t r i b u t i o n s a t a l l t h r e e l e v e l s . See Appendix I f o r t y p i c a l v a lu e s a t each d i s t r i b u t i o n l e v e l . S tim u lu s S t r u c tu r e Six v a r i a b l e s were s e l e c t e d to d e fin e th e re sp o n se a l t e r n a t i v e s f o r a l l th r e e S a t e l l i t e pro blem s. The six s tim u lu s v a r i a b l e s c o n s i s t e d o f one e f f i c i e n c y v a ria b le * one r i s k v a ria b le * and f o u r s t r u c t u r e v a r i a b l e s . The v a lu e s o f each v a r i a b l e on each a l t e r n a t i v e were d eterm in ed from th e s tim u lu s -m a tr ix c o n fig u r a tio n * th e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n * and th e number o f subsystem s in the 26 s tim u lu s m a t r i x . These v a lu e s -were d e r i v e d f o r each s tim u l u s m a tr ix p r e s e n t a t i o n , and were u s e d to compute th e d i s c r im in a n t f u n c t i o n s d i f f e r e n t i a t i n g th e s e l e c t e d from n o n s e l e c t e d a l t e r n a t i v e s . The e f f i c i e n c y v a r i a b l e i s a m easure o f th e amount o f u n c e r t a i n t y r e d u c t i o n a s s o c i a t e d w ith th e re s p o n s e a l t e r n a t i v e . I t i s th e Shannon m easure o f a v e ra g e i n f o r m a tio n (G a rn e r, 19^2, C h a p te r l) and i s computed u s in g th e b a s i c in f o r m a tio n e q u a t io n , U = - £ p ± log p ± - q± log qj, where U i s th e a v e ra g e amount o f u n c e r t a i n t y a s s o c i a t e d w ith any p a r t i c u l a r outcome among th e s e t o f e v e n t s , p^ i s th e p r o b a b i l i t y o f o c c u r re n c e o f a p a r t i c u l a r e v e n t, and q^ = 1 - p ^ . In t h i s s tu d y , p^ i s th e f a i l u r e - p r o b a b i l i t y o f th e i-^- su b sy stem c o n n e c te d to a c h a n n e l. E f f i c i e n c y i s maximum when th e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n i s d iv id e d a t th e 50 p e r c e n t p o i n t , when th e sum o f t h e p r o b a b i l i t y v a lu e s a r e e q u a l betw een th e c o n n e c te d and n o n co n n ected s u b s y ste m s. T h e r e f o r e , th e m easure i s an in d e x o f the e f f i c i e n c y o f S ' s c h o ic e r e l a t i v e to th e way he d i v i d e s th e p r o b a b i l i t y d i s t r i b u t i o n , so t h a t a h ig h e f f i c i e n c y s c o re i s r e l a t e d to m in im iz in g th e a v e ra g e number o f s t e p s to s o l u t i o n . W ith a u n ifo rm d i s t r i b u t i o n , th e m easure c o i n c i d e s w ith th e second ( h a l f - s p l i t ) v a r i a b l e . 27 The h a l f - s p l i t v a r i a b l e i s a r i s k m ea su re , th e r i s k o f u s in g a maximum number o f s t e p s to s o l u t i o n . As a m in i max s t r a t e g y , a low r i s k s c o re i s o b t a i n e d when S 's c h o ic e d iv id e s th e number o f su b sy stem s i n t o g ro u p s o f e q u a l s i z e . W ith a u n if o r m f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n , t h i s c h o ic e i s a l s o m axim ally e f f i c i e n t . As th e d i s t r i b u t i o n " d e p a r t s from u n i f o r m i t y , how ever, a s e l e c t i o n made on t h i s b a s i s i s i n e f f i c i e n t , p ro d u c in g a h i g h e r a v e ra g e number o f s t e p s , w h ile i t s t i l l te n d s to m inim ize th e maximum number o f s t e p s . The f o u r s t r u c t u r e v a r i a b l e s were r e l a t e d to th e c o n f i g u r a t i o n and p a t t e r n o f c o n n e c tio n s in th e s t im u lu s m a t r i c e s . A number v a r i a b l e sim ply m easures th e t o t a l num b e r o f su b sy stem c o n n e c tio n s ( l r s) on any c h a n n e l. A h ig h sc o re i n d i c a t e s more su b sy stem c o n n e c tio n s i n th e c h a n n e l. A w eight v a r i a b l e c o n s i d e r s t h e p r o p o r t i o n o f su bsy stem c o n n e c tio n s i n th e u p p e r h a l f o f a c h a n n e l r e l a t i v e to th e t o t a l number o f s u b s y ste m s. S e l e c t i o n o f r e s p o n s e a l t e r n a t i v e s w ith a h i g h e r s c o re on t h i s v a r i a b l e i n d i c a t e s a p r e f e re n c e f o r a c h a n n e l w ith more subsystem c o n n e c tio n s i n th e u p p e r h a l f . ■ A p r o p o r t i o n v a r i a b l e m easu res th e te n d e n c y o f S to s e l e c t c h a n n e ls w ith a maximum r a t i o o f sub system c o n n e c t i o n s i n th e u p p e r h a l f o f th e c h a n n e l. I t i s th e number o f l ’ s i n t h e u p p e r h a l f d iv id e d by th e t o t a l number o f l ’ s i n the c h a n n e l. 28 An a l t e r n a t i o n v a r i a b l e was in c lu d e d to d e te rm in e th e e f f e c t o f a l t e r n a t i n g p a t t e r n o f l ' s and- 0 ' s in th e c h a n n e l. A h ig h sc o re i n d i c a t e s f r e q u e n t a l t e r n a t i o n s , w h ile a low sc o re i n d i c a t e s c l u s t e r i n g o r g ro u p in g o f su b system c o n n e c tio n s . For example., a maximum sc o re i s o b t a i n e d when th e even-num bered subsystem s a r e c o n n e c te d and th e odd-num bered subsystem s a r e n o t c o n n ec te d to th e c h an n e l . These s t r u c t u r e v a r i a b l e s were i n c lu d e d to d e t e r mine th e e f f e c t s o f th e s tim u l u s - m a tr i x p a t t e r n on th e s e l e c t i o n o f re s p o n s e a l t e r n a t i v e s . In term s o f s tim u lu s s t r u c t u r e , th e q u e s t io n s in v o lv e d th e i n f l u e n c e on S o f th e t o t a l number o f c o n n e c tio n s , c o n n e c tio n s in o n e - h a l f o f th e c h a n n e l, th e r e l a t i v e number o f c o n n e c tio n s , and the g ro u p in g s o f th e c o n n e c tio n s . In C h ap ter I and C h a p te r I I o f t h i s s tu d y i t was r e p o r t e d t h a t Ss do re sp o n d to p r o p e r t i e s o f th e s tim u lu s s e t . I t was a ls o r e p o r t e d t h a t Ss te n d to group s tim u lu s e le m e n ts by a minimax s t r a t e g y , so th e h a l f s p l i t v a r i a b l e was in c lu d e d to e v a l u a t e t h i s e f f e c t . In a d d i t i o n , th e Shannon in f o r m a tio n m easure h a s been w id e ly a p p li e d i n p s y c h o l o g ic a l e x p e rim e n ts to stu d y th e e f f i c i e n c y o f Ss cho osin g betw een a l t e r n a t i v e s w ith u n c e r t a i n o u t comes (G a rn er, 1 9 62 ). A ll t h r e e , e f f i c i e n c y , r i s k , and s t r u c t u r e , were t h e r e f o r e employed in t h i s stu d y to e v a l u a te t h e i r r e l a t i v e c o n t r i b u t i o n s to p ro b le m -s o lv in g by th e d i s c r i m i n a n t m odel. 29 A d m in is tr a tio n o f Experim ent by Computer E x p e rim e n ta l P rocedure A ll s e s s io n s were d e sig n ed to allo w com puter a d m in -- i s t r a t i o n o f th e experim ent., a s w e ll as c o m p u te r - c o n tr o lle d d a ta c o l l e c t i o n and f o r m a ttin g . The e x p e rim e n te r was p r e s e n t o n ly to g iv e and i n t e r p r e t th e i n s t r u c t i o n s , and to i n i t i a t e th e com puter o p e r a t i o n s . On i n f r e q u e n t o c c a s io n s , th e e x p e rim e n te r r e s e t th e com puter program to th e c o r r e c t s te p when a hardw are m al f u n c tio n i n t e r r u p t e d th e e x p e rim e n ta l s e s s io n . Once th e i n i t i a l c o n d it i o n s were s e t by th e e x p e rim e n te r, th e e x p e r i ment was co ndu cted e n t i r e l y by th e com puter. The com puter th u s took th e r o l e o f th e e x p e rim e n te r, working i n t e r a c t i v e ly w ith th e S, y e t p ro v id in g c o m p lete ly o b j e c t i v e and i d e n t i c a l in f o r m a tio n to each S. The e x p e rim e n ta l p ro ced u re i s i l l u s t r a t e d i n F ig u re 2, a flow diagram l i s t i n g the m ajor f u n c t i o n s i n th e e x p e rim e n ta l sequence. The c i r c l e s i d e n t i f i e d by "SUBJ" i n d i c a t e i n p u t s by S. In a ste p w ise manner, th e computer ty p ed i n s t r u c t i o n s to Ss, d is p la y e d th e stim u lu s m a tr ix , r e q u e s te d i n p u t s , p ro c e s s e d them, ty ped th e r e s u l t s o r an sw ers, pau sin g as n e c e s s a ry to w a it f o r th e in p u t by Ss. The S s' i n p u ts were sim ply one d i g i t numbers f o r c h a n n e ls , o r o n e - o r two- d i g i t numbers f o r su bsystem s. For each in p u t, th e computer EXPERIMENTER INITIALIZES FOR SATELLITE AND TRIAL NUMBER "SU 8J" START I = SEQUENCE NUMBER K = STEP NUMBER READ FILE OF STIMULUS DATA NEXT PROBLEM DISPLAY STIMULUS MATRIX REQUEST CHOICE REQUEST SUBSYSTEM NUMBER ■SUBJ" :h o ic e CHANNEL SUBSYSTEM SUBSYSTEM / W A S X CHOICE A CHANNEL OR . A SUBSYSTEM MATRIX WHICH O PTIO N WAS SELECTED •SUBJA s s N O . REPAIR TEAM ACKNOWLEDGES MESSAGE CHANNEL (1 -8 ) REPAIR TEAM REPORTS ERROR GIVES THREE OPTIONS PRINT CHANNEL STATUS, U n o r m a l / a b n o r m a l ) N O WAS CHOICE CORRECT REMOVE SUBSYSTEMS FROM STIMULUS MATRIX PER CHANNEL STATUS YES REPAIR TEAM REPORTS SYSTEM OK ^D U M B E R ( N ) ^ OF SUBSYSTEMS REMAINING YES ^ PRINT REDUCED MATRIX END N O YES O PTIO N TO PRINT REDUCED 5TIMULUS- MATRIX DATA FOR SESSION O N PUNCHED TAPE N O (0 , 1) END F i g . 2 . — Flow Diagram f o r C o m p u te r-A d m in is te re d E x p e r im e n ta l S eq uence. 31 g e n e r a t e d a new, re d u c e d m a t r i x , f o r d i s p l a y on th e s u b s e q u e n t s t e p . T h is o p e r a t i o n removed th o s e su b sy stem s w hich a re l o g i c a l l y NORMAL, b a se d on th e s t a t u s i n f o r m a tio n f o r th e c h a n n e l s e l e c t e d by S. The com puter program f o r th e e x p e rim e n t was w r i t t e n i n CAL ( C o n v e r s a t i o n a l A lg e b ra ic L an guag e), a langu ag e s p e c i a l l y s u i t e d f o r th e i n t e r a c t i v e r e q u i r e m e n ts o f t h i s s tu d y . O r d i n a r i l y , when a program i s e x e c u te d , v a r i a b l e s a re i n p u t a s d a t a , o r computed from d a t a , and th e program o p e r a t e s w i t h o u t i n t e r r u p t i o n to p ro d u ce th e r e s u l t s . I n t h i s c a s e , th e d a ta d e s i r e d w ere th e s u b j e c t ' s r e s p o n s e s , which c a n n o t be p r e d i c t e d . The c o n v e r s a t i o n a l language p e r m i t t e d th e program to p a u se and demand th e i n p u t when r e q u i r e d , and th en p ro c e e d e d u n t i l th e n e x t i n p u t was r e q u i r e d . The program l i s t i n g i s i n Appendix I I . A . Equipm ent The com puter u se d i n th e e x p e rim e n t was an SDS 9^0, a m ed iu m -size d , h ig h - s p e e d d i g i t a l com pu ter. A t e l e t y p e c o n s o le , th e ASR 33* c o n ta in i n g a t y p e w r i t e r k ey board w ith s p e c i a l c o n t r o l c h a r a c t e r s , a t y p e w r i t e r p r i n t o u t and a p a p e r - t a p e r e a d and punch u n i t , was c o n n e c te d to th e c e n t r a l com puter by te le p h o n e l i n e s . The t e l e t y p e was l o c a t e d in a sm all', i s o l a t e d room i n th e P sychology D epartm ent a t th e U n i v e r s i t y o f S o u th e rn C a l i f o r n i a . S tim u lu s Data and P r e s e n t a t io n 32 S tim u lu s in fo r m a tio n was sto re d on d is c a s stim u lu s d a ta f i l e s * to be r e c a l l e d f o r t h e p r e s e n t a t i o n o f each s tim u lu s m a tr ix . The d a ta f i l e c o n ta in e d th e fo llo w in g d a ta : th e o r d e r o f p r e s e n t a t i o n o f the p ro b lem s; th e f a i l u r e - p r o b a b i l i t i e s o f each subsystem ; the l i s t o f m a lfu n c t io n i n g subsystem s* and th e c o n fig u r a tio n o f c o n n e c tio n s in th e s tim u lu s m a t r i c e s . These d a ta are combined i n a p r e d e te rm in e d o r d e r by th e computer program to e s t a b l i s h th e s tim u lu s m a trix f o r each problem . D e t a i ls o f th e p ro ce d u re a r e s e t f o r t h i n Appendix I I I . A . The f i l e o f s tim u lu s i n fo rm a tio n i s i n Appendix I I I . B through I I I . D . Data H andling The d a ta f o r the th r e e problem s i t u a t i o n s c o n s i s t e d o f c h an n el number r e s p o n s e s made by each S f o r eac h s te p of h i s p ro b le m -s o lv in g sequence on each System. These were s to r e d by th e com puter as th e experim ent p ro g re sse d * and f i n a l l y punched on p a p e r ta p e when each s e s s io n was com p lete.-^ Appendix IV c o n ta in s th e t a b le s o f raw d a t a accumu l a t e d f o r each S o v e r a l l t r i a l s . •^These d a ta c o u ld have been r e t a i n e d in th e computer d is c f i l e s ; however* the e x p e rim e n ta l s e s s io n s e x ten d ed o v e r a p e r i o d o f weeks f o r each S* and i t was c o n s id e re d more econom ical to t r a n s f e r the d a ta to e x t e r n a l s to r a g e u n t i l a l l the d a ta had been accum ulated and were read y f o r a n a l y s i s . S u b je c t d a ta on punched ta p e were t r a n s f e r r e d to th e com puter f i l e s . The program used to a d m in is te r th e e x p e r i ment was m o d ified to a cc ep t th e i n p u t s from the d a ta f i l e i n s t e a d o f r e a l - t i m e S re s p o n s e s . The l i s t i n g o f th e modi f i e d program i s in Appendix I I .B and the flow diagram i s i l l u s t r a t e d in F ig u re 3 . S ince a l l the n e c e s s a r y d a ta were a v a i l a b l e in th e com puter, i t o p e ra te d w ith o u t i n t e r r u p t i o n , r e p e a t i n g th e m atrix r e d u c t io n o p e r a t io n s p r e v io u s ly p e r formed w ith th e S. T h is tim e , however, i n a d d it i o n to the m a trix r e d u c t io n , i t computed v a lu e s fo r th e v a r i a b l e s d e ll f i n in g th e a l t e r n a t i v e s in each s tim u lu s m a tr ix . For each s te p , up to e ig h t se ts, o f v a lu e s were computed, one s e t f o r each a l t e r n a t e c h a n n e l. Each s e t was fo rm a tte d to a p p e a r a s a c a rd image, along w ith i d e n t i f i c a t i o n numbers f o r a sequence. System, c h a n n e l, s t e p , S, and chan n el s e l e c t i o n . Channel v a lu e s were n o t computed i f the c h a n n e l c o n ta in e d a l l l ' s o r a l l 0 ' s , s in c e no in fo rm a tio n was t r a n s m i t t e d in th e s e c a s e s . Once a c h an n el was s e l e c t e d , the program r e duced th e s tim u lu s -m a trix by d e l e t i n g subsystem s w ith e i t h e r a 1 o r 0 in t h a t c h a n n e l, depending on th e s t a t u s re a d in g . In succeed ing s te p s , th e chan n el would n e c e s s a r i l y c o n ta in e i t h e r a l l l ’ s o r O 's , so i t was a l s o excluded in succeeding c o m p u tatio n s. These a re th e in dependent v a r i a b l e s f o r th e d i s c rim in a n t a n a l y s i s d e s c r i b e d l a t e r . These v a r i a b l e s a re o b ta in e d from the i n t e r r e l a t i o n o f c o n f i g u r a ti o n , f a i l u r e = SEQUENCE NUMBER = STEP NUMBER DISC FILES 1. STIMULUS DATA 2 . SUBJECT DATA SUBJECT DATA FROM EXPERIMENTAL SESSIONS O N PUNCHED TAPE j NEXT PROBLEM LAST STEP OF PROBLEM-TRIAL COMPLETED YES N O N O LAST TRIAL ! YES END DISC FILE ID, \ 'C H O IC E , AND STIMULUS VARIABLE VALUES ) PRINT SELECTED STIMULUS-VARIABLE VALUES NUMBER (N ) O F SUBSYSTEMS ^ REMAINING N > 4 COMPUTE VARIABLE VALUES FOR "SELECTED" AND " N O N SELECTED" ALTERNATIVES REMOVE SUBSYSTEMS FROM STIMULUS MATRIX PER CHANN EL STATUS ACCEPT SUBJECTS CHOICE AT STEP K READ SUBJECT DATA READ STIMULUS DATA EXPERIMENTER INITIALIZES FOR SATELLITE, TRIAL, AND SUBJECT NUMBER OFF LINE DATA TRANSFER, DISC TO CARD P i g . 3 •--P lo w Diagram o f Com putation o f S tim u lu s V a r i a b l e s V alues 35 As th e p ro gram p r o c e e d e d , i t t r a n s f e r r e d th e com p u t e d d a t a to th e c o m p u ter d i s c f o r s t o r a g e i n a d a t a f i l e . W ith up to 72 p r o b l e m - s o l v in g t r i a l s on each S a t e l l i t e , t h r e e s t e p s p e r p ro b le m , and up to e i g h t l i n e s o f d a t a p e r s t e p , a maximum o f 1 ,7 2 8 l i n e s o f d a t a w ere g e n e r a t e d p e r S p e r S a t e l l i t e . The f i l e s were c o n v e r t e d o f f - l i n e from d i s c to c a r d . Each l i n e o f d a t a was pu nched on a s e p a r a t e IBM c a r d . T h is p r o c e d u r e f o r g e n e r a t i n g th e d a t a was r e p e a t e d f o r th e f i v e Ss on th e t h r e e S a t e l l i t e s . The c a r d s were a r r a n g e d f o r p r o c e s s i n g o f th e d a t a on an a n a l y s i s o f v a r i ance p ro g ram and d i s c r i m i n a n t a n a l y s i s p ro g ram . p r o b a b i l i t y d i s t r i b u t i o n , and s i z e o f th e s t i m u l u s m a t r i x . The s t i m u l u s m a t r ix c a n n o t be d e f i n e d ah ead o f tim e b e c a u s e i t s s t r u c t u r e i s a f u n c t i o n o f th e a l t e r n a t i v e ch o sen i n th e p r e v i o u s s t e p . CHAPTER IV EFFICIENCY ANALYSIS The d a ta o f t h i s e x p e rim e n t were s u b j e c t e d to group a n a ly s e s to o b t a i n d e s c r i p t i v e m easures o f th e d a ta a s fu n c t i o n s o f e x p e r im e n ta l c o n d it i o n s , and to compare th e r e s u l t s to f i n d i n g s from r e l a t e d p ro b le m -s o lv in g s t u d i e s . E f f i c i e n c y was d e fin e d a s a m easure o f th e amount o f u n c e r t a i n t y r e d u c t i o n a s s o c i a t e d w ith each s t e p o f p r o b le m - s o lv in g . Inasmuch a s th e p ro b le m -s o lv in g p r o c e s s had been p o sed as a q u e s t io n o f c h o ic e between a l t e r n a t i v e s w ith u n c e r t a i n outcom es, a s t r a i g h t f o r w a r d t e s t o f S 's a b i l i t y to u se in f o r m a tio n e f f i c i e n t l y was r e q u i r e d . The Shannon meas u r e o f a v e ra g e u n c e r t a i n t y o r in f o rm a tio n i s such a m easure f o r s i t u a t i o n s in v o lv i n g a c h o ic e betw een a l t e r n a t i v e s . Be cause o f th e wide a p p l i c a t i o n o f t h i s m easure o f e f f i c i e n c y in th e p s y c h o lo g ic a l l i t e r a t u r e , th e group a n a ly s e s d e s c r i b e d h e re employed th e e f f i c i e n c y v a r i a b l e f o r com parison p u rp o s e s . In th e s e a n a l y s e s , e f f i c i e n c y i s u se d as th e d e p e n d en t v a r i a b l e . The e f f i c i e n c y o f Ss was e v a lu a te d by a n a l y s i s o f v a r ia n c e to d e te rm in e th e e f f e c t s o f s e v e r a l e x p e r im e n ta l c o n d i t i o n s . I t was im p o rta n t to d e te rm in e i f t h e r e were 36 any l e a r n i n g e f f e c t s b e c a u se i t was a n e c e s s a r y c o n d it i o n f o r th e d i s c r im i n a n t model t h a t s t a b l e perfo rm an ce be e x h i b i t e d th ro u g h th e e x p e rim e n t. The p r o b l e m - t r i a l b lo c k s e f f e c t e v a lu a te d e f f i c i e n c y chang es o v e r th e e x p e rim e n t. A m easure o f th e f a i l u r e - d i s t r i b u t i o n e f f e c t was i n c lu d e d to d e te rm in e i f t h e r e were any changes i n e f f i c i e n c y a s th e d i s t r i b u t i o n o f p r o b a b i l i t i e s changed from u n ifo rm to skewed. The p a t t e r n o f c o n n e c tio n s i n th e s tim u lu s m a trix may have a f f e c t e d e f f i c i e n c y and a m easure o f c o n f i g u r a ti o n e f f e c t was in c lu d e d f o r t h i s a n a l y s i s . I t was a ls o e x p e c te d t h a t e f f i c i e n c y would change w ith s u c c e s s iv e s t e p s i n t o th e s o l u t i o n sequence.*^ T h is was a n a ly z e d by th e ste p e f f e c t . A r e p l i c a t i o n e f f e c t was in c lu d e d t o check th e r e l i a b i l i t y o f p e rfo rm an c e , and f i n a l l y , th e i n f lu e n c e of o r d e r o f p r e s e n t a t i o n was d e te rm in e d by a problem o r d e r e f f e c t . Two a n a l y s i s o f v a r i a n c e d e s ig n s c o n s id e re d th e s e e f f e c t s . ^ A n a ly s is 1 In t h i s a n a l y s i s , e f f i c i e n c y was e v a l u a t e d a s a I t was found i n c o n c e p t f o rm a tio n s t u d i e s and in i n f o r m a ti o n - p r o c e s s in g s t u d i e s t h a t th e type o f h y p o th e s e s b e in g t e s t e d changes w ith p r o g r e s s i v e s t a g e s tow ard th e s o l u t i o n . The change i s tow ard s s p e c i f i c i t y , which should r e s u l t in l e s s e f f i c i e n c y . 2 The BMD 08V A n a ly s is o f V a ria n c e program was ru n on th e H oneywell 800 com puter a t th e USC Computer S c ie n c e s L a b o ra to ry . The program i s d e s c r i b e d by Dixon ( 1 9 6 7 * pp. 587- 600). f u n c t i o n o f c o n f i g u r a t i o n and d i s t r i b u t i o n . The a n a l y s i s was p e rfo rm e d u n d e r a 5 x 2 x 3 x 2 ' x 5 d e s i g n f o r block., c o n f i g u r a ti o n ., d i s t r i b u t i o n , p ro b lem r e p l i c a t i o n . , and s u b j e c t . The d e s i g n i s i l l u s t r a t e d i n T able 1.^ The a n a l y s i s was p e rfo r m e d s e p a r a t e l y f o r SAT1 and SAT2, and th e s e p a r a t e a n a l y s e s a r e r e f e r r e d to a s AV l a and AV l b , r e s p e c t i v e l y . Only th e d a ta from th e f i r s t s t e p were u s e d , s i n c e th e c o n f i g u r a t i o n s and d i s t r i b u t i o n s c o u ld n o t be c o n t r o l l e d on su b s e q u e n t s t e p s . I t was h y p o t h e s iz e d t h a t t h e r e w ould be no d i f f e r e n c e s f o r th e two c o n f i g u r a t i o n s b e c a u se o f th e random method u s e d to e s t a b l i s h them . S i g n i f i c a n t d i f f e r e n c e s were e x p e c te d b e tw ee n th e t h r e e d i s t r i b u t i o n l e v e l s b a se d on p r e v i o u s f i n d i n g s i n a s i m i l a r e x p e rim e n t on e f f i c i e n c y (D a v is , 1 9 6 8 ) . I t was r e p o r t e d t h a t e f f i c i e n c y d e c r e a s e s w ith i n c r e a s i n g skew ness o f th e p r o b a b i l i t y d i s t r i b u t i o n . R e s u l t s and d i s c u s s i o n o f A n a l y s i s 1 . The r e s u l t s o f A n a l y s i s 1 a r e sum m arized i n T a b le s 2 and 3- Four s i g n i f i c a n t Fs f o r AV l a (P < . 0 5 ) w ere fo u n d . The s i g n i f i c a n t d i f f e r e n c e s in v o lv e th e d i s t r i b u t i o n main e f f e c t and t h r e e i n t e r a c t i o n s , i n c l u d i n g two i n t e r a c t i o n s w ith d i s t r i b u t i o n . Two s i g n i f i c a n t Fs ( P C . 0 5 ) were fo u n d f o r th e p a r a l l e l a n a l y s i s , AV l b . T hese in v o lv e d th e d i s t r i b u t i o n main e f f e c t and an i n t e r a c t i o n o f c o n f i g u r a t i o n w i t h p r o b lem r e p l i c a t i o n . 39 TABLE 1 ANALYSIS OP VARIANCE DESIGN ANALYSIS 1. BCDPS ( 5 x 2 x 3 x 2 x 5 . ) B locks 1 C o n f ig u r a tio n s 1 2 D i s t r i b u t i o n s 1 2 3 1 2 3 Problem R e p l i c a t i o n s 1 2 1 2 1 2 1 2 1 2 1 2 S u b je c ts 1 a 2 b 3 4 5 i 1. Plan I l l u s t r a t e s th e f i r s t b lo ck on ly o f the 5 - l e v e l b lo c k s d e s ig n . a C e ll e n tr y i s X1111;L XBCDPS b C e ll e n t r y i s x 1:q 22 i C e ll e n tr y i s Xloooc 40 T A B L E 2 AV la SUMMARY OF ANALYSIS, SAT1 Source Sum of Squares Degrees of Freedom Mean Square F B . Blocks 65.49 4 15.87 - C Configurations 75-00 1 75-00 - D Distributions 734.65 2 367.32 5.51* P Problem Replications 85.33 1 85.33 ' ' — S Subjects 597.88 4 149.47 — BC 18 1 .2 2 4 45.30 4.o4* BD 216.46 8 27.05 2. 26* CD 1307.65 2 653.82 7. 88* BP 319.36 4 79.84 5. 58* CP 164.28 1 164.28 — DP 2 2 6 .2 8 . 2 115.14 BS 524.70 16 3 2 .7 9 CS 2 8 4 .5 6 4 71.14 DS 534.27 8 6 6 .7 8 PS 127.76 4 31.9^ BCD 196.60 8 24.57 BCP 141.22 4 35.30 BDP 179.71 8 22.46 CDP 365.17 2 182.58 BCS 179.37 16 1 1 .2 1 BDS 585.42 52. 1 1 .9 8 CDS 66 5 .6 6 8 8 2 .9 5 BPS 357.56 16 2 2 .5 3 CPS 2 2 7 .8 8 4 56.97 DPS 454.51 8 54.28 BCDP 22- 8 .6 1 8 28.57 BCDS 756.79 32 2 5 .6 4 BCPS 4l4.4o 16 2 5 .9 0 BDPS 498.76 32 15.58 CDPS 401.94 8 50.24 BCDPS 576.85 32 1 8 .0 2 *P < .05 41 T A B L E 3 AV lb SUMMARY OR ANALYSIS, SAT2 Source Sum of Squares Degrees of Freedom Mean Square F B Blocks 49.88 4 12.47 --- C Configurations 77-01 1 77-01 --- D Distributions 142.60 2 71.30 8 . 61* P Problem Replications 8 .3 3 1 8.33 --- S Subjects 2 8 3 .5 2 4 . 7 0 .8 8 --- BC 2 3 .6 8 4 5.92 --- BD 2 7 .3 9 8 3.42 --- CD 9.24 2 4.62 --- BP 1 9 .0 3 4 4.75 --- CP 15.41 1 15.41 12.88* DP 39.60 2 1 9 .8 0 — BS 264.94 16 16.55 CS 57-18 4 14.29 DS 6 6 .2 6 8 8.28 PS 19.73 4 4,93 BCD 24.75 8 3 .0 9 BCP 1 9 .0 2 4 4.75 BDP 56.32 8 7.04 CDP 21.20 2 1 0.60 BCS 37-61 16 2 .3 5 BDS 2 3 6 .0 7 32 7-37 CDS 86.35 8 10.79 BPS 3 0 .0 6 16 1 .8 7 CPS 4 .7 8 4 I.19 DPS 85.32 8 10.66 BCDP 56.46 8 7.05 BCDS 99.64 32 3 .1 1 BCPS 48.94 16 3.05 BDPS 2 0 9 .0 7 32 6.53 CDPS 56.59 8 7.07 BCDPS 1 9 9 .0 7 32 6.22 *P < .05 42 The d i s t r i b u t i o n e f f e c t was th e o n ly one s i g n i f i c a n t on b o th a n aly se s* and a p l o t o f - t h e means i s shown i n F i g u r e 4. T h is f i g u r e shows t h a t e f f i c i e n c y te n d s to i n c r e a s e as th e f a i l u r e - p r o b a b i l i t y v a lu e s f o r th e su bsy stem s a p p ro a c h a more u n ifo rm d i s t r i b u t i o n . I t a ls o shows th e means o f SAT2 to be l a r g e r th an SAT1* b u t c o n v e rg in g a t th e u n ifo rm d i s t r i b u t i o n c o n d it i o n . When th e d i s t r i b u t i o n i s uniform * Ss te n d to s p l i t th e p r o b a b i l i t y d im ension a t th e 50 p e r c e n t p o i n t and ten d to d iv e rg e from t h a t p o i n t a s th e d i s t r i b u t i o n becomes skewed. T his r e s u l t i s in ag reem ent w ith th e f i n d in g o f D a v is. , I f Ss a re te n d in g to make r e sponses w hich d i v id e th e subsystem s i n t o g ro u p s o f e q u a l number* th en e f f i c i e n c y would d e c re a se as th e skewness o f th e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n in c re a s e d * and e f f i c ie n c y would be h i g h e s t on a u n ifo rm d i s t r i b u t i o n . T h is p o s s i b i l i t y was c o n s id e r e d in the d i s c r im i n a n t a n a l y s i s l a t e r * where th e r e l a t i v e c o n t r i b u t i o n s o f e f f i c i e n c y and h a l f - s p l i t v a r i a b l e s may be d e te rm in e d . The la c k o f s i g n i f i c a n c e on th e b lo c k e f f e c t c o n firm s t h a t a s t a b l e l e v e l o f perform ance was m a in ta in e d th ro u g h o u t th e e x p e rim e n t. E f f e c t s n o t s i g n i f i c a n t in b o th a n a ly s e s were n o t in c lu d e d and were n o t I n t e r p r e t e d . 43 EFFICIENCY (RELATIVE UNITS) 100 SAT 1 UNIFORM MODERATE SKEWED SKEW DISTRIBUTION F ig . 4 . - - E f f i c i e n c y as a F u n c tio n o f I n c r e a s i n g F a i l u r e - P r o b a b i l i t y D i s t r i b u t i o n Skewness. A n a ly s is 2 E f f i c i e n c y was e v a l u a t e d a s a f u n c t i o n o f s t e p ( p o s i t i o n In sequence o f s t e p s ) and o r d e r o f p r e s e n t a t i o n . The a n a l y s i s was p e rfo rm e d u n d e r a 5 x 12 x 3 x 5 d e s ig n f o r b lo c k s * p ro b le m o rd e r* s t e p and s u b j e c t s . The a n a l y s i s o f v a r i a n c e d e s i g n i s i l l u s t r a t e d in T a b le 4 . The a n a l y s i s was p e rfo rm e d s e p a r a t e l y f o r SAT1 and SAT2* and a r e r e f e r r e d to a s AV 2a an d AV 2b. Of p r im a r y i n t e r e s t i n t h i s a n a l y s i s was th e i n f l u en ce o f s t e p seq u en c e p o s i t i o n on e f f i c i e n c y . F i r s t * i f Ss change t h e i r s t r a t e g y a s t h e y pro ceed* a s r e p o r t e d in t h e d e s c r i p t i o n s o f b e h a v i o r i n c o n c e p t f o r m a tio n s t u d i e s and th e i n f o r m a t i o n - p r o c e s s i n g s t u d i e s ( C h a p te r I I ) i t w ould be o f i n t e r e s t to d e te r m in e i f th e ch ang e i s a l s o p r e s e n t i n t h i s stu d y and i f i t i s r e f l e c t e d by th e e f f i c i e n c y m e a s u re . Second* i f t h e r e i s a d i f f e r e n c e e v id e n c e d by a change i n e f f i c i e n c y * i t s h o u ld be d e te r m in e d w h e th e r e f f i c i e n c y i n c r e a s e d o r d e c r e a s e d . < R e s u l t s and d i s c u s s i o n o f A n a l y s i s 2 . T a b le s 5 and 6 sum m arize th e r e s u l t s o f A n a ly s is 2. S i g n i f i c a n t F ' s common to b o t h a n a l y s e s in v o lv e th e s t e p sequence* p o s i t i o n * p ro b le m o rd e r* and t h e i n t e r a c t i o n o f b l o c k s and p ro b lem o r d e r . - The means f o r th e s t e p e f f e c t were p l o t t e d in F i g u r e 5. T h is f i g u r e shows t h a t e f f i c i e n c y p r o g r e s s i v e l y TABLE k - ANALYSIS OF VARIANCE DESIGN ANALYSIS 2 BPQS (5 x 12 x 3 x 5) Blocks* 1 Problem ^ Order 2 3 b 5 6 7 8 9 10 11 12 Step 12 3 12 3 1 2 3 1 2 3 1 2 3 12 3 1 2 3 1 2 3 12 3 1 2 3 1 2 3 1 2 3 Subjects 1 a 2 b 3 k 5 i *The plan illustrates Block 1 only of 5 blocks, a Cell entry is X1 ^ ^ = XgpQg b Cell entry is X - | - | - | ? i Cell entry is X1 _ \ 46 TABLE 5 AV 2a SUMMARY OF ANALYSIS, SAT1 Source Sum of Squares Degrees of Freedom Mean Square F B Blocks 1038.49 4 259.62 5.07** P Problem Order 5258.22 11 478.02 4.82** Q Steps 3091.74 1 3091.74 — 3 Subjects 1805.35 4 451.33 BP 10571.43 44 240.25 2. 97** BQ 1081.01 4 270.25 3.41** PQ 3459.02 11 314.45 3.50** BS 2359.02 16 147.43 PS 4l4o.36 44 94.09 QS 2 5 6 .3 7 4 64.09 BPQ 7602.43 44 172.78 1.74** BPS 14252.65 176 8 0 .9 8 BQS 1268.04 16 79-25 PQS 3951.26 44 89.80 BPQS 17468.11 176 99-25 *P < .65 ' **P < .01 47 TABLE 6 AV 2b SUMMARY OF ANALYSIS, SAT2 Source Sum of Squares Degrees of Freedom Mean Square F B Blocks 270.72 4 67.68 P Problem Order 762.78 11 69.34 2 . 62* Q Steps 1992.33 2 996.16 7.96* s Subjects 597.65 4 149.4l BP 3371.43 44 76.62 2 . 17** BQ 54.79 8 6.84 — PQ 1012.19 22 46.00 — BS 515.41 16 32.21 PS 1165.04 44 26.47 QS 1000.90 8 125.11 BPQ 4259.60 88 48.4o — BPS 6204.15 176 35.25 BQS 981.62 32 . 30.67 PQS 3253.35 88 36.97 BPQS 12895.84 352 36.63 *P < .05 **P < .01 48 EFFICIENCY (RELATIVE UNITS) 100 98 96 SAT 2 94 92 SAT 1 90 2 3 STEP NUMBER F i g . 5 • - - E f f i c i e n c y a s a F u n c tio n o f S u c c e s s iv e S te p s i n R esponse S equen ce. 49 d e c re a s e d from th e f i r s t s t e p to th e t h i r d s te p o f t h e 3 s o l u t i o n s e q u e n c e . T h i s r e s u l t s u g g e s ts t h a t th e i n f l u ence o f e f f i c i e n c y l e s s e n s a s S p r o g r e s s e s th ro u g h t h e p r o b le m -s o lv in g se q u e n c e . T h is c o n c lu s io n can be r e l a t e d to th e d e s c r i p t i v e s t u d i e s re v ie w e d i n C h a p te r I I . I f , a s Johnson r e p o r t e d , Ss s t a r t w ith sim p le g e n e r a l h y p o th e s e s and th e n s u b s e q u e n t ly form more s p e c i f i c and complex t e s t s , t h i s k in d o f change would be e x p e c te d to r e s u l t in l e s s e f f i c i e n c y i n th e i n f o r m a t i o n s e n s e . In th e same v e in , K le in - muntz summarized S s ' b e h a v io r a s a d i v i d i n g o f th e problem i n t o s u b s e t s by a g e n e r a l to s p e c i f i c p r o c e d u r e . T h is would a ls o s u g g e s t l e s s e f f i c i e n t in f o r m a tio n a c q u i s i t i o n in l a t e r s t e p s . B endig (1953).* to o , found t h a t l a t e r q u e s t i o n s were n o t as e f f i c i e n t a s e a r l i e r o n e s, i n a " tw e n ty - q u e s tio n s " e x p e r im e n t. The s te p e f f e c t i s v i t a l to i n t e r p r e t a t i o n o f th e d a ta i n th e d i s c r i m i n a n t a n a l y s i s . I f e f f i c i e n c y changes as a f u n c t i o n o f s t e p , th e n one sh o u ld e x p e c t th e d i s c r i m i n a n t model t o v a ry o v e r s t e p s i n th e s o l u t i o n se q u e n c e . T his f a c t o r was c o n s i d e r e d and i s d is c u s s e d l a t e r . The p ro b lem o r d e r e f f e c t sh o u ld r e f l e c t any changes in e f f i c i e n c y a t t r i b u t a b l e to o r d e r o f p r e s e n t i n g pro b lem s in th e b lo c k s o f tw e lv e p ro b le m s . ^Only two s t e p s w ere a n a ly z e d i n AV 2a. B ecau se of th e s m a lle r s t im u lu s m a tr ix i n SAT1, t h e r e were i n s u f f i c i e n t c a s e s i n s t e p t h r e e to p e r m i t i t s i n c l u s i o n i n th e a n a l y s i s o f v a r i a n c e . 50 T h is e f f e c t was p l o t t e d and showed wide f l u c t u a t i o n s i n e f f i c i e n c y f o r problem s i n SAT1 and no d i s c e r n i b l e t r e n d f o r e i t h e r SAT1 o r SAT2. For SAT1, th e p roblem s p r e s e n te d a t eac h o f th e tw elv e l e v e l s were i d e n t i f i e d . I t was o b se rv e d t h a t p ro b lem s i n v o lv in g system s w ith skewed f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n s p re d o m in a te d a t th o s e l e v e l s which c o rre sp o n d e d w ith th e low e f f i c i e n c y p o i n t s o f th e SAT1 c u rv e . A n a ly s is 1 showed t h a t d i s t r i b u t i o n e f f e c t s were s i g n i f i c a n t , w ith skewed d i s t r i b u t i o n s p ro d u c in g low er e f f i c i e n c i e s th an u n ifo rm d i s t r i b u t i o n s . T h e re fo r e , i t a p p e a rs t h a t d i s t r i b u t i o n e f f e c t s were confounded in prob lem o r d e r . T h is c o n c lu s io n i s r e a s o n a b le s in c e no a t tem pt was made to c o u n te r b a la n c e d i s t r i b u t i o n in th e r a n d o m iz a tio n o f th e problem o r d e r . Of th e re m a in in g s i g n i f i c a n t F v a lu e s , o n ly th e b lo c k s and p r o b le m -o r d e r i n t e r a c t i o n was s i g n i f i c a n t on b o th a n a l y s e s . T h is was a ls o i n t e r p r e t e d a s th e c o n fo u n d in g o f d i s t r i b u t i o n e f f e c t s w ith problem o r d e r . The o t h e r t h r e e s i g n i f i c a n t F ' s a p p e a r o n ly i n th e SAT1 a n a l y s i s and a l l t h r e e in v o lv e i n t e r a c t i o n w ith th e p r o b le m - o r d e r e f f e c t . In summary, th e r e s u l t s o f two a n a ly s e s o f v a r ia n c e showed t h a t e f f i c i e n c y s y s t e m a t i c a l l y d e c r e a s e d a s a f u n c t i o n o f i n c r e a s i n g d i s t r i b u t i o n skew ness, and a ls o sy ste m a t i c a l l y d e c r e a s e d a s a f u n c t i o n o f number o f s t e p s ta k e n tow ard s o l u t i o n o f th e p roblem . Both o f th e s e r e s u l t s were a n t i c i p a t e d and were r e l a t e d to p r e v io u s f i n d i n g s . There were no p r a c t i c e o r le a r n in g i n f l u e n c e s so t h a t s t a b l e p e r formance i s assumed f o r m odeling p u rp o s e s . T h is i s an Im p o r t a n t c o n d itio n f o r th e d i s c r im i n a n t a n a l y s i s which i s b a se d on d a ta c o l l e c t e d th ro u g h o u t th e e x p e rim e n t. The a n a ly s e s o f v a ria n c e p ro v id e s u p p o rtin g i n t e r p r e t a t i o n s o f th e d a ta to a id in th e e v a l u a t i o n o f th e d i s c r im i n a n t fu n c t i o n . CHAPTER V THE DISCRIMINANT MODEL The model o f d i a g n o s t i c p ro b le m -s o lv in g i s p r e s e n te d i n t h i s c h a p t e r . The f i r s t p a r t d i s c u s s e s th e d i s c r i m in a t o r y problem and th e s t a t i s t i c a l b a s i s o f th e d i s c r im in a n t f u n c t i o n ; th e second p a r t d e s c r i b e s th e model; and th e t h i r d p a r t p r e s e n t s th e e v a l u a t i o n and t e s t s o f the adequacy o f th e m odel. D is c r im in a to r y A n a ly s is In th e d i s c r i m i n a t o r y problem , a sample o f members from each o f two p o p u l a t i o n s i s g iv e n . The v a lu e s o f n number o f v a r i a b l e s f o r each member i s a ls o g iv e n . The problem i s to a s s i g n a new member to th e c o r r e c t p o p u la tio n on th e b a s i s o f th e v a lu e s i t e x h i b i t s on th e n_ v a r i a b l e s . T h is in v o lv e s f i n d i n g an o p tim a l co m bination o f th e g iv e n v a lu e s to b e s t d i f f e r e n t i a t e one p o p u la tio n from th e o t h e r . 1 The d i s c r i m i n a n t f u n c t i o n i s a w eig h ted l i n e a r c o m b in atio n The p r e s e n t stu d y c o n s i d e r s th e d i s c r i m i n a n t f u n c t i o n d e r iv e d from two p o p u l a t i o n s . M u ltip le d i s c r i m i n a t o r y a n a l y s i s g e n e r a l i z e s th e tw o -c a te g o ry a n a l y s i s to a k - c a t e - g o ry a n a l y s i s . 52 53 o f th e n. v a r i a b l e s ., w here th e w e i g h ti n g c o e f f i c i e n t s a r e cho sen to m ax im ally d i s c r i m i n a t e betw een th e two p o p u l a t i o n s . The b a s i s f o r d i f f e r e n t i a t i o n i s a m a x im iz a tio n o f v a r i a n c e betw een g ro u p s and a m in im iz a tio n o f v a r i a n c e w i t h in g r o u p s . As one ty p e o f m u l t i v a r i a t e a n a l y s i s , t h i s m ethod i s r e l a t e d to m u l t i p l e r e g r e s s i o n p r e d i c t i o n m e th o d s. W hile th e l a t t e r g i v e s maximum p r e d i c t a b i l i t y b a se d on m axim izing a c o r r e l a t i o n betw een a c r i t e r i o n and a w e ig h te d sum o f n. p r e d i c t o r v a r i a b le s ., t h e d i s c r i m i n a n t f u n c t i o n i s a l s o a w e ig h te d sum, b u t p r o v i d e s th e b e s t d i f f e r e n t i a t i o n o f a dich o to m o u s c r i t e r i o n v a r i a b l e . I t was s t a t e d t h a t th e two p o p u l a t i o n s were p r e d e te r m in e d in th e d i s c r i m i n a t o r y a n a l y s i s p ro b le m . I f th e two p o p u l a t i o n s were a l r e a d y s e p a r a t e d i n t o A and B, i t w ould seem l o g i c a l to u s e th e o r i g i n a l and unam biguous b a s e s f o r s e p a r a t i n g th e s a m p le s . The d i s c r i m i n a n t f u n c t i o n i s u s e d when t h i s c a n n o t be done; p r e d i c t i o n and d i a g n o s i s a r e two a p p l i c a b l e e x am p le s. W ith p r e d i c t i o n , i t may be p o s s i b l e to d i f f e r e n t i a t e two c o n d i t i o n s w ith o u t e r r o r a f t e r th e y o c c u r , b u t one o f t e n w is h e s to d i s c r i m i n a t e b e f o r e th e y o c c u r . As an ex am p le, one may w ish to s e l e c t from among a p p l i c a n t s f o r a d m is s io n to c o l l e g e , to d i s c r i m i n a t e betw een th o s e who w i l l s u c c e s s f u l l y com p lete c o l l e g e and th o s e who w i l l n o t . A d i s c r i m i n a n t f u n c t i o n (com puted f o r m i n d i v i d u a l s m easured on a l i n e a r f u n c t i o n o f n v a r i a b l e s ^ 54 such a s t e s t r e s u l t s * b i o g r a p h i c a l d a ta * e t c . ) I s u s e d to m axim ally d i s c r i m i n a t e t h e two c a t e g o r i e s and to a s s i g n f u t u r e a p p l i c a n t s i n t o one o f th e two c a t e g o r i e s . In t h e c a s e o f d ia g n o s is * th e p r e s e n c e o f some d i s e a s e may be h id d e n to t h e e x t e n t t h a t o n l y e x tre m e m eas u r e s such a s s u r g e r y o r p o s t-m o rte m a n a l y s i s c o u ld d e t e c t i t s p r e s e n c e . One w ould o f c o u r s e w ish to d ia g n o s e such a c o n d i t i o n i n s u s p e c t e d c a s e s by e x t e r n a l symptoms. The d i s c r i m i n a n t f u n c t i o n c o u ld be a p p l i e d a s d e s c r i b e d f o r p r e d i c t i o n * b u t i n t h i s i n s t a n c e to y i e l d a m a x im a lly r e l i a b le d i a g n o s i s o f t h e . s t a t e o f h e a l t h . D i s c r i m i n a n t f u n c t i o n . The i n t r o d u c t i o n o f th e d i s c r i m i n a n t f u n c t i o n by F i s h e r i n 1336* e x te n d e d t h e u n i v a r i a t e a n a l y s i s o f v a r i a n c e t e c h n i q u e s to t h e c a se o f m ul t i p l e v a r i a t e s . The m ethod i s b a s e d on th e p r o d u c t i o n o f a d i s c r i m i n a n t f u n c tio n * Z* o f th e v a r i a b l e s x^* x 2 • x w here P z = Y . i i x j so t h e r a t i o o f v a r i a n c e s betw een and w i t h i n c l a s s e s i s m axim ized. The c o e f f i c i e n t s * £ y a r e d e r i v e d on th e a s sum ption t h a t two p o p u l a t i o n s A and B a r e m u l t i v a r i a t e n o r mal* w ith common v a r i a n c e . The f u n c t i o n Z i s u s e d t o s e p a r a t e th e two p o p u l a t i o n s * and may be m u l t i p l i e d by an a r b i - 55 t r a r y c o n s t a n t i f a d i s t a n c e m easure betw een p o p u l a t i o n s i s d e s i r e d . I f we c o n s i d e r a space o f p d im en sio n s i n w hich th e sample member i s r e p r e s e n t e d by a p o i n t , th e two p o p u la t i o n s may be th o u g h t o f a s c l u s t e r s o f p o i n t s aro u n d two c e n t r a l v a lu e s . The s o l u t i o n to t h e problem i n v o lv e s f i n d in g t h e l i n e s o f means, o n to which a l l p o i n t s a r e p r o j e c t e d , which m axim izes th e d i f f e r e n c e betw een th e two m eans. T his i s done by m axim izing th e v a r ia n c e betw een th e two means and m in im iz in g th e v a r i a n c e w ith in each p o p u l a t i o n . Rodwan and Hake (1964) p r e s e n t a sc h em atic to i l l u s t r a t e t h i s f o r th e tw o -sp a c e c a s e , where th e u se o f e i t h e r v a r i a b l e alo ne (x^ o r Xg) would n o t d i s c r i m i n a t e betw een p o p u l a t i o n s o r " c o n c e p ts " (Y& and Yfo) as w e ll as u s in g b o th v a r i a b l e s . See F ig u r e 6 . Each v a r i a b l e i s w e ig h te d such t h a t th e d i s c r i m in a n t f u n c t i o n h a s th e p r o p e r t y t h a t i t " w i l l d i s c r i m i n a te b e t t e r th a n any o t h e r l i n e a r f u n c t i o n " betw een th e two p o p u l a t i o n s . The d i s t a n c e betw een m u l t i v a r i a t e means (YaJYb ) i s g iv e n by y a - h - d “ h h + * a d2 ••• + V p where d., = x n„ - x n. 1 l a lb and x-^a e q u a ls th e mean o f p o p u la tio n Y& on th e f i r s t v a r i a b le . 56 P ig . 6 . —D ecisio n Axis f o r 2-Space Case I l l u s t r a t i n g L in e a r D isc rim in a n t F unctio n Concept. (A fte r Rodwan & Hake) 57 The Model D e s c r ip tio n o f th e Model The d i s c r im i n a n t f u n c t i o n , as a model o f d i a g n o s ti c p ro b le m -s o lv in g , i s a q u a n t i t a t i v e sta te m e n t abou t th e r e l a t i v e c o n t r i b u t i o n o f each s tim u lu s v a r i a b l e to S 's r e s p o n s e . The model i s d e riv e d i n a manner s i m i l a r to Rodwan and Hake. I t i s assumed t h a t : 1. S can d i s t i n g u i s h th e stim u lu s s i t u a t i o n along each o f th e n - v a r i a b l e dim ensions 2. S u s e s a l i n e a r com bination o f th e v a r i a b l e s i n s t e a d o f u s in g th e v a r i a b l e s s e p a r a t e l y 3 - The w e ig h ts a s s o c i a t e d w ith the l i n e a r com bi n a tio n o f v a r i a b l e s r e p r e s e n t s S 's a ssig n m en t o f r e l a t i v e im p o rtan ce to th e v a r i a b l e s in making h i s r e s p o n s e . In th e p ro b le m -s o lv in g t a s k , S makes a s e r i e s o f r e s p o n s e s to s p e c i f i c ta s k s tim u lu s s i t u a t i o n s . I f the s i t u a t i o n i s d e s c r ib e d by n _ v a r i a b l e s , th en S c o u ld d i s c r im in a te th e problem in n -d im e n sio n a l sp ace, so th e r e sponse made by S can be d e fin e d a s a p o i n t in m u ltid im e n s i o n a l space d e te rm in e d by th e v a lu e s o f each v a r i a b l e . SsT r e s p o n s e s p la c e a s e t o f a s s o c i a t e d - ^ a r i a b l e s i n t o a s e l e c t e d c a te g o ry and a n o th e r s e t i n t o a n o n s e le c te d c a t e g o ry . The d is c r im i n a n t fu n c tio n I s a s t a t i s t i c which m axi- m izes th e d i s t a n c e between th e s e two c a t e g o r i e s by c o n s id e r - 58 ing th e v a lu e s o f v a r i a b l e s in each c a t e g o r y . I t does t h i s by a p p r o p r i a t e l y w e ig h tin g th e v a r i a b l e s . The w e ig h tin g c o e f f i c i e n t s o f th e d i s c r im i n a n t f u n c tio n i n d i c a t e th e r e l a t i v e c o n t r i b u t i o n o f each s tim u lu s v a r i a b l e . These are computed f o r as many d a ta p o i n t s in th e s o l u t i o n p r o c e s s a s th e e x p e rim e n te r c a r e s to sam ple. In t h i s stu d y , t h e sam p le c o n s i s t e d o f th e f i r s t t h r e e s t e p s f o r each o f f i v e Ss on t h r e e d i f f e r e n t e x p e rim e n ta l c o n d i t i o n s . The c o e f f i c i e n t s a r e i n t e r p r e t e d as th e r e l a t i v e im p o rtan c e a t t r i b u t e d by S to each v a r i a b l e i n making h i s r e s p o n s e . Thus, th e model q u a n t i t a t i v e l y d e s c r i b e s S 's b e h a v io r in term s o f th e s tim u lu s s t r u c t u r e . S tim u lu s D im ensions The d i s c r i m i n a n t f u n c t i o n was d e r iv e d by a l i n e a r co m b in atio n o f s i x v a r i a b l e s to d i f f e r e n t i a t e the s e l e c t e d a l t e r n a t i v e s from th e n o n s e le c te d re s p o n se a l t e r n a t i v e s . The s ix v a r i a b l e d im e n sio n s, d e s c r i b e d in C h ap ter I I I , page 2 5, a r e summarized below: 1. Number. A m easure o f th e number o f su bsy stem s f c o n n ec te d to the c h a n n e l. The t o t a l number o f l ’s i n each —c h a n n e l . 2. E f f i c i e n c y . A m easure o f th e ten d e n cy o f S to m inim ize th e av erag e number o f s t e p s to s o l u t i o n . I t i s the Shannon i n f o r m a t i o n - s t a t i s t i c d e s c r i b i n g the amount o f u n c e r t a i n t y in each c h a n n e l. 59 3- W eig h t. The w e ig h tin g o f su b sy stem c o n n e c ti o n s in th e u p p e r h a l f o f th e c h a n n e l. I t i s th e r a t i o o f sub*- sy stem s c o n n e c tio n s in th e u p p e r h a l f to th e t o t a l number o f su b sy stem s i n th e c h a n n e l. 4. H a l f - s p l i t . A m easure o f th e te n d e n c y to m i n i mize t h e maximum number o f s t e p s to s o l u t i o n by s p l i t t i n g th e number o f su b sy stem s i n t o g ro u p s o f e q u a l s i z e . I t i s m easured by t h e a b s o l u t e d i f f e r e n c e betw een th e p r o p o r t i o n o f su b sy stem c o n n e c ti o n s m inus 0 . 5 . 5. P r o p o r t i o n . T h is i s a m easure o f t h e r e l a t i v e number o f su b sy stem c o n n e c tio n s i n th e u p p e r h a l f o f th e c h a n n e l. I t i s the r a t i o o f th e number o f l ' s i n th e u p p e r h a l f to th e t o t a l number o f l r s in th e c h a n n e l. 6 . A l t e r n a t i o n . T h is i s an i n d i c a t i o n o f th e d e g re e o f c l u s t e r i n g o r g ro u p in g o f su b sy stem s a s t h e y a r e p r i n t e d f o r d i s p l a y . I t i s a r a t i o e x p re s s e d as th e number o f a l t e r n a t i o n s betw een l ' s and 0 's to th e number o f p o s s i b l e a l t e r n a t i o n s ' i n the c h a n n e l. A f t e r eac h r e s p o n s e o f S, th e s t im u lu s m a t r ix was re d u c e d and th e v a r i a b l e v a lu e s recom p uted i n te rm s o f th e r e l a t i o n s e x h i b i t e d by th e re d u c e d s t i m u lu s m a t r i x . The c o m p u ta tio n s o f v a r i a b l e v a lu e s were p e rfo rm e d i n th e c o u rs e o f th e e x p e rim e n t b e c a u se th e d e s c r i p t i o n o f su c c e e d in g s t i m u lu s m a t r i c e s was d e p en d e n t on th e S ' s c h o ic e o f a l t e r n a t i v e s in th e p r e v i o u s r e s p o n s e . The r e s u l t i n g v a lu e s were s t a n d a r d i z e d f o r each v a r i a b l e . Each v a lu e was d i - 60 v id ed by th e maximum value on th e r e s p e c t i v e v a r i a b l e d i mensions to tra n sfo rm the o b ta in e d v a lu e s to a s c a le o f p r o p o r t io n a l v a lu e s . E v a lu a tin g th e Model T reatm ent o f the Data The d ata were a n aly zed s e p a r a t e l y f o r each combina t i o n o f s u b j e c t , S a t e l l i t e , and ste p sequence p o s i t i o n . A t o t a l o f 45 s e p a r a te d is c r im in a n t f u n c tio n s were computed. Each a n a l y s i s c o n s is te d o f 48-60 p ro b le m -so lv in g t r i a l s f o r S a t e l l i t e s 1 and 2, and 30 f o r S a t e l l i t e 3 . The d is c r im in a to r y a n a l y s i s was perform ed on a l a r g e , h ig h -sp e e d d i g i t a l com puter.^ Each a n a l y s i s r e p r e s e n te d a c r o s s - s e c t i o n o f an i n d iv id u a l S 's p ro b le m -so lv in g b e h a v io r, i . e ., p ro b le m -s o lv ing on one S a t e l l i t e , a t one s t e p , b ased on a sample o f 48 to 60 t r i a l s . I n t e r p r e t a t i o n s o f b e h a v io r a l p ro c e s s were made by e v a lu a tin g d is c r im in a n t f u n c tio n s a c r o s s s te p s ; o f r e l i a b i l i t y , by comparing d is c r im in a n t f u n c tio n s a c ro s s s i m i l a r S a t e l l i t e s ; and o f v a l i d i t y , by p r e d i c t i o n o f b e h a v io r w ith o b ta in e d d is c r im in a n t f u n c tio n s . The computed d is c r im in a n t f u n c tio n s in Appendix V show the o b ta in e d c o e f f i c i e n t s a s s o c i a t e d w ith v a r i a b l e . 2 A n a ly sis was perform ed a t the W estern Data P r o c e s s ing C e n te r, U n iv e rs ity o f C a l i f o r n i a , Los A ngeles, on an IBM 3 6 0 . The program was a s t e p - b y - s t e p d is c r im in a n t a n a l y s i s p ro c e d u re , d e s c rib e d i n Dixon, op. c i t ., pp. 2 l4 a - 2 l4 e . 6 l These w i l l be e v a l u a t e d in th e s e r i e s o f t e s t s d e s c r i b e d l a t e r i n t h i s c h a p t e r . D e s c r i p t i v e s t a t i s t i c s f o r each v a r i a b l e a r e i n c l u d e d i n Appendix VI., w hich t a b u l a t e s th e means and s t a n d a r d d e v i a t i o n s . T e s tin g th e Agreement betw een S u b j e c t s The d i s c r i m i n a n t f u n c t i o n i s p ro p o s e d as a model f o r i n d i v i d u a l S s. I t i s a ls o o f i n t e r e s t , h ow ever, to know w h e th e r d i f f e r e n t Ss u se th e same a p p ro a c h . I f Ss do u se s i m i l a r a p p ro a c h e s , i . e . , i f th e y te n d to p l a c e p r o p o r t i o n a t e w e ig h t on th e same v a r i a b l e s , th e n a h ig h c o r r e l a t i o n s h o u ld e x i s t betw een the s e t s o f c o e f f i c i e n t s . The c o e f f i c i e n t d im en sion was f i r s t s t a n d a r d i z e d by m u l t i p l y i n g eac h one by th e s t a n d a r d d e v i a t i o n o f t h e i r r e s p e c t i v e v a r i a b l e s . A c o r r e l a t i o n u s i n g K e n d a l l 's W s t a t i s t i c , th e c o e f f i c i e n t o f c o n c o rd a n c e , was p e rfo rm e d on th e r a n k - o r d e r e d s e t s o f d i s c r i m i n a n t w e i g h ts . Appendix V II p r e s e n t s th e r a n k - o r d e r i n g f o r a l l Ss. The c o r r e l a t i o n was p e rfo rm e d f o r th e t h r e e s t e p s on SAT1 and SAT2. The r e s u l t s a re sum m arized i n T ab le 7* The t a b l e shows t h a t W (k = 5* N = 6 ), i s s i g n i f i c a n t f o r a l l c a s e s e x c e p t o ne. T h is f i n d i n g i n d i c a t e s t h a t th e r e l a t i v e co n t r i b u t i o n o f th e v a r i a b l e s d id n o t change among S s. I t a p p e a r s t h a t p ro b lem s in b o th S a t e l l i t e s and a t a l l s t e p s w ere s o lv e d I n a s i m i l a r way by a l l Ss. 62 TABLE 7 AGREEMENT OP DISCRIMINANT FUNCTIONS OVER SUBJECTS KENDALL W S te p Number S a t e l l i t e 1 2 3 ¥ .90 .56 .56 SAT1 Sum. Sq. 393-5 243.5 243.5 S i g n i f . .01 .01 .01 W • 59 • 35 .60 SAT2 Sum. Sq. 257.5 153.5 2 6 1 .5 S i g n i f . .01 - .01 k = 5 s u b j e c t s N = 6 c o e f f i c i e n t s S i g n i f i c a n c e L ev el: P < .05 , 182.4 P < .01 , 229.4 63 T e s tin g th e Agreement betw een S teps T his t e s t was perform ed to d e term in e th e r e l a t i o n ship between ste p and r e l a t i v e w e ig h tin g o f th e d is c r im i n a n t c o e f f i c i e n t s . The a n a l y s i s o f v a ria n c e had a lr e a d y p o in te d to a d e c re a s e in e f f i c i e n c y from one s te p to a n o th e r . A low and s i g n i f i c a n t c o r r e l a t i o n would be e x p e c te d between s e t s o f c o e f f i c i e n t s d e riv e d from d i f f e r e n t s te p s i f th e e f f i c i e n c y r e s u l t can be i n t e r p r e t e d as an i n d i c a t o r o f changed b e h a v io r . The s ta n d a r d iz e d c o e f f i c i e n t s f o r SAT1 and SAT2 were r a n k - o r d e r e d and th e K endall s t a t i s t i c was a p p lie d . T able 8 shows o n ly th r e e s i g n i f i c a n t c o r r e l a t i o n s (k = 3, N = 6 ). The la c k o f g e n e r a l c o r r e l a t i o n i n d i c a t e s t h a t th e ra n k o rd e r in g o f th e c o e f f i c i e n t s ( i . e . , r e l a t i v e c o n t r i b u t i o n o f the v a r i a b l e s ) changed a c r o s s s t e p s . This i s i n t e r p r e t e d u n d e r th e d is c r im i n a n t model as a change in S 's a p p ro a c h --a change i n th e r e l a t i v e im po rtan ce t h a t S a t t r i b u t e d to th e v a r i a b l e s — a t d i f f e r e n t s ta g e s o f p ro b le m -s o lv in g . The a n a l y s i s o f v a ria n c e had su g g e ste d t h a t agreem ent should n o t be e x p e c te d o v e r s t e p s . T his was con firm ed . The c o e f f i c i e n t s a s s o c i a t e d w ith e f f i c i e n c y , how e v e r, do n o t e x h i b i t th e same sy s te m a tic d e c r e a s e . I n s t e a d , t h e i r m agnitude i s low and p o s i t i v e w ith no tr e n d t h a t could be r e l a t e d to s te p . This, i s i n t e r p r e t e d sim ply and d i r e c t l y : th e e f f i c i e n c y v a r i a b l e c o n t r i b u t e s l i t t l e to S s 1 re s p o n s e s r e l a t i v e to the s e t o f v a r i a b l e s . 64 TABLE 8 AGREEMENT OF DISCRIMINANT FUNCTIONS OVER STEPS KENDALL W S u b je c ts S a t e l l i t e 1 2 3 4 5 W .58 .56 ,4o .80 .48 SAT1 Sum. Sq. 9 1 .5 8 7 .5 6 3 .5 125.5 7 5 .5 S ig n if. - - - .01 - W .57 .81 • 83 .3^' .42 SAT2 Sum. Sq. 89-5 127.5 131.5 53-5 6 5 .5 S i g n i f . - .01 .01 - - k = 3 s te p s N =~ 6 ' c o e f f i c i e n t s S i g n i f i c a n c e l e v e l : P <.05 , 103-9 P <.01 , 122.8 65 T e s tin g th e D e riv e d D is c r i m i n a n t F u n c tio n The p u rp o se o f t h i s t e s t was to d e te rm in e how w e l l th e d i s c r i m i n a n t f u n c t i o n f i t t e d th e d a ta from w hich i t was d e r i v e d . The t e s t in v o lv e d a t r i a l - h y - t r i a l co m parison o f th e r e s p o n s e s p r e d i c t e d by th e d i s c r i m i n a n t f u n c t i o n w ith th e S s ' a c t u a l r e s p o n s e s . A d i s c r i m i n a n t f u n c t i o n , com p u te d f o r e ac h r e s p o n s e a l t e r n a t i v e on each t r i a l , was a v a i l a b l e a s o u tp u t o f th e d i s c r i m i n a n t a n a l y s i s program . The e i g h t a l t e r n a t i v e s in eac h t r i a l were r a n k - o r d e r e d by m agn itu de o f t h e i r d i s c r i m i n a n t f u n c t i o n , form ing th e o r d e r o f th e m o d e l's p r e d i c t i o n s : th e a l t e r n a t i v e h a v in g th e h i g h e s t v a lu e i s th e f i r s t c h o ic e o f th e m odel. S 's a c t u a l c h o ic e was th e n l o c a t e d on th e m o d e l's p r e d i c t i o n o r d e r . The t e s t was p e rfo rm e d f o r a l l t h r e e S a t e l l i t e s , and a f r e quency d i s t r i b u t i o n o f S s' c h o ic e s on th e model c h o ic e o r d e r was form ed. I f th e model were p e r f e c t , a l l o f S s' c h o ic e s would m atch t h e m o d e l's f i r s t c h o ic e . I f random, a u n ifo rm d i s t r i b u t i o n o f S s ' c h o ic e s o v e r the e i g h t r a n k s o f th e m o d e l's p r e d i c t i o n s would be e x p e c te d . The r e s u l t s a r e shown in T able 9j where th e d a ta a re sum m arized by p o o lin g S a t e l l i t e s , s u b j e c t s , and s t e p s . The t a b l e shows t h a t 49 p e r c e n t o f S s' c h o ic e s m atched th e m o d e l's f i r s t c h o ic e , and 74 p e r c e n t o f t h e i r c h o ic e s w ere i n c l u d e d in th e f i r s t two c h o ic e s o f th e m odel. The t o t a l number o f c o m p a riso n s was 2 0 0 3 . I t was c o n c lu d e d t h a t th e TABLE 9 AGREEMENT OE S s' RESPONSES WITH DERIVED DISCRIMINANT FUNCTION PREDICTIONS Model Frequency Choice o f S s 1 Cum. Cum. Order R esponses Freq. P ercent 1 977 977 49 2 506 1483 74 3 245 1728 86 4 l 4 l 1869 93 5 64 1933 96 6 41 1974 99 7 25 1999 99 8 4 2003 100 2003 67 model d e s c r ib e d th e d a ta adequ ately* s i g n i f i c a n t l y above chance. The r e s u l t s showing th e d i s t r i b u t i o n s e p a r a t e l y by s u b j e c t s and s te p p o s i t i o n a re in Appendix V I I I . T e s ts to V a lid a te th e D is c r im in a n t F u n ctio n The purpose o f t h i s t e s t was to p r e d i c t th e r e sp onses o f Ss from one problem , u s in g th e d is c r im i n a n t f u n c tio n d e riv e d from th e d a ta o f a n o th e r problem . The c o e f f i c i e n t s d e riv e d from SAT1 and SAT2 were a p p lie d to th e d a ta o f SAT3. The mean o f th e s t a n d a r d iz e d c o e f f i c i e n t s from SAT1 and SAT2 were u se d , and a new d i s c r im in a n t f u n c tio n was computed f o r each re sp o n se a l t e r n a t i v e f o r each t r i a l . S s 1 a c t u a l s e l e c t i o n s on SAT3 were compared w ith the o r d e r o f p r e d i c t i o n s by th e m odel. The r e s u l t s a re shown i n T able 10. The number o f S s 1 c h o ic e s on SAT3, p r e d i c t e d by th e model d e riv e d from SAT1 and SAT2, i n c l u d e s 51 p e r c e n t and 73 p e r c e n t on th e f i r s t two c h o ic e s o f the model. T h is p r e d i c t i o n i s a s good as th e p re v io u s t e s t , ap p ly in g the model back to d e s c r ib e i t s own d a ta . To d e te rm in e i f t h i s a s s ig n e d model p r e d i c t s a s w e ll as one d e riv e d from th e SAT3 d a ta , th e freq u e n cy d i s t r i b u t i o n f o r th e SAT3 model i s shown f o r com parison on th e r i g h t h a l f o f T able 10. T his p r e d i c t i o n i s b e t t e r , in c lu d in g 66 p e r c e n t and 81 p e r c e n t o f S s 1 c h o ic e s w ith i t s f i r s t two p r e d i c t i o n s . TABLE 1 0 AGEEEMEPJT OF Ss' RESPONSES WITH DISCRIMINANT FUNCTION PREDICTIONS ON SAT3 DATA Model Choice Order Prediction on SAT3 by Assigning SAT1-2 Discriminant Function Prediction on SAT3 Using SAT3 Derived Discriminant Function Frequency of Ss ’ Responses Cumulative Frequency Cumulative Percent Frequency of Ss’ Responses Cumulative Frequency Cumulative Percent 1 2l4 214 51 280 280 66 2 103 217 72 62 2^2 81 5 42 259 85 29 272 88 i f 38 297 95 22 394 92 5 12 410 97' 22 4l6 98 6 11 421 100 6 422 100 7 2 423 100 1 423 100 8 0 423 100 0 423 100 423 423 O N 00 The above com parisons were p o o led f o r s u b j e c t s and s t e p s . F ig u re 7 compares th e p r e d ic t io n s o f th e two m odels s e p a r a t e ly fo r th r e e p r o b le m -so lv in g s t e p s . The c u r v es i l l u s t r a t e th e co rresp on d en ce between the SAT3 model and the SAT1 - SAT2 model a s s ig n e d to SAT3 d a ta . Rao (1952, pp. 248-249) g i v e s a s t a t i s t i c a l t e s t o f s i g n i f i c a n c e between two d is c r im in a n t f u n c t io n s ; however,, the t e s t e v a lu a t e s the d is c r im in a n t s at t h e i r means, whereas t h i s stu dy is- i n t e r e s t e d in v e r i f y i n g the a b i l i t y o f t h e . d is c r im in a n t fu n c tio n to accou n t fo r a c t u a l b e h a v io r o f S s. The t e s t performed here v a l i d a t e s th e model on a new s e t o f d a ta . T his a g r e e ment s u g g e s t s th a t the model i s not s p e c i f i c to a p a r t i c u la r s i t u a t i o n , b u t can be u sed to p r e d i c t over d i f f e r e n t p ro b lem s. N U M B E R O F S s' R E S P O N S E S N U M B E R O F Ss1 RESPON SES 70 S T E P I 120 100 80 60 40 20 \ \ \ M I “ \ t % * - 1 2 3 4 5 6 M ODEL CHOICE O R D E R S T E P 3 120 < /> u . a £ UJ m 2 3 4 5 0 6 M O D EL CHOICE O R D E R S T E P 2 100 80 60 40 20 0 LEGEND: ASSIGNED D.F. {S A T 1 & 2) D E R IV E D D.F. (SA T 3) 2 3 4 5 6 7 M O D EL CHOICE O R D ER F ig . 7 . — Comparison o f P r e d i c t i o n A b i l i t y on SAT3 D ata betw een a SAT3 D is c r im in a n t F u n c tio n and an A ssigned (SAT1-SAT2) D is c r im in a n t F u n c tio n . CHAPTER VI DISCUSSION AND SUMMARY An e x p e rim e n t was d e s ig n e d and c o n d u c te d to o b t a i n d a ta on a d i a g n o s t i c p r o b le m - s o lv in g t a s k . The d a ta were a n a ly z e d i n two ways: f i r s t , , group a n a l y s e s w ere p e rfo rm ed to d e te rm in e th e e f f e c t s o f e x p e r im e n ta l c o n d i t i o n s on e f f i c i e n c y o f p e rfo rm a n c e . Second., th e model o f p ro b le m s o lv in g was t e s t e d f o r c o n s i s t e n c y and was v a l i d a t e d on e x p e r i m e n t a l d a t a . The c o n c l u s i o n s a r e p r e s e n t e d i n t h i s c h a p t e r , fo llo w e d by a d i s c u s s i o n o f i m p l i c a t i o n s , and th e summary o f th e s tu d y . C o n c lu s io n s 1. E f f i c i e n c y d e c r e a s e d a s a f u n c t i o n o f i n c r e a s i n g skew ness o f th e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n . S in ce th e Shannon m easure i s a s ta te m e n t o f th e number o f e q u a l ly l i k e l y b i n a r y s t e p s o r d e c i s i o n s w hich must be made to i s o l a t e th e c o r r e c t su b sy stem , th e r e s u l t i n d i c a t e s t h a t th e a v e ra g e number o f s t e p s was m in im ized when th e d i s t r i b u t i o n was u n ifo rm . But th e a v e ra g e number o f s t e p s i n c r e a s e d a s th e d i s t r i b u t i o n became skewed. T h e r e f o r e , Ss were becom in g l e s s e f f i c i e n t by n o t making t h e i r r e s p o n s e s on th e 71 72 b a s i s o f an optimum s p l i t o f t h e p r o b a b i l i t y d i s t r i b u t i o n . 2. E f f i c i e n c y d e c r e a s e d a s a f u n c t i o n o f s u c c e s s i v e s t e p s to s o l u t i o n . T h is f i n d i n g was n o t e d i n th e t w e n t y - q u e s t i o n s e x p e rim e n t (B e n d ig , 1953)* i n w h ich e a r l i e r q u e s t i o n s w ere e f f i c i e n t b u t l a t e r o n e s w ere n o t . S i m i l a r c o n c l u s i o n s w ere drawn from Jo h n so n (a b o v e , page 14) and K le in m u n tz (ab o v e , page 13) . These r e s u l t s i n d i c a t e t h e p r o b l e m - s o l v in g p r o c e s s to be c h a r a c t e r i z e d by a r e s p o n s e , s u c c e s s i v e l y more s p e c i f i c , to p r o p e r t i e s o f th e s t i m u l u s s e t r a t h e r th a n a r e s p o n s e to e f f i c i e n c y . The o b t a i n e d s y s t e m a t i c d e c r e a s e i n e f f i c i e n c y i s e n t i r e l y c o n s i s t e n t w i t h t h e s e f i n d i n g s . 3. The p e rfo rm a n c e o f Ss i n t h i s e x p e r im e n t was r e l i a b l e and s t a b l e . The l a c k o f s i g n i f i c a n c e on c o n f i g u r a t i o n s and r e p l i c a t i o n s i n t h e a n a l y s i s o f v a r i a n c e s u g g e s t s t h a t th e d i f f e r e n t p r e s e n t a t i o n s r e p r e s e n t e s s e n t i a l l y ^homogeneous t a s k c o n d i t i o n s . The l a c k o f s i g n i f i - . c an c e i n th e b l o c k e f f e c t means t h a t p e rfo rm a n c e was s t a b l e th r o u g h o u t th e e x p e r im e n t. The r e s u l t s on t h e s e c o n d i t i o n s a r e i m p o r t a n t f o r th e i n t e r p r e t a t i o n o f th e m odel, a s i t i s b a s e d on d a t a o b t a i n e d th ro u g h th e e n t i r e e x p e r im e n t. In summary, th e g ro u p a n a l y s e s p r o v i d e d a d e s c r i p t i o n o f th e d a t a i n r e l a t i o n to th e e x p e r i m e n t a l c o n d i t i o n s and i n r e l a t i o n to o t h e r p r o b le m - s o lv in g s t u d i e s . The i n t e r p r e t a t i o n o f th e m odel can be made u n d e r t h i s d e s c r i p t i v e b a s e l i n e . 73 4. The a b i l i t y o f th e d is c r im i n a n t f u n c tio n to d i s c r im i n a t e th e d a ta from which I t was d e riv e d was e x p e r i m e n ta lly v e r i f i e d . The S s ' c h o ic e s were matched w ith the o r d e r o f p r e d i c t i o n o f th e m o d e l's c h o ic e s , s t e p - b y - s t e p f o r o v e r 2000 s t e p s f o r a l l Ss. Of th e s e , th e m o d e l's f i r s t c h o ice c o r r e c t l y p r e d i c t e d h a l f o f th e Ss' a c t u a l c h o ic e s ; th e f i r s t two c h o ic e s o f th e model a cc o u n ted f o r t h r e e - f o u r t h s o f S s ' c h o ic e s . W ith e i g h t a l t e r n a t i v e s from which to choose, t h i s fre q u e n c y i s w e ll above chance. The agreem ent betw een S s ' c h o ic e b e h a v io r and th e m o d e l's p r e d i c t i o n o f S s' c h o ic e behavior- i n d i c a t e s t h a t th e model can in d ee d s e p a r a te th e a l t e r n a t i v e s i n t o two groups i n a c c o rd ance w ith the S s ' a c t u a l c l a s s i f i c a t i o n . 5. The a b i l i t y o f th e d i s c r im i n a n t f u n c tio n to p r e d i c t S s 1 c h o ic e b e h a v io r on a new s e t o f d a ta was e x p e r im e n t a l ly v e r i f i e d . F i r s t , i t was shown t h a t th e SAT3 d i s c r im in a n t f u n c tio n p r e d i c t e d S s' c h o ic e b e h a v io r . T his r e s u l t was th en compared to th e r e s u l t o f th e t e s t a s s ig n in g th e SAT1 - SAT2 d is c r im i n a n t f u n c tio n to p r e d i c t S s 1 c h o ic e s on SAT3. T his t e s t showed t h a t th e a s s ig n e d d i s c r im in a n t fu n c tio n r e l i a b l y p r e d i c t e d S s' c h o ice b e h a v io r on SAT3. H a lf o f S s' c h o ic e s a g re e d w ith th e m o d e l's f i r s t c h o ic e s , and a lm o st t h r e e - f o u r t h s o f S s' c h o ic e s were i n clu d e d i n the m o d e l's f i r s t two p r e d i c t i o n s . In comparing th e s e r e s u l t s , th e d a ta o b ta in e d from Ss f o r SAT3 f i t the a s s ig n e d SAT1 - SAT2 model, b u t th e d i f f e r e n c e was n o t g r e a t . The m odels converge by th e t h i r d p r e d i c ti o n ., a c c o u n tin g f o r 85 p e r c e n t v e rs u s 88 p e r c e n t o f S s ' c h o ic e s . I t i s im p o r ta n t to c o n s id e r th e r e s u l t s h e re i n r e l a t i o n to th e e a r l i e r t e s t , which v e r i f i e d the a b i l i t y o f th e model to p r e d i c t S s' b e h a v io r on i t s own s e t o f d a t a . The p r e d i c t i v e a b i l i t y o f the a s s ig n e d model on SAT3 i s i d e n t i c a l to th e d e s c r i p t i v e a b i l i t y of th e m odels p o o le d o v e r a l l c o n d i t i o n s : 49 p e r c e n t v e rs u s 5 1 p e r c e n t on th e f i r s t p r e d i c t i o n , and 74 v e rs u s 7 3 p e r c e n t on t h e f i r s t two p r e d i c t i o n s . Prom a c o n s i d e r a t i o n o f th e s e f r e q u e n c i e s i t a p p e a r s t h a t a d i s c r i m i n a n t f u n c tio n p r e d i c t s S s ' b e h a v io r on new d a t a as w e l l as a d i s c r im in a n t f u n c t i o n d e s c r i b e s i t s own d a t a . 6 . There were no d i f f e r e n c e s i n the p r o b le m - s o lv in g b e h a v io r among s u b j e c t s . Models o f i n d i v i d u a l Ss were in ag re em e n t a t e a c h s t e p o f each p roblem . The s i g n i f i c a n t c o r r e l a t i o n s i n d i c a t e t h a t each v a r i a b l e has been g iv e n p r o p o r t i o n a l w e ig h ts by th e s e v e r a l Ss. Thus, i t can be con c lu d e d t h a t Ss work by s i m i l a r a p p ro a c h e s in term s o f com b in in g t h e v a r i a b l e s i n s i m i l a r ways f o r making t h e i r c h o i c e s . 7• I n d i v i d u a l Ss change t h e i r a p p ro a c h on su c c e e d in g s te p s o f th e s o l u t i o n s e q u e n c e . T here was g e n e r a l l y no agreem ent in th e S s r m odels d e riv e d f o r d i f f e r e n t s t e p s f o r ea c h p ro b lem . T h is c o n c lu sio n i s s u p p o rte d by r e s u l t s from th e a n a l y s i s o f v a r ia n c e and by th e s t u d i e s r e p o r t e d in 75 C h a p te r I I . Combining th e I n t e r p r e t a t i o n o f t h i s r e s u l t w i t h the a g re em e n t o b ta in e d o v e r s u b je c ts ., abo v e, i t seems t h a t n ot o n ly do Ss change a t each s t e p , b u t th ey change In t h e same w ay . I n summary* th e u s e o f th e d i s c r i m i n a n t f u n c t i o n a s a model f o r d e s c r i b i n g human p ro b le m - s o lv in g was e x p e r i m e n ta lly v e r i f i e d . The model a d e q u a te ly d i s c r i m i n a t e d th e d a t a from which I t was d e riv e d * and t h e model a d e q u a te ly p r e d i c t e d c h o ic e b e h a v io r on a new t a s k . The c o n s ta n c y o f t h e d i s c r i m i n a n t f u n c t i o n s was e v a l u a t e d o v e r s u b j e c t s and s t e p s by t e s t i n g th e i n v a r i a n c e o f t h e w e ig h tin g c o e f f i c i e n t s . C o r r e l a t i o n a l r e s u l t s were s u b s t a n t i a t e d by b e h a v i o r a l i n t e r p r e t a t i o n s . D is c u s s io n L i m i t a t i o n s Two l i m i t a t i o n s i n th e u se o f th e d i s c r i m i n a n t model a r e i d e n t i f i e d . One* in e v a l u a t i n g p ro b le m - s o lv in g a s a s e q u e n t i a l p ro c e ss * th e d i s c r i m i n a n t f u n c t i o n i s a s e r i e s o f c r o s s - s e c t i o n a l sam ples o f th e p r o c e s s . I t p r o v i d e s d e s c r i p t i v e m easurem ents a t a s e l e c t e d number o f p o i n t s . W hile i t i s p o s s i b l e to sam ple a r e p r e s e n t a t i v e number o f p o i n t s i n a b e h a v i o r a l sequence* f o r s u f f i c i e n t l y l a r g e N i t may be i m p r a c t i c a l . T h is l i m i t s i t s a p p l i c a b i l i t y when b e h a v i o r in v o lv e s long c h a i n s o f r e s p o n s e s . The second l i m i t a t i o n in v o lv e s the c l a s s i f i c a t i o n o f a l t e r n a t i v e s i n t o two g ro u p s. The d i s c r im i n a t io n t a s k o r d i n a r i l y in v o lv e s th e assignm ent o f a stim u lu s o b j e c t to one c a te g o ry (say., A) o r a n o th e r (sa y , B) . In t h i s stu d y , th e ta s k was d i f f e r e n t . A s e t o f e ig h t a l t e r n a t i v e s was p r e s e n te d as th e stim u lu s o b j e c t ; one a l t e r n a t i v e was s e l e c t e d f o r C ategory A, and th e rem ainder were a u to m a tic a lly p la c e d i n C ategory B. T h is p ro ced u re r a i s e s the q u e s tio n con cern in g the b a s i s f o r s e l e c t i o n o f an a l t e r n a t i v e . F i r s t s i t i s p o s s i b l e t h a t more than one a l t e r n a t i v e could be c l a s s i f i e d in C ategory A. For example, S may be s e l e c t ing between s e v e r a l a l t e r n a t i v e s , a l l o f which he would p la c e in C ategory A, r a t h e r than s e p a r a tin g th e a l t e r n a t i v e s i n t o A o r B. T his s i t u a t i o n would e x i s t i f two a l t e r n a t i v e s were i d e n t i c a l , o r a ppeared e q u a lly a c c e p ta b le to S. Sec ond, the p ro ce d u re le a v e s th e i n t e r p r e t a t i o n o f C ategory B ambiguous. While S made an o v e r t resp o n se to s e l e c t an a l t e r n a t i v e f o r C ategory A, th e c a se s in C ategory B were c l a s s i f i e d by d e f a u l t . I m p lic a tio n s The d is c r im in a n t model o f p ro b le m -so lv in g was e x p e r im e n ta lly v e r i f i e d . Some im p l i c a ti o n s , b a se d on th e a s sum ptions o f the model, can be c o n sid e re d . F i r s t , i t was assumed t h a t S could d i s c r im i n a t e along th e stim u lu s d i mensions e x i s t i n g in the stim u lu s s e t . By p ro v id in g a s u i t a b l e s e t o f s tim u lu s v a r i a b l e s , an i n v e s t i g a t o r can o b t a i n d i r e c t e s t i m a t e s o f th e q u a n t i t a t i v e c o n t r i b u t i o n o f f a c t o r s e n t e r i n g i n t o th e o b ta in e d r e s p o n s e . I n f e r e n c e s a b o u t th e c o g n i t i v e p r o c e s s e s i n f l u e n c i n g an o b t a i n e d r e sponse w i l l be b a se d upon th e s e t o f v a r i a b l e s u s e d , o r n o t u s e d , i n th e d i s c r i m i n a t i o n . T h is i n f e r e n c e can be made w ith o u t an i n t e r v e n i n g , s u b j e c t i v e i n t e r p r e t a t i o n o f th e S Ts s t r u c t u r i n g o f th e en v iro n m en t. S in c e th e a c t u a l cog n i t i o n s o f an i n d i v i d u a l a re n o t a c c e s s i b l e o r o b j e c t i v e l y v e r i f i a b l e , i t would be w e ll to have some sim p le , q u a n t i t a t i v e d e s c r i p t i o n o f b e h a v io r t h a t i s t i e d to o b s e r v a b l e s . I t I s b e li e v e d t h a t th e d i s c r i m i n a n t f u n c t i o n p r o v id e s such a d e s c r i p t i v e m odel. Second, i t was assumed t h a t an i n d i v i d u a l u se d a l i n e a r c o m b in atio n o f v a r i a b l e s i n s t e a d o f u s in g o n ly one s tim u lu s v a r i a b l e in making h i s r e s p o n s e . The d e r iv e d d i s c r im in a n t f u n c t i o n c o n s i s t s o f th o se v a r i a b l e s w hich s i g n i f i c a n t l y c o n t r i b u t e to th e d i s c r i m i n a t i o n ; v a r i a b l e s which do n o t c o n t r i b u t e s i g n i f i c a n t v a r ia n c e a r e s t a t i s t i c a l l y e l i m i n a t e d . The n e g a tiv e I n fo r m a tio n i s I m p o rta n t; i t i n d i c a t e s what th e s u b j e c t t h in k s i s n o t im p o r ta n t, b u t th e o b s e rv e d b e h a v io r i s e v e n t u a l l y i n t e r p r e t e d i n term s o f th e s e t o f re m a in in g v a r i a b l e s . The b a s i c q u e s tio n I s w h e th e r o r n o t a s u f f i c i e n t s e t o f v a r i a b l e s was in c lu d e d in th e f i r s t p l a c e ; w h e th e r an im p o r ta n t v a r i a b l e was o m it t e d . The r i s k in i n c lu d in g a d d i t i o n a l v a r i a b l e s i s n o t a 78 s e r i o u s p r o b le m - - p e r h a p s o n ly a p r a c t i c a l one i n te rm s o f h a n d li n g more d a t a i n t h e m e c h a n ic s o f e x p e r i m e n t a t io n and ,d a ta t r e a t m e n t — s i n c e an y v a r i a b l e s w hich do n o t c o n t r i b u t e to t h e d i s c r i m i n a t i o n w i l l be e x c lu d e d . I t i s i m p o r t a n t , h o w ev er, to have enough v a r i a b l e s ; to have s u f f i c i e n t i n f o r m a tio n f o r making a d i s c r i m i n a t i o n , b u t t h i s p o i n t i s one t h a t i s n o t l i m i t e d to d i s c r i m i n a t o r y a n a l y s i s . I t i s one w hich m u s t 'b e c o n s i d e r e d i n d e s i g n in g any e x p e r im e n t. In a d d it io n , th e method o f d is c r im in a t o r y a n a l y s i s i s n ot l i m i t e d to the assum ption o f l i n e a r i t y , which i s made in common u s a g e . A d i s t r i b u t i o n - f r e e method o f com p u tin g th e d is c r im in a n t f u n c t io n was d e s c r ib e d (K en d all, 1 9 6 6 ) which makes th e d is c r im in a t io n a t each s t e p in s t e a d o f c o n s id e r in g a l i n e a r com b ination o f the v a r i a b l e s .. T his method e v a lu a t e s th e s e t o f v a r i a b l e s in terms o f t h e i r o r der o f c o n s id e r a t io n and the r e l a t i v e number o f c a s e s d i s c r im in a te d . I t produced r e s u l t s v e r y s im ila r to th e l i n e a r com bination method. T h ir d , i t was assum ed t h a t th e c o e f f i c i e n t s a s s o c i a t e d w i t h e a c h v a r i a b l e r e p r e s e n t e d an i n d i v i d u a l ' s a s s i g n ment o f im p o rta n c e to e a c h v a r i a b l e . T h is i s th e i m p o r t a n t p o i n t i n i n t e r p r e t i n g th e m odel. I f i t i s v a l i d , th e n s i m i l a r i t i e s and c o n s i s t e n c i e s o f t h e b e h a v i o r a l p r o c e s s can be known by c o n s i d e r i n g th e p r o p o r t i o n a t e m ag n itu d e o f each c o e f f i c i e n t i n com paring b e h a v i o r u n d e r d i f f e r e n t t a s k s i t u a t i o n s . V a r i a t i o n s and c o n s i s t e n c i e s o f b e h a v i o r o v e r 79 th e c o n d i t i o n s o f th e e x p e r im e n t co/uld he r e l a t e d to t h e p r o p o r t i o n a t e c o n t r i b u t i o n o f th e v a r i a b l e s i n th e d i s c r i m i n a n t f u n c t i o n m odel. In th e p r e s e n t study., Ss u s e d a c o m b in a tio n o f v a r i a b l e s i n t h e i r r e s p o n s e s , b u t one v a r i a b l e was c o n s i s t e n t l y more i m p o r t a n t th a n any o t h e r . T h is v a r i a b l e was th e h a l f - s p l i t , w hich r e p r e s e n t s th e te n d e n c y to m in im iz e th e m a x i mum number o f s t e p s to s o l u t i o n ( v a r i a b l e 4 ) . T h is t e n d ency was e v id e n c e d by c h o i c e s t h a t s p l i t t h e number o f s u b sy ste m s i n t o e q u a l s i z e g r o u p s . The c o e f f i c i e n t f o r t h i s v a r i a b l e was c o n s i s t e n t l y h i g h e s t i n ra n k and i t s m a g n itu d e was d i s p r o p o r t i o n a t e l y l a r g e r th a n .a n y o t h e r . I t d i d n o t c h a n g e * it s o r d e r o v e r S a t e l l i t e s , s u b j e c t s , o r s t e p s . A p o s t - t e s t q u e s t i o n n a i r e s u p p o r te d t h i s c o n c lu s io n t h a t S s ' a t t e n d p r i m a r i l y to th e h a l f - s p l i t v a r i a b l e . E f f i c i e n c y , on th e o t h e r h a n d , c o n t r i b u t e d r e l a t i v e l y l i t t l e to th e d i s c r i m i n a t i o n . The f a i l u r e to use th e e f f i c i e n c y v a r i a b l e i s c o n s i s t e n t w i t h c o n c l u s i o n s from th e g ro u p a n a l y s e s . A s t r u c t u r e v a r i a b l e , th e t o t a l number o f c o n n e c ti o n s , was p o s i t i v e l y r e l a t e d to t h e c h o ic e , c o n t r i b u t i n g m o d e r a te ly on th e f i r s t s t e p and s l i g h t l y on th e n e x t two s t e p s . One p l a u s i b l e i n t e r p r e t a t i o n o f t h i s r e l a t i o n s h i p i s t h a t th e Ss, i n t h i s t a s k to l o c a t e a m a l f u n c t i o n , te n d to s e e k c o n f ir m in g i n f o r m a t i o n , i . e . , th e more c o n n e c ti o n s t h e r e a r e i n a c h a n n e l, th e more l i k e l y i t i s to r e c e i v e i n f o r m a t i o n t h a t a m a l f u n c t i o n e x i s t s in t h a t c h a n n e l. I t would a l s o i n d i c a t e t h a t S i s p a y in g more a t t e n t i o n to th e su b sy stem c o n n e c tio n s ( th e I ’ s) th a n to th e 0 r s. The re m a in in g v a r i a b l e s w ere r e l a t e d to s m a ll c o e f f i c i e n t s w hich v a r i e d i n t h e i r r a n k o r d e r . In f u t u r e s tu d y , t h e s e c o e f f i c i e n t s w i l l be removed from t h e a n a l y s i s on th e b a s i s o f t h e i r la c k o f c o n t r i b u t i o n to th e d i s c r i m i n a t i o n , o r on th e p r a c t i c a l b a s i s t h a t th e c o s t o r e f f o r t to i n c l u d e them i s n o t J u s t i f i e d by th e r e l a t i v e l y s m a ll i n c r e a s e i n d i s c r i m i n a t i o n . M oreover, some c o r r e l a t i o n was o b s e r v e d , and c o r r e l a t e d v a r i a b l e s have th e e f f e c t o f d e p re s s in g t h e w e ig h t p e r v a r i a b l e . I n v e s t i g a t i o n s h o u ld be c o n tin u e d w ith o u t th e s e v a r i a b l e s to d e te rm in e how and i f th e re m a in in g v a r i a b l e s change in p r o p o r t i o n a t e c o n t r i b u t i o n . I t may be p o s s i b l e to i n c r e a s e th e p e r c e n ta g e o f c a s e s th e m odel p r e d i c t s . I t would a ls o b e d e s i r a b l e to t e s t th e model u n d e r d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s . For exam ple, m o d ify in g th e f a i l u r e - p r o b a b i l i t y d i s t r i b u t i o n to i n c l u d e e x trem e skew ness m ig h t i n f l u e n c e Ss to a t t r i b u t e m o r e .im p o rta n c e to th e e f f i c i e n c y v a r i a b l e . C e r t a i n l y s p e c i f i c i n s t r u c t i o n s o r d i r e c t i o n s to a t t e n d to a v a r i a b l e sh o u ld b e r e f l e c t e d in i t s w e ig h tin g c o e f f i c i e n t . S i m i l a r l y , b e h a v io r c o u ld be a n a l y zed a s a f u n c t i o n o f th e v a r i o u s g o a ls and m o ti v a tio n s e s t a b l i s h e d by i n s t r u c t i o n s . A n o th e r c o n d i t i o n i s to i n c r e a s e th e f u n c t i o n a l c o m p le x ity o f th e p ro blem s i t u a t i o n . F i 81 n a l l y , the model can be a p p l i e d to r e a l - l i f e d i a g n o s t i c and tr o u b le s h o o t i n g s i t u a t i o n s . Summary The p r e s e n t stu d y p ro p o se d th e d i s c r i m i n a n t f u n c tio n (a m u l t i v a r i a t e a n a l y s i s method) a s a model f o r d i a g n o s t i c p r o b le m - s o lv in g . The model h a s th e f o llo w in g c h a r a c t e r i s t i c s : I t i s d e s c r i p t i v e and in d iv id u a l., b e in g con c e rn e d w ith b e h a v io r o v e r th e s e v e r a l s t e p s o f th e s o l u t i o n p r o c e s s f o r i n d i v i d u a l s u b j e c t s . I t r e l i e s on o b j e c t i v e d a ta , d e s c r i b i n g b e h a v i o r a l r e s p o n s e s in term s o f th e s t i m u l u s v a r i a b l e s w ith o u t i n t e r v e n i n g , s u b j e c t i v e i n t e r p r e t a t i o n . I t i s m u l t i v a r i a t e , u s in g a s e t . o f m u l t i p l e m ea su re ments o f th e p r o p e r t i e s o f th e s tim u lu s s t r u c t u r e . And i t i s q u a n t i t a t i v e and s im p le . The model p a ra m e te r s a re d i r e c t l y q u a n t i f i e d a s c o e f f i c i e n t s a s s o c i a t e d w ith s tim u lu s v a r i a b l e s . The b e h a v io r o f an i n d i v i d u a l i s i n f e r r e d from th e s e t o f c o e f f i c i e n t s : th e r e l a t i v e m agnitude o f th e c o e f f i c i e n t s i s i n t e r p r e t e d a s th e r e l a t i v e im p o rtan c e th e i n d i v i d u a l h as a t t r i b u t e d to th e a s s o c i a t e d v a r i a b l e in con s i d e r i n g h i s r e s p o n s e . The model was t e s t e d by d a t a c o l l e c t e d in a d ia g n o s t i c p r o b le m - s o lv in g t a s k . T h is k in d o f p r o b le m - s o lv in g i n v o lv e s : a r e q u ir e m e n t f o r a sequence o f i n f o r m a t i o n - a c q u i r ing s t e p s ; a s t r u c t u r e d t a s k w ith a s p e c i f i e d s e t o f r e sponse a l t e r n a t i v e s ; and th e u se o f o b j e c t i v e d a ta . 82 An e x p e r im e n t was d e s ig n e d to a d m i n i s t e r t h i s t a s k u n d e r c o m p u ter c o n t r o l , to p e r m i t e x te n d e d t e s t i n g s e s s i o n s on i n d i v i d u a l s u b j e c t s , and to com pute and g e n e r a t e s e q u e n - t i a l l y - d e p e n d e n t s t i m u l u s p r e s e n t a t i o n s . The d a t a from t h i s e x p e rim e n t w ere u s e d to t e s t th e ad eq u acy o f th e m odel. Group a n a l y s e s w ere p e rfo rm e d f i r s t , to p r o v i d e d e s c r i p t i v e s t a t i s t i c s t h a t c o u ld be r e l a t e d to r e s u l t s o f o t h e r p r o b l e m - s o l v in g e x p e r i m e n t s . U sing e f f i c ie n c y a s m easu red by an i n f o r m a t i o n s t a t i s t i c , i t was c o n f ir m e d t h a t e f f i c i e n c y d e c r e a s e s w ith i n c r e a s i n g v a r i a b i l i t y o f f a i l u r e . p r o b a b i l i t i e s among t h e s e t o f p o s s i b l e e v e n t s , and t h a t i t a l s o d e c r e a s e d w ith s u c c e s s i v e s t e p s o f th e p ro b lem s o l u t i o n s e q u e n c e . The d i s c r i m i n a n t f u n c t i o n was th e n v e r i f i e d a s an a d e q u a te m odel o f d i a g n o s t i c p r o b l e m - s o l v i n g . A ssu m p tio n s c o n c e rn in g th e i n t e r p r e t a t i o n o f th e c o e f f i c i e n t s were t e s t e d . C o r r e l a t i o n a l r e s u l t s w ere i n a g re e m e n t w ith th e a s s u m p tio n s , and w i t h th e f i n d i n g s o f Rodwan and Hake r e l a t i v e to t h e p r o p o r t i o n a t e c o n t r i b u t i o n s o f th e c o e f f i c i e n t s d e r i v e d f o r d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s . I f b e h a v i o r i s s t a b l e , and i f i n d i v i d u a l s u se a s i m i l a r c o m b in a tio n o f th e v a r i a b l e s f o r t h e i r r e s p o n s e s , t h e p r o p o r t i o n a t e c o n t r i b u t i o n o f th e v a r i a b l e s to th e d i s c r i m i n a n t f u n c t i o n s h o u ld be i n v a r i a n t . C o r r e l a t i o n s b etw een s e t s o f c o e f f i - . c i e n t s showed th e e x p e c te d i n v a r i a n c e when b e h a v i o r was 8 3 s t a b l e , and showed a change when r e s p o n s e b e h a v i o r chan g ed . I n t e r p r e t a t i o n s o f th e im p o rta n c e o f t h e v a r i a b l e s were b a s e d upon th e r e l a t i v e o r d e r and m ag n itu d e o f th e c o e f f i c i e n t s . T hese i n t e r p r e t a t i o n s w ere c o n s i s t e n t w i t h f i n d i n g s o f p r e v i o u s e x p e r im e n ts and w ere s u p p o r te d by i n d e p e n d e n t d e s c r i p t i v e g ro u p a n a l y s e s p e rfo rm e d i n t h i s s t u d y . V a l i d a t i o n t e s t s d e te r m in e d t h e a b i l i t y o f th e mod e l to a c c o u n t f o r t h e o b t a i n e d d a t a . A greem ent was fo und betw een o b t a i n e d r e s p o n s e s and p r e d i c t i o n s o f th e m odel, v a l i d a t i n g th e a b i l i t y o f th e m odel to d e s c r i b e i t s own d a t a a s w e l l a s to p r e d i c t b e h a v i o r on a new s e t o f d a t a . T hese c o n c l u s i o n s s u g g e s t t h a t th e d i s c r i m i n a n t f u n c t i o n i s a sim p le and a d e q u a te m odel f o r d e s c r i b i n g p r o b l e m - s o l v in g b e h a v i o r . B e h a v io r can be d i r e c t l y q u a n t i f i e d by t h i s a p p ro a c h and m e a n in g f u l l y i n t e r p r e t e d a s a f u n c t i o n o f p r o p e r t i e s o f th e s t i m u l u s s e t . The m odel i s a l s o g e n e r a l , a s i n d i c a t e d by th e r e s u l t s o f v a l i d a t i o n on d i f f e r e n t p ro b le m s . T h is s tu d y h a s p r o v i d e d f i n d i n g s , t h e r e f o r e , to recommend th e d i s c r i m i n a n t f u n c t i o n a s a sim p l e and l o g i c a l e x t e n s i o n o f th e d e s c r i p t i v e a p p ro a c h to p r o b l e m - s o l v i n g . L I S T 01 R E F E R E N C E S 8 4 REFERENCES 1. B e c k e r, G. M., & M cC lintock, C. G. V alue: b e h a v i o r a l d e c i s i o n t h e o r y . Annual Review o f Psycho logy., 1 9 6 7 , 18, 2 39-286. 2. B en d ig , A. ¥. Twenty q u e s t i o n s : an i n f o r m a tio n a n a l y s i s . J o u r n a l o f E x p e r im e n ta l P sy c h o lo g y , 1953* 46, 3 4 5 - 3 485 3 . B r a u n s t e i n , M. L . , & Coleman, 0. P. An i n f o r m a t i o n - p r o c e s s in g m odel o f the a i r c r a f t a c c i d e n t i n v e s t i g a t o r . P a p e r p r e s e n t e d t o th e Human F a c t o r s S o c i e t y , 10th A nnual M e etin g , Anaheim, C a l i f o r n i a , November 1 9 6 6 . 4 . B ru n e r, J . S ., Goodnow, J . J . , & A u s tin , G. A. A s tu d y of t h i n k i n g . New York: W iley , 1956. 5- D a v is , D. J . S t r u c t u r e o f t h e e n v iro n m en t and s t r a t e g i e s f o r a c q u i r i n g i n f o r m a t i o n . J o u r n a l o f E x p e r i m e n ta l P sy ch o lo g y , 1 9 6 7, 7 3 j 2 2 7 - 2 3 1 . 6 . D a v is, D. J . E f f i c i e n c y and r i s k i n human i n f o r m a t i o n - a c q u i s i t i o n . P ap er p r e s e n t e d a t th e m ee tin g o f th e W este rn P s y c h o l o g i c a l A s s o c i a t i o n , San D iego, March 1968. 7 . D ixon, W. J . ( E d .) BMD b io m e d ic a l com p uter program s. (2nd e d .) B e r k e l e y : U n i v e r s i t y o f C a l i f o r n i a P r e s s , 1967. 8 . E dw ards, W. B e h a v i o r a l d e c i s i o n t h e o r y . Annual Re view o f P sy c h o lo g y , 1961, 12., 473-498* 9 . G a rn e r, W. R. To p e r c e i v e i s to know. Am erican Psy c h o l o g i s t , 1 9 6 6 , 2 1 , 11- 1 9 * 10. H unt, E. B. C oncept l e a r n i n g ; an i n f o r m a ti o n p r o c e s s in g p ro b lem ! New Y o rk : W iley , 1 9 6 2 . 11. H unt, E. B ., M arin , J . , & S to n e , P. J . E x p e rim e n ts - i n i n d u c t i o n . New York: Academic P r e s s , 1 9 6 6 . " 85 86 1 2 . 13. 14. 15. 1 6 . 17. 18 . 19- 2 0 . Johnson., E. S. An in f o r m a ti o n - p r o c e s s in g model o f one k ind o f problem s o lv in g . P s y c h o lo g ic a l Mono g r a p h s , 1964, 78 (4 , whole n o . 5 8 1 ). K e n d a ll, M. G. A c o u rse in m u l t i v a r i a t e a n a l y s i s . New York: H afner, 1957- Pp. 144-170. K e n d a ll, M . G. D is c r im in a tio n and c l a s s i f i c a t i o n . In P. R. K ris h n a ia h ( E d .) , M u l t i v a r i a t e a n a l y s i s . New York: Academic P re s s , 1 9 6 6 . P p . I 6 5 - I 8 5 . K leinm untz, B. D ia g n o stic problem s o lv in g by com puter. U n pub lished m a n u sc rip t, 1 9 6 2, C arn eg ie I n s t i t u t e o f T echno logy . K leinm untz, B. Problem s o lv in g : r e s e a r c h , method, and th e o r y . New York: W iley, 1 9 6 6 . Rao, C. R. Advanced s t a t i s t i c a l methods in b io m e tric r e s e a r c h . New York: W iley, 1952. P p . 2 3 6- 2 7 2 . R igney, J . W., e t a l . Measurement and p r e d i c t i o n of c o g n itiv e lo a d in g s in c o r r e c t i v e m ain ten ance ta s k s : I . A B ayesian approach . T e c h n ic a l R e p o rt No. 46, 1966, Departm ent o f Psychology, U n i v e r s i t y o f S outhern C a l i f o r n i a . Rodwan, A. S . , & Hake, H. ¥ . The d i s c r im i n a n t f u n c t i o n as a model f o r p e r c e p t i o n . American J o u r n a l o f P sycholo gy, 1964, 77* 3 8 0- 3 9 2 . Simon, H. A. R a ti o n a l c h o ic e and th e s t r u c t u r e o f the e n v iro n m en t. P s y c h o lo g ic a l Review, 1956, 6 3 , 129- 138. 21. Wertman, P. M. R e p r e s e n ta tio n and s t r a t e g y in d ia g n o s t i c problem s o lv in g . Human F a c t o r s , 1966, 8 , 48-53. A P P E N D I C E S 87 88 APPENDIX I.A SATELLITE 1: TYPICAL STIMULUS MATRIX (C o n fig u ra tio n A , D i s t r i b u t i o n Skewed, N = l 6 ) SYSTEM NUMBER I SUBSYST 00 1 2 3 CHANNEL 4 5 6 7 8 probab: SS 1 0 0 0 0 1 0 1 0 26 SS 2 . 1 0 0 1 0 1 0 1 25 SS 3 1 0 0 0 0 0 0 1 14 SS 4 1 0 0 1 0 1 1 1 11 SS 5 1 0 0 1 0 0 1 0 6 SS 6 1 0 1 1 1 0 1 1 5 SS 7 1 0 1 1 1 0 1 1 4 SS 8 1 1 0 0 0 0 1 0 3 ss 9 1 1 0 1 1 0 1 0 1 ss 10 1 0 0 0 0 1 1 1 . 1 ss 11 0 0 1 0 1 0 0 1 1 ss 12 1 0 1 1 1 0 0 1 1 ss 13 0 0 0 0 1 0 0 0 1 ss 14 0 0 0 1 0 0 0 1 1 ss 15 1 1 1 0 1 0 1 0 1 ss 16 1 1 0 1 1 1 1 0 1 89 APPENDIX I .B SATELLITE 2: TYPICAL STIMULUS MATRIX ( C o n fig u r a tio n A, D i s t r i b u t i o n U niform , N = 24) SYSTEM NUMBER 5 SUBSYST 00 1 2 3 CHANNEL 4 5 6 7 8 PROBABILITY SS 1 1 0 0 1 1 1 0 0 5 SS 2 0 1 0 1 1 0 1 0 5 SS 3 0 0 0 0 1 0 1 1 5 SS 4 0 0 0 1 0 0 0 0 4 ss 5 0 1 0 0 0 1 0 0 4 ss 6 0 0 1 0 0 0 0 1 4 ss 7 1 0 0 0 0 1 1 0 4 ' ss 8 1 0 1 ■ 1 1 0 0 1 4 ss 9 1 1 1 1 0 0 1 1 4 ss 10 0 0 0 1 1 0 0 1 4 ss 11 1 1 1 1 0 1 0 1 4 ss 12 1 1 1 0 0 0 1 1 4 ss 13 0 0 1 0 0 1 0 0 4 ss 14 0 0 1 0 1 1 0 1 4 ss 15 1 0 1 0 0 1 0 1 4 ss 16 1 1 1 0 1 0 1 0 4 ss 17 0 0 1 0 0 0 1 1 4 ss 18 1 0 1 1 0 1 1 0 4 ss 19 0 0 0 1 1 1 0 0 4 ss 20 1 1 0 1 1 1 0 1 4 ss 21 0 0 0 0 1 1 0 0 4 ss 22 1 0 1 1 0 1 1 0 4 ss 23 1 0 1 0 0 0 1 1 4 ss 24 1 1 0 1 1 1 0 0 4 /X 90 APPENDIX I.C SATELLITE 3: TYPICAL STIMULUS MATRIX ( C o n f i g u r a t io n A, D i s t r i b u t i o n M o d e ra te ly Skewed, N = 20) SYSTEM NUMBER 3 SUBSYST 00 1 2 3 CHANNEL 4 5 6 7 8 PROBABILITY SS 1 1 0 1 1 1 1 0 0 16 SS 2 1 0 0 0 0 1 0 0 13 SS 3 0 0 0 1 1 1 1 1 8 SS 4 1 0 1 1 0 1 1 1 8 SS 5 0 0 1 0 1 0 1 1 7 SS 6 1 0 1 1 0 0 0 1 6 SS 7 0 0 0 1 0 0 0 1 6 SS 8 1 1 0 1 0 0 1 0 4 SS 9 0 0 0 1 0 0 0 1 4 ss 10 0 1 0 0 1 0 0 1 3 ss 11 1 1 0 0 1 0 0 1 3 ss 12 0 0 0 1 0 1 1 1 3 ss 13 0 0 0 1 0 1 1 0 3 ss 14 0 1 0- 0 0 1 1 0 3 ss 15 1 0 0 1 0 1 0 1 3 ss 16 0 1 0 1 1 1 1 0 2 ss 17 0 0 0 0 0 1 1 0 2 ss 18 0 0 0 1 1 1 1 0 2 ss 19 1 0 0 1 0 1 1 0 2 ss 20 1 1 0 0 1 0 0 0 2 91 APPENDIX I I .A COMPUTER PROGRAM FOR ADMINISTRATION OF THE EXPERIMENT 0 .0 DEMAND M 0 .2 SET N=10 - - 0 .3 OPEN "MF2" FOR INPUT AS FILE 2 0 .3 1 READ FROM 2: S ( j) FOR J=1 TO 48 0 .4 READ FROM 2: F{j,K) FOR J=1 TO 20 FOR K=1 TO 6 0 .4 1 READ FROM 2: R(J,K) FOR J=1 TO M FOR K=1 TO 6 0 .4 2 CLOSE 2 0 .5 SET T=1 0 .7 1=1 0 .8 Z l= l 0 .9 PAUSE 1.0 OPEN "MAT2" FOR INPUT AS FILE 1 1.6 READ FROM 1: A(J,K) FOR K=1 TO N FOR J=1 TO M 1.7 READ FROM 1: A1(J,K) FOR K=1 TO N FOR J=1 TO M 1.8 CLOSE 1 1.9 SET A(J,K) = A1(J,K) FOR K=1 TO N FOR J-=l TO M IF S (I)> 6 2.0 XI = IF S (I)> 6 THEN S ( I ) -6 ELSE S ( l) 2.1 X = IF I>40 THEN F ( l- 4 0 ,X l) ELSE IF I>20 THEN F (1 -2 0 jXl) ELSE F(I,X 1) 2.2 A(J,N) = R(J,X1) FOR J=1 TO M 2.21 TYPE IN FORM l4 : S (l) 2.7 TYPE " CHANNEL READING: TYPE ( l- 8 ) REPAIR SUBSYSTEM: TYPE '0 0 ' " 2.9 DEMAND IN FORM 2: C IF T M OD 2=0 2.92 DEM AND IN FORM 10: C IF T M OD 2#0 3.0 TO STEP 2.9 IF C>=N-1 3 .1 q(t)=C 3.11 T=T+1 3 .2 TO STEP 3.6 IF C=0 3.4 TO PART 23 IF A(X,C+1)=0 3.5 TO PART 24 IF A(X,C+l)=l 3.6 DEM AND IN FORM 5: C IF I M OD 2=0 3.7 DEMAND IN FORM 11: C IF I M OD 2#0 4.0 TO STEP 3.6 IF C>M - 4 .1 SET Q(T)=C 4 .2 T=T+1 4 .3 TYPE IN FORM 6: C 92 APPENDIX I I .A — C on tin u ed COM PUTER PR O G RA M FOR ADMINISTRATION OF THE EXPERIMENT 5-0 Y=IF A(C,N)>3 THEN 8 l 6/M ELSE 432/M 5 .0 1 DO STEP 4 0 .0 FOR V=1 TO Y/4 5 .0 2 TYPE "CORRECTIVE ACTION COMPLETED" 5 .2 DEMAND IN FORM 15: SI 5-3 TO STEP 5-2 IF S l # l 5.4 TO STEP 25.0 IF C=X 5.41 TYPE IN FORM 7: C IF (X+C) M OD 2=0 5.42 TYPE IN FORM 8 : C IF (X+C) M OD 2#0 5.5 A(C,K)=99 f o r K=1 TO n 5.51 DEMAND IN FORM 12: C 5-52 TO STEP 5 .5 1 IF C>3 5.6 Q(T)=C 5 .6 1 T=T+1 5.7 TO STEP 3 .6 IF C=1 5-71 TO STEP 2 .9 IF C=2 5.72 TO STEP 31.05 IF C=3~ 23.0 TYPE IN FORM 3: C 23.1 SET J=1 23.5 SET A(J,K ) = IF A (J,C+1)=1 THEN 99 ELSE IF A(J,C+1)=99 THEN 99 ELSE A(J,K) FOR K=1 TO N 23.51 Z1=Z1+1 IF A(J j l ) # 9 9 2 3.6 J=J+1 2 3 .8 TO STEP 2 3 .5 IF J<=M 23.9 TO STEP 31 24.0 TYPE IN FORM 4: C 24.1 SET J=1 24.5 SET A (J.K )= IF A(J,C+1)=0 THEN 99 A( J , C + 1 ) = 9 9 THEN 99 ELSE A( J , K ) FOR ELSE; IF — K=1 TO N 24.51 Z1=Z1+1 -IF A (J,1 )# 9 9 24.6 J=J+1 24.8 TO STEP 24.5 IF J<=M 24.9 TO STEP 31 2 5 .O TYPE IN FORM 16: C 25.1 TYPE IN FORM 9: S ( l) 25.6 SET 1=1+1 2 5 .Y I= IF I >48 THEN 1 ELSE I 2 5 .8 TYPE "STANDBY FOR NEXT ALARM" 2 5 .8 2 q ( t ) =98 2 5 .8 3 LINE 25.85 T=T+1 25.86 Z l= l 3 0.0 Y=IF A(C,N)<3 THEN 8 l 6/M ELSE 432/M 30.1 DO STEP 4 0 .0 FOR V=1 TO Y/4 30.3 TO PART 1 9 3 APPENDIX I I .A — C o n tin u ed COMPUTER PROGRAM FOR ADMINISTRATION OF THE EXPERIMENT 3 1 .0 TO STEP 3 1 .0 5 IF Zl>4 3 1 .0 0 1 Z l= l 3 1 .0 1 DEMAND IN FORM 13: W 3 1 .0 2 TO STEP 2 .9 IF W#1 3 1 .0 5 TYPE " . . SUBSYST CHANNEL 00 1 2 3 4 5 6 7 8 PROBABILITY " 3 1 .0 6 Z l= l 3 1 .1 j = i ~ ■ 3 1 .2 TO STEP 3 1 .7 I F A (J ,1 )= 9 9 3 1 .4 TYPE IN FORM 1: A (J,K ) FOR K=1 TO N 3 1 .7 J=J+1 3 1 .8 TO STEP 3 1 .2 IF J<=M 3 1 .9 2 TO STEP 2 .9 4 0 .0 A 1(J,K ) - A 1(J,K ) FOR K=1 TO N FOR J=1 TO M 50 TYPE IN FORM 22: Q (j) FOR J=1 TO T - l FORM 1: S S %% ^0% %% %% 0 %% %% c 0 fo c 0 fo %%% FORM 2: CHANNEL NUMBER ? ## FORM 3 : THE CHANNEL 0 READING IS NORMAL THE POSSIBLE FAULTY SUBSYSTEMS ARE FORM 4: THE READING ON CHANNEL 0 I S ABNORMAL THE POSSIBLE FAULTY SUBSYSTEMS ARE FORM 5: FIX SS NUMBER ? # # FORM 6 : REPAIR ON SS 0 o HAS BEEN INITIATED. WAIT FOR STATUS MESSAGE. FORM 7: SS 0 WAS CHECKED OUT AND IT WAS OK. THE SYSTEM IS STILL NOT WORKING. ANY INSTRUCTIONS? FORM 8 : SS 0 o WAS WORKING OK. SOME OTHER SUBSYSTEM MUST BE MAL FUNCTIONING BECAUSE THE SYSTEM STATUS IS STILL NO-GO. 9 4 APPENDIX I I .A — C o n tin u ed COM PUTERPROGRAM FOR ADMINISTRATION OF THE EXPERIMENT FORM 9: SYSTEM %% IS NOW WORKING OK. FORM 10: CHANNEL ? ## FORM 11: SUBSYSTEM NUMBER ? ## FORM 12: CHOOSE FROM THE FOLLOWING 3 STEPS: (1) FIX ANOTHER SUBSYSTEM (2) GET A CHANNEL READING (3) DISPLAY THE REMAINING SUBSYSTEMS TYPE A STEP NUMBER HERE: ## FORM 13: AVAILABLE FOR PRINTOUT. PRINT? YES=1 N0=0 ?## FORM 14: W E HAVE A 'NO-GO' READING FOR SYSTEM % % REFER TO THE SYSTEM TABLE FORM 15: TYPE A '1 ' TO CHECK THE SYSTEM GO/NO-GO STATUS. #. FORM 16: SS %% HAS BEEN REPAIRED FORM 22: i o i o i o < ? ( # $ > % 0> i oi o% < $ $ $ > %%% %%% < $ $ $ > APPENDIX II.B COMPUTER PROGRAM TO DERIVE STIMULUS VARIABLE VALUES 0 . 0 DEMAND M ,I2 ,T 2 ,0 0 . 1 DEMAND I 0 . 2 SET N=10 0 .3 OPEN "MP3" FOR INPUT AS PILE 2 0 .3 1 READ FROM 2: S ( j) FOR J=1 TO 48 0 .4 READ FROM 2: F (J,K ) FOR J=1 TO 20 FOR K=1 TO 6 0 .41 READ FROM 2: R (J,K ) FOR J=1 TO M FOR K=1 TO 6 0 .4 2 CLOSE 2 0 .4 5 OPEN/SEL/FOR INPUT AS FILE 3 0 .5 OPEN/BMD/FOR OUTPUT AS FILE 4 0 . 6 TYPE "K2 N2 I SI T1 M5 CM 0 . 8 N l= l 0 .9 N2=0 1 .0 OPEN "MAT3" FOR INPUT AS FILE 1 1 .2 1=1F I>48 THEN 1 ELSE I 1 .6 READ FROM 1: A U j K) FOR K=1 TO N FOR J=1 TO M 1 .6 5 TO STEP 1 .8 IF S (I)< 7 1 .7 READ FROM 1: A(J,K) FOR K=1 TO N FOR J=1 TO M 1 .8 CLOSE 1 2 .0 XI = IF S ( l )>6 THEN S (I )-6 ELSE S ( l ) 2 .1 X = IF I>40 THEN F (1 - 4 0 ,XI) ELSE I F I>20 THEN F (I-2 0 ,X 1 ) ELSE F (I,X 1 ) 2 .2 A(J,N) = R (J,X 1) FOR J=1 TO M 2 .3 READ FROM 3 : Q(Tl) FOR T l= l TO T2 2 .4 T l= l 2 .5 C=Q,(Tl) 2 .6 TO STEP 9 IF C=0 2 .7 Z l= l 4 .0 M5=0 4 .1 M5 = IF A ( J ,1 )# 9 9 THEN M5+1 ELSE M5 FOR J=1 TO M 4 .2 B(K1,K)=0 FOR K l=l TO 12 FOR K=2 TO 9 4 .3 P1=0 4 .4 P1=IF a( j , n )#99 then p i +a ( j , n ) e l s e PI FOR J=1 TO 5-0 DO PART 83 FOR K=2 TO 9 5-1 DO PART 84 FOR K=2 TO 9 5-3 DO PART 85 FOR K=2 TO 9 5-5 DO PART 87 FOR Kl=5 TO 10 5 .7 K2=0 5 .8 K2=IF B (10,K )#0 THEN K2+1 ELSE K2 FOR K=2 TO 9 5 .9 N2=N2+K2 96 APPENDIX I I . B - - C o n tin u ed COM PUTER PR O G R A M T O DERIVE STIMULUS VARIABLE VALUES 6 .1 DO PART 30 FOR K=2 TO 9 6 . 3 TYPE IN FORM 2: K 2,N 2, I , S ( l ) , T1,M5,C 7 .0 H=IF A(X, C +l)=0 THEN 1 ELSE 0 7 .2 TO PART 23 8 .0 T1=T1+1 8 .5 TO STEP 2 .5 9 .0 1= 1+1 9 .1 N1=N1+1 9 .5 TO STEP 1 IF Nl<=12 9 .6 CLOSE 4 9-7 CLOSE 3 10.0 PAUSE 23 .1 SET J=1 2 3 .5 SET A(J.K) = I F A(J , C+l) = H THEN 99 ELSE IF A(J,C+1J = .99 THEN 99 ELSE A(J,K) FOR K=1 TO N 2 3 .5 1 Z1=Z1+1 IF A ( J ,l ) # 9 9 2 3 .6 J= J+1 2 3 .8 TO STEP 2 3 .5 I F J<=M 23 .9 TO STEP 8 IF Zl>4 23.91 TO STEP 9 30.0 WRITE ON 4 IN FORM 1: B(K1,K) FOR K1=0 TO 12 IF b ( 10j k)#o 3 1 .0 TYPE IN FORM 1 : B(K1,K) FOR K1=0 TO 12 IF B U O jK ^O 8 3 .0 B(0,K)=1 8 3 .1 BC1 ,K )= S (I) 8 3 .2 B 2,K =T1 8 3 .3 B (3 j K)=M5 8 3 .4 B(4, k ) =K-1 8 3 .5 P5(K)=0 8 3 .6 I 5 (K)=0 8 3 .7 B (1 2 , K) =0 84 .0 P5(K) = IF A (J,K )#99 THEN (P5(K) + A(J,K)- * A(j,N)) ELSE P5(K) FOR J=1 TO M - 8 4 .0 1 P(K)=P5(K)/P1 8 4 .1 B(5,K)' = IF A(J,K) = 1 THEN B(5,K) + 1 ELSE B(5,K) FOR J= 1 TO M 8 4 .1 2 B(6 ,K) = IF P(K) = 0 THEN 0 ELSE I F P(K) = 1 THEN ELSE -(P(K) * (LOGlO(PfK ))/L0G10(2)) + ( l - P(K)) ( LOGIO(1 - P( Kj )/LOG 10 ( 2 ))) 8 4 .2 B(7,K) = IF A (J,K )#99 THEN ( 6 ( 7 ^ ) + A (J,K )) ELSE B(7,K) FOR J=1 TO IP(M 5/2) * o 9 7 APPENDIX I I . B - - C o n tin u ed COM PUTER PROGRAM TO DERIVE STIMULUS VARIABLE VALUES 8 4 .3 T (J) = IP A (J,K )# 9 9 then A (J,K ) ELSE I P J=1 THEN 99 ELSE T (J - 1) FOR J=1 TO M 8 4 .4 I5(K ) = 0 8 4 .4 2 T(M+1) = T(M) 8 4 .5 I5(K ) = IF ABS(T{j) - T ( J +1)) = 1 THEN I5 (K ) + 1 ELSE 1 5 (K) FOR J= 1 TO M 85-0 Y=B(5.K)/M5 8 5 .1 B f8 jKJ = ABS(Y - . 5 ) 8 5 .2 B(9,K) = IF B(5jK) = 0 THEN 0 ELSE B{ 7 ,K )/B (5 , K) 8 5 .3 Z4 = M5 - B (5 ,K) 8 5 .4 Z3 = IF Z4>B(5,K) THEN 2 * 3 ( 5 ^ ) ELSE IF B (5,K ) = IP(M 5/2) THEN 2 * B(5,K) - 1 ELSE 2 * Z4 8 5 .5 B(lO,K) = IF Z3 = 0 THEN 0 ELSE I 5 (K )/Z 3 8 5 .6 B (1 1 ,K) = IF C = K - 1 THEN 1 ELSE 0 8 7 .0 B2(K1) = MAX ( K=2 TO 9: B(K1,K)) 8 7 .1 B(K1J K) = I F B2(K1) = 0 THEN 0 ELSE IP(B (K 1,K ) * 100/B 2(K I)) FOR K=2 TO 9 FORM 1: FORM 2 9 8 APPENDIX I I I . A STIMULUS DATA AND STIMULUS PRESENTATION S tim u lu s d a t a . The f o l lo w in g s t i m u l u s i n f o r m a t i o n was s t o r e d i n t h e d i s c f i l e o f th e c o m p u ter: The o r d e r o f p r e s e n t a t i o n o f th e 12 s y s te m s ( t r i a l s ) f o r t h e f o u r b l o c k s o f th e e x p e r im e n t. The i n f o r m a t i o n i s i n a v e c t o r S ( i ) , i = 1* 4 8 . The f a i l u r e p r o b a b i l i t y v a l u e s f o r th e N su b s y ste m s i n eac h e x p e r im e n t. The I n f o r m a t i o n i s i n a m a t r i x R ( l , j ) j i = N, j = 6 . The s i x colum ns c o r r e s p o n d to t h e two r e p l i c a t i o n s on th e t h r e e d i s t r i b u t i o n l e v e l s . The su b s y ste m s to be s e l e c t e d a s m a l f u n c t i o n i n g . T h is I n f o r m a t i o n i s i n a m a t r i x F ( i . , j ) , k = 20., j = 6 . T hese su b s y s te m s o c c u r i n f r e q u e n c y c o r r e s p o n d i n g to th e p r o b a b i l i t i e s o f f a i l u r e l i s t e d I n th e r e s p e c t i v e 6 colum ns o f th e m a t r i x R ( i , j ) . The c o n f i g u r a t i o n s o f l ' s and O ’ s . C o n n e c tio n s betw een th e N s u b s y ste m s and 8 i n f o r m a t i o n c h a n n e ls c o n t a i n e d i n two m a t r i c e s t A ( i j j ) and A l ( i , j ) j i = N, j = 1 0 . The f i r s t column o f t h e m a t r i c e s l i s t s th e su b s y ste m ID number from 1 to N. The l a s t column i s b l a n k — th e p r o b a b i l i t y v a l u e s b e in g i n s e r t e d a t th e tim e o f p ro g ram e x e c u t i o n . The l ' s and 0 ' s a r e c o n t a i n e d i n colum ns 2 to 9• 9 9 T h is f i l e o f s tim u lu s in fo rm a tio n , i s found in Ap p e n d ix I I I . B th ro u g h I I I . D . S tim u lu s p r e s e n t a t i o n . I n f o r m a tio n i n the f i l e i s r e l a t e d a s shown in T able 11. I t I s p r o c e s s e d f o r problem p r e s e n t a t i o n a s f o llo w s : an in d e x o r c o u n te r , K, i s e s t a b l i s h e d to i n d i c a t e th e sequence o f t r i a l s on system s. The in d ex in c re m e n ts 1 f o r each pro b lem from 1 to 48, th e n r e t u r n s to 1 and c o n ti n u e s . F o r K - 1, th e in d e x K a d d r e s s e s th e f i r s t system i n v e c t o r S ( i ) , w hich happens to be System 3 f o r S a t e l l i t e 1. The v a lu e , S ( k), i s u se d to s e l e c t th e c o n f i g u r a t i o n and d i s t r i b u t i o n l e v e l . To s e l e c t a c o n f ig u r a t i o n , A i s chosen i f th e system number, S(K ), i s s ix o r l e s s , and A1 i s chosen i f S(K) i s g r e a t e r th a n s ix . To s e l e c t a d i s t r i b u t i o n ( e . g . , to s e l e c t a column from R ( i , j ) ) column j i s s e t e q u a l to S(K). B ecause the same s e t o f d i s t r i b u t i o n s a r e u s e d i n c o n f i g u r a t i o n s A and A l, J i s s e t e q u a l to S(k) - 6 when th e system number i s g r e a t e r th a n s i x . To s e l e c t a m a lf u n c tio n in g subsystem from c e l l in m a tr ix F ( i , j ) , i i s s e t e q u a l to K and j s e t to S(k) o r S(K) - 6 a s b e f o r e . T h e r e fo re , f o r th e f i r s t t r i a l (K = l ) , th e system number i s t h r e e , th e c o n f i g u r a t i o n i s m a trix A, th e d i s t r i b u tio n i s column t h r e e o f m a tr ix R, and the m a lf u n c tio n i s th e c e l l v a lu e a t row one and column t h r e e o f m a trix F. 100 RELATION TABLE 11 OP STIMULUS INFORMATION System Number* S(I) C o n f ig u r a t i o n Problem D i s t r i b u t i o n F a u l t 1 A R ( i ,S ( K ) ) F (K ,S (K )) 2 1 ? It 1 1 3 II It 1 1 4 I I II !t 5 II It 1 1 6 II It 1 1 7 A1 R ( i ,S ( K ) - 6 ) F (K ,S (K )-6 ) 8 1 ! II M 9 II It II 1° II II I T 11 II 1 1 1 1 12 II It 1 1 *The sy stem num bers 1 -1 2 a re ra n d o m ly o r d e r e d in 4 b l o c k s . P r o c e d u re d e s c r i b e d i n t e x t . 1 0 1 APPENDIX I I I . B SATELLITE 1. STIMULUS DATA SEQUENCE OF PRESENTATION OF SYSTEMS 3 . 2 . 1 0 . 6 . 8 . 1 . 1 1 . 9 . 5 . 1 2 . 7 . 4 , 2 . 1 0 . 1 2 . 3 . 4 . 8 . 6 . 1 . 7 . 9 . 1 1 . 5 , 1 1 . 9 . 5 , - 1 , 1 0 , 8 , 3 , 7 , 6 , 2 , 1 2 , 4 , 2 , 6 , 9 , 1 1 , 12, 1 , 7 , 4 , 5 , 1 0 , 8 , 3 , LIST OF MALFUNCTIONING SUBSYSTEMS 1 5 . 2 . 2 . 3 . 1 . 3 . 1 . 3 . 6 . 2 . 4 . 3 . 1 . 3 . 1 . 2 . 1 . 1. 2 . 2 , 8 . 1 . 1 . 2 . 3 . 7 . 2 . 1 . 6 . 4 . 8 . 1 . 1 . 4 . 7 . 1 . 1 6 . 4 . 4 . 2 , 2 , 3 , 1 3 , 1 4 , 2 , 1 , 6 , 1 2 , 7 , 2 , 7 , 1 4 , 1 , 8 , 2 , 1 , 9 , 3 , 8 , 1 0 , 4 . 6 . 7 . 1 4 . 3 . 2 . 4 . 1 . 2 . 9 . 2 . 8 . 1 0 . 5 . 3 . 8 . 4 . 2 . 1 . 2 , 9 , 1 , 2 , 1 4 , 1 5 , 3 , 6 , 4 , 6 , 5 , 1 6 , 1 0 , 1 4 , 2 , 7 , 8 , 1 1 , 7 , 1 5 , 1 , 4 , 8 , 3 , 1 3 , 1 4 , 8 , 1 1 , 7 , 1 4 , 5 , 1 2 , 1 , 2 , 8 , 9 , 1 0 , 4 , 1 3 , 1 5 , 6 , FAILURE-PROBABILITY DISTRIBUTIONS 2 6 . 2 5 . 1 4 . 1 1 . 6 . 5 . 4 . 3 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 , 2 9 . 2 2 . 1 0 . 8 . 7 . 6 . 4 . 4 . 2 . 2 . 1 . 1 . 1 . 1 . 1 . 1 , 1 7 . 1 6 . 1 1 . 9 . 8 . 7 . 6 . 5 . 5 . 4 . 3 . 3 . 3 . 3 . 3 . 1 , 1 4 , 1 3 , 1 2 , 1 0 , 8 , 6 , 6 , 5 , 4 , 4 , 4 , 4 , 3 , 3 , 2 , 2 , 8 , 7 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , CONFIGURATIONS A 1 , 0 , 0 , 0 , 0 , 1 , 0 , 1 , 0 , 0 , 2 , 1 , 0 , 0 , 1, 0 , 1 , 0 , 1 , 0 , 3 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 4 . 1 . 0 . 0 . 1 . 0 . 1 . 1 . 1 . 0 , 5 .1.0 .0 .1.0 .0 . 1.0 .0 , 6 ,1,0 , 1,1, 1,0 , 1,1,0 , 7, 1,0 , 1,1, 1,0 , 1,1,0 , 8 ,1, 1,0 ,0,0 ,0 , 1,0,0 , 9 ,1, 1,0 ,1, 1,0 , 1,0 ,0 , 10, 1,0 ,0,0 ,0 ,1,1,1,0 , 11,0 ,0 , 1,0 , 1,0 ,0, 1,0 , 12,1,0 ,1,1, 1,0 ,0,1,0 , 1 3 . 0 . 0 . 0 . 0 . 1 . 0 . 0 . 0 . 0 , 1 4 . 0 . 0 . 0 . 1 . 0 . 0 . 0 . 1 . 0 , 1 5 . 1 . 1 . 1. 0 . 1 . 0 . 1. 0 . 0 , 1 6 , 1 , 1 , 0 , 1 , 1 , 1 , 1, 0 , 0 , A1 1, 0 , 1 , 0 , 1, 1 , 1, 0 , 1 , 0 , 2 , 1 , 0 , 1, 1 , 0 , 1, 0 , 0 , 0 , 3,0 ,0 ,1,1,0 ,0 ,0 ,0 ,0 , 4 . 0 . 1 . 0 . 0 . 0 . 1 . 0 . 0 . 0 , 5. 0 . 1. 1. 0. 0 . 0 . 1. 1. 0, 6 , 0 , 1, 1, 0, 1, 0 , 1, 0 , 0 , 7, 0 , 1, 0, 0 , 1, 1, 0, 0 , 0 , 8, 0 , 1, 0 , 1, 1, 0 , 1, 0 , 0 , 9, 1, 0 , 0 , 1, 0 , 1, 1, 0 , 0 , 10, 1, 1, 0 , 0 , 0 , 1, 0 , 0 , 0 , 11, 0 , 0 , 1, 0 , 1, 0 , 1, 0 , 0, 12, 1, 0 , 0, 1, 0 , 0 , 0 , 0 , 0 , 1 3 . 1 . 1 . 1. 1 . 0 . 1 . 0 . 0 . 0 , 1 4 . 0 . 1 . 1 . 0 . 0 . 0 . 0 . 0 . 0 , 1 5 . 0 . 1. 0 . 0 . 0 . 1 . 0 . 1 . 0 , 1 6 , 1 , 1 , 0 , 1 , 0 , 0 , 1 , 0 , 0 , C M O i — 1 , — 1 r\ rv C M I --1 1 — 1 rv rv rv r v -=r i — 1 iH rH ^ rH ^ * \ * v ry rv £M * v ■ > ^0 0 LP\ i — I i — 1 i — I * V - Z j“ -Z j" •vV D C M rH rH rv » v • > C M * v r v LP\,— 1 C M * > 1 --1 I — I I — I rv _ H ~ -H" a y •i * \ »\C M aa)- r > rv ry C M rv r v S C O s f t i — 1 rH M O rH ,— 1 H ^ * \ ^ ^ VO L T V H LAVO C O ft; o i — 1 i — 1 i — I * v _ H " ftj- r\ rv rvC M ^ r \ H C M C M * > ftH * -=t 00 r v rv r > rv f t ^ » \ » , H r\ * > • > C M * v r v f t >H i — 1 id- cocm co VO rH O f t - tf t C M E H rH C M C M r\-H* E H co •> •> •> i — i f t ^ ft) * V rv rv C M * > * V f t <H CT\ D — * > C M CT\ C M O -f t CO PQ iH C M C M r\-H" j z t f t Ph 1 — 1 • > •> !— 1 f t ^ ,— 1 n » \ H * v * > * > C M * > r > o *>rHVO » > ft) H C M VO •'VO CO f t rH C M OO * > jH" -H* C O Q \ i — ! * > £ — C O ,— 1 LA ^ * > * \ * v « v C M * > r v o f t ft: • > r\ C M • > o n *\LA rH VO CO C O rH C M -H" *\^j“ -H" • f t o Lf\ L C\ *>-^- ft! » V OV ^ ^ 1 — 1 H * V rv rv (Y D • > » v C O H j > M • > * > C M • > VO • > CO rH * » C M Q rH C M -zt * \-zJ~ -= t H s f t C M C O H m H •'ft- • > rH OV rH r\ • > rv_ zj" rv r v o H H f t rH • > • > ft; CO •'VO »>•>•< >H H C M -H- *>hT -zj* H f t f t •> v o ^r cm o •wft H 0 > 0 LA Eh • V rv rv J Z J * rv * v X C O ft; £ • > — rv rv rv H CO • » *»i— 1 i — 1 • » H C M C M -H" H r f t H w • > i — 1 rH M O Eh i — 1 CO * > t— f t • > rv rvJ^j" rv rv E p ) • C O -Zj" * \ i — 1 * > O ft" rH 0> LA ^ H C M C M ft- **ft- -ft > -5 C M pd * > C M » \ CT\ ft; •\ *rO O i — I rH C7\ PQ •\ ^ft" C5 w E CO *>0^ •» 5 — J — J ^ < C M OO-ft *Nft- -ft H PH w f t » > O i — 1 f t » \ rH C M rH rH pq • > * \ •'ft" ^ Ph P L , f t C M i — 1 LP\ i— 1 f t CO ^ C M i — I * a i — 1 o C M ft- ft- -vft- ft- E f t H P h rv rv r > r v ca; * \ CO ^ f t ^ » \ -'ft* O f t o o C M rH O f t CO *»b— CO »CM PH M O - f t -ft •'•ft ft- o f t 1 — 1 1 — 1 • > 1 — 1 ^ rH ^ LA , — 1 i •, -\ft" • > & w * v rv Q rv f t LA *\ft" C M r— 1 » \ M t>- LA LA • 'f t' ft- f t o M O COH CO O » \ C M "\ft- S •\ * \ •'ft- ^ ^ f t ft: • > • > * N « \ ft- *\V0 VO rH f t CD LA LA •'ft- -ft C O CO -^i" CO CO E H C M LA , — 1 i — I • ' • ' • ' LA ^ ^ 1 CO C M i— 1 H C T V M O M O •'ft" ft" H ' ' O f t ' f t - f t - • > f t • ' • ' • ' LA ^ ^ f t f t t— i — 1 i — 1 rH rH C 5 > f t O i — 1 M O •'ft" ft" C O ^ OV LA rH COCOrH * M — I ^ rH CO ^ C M CO ft" rH ft" rH •>H VO * * ^ *\C0 • > D — C M rH "i CO C M * * * \ n t1 — t— 1 •iCM C M i — 1 h h C M C M H H C M H rH rH •'M O • > ^ •\ » \ [^— •'ft- ft" C M C M • > P — • » • » i— 1 rH CO ^ LAft" ^ •x •'CO ^ ^ CO OO O - LA-ft rH i — 1 i — I CO * > • > ^ LAft" LAft" rH O ^ • > H H H H LA-ft •n *v *v *>000000000000000 O O O O O O O O O • v * v ^ ^ * , ^ » , ^ i — ! 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I— I O O O 1 — 1 O --1-----1 I — I O 1 — I O I — it— I O O 1 — I rvrvrvrvrvrvrvrv rvrvrvrvrvrvrv - v r v - v r v r v r v r v r v •> fH i H O O O O O O O O O O O O O I — I O I — i O I — I I — I O O 1 — i rv' *v*\ *\ «\ «\ r\ *v»\ *\ *i *\ *\ *\ *V rv rv rv rv rv rv rv rv rv (^ )| 1 C M CO-H“ LO \V £) £ CQ O * 1 C M CO-H" i— i cm c n ^ r lomd t>~oo o > h h h h h h h h h h c j ( M w wcm O r v r v r v r v ^ r v ^ r v - V^ - > - > ^ ^ ^ » V rv r, rv -v r, r, *>000000000000000 (D O O O O O 1 —1 O *>•>•>•>•>*>*>*>*>•>•>*>*>•>•> * v rv * v » V • > ^ # v rv rv( 1 I l O O 1 1 < 1 O 1 1 O O I i O O I I O CD O I 1 O O ■ 1 O O I 1 *V*>rV*>*V*>*>*V*>*>*>*V*>*>*V rv rv rv rv rv rv »v rv *>OCDl“H O C D O r-ll—I H O O O H H O CD*— I H O O O--I--1 O 1 — 1 rvrvrvrvrvrvrvrvrvrvrvrvrvrvrv rv n rv ^ rv n *v n ^ O H O H H r l O O ^ H H H r l O H I—i < D I I I--I I I rvrvrvrvrvrvrvrvrvrvrvrvrvrvrv rv rv rv »V *> »> *> ^ *\ I—I O O O 1 1 O 1 —l O O H H H O O H i— 11— 1 1— i o o o o i— i o *»*>*>*>*>r' *># > # >*>*\*>,>*>*> • v » v * v -v ^ ^ ^ » v r v r H r H O O C D O O O r H r H r H O r H O i - ! 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V . - ' OOOOMOMOI-I 1> H O H 'O h -'O O O O l— 'H 1 - - - - - * - - - - - - - - - - - - - - O O O O O l ' M l —1 ! ‘ O h I -'H I-'H I-'H H O O '- v * * • v * * * v * v * v * v * — — — — — — — — — — — O I — ‘ O O | !|— 1 H O O OMMMMOMMMOO'' - - - - - - - - - - - - - - - - - - - | |Q|_J|_1J_1|_]| I O O 0 0 0 0 0 1 — ‘ O O m i— ■i — 1 ' * * • v * * • v * > • v * * • --- -- - — — — - — Q Q O O O O O O O O O O O O O O O O O O — — — — — — — — — w h h h m h h h h p h v d oo-o cm v ji 4hjo ro m o vo oo-o onui -t^oo ro i — ' O — — — — — — — — — — — — — — — — — — — — O l— ‘ O |— 1 O_ _| _*01_ _1 | 1 1 — ■ i— 1 ( O 1 —-* ^ 0 C ) I— * O — — — — — — — — — - - - - - - - - - - - o i— ‘O O O O O O O H O O O h O m OOHH'* - v * - v * - - - i* - - - - - - - - - - - O O O l— ■ (— ’ 1 — 'O O l— 1 O O C O C O C O C O C O C O C O C O C O - - - - - - - - - - - | I I 1 I—I |J O (.J I I O | 1 O h h O h H O h m O O 1 * - - - i* - - - - .. - - - - - - - - - - - O O O O l— ‘ O l— 'O h-• I I — ‘ Oh-‘ O l— ‘ O O O O h -‘ I — I'* ' * - • * - v * - - i * 1 1 — 1 - - - - - - - - - - - O O O O O h1 H‘ I — 1 'I— 1 O H 1 1 — ' H1 H1 H1 H1 I — 1 1 H1 O O - - - - - - - - - - - - - - - - - - - - O H O O H H H O O O h h M H O h h I-'OO'- - - - - V i v. i. v. - - - - - - - - - - - p O H n H M H O O O O O O O h -‘ O O l-'l-, h -‘' * v * * • V i - i* V . v . v * - — — — — - — — O O O O O O O O O O O O O O O O O O O O — — — — — — — — — V * U V * V 4 V * V a V * V » l « V « W CONFIGURATIONS H 1 H 1 H VJI M -Pr VO ID H '* v * v. v . v. | _ i ro v ji H 1 H 1 1 — 1 -trv v . vji O O h h ro ro v . Q v v . j — i (jO v * v * VJI On— q On i — 1 v . ro H 1 * * * VJI OV* Vi Vi - 4^ avv- vo o o no >. V. H M H ro V. V * Py3 V. V. V * VJI VJI I — 1 C D O O 1 — 1 1 -1 I— 1 Vi VO H 0 0 C O V. V # V * Vi v. — r x i rO C D -H v O ' - tH M v jiv ji v o c d i — 1 h 1 > Vi v, Vi |__ 1 Vi 0 Q HI O Vi Vi Vi Vi J i - l j O H 1 — 1 1 — 1 - o v. O0v C O VJ1VJI - o C O " " y OM— “ • VD v * H* i -3 CD 4= " 4^ ro 0 C O Vi Vi Vi v. V O V O v . u 1 — “ * ro v * V * l« C« V a s ; > VJI VJI VJI - o v. Vi s 4=-H> (JO —q > * H O 0 0 1 — * — - 4 1 — 1 o h3 Vi Vi Vi Vi C T v Qv w Vi (jOv- v. VOv- *1 - r o - ro M t?3 VJI VJI VJI G \ v . V. i VJIV. I — 1 H v OO I__1 V i { --- 1 V i f V. Vi V. V. v j l - f c r Vi —V] V. V. f Q V , o ro rocD O f v jiv jiv ji a v v v SJ H v H r o - H 1 V. V i Vi Vi Pd H v v v v LO ^ r O C JV V JI O - VJI- t-* h 1 o n vji 4=- H 3 VJI VJI VJI - p r v . V. w Vi Vi Vi |--- 1 Vi |— t j--- 1 V * Vi v« > T ) td Vi V. v. Vi ( j j > VO H 1 I —1 O LO - <3 - -HVO VO W V J I V J I - C r - t ^ v . V i tu v * O O O O v. V. 4 r Si v o - — - H C D Vi V. V. Vi ( J f J H I r o - - — 4 r o - o - C D H - H w • V J I V J I - P O j O v. V. It * - r o v o - - h 3 o n - h 1 - W V V V. v. [ \ 3 | \ ) I H V O O '* O M - " * H - 0 0 - V J I ' DO V J I V J I - f c T U ) v- v* lO - - r o - - o o o r o - h - i -3 V * V * V * V * py^) |__1 IO OV-pr- H H 1- s j - h 1- on > H VJI VJI -£-U0 v v - - -PrOOH'OO H V J I o o o - f-3 g Vi V. V. Vi |__ | |— 1 « 0 0 VO- - - - S i — — — i__i H O VJI VJI - t O j O v . v. H I v- - 4r | \ ) H H Q 4=-Hi o n - O t r 1 Vi Vi v« Vi |--- 1 J --- 1 D O 1 —1 H 1 - - VOVJI \* \ a \* |_1 s ; c i V J I V J I - p r u o v. v. iH ro - t ^ h - * r o - - c a - " 4 V J I H 1 O DO Vi Vi Vi Vi |__1 |__1 ^ 0 Vi Vi V, V. |__| | _ | cd — — o — o VJlVJIUO CD v. v H H H H U I - - 0 1 — 1 VO — H O V i V i V i V i [ _ _ _ 1 J _ _ _ | bd - - o o - r o o o b9 - - w h > v jiv jio o r o 1 - v - a H CO- 4=-- - i ___1 1_i — - i -3 V i V i V i V . |_ _ _ | |_ _ _ | 0 0 - H1- -HVD C D ro H C D 0 0 > v jiv ji ro r o v v H V * - V ] 1 — 1 1 — 1 - - i H v« v* v« v« X fx V i V i V i v« |__1 I__1 O v o - - - u o ro M i-3 vji -tr ro ro v - v s : v « |_1 |_1 \« v« S M V i v , V i V . |_ _ _ 1 1 C D CD VJI O n- 4= - D O g vji ro ro>- v V * V * V. |__1 v » W V i V i V i V i |_ _ _ 1 |_ _ _ 1 H 1 OVCD- ro rov. v. C D - - V i V . |_ _ _ 1 |_ _ _ | - H H V i V i ID CD VJI O - - - H1 - t V . H1 o cd APPENDIX I I I . 104 LEG END FOR APPENDIX IV Response numbers are in te r p r e te d as fo llo w s : 1 . A number p reced in g th e f i r s t "0" i s a channel number. 2 . A "0" i s a subsystem r e p a ir r e q u e st. J . The f i r s t number fo llo w in g a "0" i s a subsystem number. 4. The second number fo llo w in g a "0," i f any, i s th e s e le c t io n a f t e r an erroneous subsystem c h o ic e , i t i s : a . I f "1," a subsystem r e q u e st; th e n ext number i s a subsystem b . I f "2," a channel req u est; th e n ex t number i s a channel c . I f "3," a req u est f o r d is p la y o f th e m atrix 5 . Subsequent numbers are d e fin e d a s in th e above fo u r r u le s . 105 A PPEN D IX IV.A SU B JE C T 1 R E SPO N SE S O N SA T 1 S e- S y s- quence tern Response Number 1 3 1 7 i f 6 0 12 1 2 2 2 1 5 7 0 1 - 3 10 2 6 8 1 5 0 5 1 i f 6 7 1 8 0 13 - 5 8 2 i f 1 0 3 - 6 1 1 8 i f 6 0 3 - 7 ll 2 6 3 7 5 0 6 - 8 9 2 i f 1 3 6 0 12 - 9 5 1 i f 5 3 2 7 0 6 10 12 6 7 2 i f 5 0 5 — ll 7 2 3 6 8 5 l 0 i f 12 k k 7 1 2 3 0 8 — 13 2 1 5 3 7 0 1 - I k 10 6 3 2 8 0 5 - 15 12 . 2 i f 1 6 7 0 9 - 16 3 5 7 3 2 0 1 - IT k 2 i f 7 8 3 0 5 3 18 8 2 6 8 l 5 0 i f - 19 6 7 1 2 3 0 15 - 20 1 8 6 i f 7 0 2 - 21 7 A 6 8 0 15 — 22 9 i f 6 7 l 0 3 - 23 11 i f 1 3 2 0 2 - 2 k 5 7 i f l 0 I l f - 25 11 2 6 A 5 8 0 15 - 26 9 i f 6 2 1 0 1 - 27 5 i f 8 7 3 0 7 l 6 2 8 l 8 3 6 i f 0 3 - - 2 9 10 i f 2 3 1 0 2 30 8 i f 3 5 1 8 0 i f 31 3 7 i f 8 3 0 6 l 7 32 7 i f 1 5 0 3 - 33 6 8 i f 3 6 7 0 2 - 3k 2 i f 8 7 6 0 i f - 106 APPENDIX I V .A — C o n t in u e d SUBJECT 1 RESPONSES ON SAT1 S e - S y s- quence tem Response Number 35 12 4 6 2 3 0 9 — 36 4 2 4 3 0 8 — 37 2 8 2 4 6 0 16 — 38 6 5 7 8 0 13 - 39 9 6 3 1 0 8 - t o 11 5 3 6 8 0 1 — 4i 12 6 4 1 5 8 0 4 — t o 1 8 5 4 6 0 4 l 2 — 43 7 l 2 4 3 0 13 3 0 2 t o 4 3 4 5 7 6 0 5 1 14 to 5 4 7 5 3 0 15 - to 10 3 2 4 6 0 2 — t o 8 6 4 3 2 0 2 — t o 3 8 3 7 4 0 12 — t o 3 4 5 6 7 0 2 - 50 2 8 2 5 7 0 1 - 51 10 4 3 1 8 0 4 1 7 52 6 4 7 5 3 0 13 53 8 6 4 2 1 0 3 54 1 8 3 6 4 0 3 55 11 6 3 5 2 0 6 56 9 4 2 3 7 0 12 57 5 5 4 8 7 0 7 l 6 - 58 12 6 2 3 7 8 0 5 - 59 7 5 2 3 l 8 0 4 - 60 4 5 6 4 2 0 8 — 61 2 4 5 3 7 0 1 — 62 10 4 3 5 2 8 0 5 63 12 4 6 2 3 0 9 64 3 8 4 1 7 0 1 65 4 4 5 6 7 0 4 66 8 4 3 5 8 1 0 — 67 6 5 3 l 2 0 15 — 68 l 5 4 7 6 0 2 - 1 0 7 APPENDIX IV.A SUBJECT 1 RESPONSES O N SAT2 Se- Sys- quence tem Response Numbers 1 8 4 6 5 8 2 0 2 6 l 5 3 8 0 13 — 10 6 3 2 4 0 12 - 4 2 5 7 6 2 1 0 5 5 3 6 7 2 5 4 3 0 l4 6 4 8 7 3 6 0 16 — 7 7 3 2 6 5 8 0 2 — 8 12 2 6 3 4 0 12 — 9 5 1 3 4 6 0 3 — 10 9 4 6 7 8 2 0 8 ll 11 4 8 1 2 6 0 15 — 12 l 3 5 6 0 4 — 13 4 4 1 7 0 15 - 14 3 6 5 7 2 l 0 5 15 12 4 1 5 6 7 0 3 1 6 10 7 3 5 6 0 1 - 17 2 8 5 1 2 0 1 - 1 8 1 1 6 4 3 2 0 1 — 19 6 8 1 3 5 0 14 - 20 8 6 3 7 5 0 1 l 5 21 5 1 5 6 4 2 0 2 - 22 11 4 6 7 5 0 7 - 23 9 4 3 2 5 6 0 4 - 24 7 3 7 5 6 0 1 - 25 8 4 5 6 3 0 10 - 26 10 6 4 2 8 0 16 27 1 7 8 3 2 0 2 28 5 6 3 1 7 2 0 15 29 9 5 8 4 2 T _ 0 22 30 ll 3 6 4 2 0 7 31 4 l 5 8 4 2 0 19 32 12 4 5 1 8 0 5 33 2 4 8 4 3 0 4 34 6 6 5 8 4 0 3 35 7 6 3 4 0 8 - 10 8 APPENDIX IV.A— Continued SUBJECT 1 RESPONSES O N SAT2 Se~ S y s- quence tem R esponse Number 36 3 1 8 5 4 2 0 2 37 3 3 6 2 8 4 0 9 - 38 8 8 4 1 5 .a 6 39 10 4 ’ 5 3 8 0 14 - 4o 11 5; 8 6 3 1 0 18 4i 9 4„:_ 7 8 2 6 0 12 — 42 6 7 8 4 3 0 13 - 43 -2 5 8 4 2 1 0 13 - 44 5 5 4 l 2 6 0 8 ^5 b . 5 4 8 7 0 14 46 7 3 6 2 4 0 7 - 47 1 5 4 1 8 6 0 2 48 12 3 2 4 8 6 0 12 49 8 6 5 2 3 4 0 22 - 50 6 8 4 7 5 3 0 13 - 51 10 4 7 2 6 0 12 - 52 2 5 4 6 l 3 0 5 - 53 3 5 4 7 8 0 14 - 5 b 4 5 4 8 2 0 16 — 5 5 7 6 7 2 4 8 O' 2 — 5 6 12 4 6 7 8 0 12 - 57 5 5 4 8 3 0 3 - 58 9 6 4 2 3 0 8 - 59 l l 6 3 4 l 5 0 15 - 60 1 5 6 7 8 0 4 — 61 b 5 4 8 7 6 0 15 - 62 3 3 4 5 7 0 5 - 83 . 12 4 5 8 6 7 0 3 - 6 b 10 5 6 4 2 l 0 1 - 65 2 5 4 8 1 2 0 1 — 66 1 5 4 3 2 0 i4 — 67 6 6 4 5 1 0 l 1 5 68 8 5 4 1 2 0 2 — 69 5 6 4 3 2 0 7 70 11 6 4 3 5 0 4 - 109 APPENDIX TV.A SUBJECT 1 RESPONSES O N SAT3 S e - S y s- quence tem R esponse Number 1 2 8 if 1 3 0 1 - 2 12 if 6 1 7 8 ' 0 1 - 3 3 7 8 2 if 5 1 0 19 if 4 7 1 if 2 0 2 - 5 9 7 if 1 3 5 0 1 — 6 7 8 3 if 2 5 0 8 — 7 5 7 1 2 0 7 - 8 6 7 5 8 2 0 16 - 9 1 7 8 3 5 0 3 - 10 10 7 8 2 5 1 if 0 13 l l l l 7 2 8 3 1 0 if — 12 8 7 6 5 2 if 0 2 — 13 if 7 5 1 2 6 8 0 if I k 7 7 8 5 3 0 3 - 15 12 7 1 if 0 9 1 7 - 16 5 7 if 3 1 0 7 - 17 9 7 3 l 0 if - 18 11 7 if 3 5 0 6 - 19 1 7 8 3 5 0 3 - 20 8 7 5 1 6 3 0 if - 21 6 7 5 l 6 3 0 19 - 22 10 7 1 6 3 0 1 — 23 2 7 6 5 0 l - 2 k 3 1 5 8 7 0 7 l 9 25 if 7 if 3 6 0 7 - 26 12 1 8 3 7 0 if — 27 2 l 7 6 if 0 2 - 28 6 1 if 5 2 0 16 — 29 7 7 8 3 5 0 3 - 110 APPENDIX IV.B SUBJECT 2 RESPONSES O N SAT1 S e- S y s- quence tern R esponse Number 1 3 7 1 2 6 0 2 - 2 2 5 7 if 1 0 1 - 3 10 1 + 6 5 0 7 - 4 6 7 1 5 3 0 13 — 3 8 6 1 3 0 3 - 6 1 5 if 8 '6 0 3 — 7 11 4. 3 5 2 0 6 - 8 9 6 if 2 3 0 12 - 9 5 5 8 7 0 6 - 10 12 if 6 5 8 0 5 - 11 7 6 5 1 8 0 if 12 k k 7 5 2 0 8 - 13 2 6 1 8 7 0 1 - I k 10 5 3 6 2 7 0 5 15 12 6 if 2 7 0 9 - 16 3 5 l 3 7 0 l - 17 k if 3 8 7 0 if 18 8 if 6 5 1 8 0 if 19 6 l if 2 6 5 0 15 20 1 5 6 7 0 2 - 21 7 6 5 3 2 1 8 0 22 9 6 3 if 0 3 - 23 l l if 6 5 3 2 0 2 2 k 5 if 8 7 3 1 0 lif 25 11 6 if 5 1 8 0 15 26 9 6 if 2 8 0 1 — 27 5 5 8 7 1 0 6 - 28 1 if 8 1 6 0 3 - 29 10 5 3 2 1 0 2 - 30 8 6 1 if 5 8 0 if 31 3 5 8 7 0 7 - 32 7 3 7 1 2 0 3 - 33 6 if 5 7 1 0 2 — 3 k 2 if 5 7 6 0 if — 35 12 6 1 3 if 0 9 - I l l APPENDIX IV . B— Continued SUBJECT 2 RESPONSES O N SAT1 S e - Sy se quence tem R esponse Number 36 4 4 1 2 5 0 8 - 37 2 5 4 8 6 0 16 — 38 6 5 4 3 7 0 13 - 39 9 4 1 2 8 0 8 - 4o l l 6 l 8 4 0 1 — in 12 6 4 8 5 1 0 4 42 1 4 5 7 6 0 2 — 43 7 4 6 2 3 0 2 — 44 4 4 5 6 7 0 14 - 45 5 4 1 2 5 0 15 - 46 10 4 2 3 6 0 12 — 47 8 4 6 2 3 0 2 — 48 3 4 5 8 7 0 12 - 49 3 4 5 6 7 0 2 - 50 2 4 1 3 7 0 1 - 51 10 4 6 5 0 7 - 52 6 4 7 5 3 0 13 - 53- 8 4 6 1 2 0 13 - 5^ 1 4 l 7 0 3 - 55 11 4 3 5 2 0 2 l 56 9 4 6 1 2 0 12 57 5 4 5 2 7 6 0 6 58 12 4 6 5 7 0 5 - 59 7 4 3 5 l 8 0 4 60 4 4 5 7 2 0 8 - 61 2 4 8 2 7 0 1 — 62 10 4 3 5 7 0 5 — 63 12 4 6 3 2 0 9 — 64 ' 3 4 8 2 7 0 1 — 65 4 4 5 6 7 0 4 — 66 8 4 6 5 1 8 0 4 67 6 4 4 1 8 3 0 15 68 l 4 5 6 7 0 2 — 69 7 4 6 5 l 8 0 15 70 9 4 6 1 2 0 3 - 71 11 4 6 2 3 0 2 - 11 2 APPENDIX IV.B SUBJECT 2 RESPONSES O N SAT2 Se- Sys- quence tem Response Number 1 8 k 5 5 2 0 22 — 2 6 5 1 6 5 0 13 5 10 6 5 5 k 0 12 1 + 2 5 8 k 2 0 5 5 5 5 k 5 6 0 1^ 6 4 1 * . 6 l 2 5 0 1 6 7 7 h 5 6 8 5 0 2 8 12 k 6 5 3 0 12 9 5 5 8 7 0 3 10 9 k 5 2 6 0 8 11 11 5 1 3 6 0 15 12 1 6 h 8 k 7 0 4 — 15 4 5 6 7 2 8 0 15 - 1J 4- 5 5 6 k 1 3 0 5 - 15 12 k 5 6 7 0 3 - 16 10 k 5 8 7 0 l — 17 2 k 6 5 2 1 0 1 - 18 1 k 5 8 2 1 0 1 19 6 k 8 7 6 5 0 i h 20 8 k 5 8 1 0 1 l 5 21 5 k 6 5 8 0 2 — 22 11 k 2 5 6 0 7 - 25 9 k 5 5 6 0 h - 2k 7 k 8 5 7 0 1 25 8 k 5 6 3 0 10 - 26 10 5 2 6 5 0 16 — 27 l k 8 7 l 0 2 — 28 5 k 6 3 8 5 0 15 29 9 k 5 6 3 2 0 22 - 50 11 k 5 2 6 0 7 - 51 k k 8 1 5 0 2 1 19 113 APPENDIX IV.B— Continued SUBJECT 2 RESPONSES ON SAT2 Se- Sys- quence tem Response Number 32 12 l + 5 3 . 6 7 0 1 1 33 2 1+ 8 5 6 0 4 - 3^ 6 4 8 7 1 3 0 3 - 35 7 l + 3 2 5 6 0 8 - 36 3 1+ 6 8 5 0 2 - 37 3 1+ 2 8 6 0 9 - 38 8 1 + 5 3 1 6 0 6 - 39 10 l + 7 5 2 6 0 l4 — 40 11 l + 3 2 5 0 18 4l 9 l + 3 2 6 0 12 — 42 6 l + l 3 6 5 0 13 1 + 3 2 l + 7 8 6 5 3 0 13 1 + 1+ 5 1+ 8 2 3 0 8 — 45 1+ 1+ 8 7 6 5 0 14 — 1 + 6 7 1+ 3 2 6 0 7 - 1+ 7 1 1+ 8 5 1 2 0 2 — 1+ 8 12 1+ 3 2 6 0 12 — 1+ 9 8 1+ 8 6 2 5 0 22 50 51 6 10 l + 1+ 7 3 8 2 5 6 3 0 0 12 13 — 52 2 1+ 7 8 3 2 0 5 53 3 ■ 1+ 7 8 2 3 0 13 2 51+ 1+ l + 8 7 5 0 16 - 55 7 1+ 3 8 5 0 2 — 56 12 l + 6 7 8 0 12 - 57 5 1+ 7 1 5 0 3 — 58 9 1+ 3 2 7 6 5 0 8 59 11 1 + 5 1 3 6 .0 15 - 60 1 4 8 5 7 0 4 — 61 l + 4 8 7 5 l 0 15 — 62 3 4 8 2 7 0 5 - 114 APPENDIX IV.B SUBJECT 2 RESPONSES ON SAT3 Se quence Sys tem Response Number 1 2 1 6 3 5 0 1 2 12 5 2 3 1 0 1 3 3 7 4 8 2 5 1 0 19 - 4 4 4 5 7 0 2 - 5 9 7 4 l 6 5 0 1 — 6 7 7 8 2 6 0 8 - 7 5 1 8 7 4 0 7 - 8 6 6 8 4 5 7 2 0 16 9 1 4 1 5 2 8 0 3 — 10 10 6 4 8 1 5 0 13 - 11 11 1 6 3 5 - 0 4 — 12 8 7 4 8 6 c 2 - 13 4 4 8 7 3 0 4 - 14 7 7 4 8 1 5 0 3 15 12 1 8 5 6 0 9 l 7 - 16 5 7 5 1 0 7 - 17 9 8 5 6 l 7 4 0 4 - 18 11 4 8 6 3 0 6 - 19 1 1 8 5 7 6 0 3 - 20 8 7 5 1 2 8 0 4 — 2 1 6 1 6 7 8 0 19 — 22 10 5 4 1 0 1 23 2 l 8 3 0 1 — 24 3 7 4 3 1 .0 7 1 9 - 25 4 1 8 5 6 0 7 — 26 12 1 8 6 3 0 4 — 27 2 1 6 5 8 7 0 2 - 28 6 1 8 4 5 2 0 16 — 29 7 1 6 8 5 0 3 - 30 3 1 5 6 3 0 10 - 31 8 7 8 5 3 0 3 - 11 5 APPENDIX IV.C SUBJECT J RESPONSES O N SAT1 Se- Sys- quence tem Response Number 1 3 7 8 1 4 3 0 2 — 2 2 8 7 5 4 1 0 1 — 3 10 6 4 1 8 5 0 4 1 4 6 8 4 1 7 0 13 — 5 8 3 2 1 4 0 3 — 6 1 4 1 2 6 0 3 7 11 3 2 7 5 0 6 — 8 9 4 6 2 0 12 — 9 5 3 7 4 0 6 - 10 12 4 3 5 7 0 5 11 7 3 4 5 0 4 - 12 4 4 7 2 3 0 8 - 13 2 5 4 0 1 - 14 10 3 4 5 7 0 5 - 15 12 4 3 7 5 2 0 9 - 16 3 5 4 7 3 0 1 — 17 4 4 6 8 7 0 4 — 18 8 8 6 4 5 1 0 4 - 19 6 4 1 8 3 0 15 - 20 l 5 6 7 0 2 — 21 7 3 4 5 0 4 3 1 0 22 9 4 6 2 1 0 3 23 11 3 2 4 1 0 2 24 5 4 3 8 6 0 14- 25 11 4 3 1 5 8 0 15 — 26 9 3 4 6 1 0 1 - 27 5 5 3 7 2 0 6 — 28 1 4 5 7 0 3 - 29 10 3 2 l 0 2 - 30 8 6 8 '4 5 1 o ' 4 — 31 3 5 3 7 2 0 6 1 7 32 7 5 3 4 1 0 3 - 33 6 5 6 4 7 0 2 - 34 2 4 6 7 2 0 4 — 35 12 4 2 6 3 0 9 — 36 4 4 5 7 2 0 8 - 116 APPENDIX IV. C — Continued SUBJECT 3 RESPONSES O N SAT1 S e - S y s- quence tem R esponse Number 37 2 4 3 6 7 2 0 16 38 6 5 3 2 7 0 13 - 39 9 4 6 7 5 0 8 4o 11 4 6 2 1 0 1 — 4 i 12 4 3 5 8 1 0 4 42 1 5 4 6 7 0 2 _ 43 7 4 6 3 0 2 — 44 4 4 6 3 1 0 14 — 45 5 5 3 7 8 0 15 46 10 4 3 1 2 0 2 Vf 8 4 6 3 2 0 2 48 3 5 3 7 4 0 12 49 3 5 4 6 7 0 2 50 2 4 3 7 1 0 1 51 10 6 4 5 0 7 52 6 5 3 1 7 0 13 - 53 8 4 6 2 1 0 3 — 54 1 8 6 4 1 0 3 — 55 11 4 3 5 2 0 6 56 9 4 6 1 2 0 12 57 5 4 5 2 7 0 6 58 12 4 7 5 0 5 59 7 6 4 5 1 8 0 4 6o 4 4 7 2 3 0 8 6 i 2 4 1 0 1 62 10 6 4 5 7 0 5 63 12 6 1 3 2 0 9 64 3 5 l 7 0 7 1 1 65 4 4 3 6 7 0 4 - 66 8 1 6 8 . 5 0 5 1 67 6 5 3 4 l 0 15 — 68 1 5 4 6 7 0 2 — 69 7 4 6 5 8 0 15 - 70 9 4 6 1 2 0 3 71 l l 4 6 2 3 0 2 — 72 5 5 4 6 7 0 14 - 117 APPENDIX IV.C SUBJECT 5 RESPONSES O N SAT2 S e - S y s- quence tern 1 8 6 5 2 6 k 6 3 10 5 i f 2 k 6 5 3 k 7 6 4 3 6 7 7 5 6 8 12 5 6 9 5 7 i f 10 9 5 i f ll ll 5 k 12 ~l k 2 13 k 5 4 l J + 3 5 7 15 12 5 3 16 10 5 6 17 2 7 1 18 1 k 2 19 6 2 I f 20 8 1 6 21 5 k 5 22 11 5 3 23 9 6 3 2 k 7 5 i f 25 8 1 5 26 10 5 3 27 1 5 I f 28 5 5 6 29 9 k 5 30 11 k 3 31 4 5 8 Response Number 3 if 2 0 22 3 8 0 13 3 2 6 u 12 3 1 2 0 5 — 8 5 0 lk — 2 if 5 1 6 — 2 8 0 2 „ 3 2 if 0 12 — 5 1 0 3 — 3 6 2 0 8 — 1 3 6 0 15 — 1 0 if — 6 l 3 0 15 - 2 1 0 5 - 6 7 0 3 - 8 7 0 1 - 0 l — 6 0 1 7 8 1 5 0 l k 5 0 1 l 5 — 8 l 2 0 2 k 2 0 7 — k 2 5 0 if — l 6 0 6 1 l 6 3 0 10 — 2 1 0 16 - l 7 0 7 1 2 k 1 3 0 15 - 8 1 2 0 22 2 6 0 7 — 1 2 if 0 19 - 11 8 APPENDIX IV. C — Continued SUBJECT 3 RESPONSES O N SAT2 S e - Sy se quence tern R esponse Number 32 12 A 5 8 7 0 1 1 5 - 33 2 5 6 1 3 0 . A - 3 A 6 5 1 A 6 0 3 — 35 7 A 3 6 2 0 8 — 36 3 5 1 A 2 0 2 - 37 3 5 6 2 A 0 9 - 38 8 5 A 6 7 0 6 — 39 10 ■ 5 3 6 A 2 0 lA Ao n 5 6 A 3 2 0 18 — A l 9 5 6 3 2 0 21 A 0 12 A 2 6 5 6 2 7 1 0 13 ^3 2 5 6 A l 2 0 13 — A A 5 5 A 8 6 1 0 6 8 - ^5 1 + 6 ' A 7 5 5 A A 8 7 7 0 0 7 lA — a t - 1 ■- 5 A l 2 0 2 - 1 + 8 12 5 A 6 2 0 12 — 1 + 9 8 5 A 8 1 2 0 22 — 50 6 5 6 A 1 2 0 13 51 10 5 A 3 2 6 0 12 - 52 2 5 A 6 3 2 0 5 — 53 3 5 1 A 6 3 0 .lA — 5A A A 6 1 2 5 0 16 55 7 A 6 7 8 0 2 — 56 12 A 6 8 7 0 7 1 12 57 5 A 6 1 3 0 3 - 58 9 A 6 8 3 2 0 8 — 59 11 A 6 5 l 3 0 15 — 6o l A 6 5 3 0 A — 61 A A 6 3 8 1 0 15 — 62 3 A 6 8 2 0 5 - 119 APPENDIX IV.C SUBJEC T 3 R ESPO N SES O N SAT} Se~ S y s- quence tem R esponse Number 1 2 1 7 if 0 1 - 2 12 1 6 3 5 0 1 - 3 3 1 6 3 if 7 0 19 — 4 if 1 6 3 if 0 if l 2 5 9 1 6 3 5 0 1 — 6 T l 6 3 5 0 8 - T 5 l 6 3 if 0 7 — 8 6 1 6 3 5 8 2 0 16 9 1 1 6 5 0 3 - 10 10 l k 5 6 8 0 13 — 11 11 1 6 3 5 0 if - 12 8 1 4 5 0 2 — 13 k 1 k 5 6 3 0 if — 1 k 7 1 k 3 5 0 3 - 15 12 1 k 5 6 0 9 l 7 16 5 1 k 5 6 0 7 - IT 9 1 k 3 6 7 0 if — 18 l l l k 3 6 0 6 - 19 1 1 k 5 8 0 3 - 20 8 1 k 3 6 7 0^ if - 21 6 l k 3 6 7 0 19 - 22 10 1 h 3 6 5 0 5 1 23 2 1 k 3 6 7 0 1 — 2 k 3 l k 5 6 0 7 1 9 25 4 1 k 5 6 0 7 - 26 12 1 k 3 6 7 0 if — 27 2 1 k 6 0 2 — 28 6 1 k 5 8 2 0 16 — 29 7 1 k 5 1 8 0 3 - 30 3 1 k 5 7 0 10 - 120 A PPEN D IX IV.D SU B JE C T U R E SPO N SE S O N SAT1 S e - S y s- quence tern R esponse Number 1 3 7 4 1 0 2 — 2 2 4 7 5 0 1 — 3 10 4 3 6 5 0 7 - 4 6 5 3 2 7 0 13 - 5 8 5 6 4 7 3 0 3 - 6 1 7 1 4 0 3 - 7 11 4 5 7 0 6 — 8 9 5 4 6 3 7 0 12 9 5 7 5 3 4 0 6 - 10 12 6 5 4 7 0 14 5 - l i 7 2 6 5 1 12 4 5 6 4 3 8 0 14 2 13 2 5 3 7 4 0 1 14 10 2 6 5 3 7 0 5 - 15 12 3 4 7 1 2 0 9 - 16 3 5 8 2 7 0 1 — 17 4 3 8 7 4 0 4 — 18 8 4 3 5 1 0- 4 — 19 6 5 8 2 4 0 15 - 20 1 4 8 3 6 7 0 2 — 21 7 3 4 5 1 8 0 15 - 22 9 2 6 4 3 0 3 23 11 2 4 0 12 3 6 0 1 24 5 4 5 6 7 0 14 — 25 11 r ~ 3 5 l 8 0 15 - 26 9 2 6 5 8 0 1 27 5 5 4 3 7 0 7 1 6 28 i k 5 7 8 0 3 - 29 10 4 l 6 7 2 0 2 - 30 8 6 3 4 5 1 8 0 4 31 3 5 1 2 8 7 0 6 1 32 7 5 l 3 2 0 3 - 33 6 7 5 6 0 2 - 34 2 7 8 6 3 4 0 4 - 1 2 1 APPENDIX IV . D — Continued SUBJECT 4 [RESPONSES O N SAT1 S e - S y s- quence tem R esponse Number 35 12 6 2 7 0 9 — 36 4 2 5 4 0 8 — 37 2 4 5 8 6 0 16 — 3 8 6 5 1 . 3 7 0 13 - 39 9 6 7 3 4 1 0 8 40 11 3 4 1 6 0 1 — in 12 4 3 5 8 1 0 4 42 1 5 4 8 7 6 0 2 43 7 - 6 2 7 0 2 — 44 4 3 4 6 7 8 0 14 45 5 5 3 7 4 0 15 46 10 6 2 3 0 2 — 47 8 6 2 7 0 2 - 48 3 7 5 3 1 0 12 - 4 9 3 5 7 4 1 0 2 - 50 2 7 8 2 1 0 1 - 51 10 4 3 5 0 7 - 52 6 5 4 3 7 0 13 - 53 8 2 7 3 6 0 3 - 5^ 1 7 5 4 0 3 - 55 11 2 6 3 7 5 0 6 56 9 3 2 6 0 12 - 57 5 5 3 4 7 0 7 1 58 12 2 6 3 5 7 0 5 — 59 7 6 4 5 1 0 4 - 60 4 3 8 5 4 0 8 - 61 2 7 1 0 1 62 10 6 7 5 4 8 0 5 6 3 12 2 3 7 0 9 64 3 7 1 0 1 - 65 4 5 7 4 6 0 4 — 66 8 3 8 7 1 5 0 4 6 7 6 7 4 2 3 0 15 68 1 4 5 7 6 0 2 - 1 2 2 APPENDIX IV.D SUBJECT 4 RESPONSES O N SAT2 S e- S y s- quence tem R esponse Number 1 8 5 2 8 6 4 0 22 - 2 6 3 2 1 6 5 0 13 - 5 10 4 7 8 6 0 12 - 4 2 6 3 5 l 0 5 - 5 3 3 2 8 1 7 6 0 i4 6 k 3 8 7 k 0 16 — 7 7 8 k 5 0 2 — 8 12 1 + 3 6 8 0 12 - 9 5 6 4 3 0 3 — 10 9 2 6 8 7 0 8 - 11 11 k 3 5 6 7 0 15 - 12 1 k 8 6 7 0 4 - 13 k 6 1 k 7 0 15 - i4 3 k 3 6 2 0 5 - 15 12 2 k 6 7 5 0 3 - 16 10 5 8 1 0 1 - 17 2 2 5 7 8 1 0 l - 18 1 2 5 8 0 1 — 19 6 5 8 4 3 0 14 - 20 8 6 5 k 8 7 0 1 l 21 5 3 k 6 8 2 0 2 — 22 11 k 3 5 7 0 7 ■ - 23 9 3 ~9 ' 7 2 6 0 4 - 24 7 5 6 4 8 1 0 1 — 25 8 3 2 8 7 0 10 - 26 10 3 6 5 k 0 16 - 27 1 3 5 8 6 0 2 — 28 5 6 3 8 5 2 0 ‘29 9 7 5 2 1 4 0 - 123 APPENDIX IV.D— Continued SUBJECT k RESPONSES O N SAT2 S e - S y s - quence tem R esponse Number 30 11 1 3 6 8 0 7 - k 1 5 8 6 if 0 19 — 32 12 3 if 6 1 5 0 5 - 33 2 2 3 5 if 0 if 3^ 6 2 5 if 3 6 0 3 35 7 3 7 6 2 0 8 - 36 3 1 if 5 2 0 2 - 37 3 3 8 7 1 if 0 9 - 38 8 5 2 8 6 3 1 0 6 39 10 if 2 6 8 0 lif - k o 11 1 2 if 6 7 5 0 18 ifi 9 7 5 6 3 2 if 0 12 if2 6 3 7 6 8 0 13 — if3 2 7 3 if 6 8 0 13 — k b 5 7 6 3 l 0 8 — ^5 k 8 1 3 6 0 lif - k 6 7 8 2 5 if 0 7 — k j 1 8 6 7 1 0 2 k 8 12 8 3 2 if 6 0 12 k 9 8 8 1 6 0 if 1 12 3 50 6 3 1 6 5 0 13 - 51 10 if 2 6 5 0 12 - 52 2 8 6 if 7 2 0 5 — 53 3 7 8 1 5 3 0 lif — 54 if 7 1 8 3 if 0 16 - 55 7 8 if 5 7 0 7 1 - 56 12 if 8 7 6 0 12 - 57 5 if 8 7 3 1 0 3 - 58 9 if 3 6 2 0 8 - 59 11 if 6 1 3 5 0 15 124 APPENDIX IV.D SUBJECT 4 RESPONSES ON SATJ B e - S y s - q u en ce tem R esponse Number 1 2 8 4 7 0 1 _ 2 12 8 4 5 7 0 1 — 3 3 4 1 7 6 3 0 19 — 4 4 5 8 7 0 2 — 3 9 8 7 4 0 1 — 6 7 8 7 6 0 8 — 7 5 8 4 7 1 0 9 l 7 - 8 6 7 8 4 5 2 0 16 9 1 8 3 7 0 3 - 10 10 8 7 6 4 5 1 0 15 - 11 11 8 5 6 7 l 0 4 — 12 8 8 7 5 0 18 1 2 13 4 8 4 6 1 3 0 4 — 14 7 8 4 6 1 5 .0 3 — 15 12 7 4 1 0 7 - 16 5 6 4 8 1 7 0 7 - 17 9 6 4 8 1 7 0 4 — 18 11 4 6 1 7 0 6 — 19 1 8 4 6 1 0 3 - 20 8 8 4 6 1 0 4 — 21 6 7 5 4 l 6 3 0 19 - 22 10 8 4 5 7 2 0 1 — 23 2 8 7 5 0 1 - 24 3 8 4 5 1 6 0 7 1 9 1 2 5 APPENDIX IV.E SUBJECT 5 RESPONSES ON'SAT1 S e - S y s- quence tem. R esponse Number 1 3 7 1 3 4 0 2 — 2 2 1 8 7 0 1 — 3 10 4 6 5 0 7 — 4 6 4 1 3 7 0 13 - 5 8 4 6 1 2 0 3 - 6 l 5 4 7 0 3 - 7 11 6 4 5 2 0 6 — 8 9 6 4 7 1 0 12 — 9 5 8 5 7 0 6 - 10 12 3 7 5 0 5 - 11 7 4 6 1 8 5 0 4 — 12 4 6 3 4 5 8 0 - 13 2 5 8 l 7 0 9 2 4 i4 10 6 4 5 7 0 5 - 15 12 6 l 2 3 0 9 16 3 8 2 5 7 0 1 - 17 4 6 8 4 0 10 2 7 0 18 8 6 4 5 8 1 0 4 19 6 8 2 4 5 0 15 - 20 1 5 4 7 6 0 2 — 21 7 6 4 1 5 8 0 15 - 22 9 6 4 2 1 0 3 - 23 11 6 4 3 2 0 2 — 24 5 8 7 4 l 0 l4 — 25 11 4 3 1 8 0 15 — 26 9 6 4 2 3 0 1 — 27 5 8 3 7 0 7 1 6 - 28 1 8 6 3 l 0 3 — 29 10 6 4 2 3 0 2 - 30 8 6 4 8 5 1 0 4 - 31 3 5 4 2 7 0 6 l 7 32 7 6 4 2 3 0 3 — 33 6 8 3 6 4 7 0 2 - 54 2 4 5 6 7 0 4 — 35 12 4 6 3 2 0 9 - 126 APPENDIX IV.E— Continued SUBJECT 5 RESPONSES O N SAT1 S e - S y s- quence tem R espon se Number 36 k k 7 5 6 0 8 37 2 k 8 5 6 0 16 — 38 6 k 8 2 7 0 13 - 39 9 k 6 2 1 0 8 - if O 11 k 6 2 1 0 1 — In 12 k 6 8 5 1 0 k if2 1 k 8 5 6 7 0 2 43 7 k 6 2 3 0 2 — ifif 4 k 5 6 7 0 Ik - k$ 5 k 5 7 3 0 15 - k6 10 if 6 2 3 0 2 — k j 8 k 6 2 3 0 P kd 3 k 5 2 7 0 12 — ks 3 k 5 7 6 0 2 - 50 2 k 5 7 3 0 1 - 51 10 k 6 8 1 5 0 7 52 6 k 5 7 3 0 13 - 53 8 k 6 2 0 3 - 5^ l k 5 7 0 3 - 55 11 k 6 5 2 0 6 - 56 9 k 6 2 1 0 12 - 57 5 if 5 2 7 0 6 - 58 12 k 6 5 8 0 5 — 59 7 k 6 5 8 1 0 if 60 if k 5 7 6 0 8 — 6 1 2 k 5 7 3 0 l — 62 10 k 6 5 8 0 5 - 63 12 k 6 2 7 0 9 - 6k 3 k 5 7 l 0 l — 65 k k 5 7 6 0 4 - 66 8 k 6 1 8 5 0 if 67 6 k 5 8 2 0 15 — 68 1 if 5 7 6 0 2 — 69 7 k 6 5 8 0 15 - 70 9 k 6 1 2 0 3 - 127 APPENDIX IV .E SUBJECT 5 RESPONSES O N SAT2 S e - S y s - quence tem R esponse Number 1 8 8 b 5 1 0 17 2 0 2 6 1 5 3 8 0 13 — 3 10 8 7 6 4 0 12 — if 2 8 1 b 2 0 5 _ 5 3 8 1 5 6 0 lif — 6 if 8 1 3 If 0 16 — 7 7 6 7 8 0 2 - 8 12 6 5 3 b 0 12 - 9 5 8 2 7 1 3 0 3 - 10 9 6 7 8 l 2 0 8 — 11 11 6 3 7 ■ 5 8 0 15 — 12 l 5 8 1 2 3 0 if — 13 if 8 5 7 b 6 0 15 _ lif 3 5 7 8 6 3 0 if 1 15 12 6 2 7 5 If 0 3 — 16 10 6 5 7 8 0 1 — 17 2 6 3 b 2 1 0 1 — 18 1 if 8 5 2 1 0 1 — 19 6 b 6 3 8 0 13 2 1 20 8 b 5 1 6 0 5 - 21 5 b 6 5 7 0 2 — 22 11 b 6 5 7 0 7 - 23 9 b 6 5 7 2 0 k — 2 ^ 4 - 7 b 5 8 7 0 1 - 25 8 b 5 6 8 3 0 10 .26 10 6 7 b 3 0 16 — 27 l k 5 2 8 6 0 2 — 28 5 k 6 3 8 1 0 15 — 29 9 it 5 8 6 2 0 22 30 11 b 7 6 5 0 7 - APPENDIX IV.E— Continued SUBJECT 5 RESPONSES O N SAT2 Se~ Sys- quence tem Response Number 31 4 4 5 2 8 1 0 19 - 32 12 4 6 1 5 0 1 1 5 33 2 4 5 2 8 7 0 4 3 ^ + 6 4 6 1 3 0 3 35 7 4 7 6 2 0 8 36 3 4 6 5 8 0 4 1 2 37 3 4 6 5 8 0 9 38 8 4 5 8 6 0 6 — 39 10 4 7 6 5 2 0 i k — 4o 11 4 7 6 2 3 0 18 — in 9 4 7 6 5 0 12 — 42 6 4 6 3 8 0 13 43 2 4 6 3 8 0 13 — 44 5 4 6 5 8 3 0 8 45 4 4 6 3 8 1 0 I k — 46 7 4 7 6 5 0 7 — 47 1 4 6 5 1 8 0 2 - 48 12 4 7 6 5 0 12 49 8 4 5 8 6 2 0 22 - 50 6 4 6 3 5 8 0 13 - 51 10 4 7 6 5 0 12 - 52 2 4 6 3 2 0 5 — 53 3 4 6 3 8 1 0 I k 54 4 4 6 1 2 5 0 16 — 55 • 7 4 7 6 8 0 2 — 56 12 4 7 6 2 6 0 12 - 57 5 4 6 1 3 0 3 - 58 9 4 7 6 2 0 8 - 59 11 4 5 8 7 6 0 15 60 l 4 6 5 3 0 4 129 APPENDIX IV.E SUBJECT 5 RESPONSES O N SAT^ Se- Sys- quence tem Response Number 1 2 : 7 4 3 6 0 1 — 2 12 8 1 6 4 3 0 l — 3 3 8 1 6 4 3 0 19 - 4 4 8 1 6 4 0 2 — 5 9 8 1 6 4 3 0 l — 6 7 8 l 3 6 4 0 8 - 7 5 8 1 5 6 0 7 - 8 6 8 1 4 5 2 0 16 9 1 8 1 7 6 0 3 - 10 10 8 1 4 5 0 13 — n n 8 1 3 6 0 4 - 12 8 8 1 3 6 7 0 2 — 13 4 8 1 3 6 0 4 — 14 7 8 1 5 3 6 0 3 - 15 12 8 1 5 6 0 9 1 7 16 5 8 1 5 0 6 2 5 6 17 9 8 7 5 1 0 4 - 18 11 8 7 4 3 0 6 - 19 1 8 7 5 4 0 3 - 20 8 8 7 5 3 0 4 - 21 6 8 l 6 4 3 0 19 - 22 10 8 1 6 4 3 0 l - 23 2 8 1 3 0 l — 24 3 8 7 4 l 0 7 l 9 25 > .. 4 8 7 1 2 0 7 - 26 12 8 7 5 3 0 4 - 27 2 8 1 6 4 0 2 — 28 6 8 l 4 5 2 0 16 - 29 7 8 7 5 3 0 3 - 30 3 8 7 l 5 0 10 - 31 8 8 7 5 3 0 3 - APPENDIX V.A SATELLITE 1 COEFFICIENTS r Coefficients Mean ( Selected Category Coordinates Nonselected Category Subject Step l 2 3 4 5 6 1 -.0 2 9 9 3 .02051 .02676 .03339 -.02649 .00384 - .8 6 2 .123 1 2 .01285 -.0 1 6 1 1 -.00154 -.0 5 3 6 9 .00330 .01463 .968 - .1 7 0 3 .00256 .01136 .00352 -.0 3 9 6 3 -.0 0 2 6 0 .00912 .785 - .2 1 2 1 - .0 2 9 7 3 .02653 .03058 .03805 -.0333^ -.0 2 0 2 9 -I.236 .177 2 2 -.0 0 1 9 6 -.014-01 -.0 0 0 2 7 -.0 5 6 3 5 .00611 . .00623 1 .1 1 0 -.185 3 -.0 0 7 6 9 .01818 .00140 -.03646 -.0 0 3 8 3 -.0 1 1 7 6 • 975 - .2 6 8 1 -.04853 -.00487 .05602 .02994 -.0 2 9 2 2 -.0 0 1 7 8 -1 .1 8 6 .169 3 2 .00723 .00940 .00034 .05565 -.0 0 9 4 3 -.02240 -1 .0 0 9 .172 3 -.0 0 7 2 2 .00966 .00505 -.0 4 3 6 6 -.00094 .00818 I.083 - .2 8 1 1 -.0 4 3 3 1 -.0 0 6 9 6 .01854 • 01575. -.0 0 1 1 8 .00484 -.712 .102 4 2 . 0^582 .01177 -.0 2 5 7 6 -.0 1 4 1 9 •00753 .00380 .857 -.148 3 .00531 .02546 -.0 1 6 0 7 -.0 2 2 5 4 .01877 .00993 .707 -. 174 1 -.0 3 5 1 6 .02762 .03611 .03870 -.0 3 2 0 5 -.0 1 9 0 5 -1.363 .195 5 2 -.0 1 0 3 3 -.0 2 0 1 0 .00881 -.0 5 6 5 2 .00480 -.0 0 1 0 0 1.312 - .2 2 5 3 -.0 1 0 7 2 .00777 .01242 -.04425 -.01145 -.00605 • 950 - .2 5 8 Note: For correlation and for interpretation over subjects, steps and problems, the signs were reversed as necessary to make the comparisons meaningful. i — 1 uo o APPENDIX V.B SATELLITE 2 COEFFICIENTS Subject Step Coefficients Mean Coordinates ■ Selected Nonselected , Category Category l 2 3 4 5 6 1 -.0 0 7 5 3 -.1 2 0 9 8 .01757 .02485 -.00624 -.04456 - .6 8 1 .097 1 2 .01002 .01191 -.0 3 1 0 7 .05574 .01927 -.0 0 3 7 8 CO £ • 1 H O 3 .01025 -.OO63O .00323 -.0 3 6 7 3 -.0 0 8 7 3 -.01019 .664 1 • H 1 .04025 -.03946 -.0 5 1 8 6 .03383 .00194 -.0 0 2 8 2 -1.584 .226 2 2 .03162 .00182 -.0 3 5 6 1 .06334 .03264 -.0 2 2 1 6 - .9 1 9 .1 6 1 3 -.0 0 2 9 2 .00548 -.00642 .05263 .00971 .00016 -1 .0 2 3 .2 2 1 1 .04421 -.0 6 7 4 0 .00751 .03482 -.0 1 8 1 9 -.0 2 7 8 7 - .6 8 1 .097 .3 2 -.0 1 0 1 6 -.0 0 7 4 1 .01673 -.0 5 8 2 0 -.01057 .03130 l.o46 - .1 8 0 3 -.0 0 1 9 2 .01172 -.0 0 0 8 1 -.04430 .00018 .01822 .801 -.172 l -.OI578 -.2 8 9 9 5 .02291 -.03333 - .00171 .314 -.045 4 2 .03462 .05629 .00436 .02480 -.01647 -.0 0 5 8 7 .520 - .0 8 8 3 .01958 .05279 .01628 -,0 0 2 1 3 -.0 1 8 7 8 .00811 . 73^ -.159* l .03719 -.0 4 6 9 8 -.0 4 5 1 6 .03518 -.0 0 0 5 2 -.0 0 7 9 6 -1.483 .212 5 2 -.01033 .00050 .00681 .06658 -.01048 .00258 - .8 7 2 .152 3 -.0 0 7 1 0 -.0 0 9 1 5 -.0 0 5 0 6 .05416 - -.0 1 5 0 6 -1 .2 1 2 .2 6 7 Note: For correlation and for interpretations oyer subjects, steps and problems, the signs were reversed as necessary to make the comparisons meaningful. i-1 uo t - J APPENDIX V.C .SATELLITE 5 COEFFICIENTS Coefficients ! Mean Coordinates ■Selected Nonselected Category Category Subject Step 1 2 3 4 5 . 6 1 .16147 -.00815 -.17453 -.0 6 0 5 9 .17002 .02685 1.483 -0 .2 1 2 1 2 .00992 -.01463 -.02449 .03193 .00308 .00149 -.755 .126 3 -.00428 .00409 .OO 675 -.0 3 7 2 7 -.0 0 9 1 3 -.0 1 9 2 6 1.433 - .3 2 1 1 -.1 6 6 7 4 .02366 .16845 .06696 -.1 9 1 3 8 -.0 4 7 2 3 -1.015 .145 2 2 -.OO777 -.0 1 6 3 0 .01929 -.04944 -.0 0 8 5 2 -.0 0 1 9 5 1 .0 2 1 - .1 7 0 3 -.00017 -.0 1 6 1 3 .00240 .04165 -.0 1 1 7 8 -.0 0 2 3 8 -1.013 .236 1 -.1 3 9 1 5 .04360 .16577 .08845 -.2 0 9 4 9 -.0 5 7 8 9 -2 .0 9 2 . 2 9 9' 3 2 .08919 -.0 1 9 0 8 -.0 3 8 5 3 -.0 3 7 2 1 .04219 .03400 1.793 -.299 3 .05144 -.01571 -.0 2 5 6 8 .03737 .00939 -.0 0 2 3 8 -1.324 .280 1 .14718 -.0 1 3 6 9 -.1 5 5 9 4 -.0 0 7 6 4 .14188 .04282 -2.024 .289 4 2 .05428 .01369 -.0 2 1 6 8 -.00141 .01753 -.0 0 0 9 9 L f \ K\ OO -.139 3 -.0 4 5 5 4 -.03379 -.00241 .00200 -.00405 - -.837 .195 1 .07208 .05384 -.07548 .05344 - .02788 -4.378 .625 5 2 -.0 2 2 8 7 -.0 1 8 0 1 .02823 -.0 4 5 9 2 -.0 1 3 9 2 -.0 1 2 0 5 1 .7 2 1 I r o 00 -3 3 -.00314 -.0 0 5 0 6 ,oi4i8 .05438 -.0 3 3 1 0 -.0 3 0 4 3 -.993 .2 2 1 Note: For correlation and for Interpretations over subjects, steps and problems, the signs were reversed as necessary to make the comparisons meaningful. M r o 133 APPENDIX VI .A M E A N S A N D STA N D A R D DEVIATIONS FOR STEP 1 Sub ject Vari able SAT1 SAT2 Mean Std. Dev. Mean Std. Dev. Gp. A* Gp. B** Gp. A Gp. B Gp. A Gp. B Gp. A Gp. B 1 1 72.23 61.32 i3.ll 22.85 8 2 .8 7 8 0 .1 2 1 1 .9 2 17.78 2 94.16 87.97 8.83 13.78 9 8 .1 0 96.25 2 .3 0 3-75 3 64.62 55-14 18.33 27.44 75-64 77.52 14.98 17.90 2 5 .1 8 55.43 2 6 .8 0 33-62 24.28 4o.oo II.69 ' 31.30 5 7 2 .6 8 72.15 18.46 2 1 .9 8 6 1 .1 2 6 7 .0 9 1 5 .0 1 2 1 .6 2 6 6 5 . 6b 6 9 .6 8 16.48 1 7 .6 8 79.81 7 6 .8 0 1 6 .2 8 I6 .3 6 2 1 7 2 .1 2 6 1 .3 2 8.39 2 3 .0 6 86.40 79-66 5.47 1 8 .0 8 2 9 6 .3 9 8 7 .7 9 4 .5 0 1 3 .6 8 9 8 .7 6 9 6 .1 8 0.43 3.78 3 65.27 55.13 1 0 .6 2 2 7 .8 2 9 2 .6 0 75-10 7 .8 2 17.46 4 1 7 .2 0 55.90 2 1 .5 8 33-02 1 0 .1 2 4 2 .4 7 9 .8 9 2 9 .8 1 5 74.32 71.55 15.93 2 2 .2 7 72.96 65.47 1 9 .8 0 2 1 .0 1 6 7 1 .9 8 6 8 .9 0 1 8 .9 0 1 7 .2 2 74.68 77.47 2 1 .8 3 15.45 3 l 71.25 61.39 7.94 2 3 .1 7 76.34 8 1 .1 0 12.84 17.63 2 9 7 .2 2 8 7 .7 0 3 .6 3 13.57 97-62 9 6 .3 4 ' 2 .8 1 3-71 3 59.38 55.95 13.36 27.91 75.74 77.51 13.14 1 8 .0 9 4 17.50 5 6 .0 7 1 7 .2 6 33-40 2 9 .2 8 39.74 2 2 .0 2 30.85 5 68.15 72.55 15.99 2 2 .2 2 67.48 6 6 .2 5 17.14 2 1 .5 0 6 67-73 69.47 1 6 .5 8 1 7 .6 2 79.70 76.76 1 8 .0 0 1 6 .1 2 4 1 74.84 60.95 1 5 .0 6 22.48 81.25 8 0 .0 4 15.47 17.50 2 9 4 .2 5 87.96 7.79 1 3 .8 6 95-79 9 6 .5 4 4.36 3.56 3 6 5 .9 1 54.95 2 1 .8 3 2 7 .0 1 79.60 7 6 .9 1 1 6 .1 4 1 7 .8 6 4 3 1 .9 6 54.46 2 5 .1 1 3 4 .5 6 36.17 3 9 .1 2 2 9 .2 5 30.17 5 7 0 .6 2 72.45 1 6 .1 9 2 2 .2 3 6 6 .6 7 6 5 .8 3 2 0 .3 6 2 1 .1 5 6 6 5 .6 1 6 9 .6 9 16.57 1 7 .6 7 77-81 77-46 1 8 .1 7 1 6 .0 5 5 l 7 2 .7 9 6 1 .2 1 5.57 2 3 .2 1 85.69 79.40 7.27 1 8 .1 0 2 9 6 .5 1 87.64 4 .1 7 1 3 .8 5 98.79 9 6.ll o.4i 3 .8 0 3 64.23 55-22 1 0 .2 0 2 8 .0 0 90.44 75-37 1 1 .4 7 1 7 .6 0 4 14.04 56.79 17.05 32.79 1 0 .5 8 42.77 9 .9 0 2 9 .7 9 5 7 2 .5 6 72.04 15.43 2 2 .3 2 71.15 65.19 2 0 .6 1 2 1 .0 1 6 71.51 6 8 .6 9 1 8 .1 5 17.43 7 6 .0 2 77.71 2 1 .5 7 15.44 *Selected category. **N onselected ca teg o ry . 134 APPENDIX V I . B M E A N S A N D STA N D A R D DEVIATIONS POR STEP 2 Sub ject Vari able SAT1 SAT2 Mean Std. Dev. Mean Std. Dev. Gp. A* Gp. B** Gp. A Gp. B Gp. A Gp. B Gp. A Gp. B 1 1 64.70 50.73 1 9 .6 1 25.65 67.40 58.90 17.99 22.97 2 90-55 79.67 1 2 .1 8 24.29 95-95 91.51 5 .2 2 II.7 6 3 48.73 37.41 41.16 40.55 64.07 49.25 34.78 35.92 4 14.18 35-75 13.43 22.85 13.31 25.34 9.46 17.79 5 41.82 3 7 .0 3 37-71 38.99 50.51 45.91 50.44 54.20 6 70.14 7 1 .6 9 1 7 .8 6 2 1 .0 1 67.48 70.25 18.64 20.49 2 1 61.46 4 9 .7 4 1 8 .6 5 2 6 .2 9 6 5 .5 0 6 2 .8 6 1 5 .9 8 2 1 .1 8 2 94.63 7 8 .2 9 7 .5 2 24.82 9 6 .5 0 89.85 5-55 14.96 3 5 2 .8 8 3 9.ll 42.08 39.91 57.96 5 2 .2 0 39.32 5 6 .8 8 i t 1 0 .0 7 3 7 .2 9 1 1 .2 2 23.25 9.96 25.24 5 .2 9 16.48 ■ 5 50.83 39.56 40.49 39.30 56.72 55-95 35.05 33-41 6 6 8 .8 6 72.24 19.85 20.19 7 1 .9 6 6 7 .8 6 2 7 .0 8 23.45 3 1 55.90 4 9 .8 3 17.56 25.32 64.92 6l.4l 13.25 2 5 .0 2 2 94.08 79.-25 10.96 24.50 97.14 9 2 .4 9 3-79 10.40 3 4 5 .9 2 37.13 5 8 .2 8 39.49 7 0 .0 6 6 0 .5 6 2 8 .4 9 5 6 .9 0 i t 13.25 35-73 1 2 .5 8 25.41 1 0 .8 2 24.51 8 .6 5 1 6.4o 5 4 5 .9 8 37.59 38.51 39.13 5 5 .8 6 5 2 .2 6 2 2 .6 2 54.46 6 7 1 .8 2 7 0 .1 6 20.14 2 0 .1 8 8 0 .7 0 69.4l 1 8 .8 8 19.77 I t 1 6 3 .9 2 17.04 4 9 .9 9 24.54 73.25 6 2 .6 6 20.44 2 2 .2 0 2 9 1 .4 3 13-55 78.64 24.57 95.25 9 1 .8 5 4 .9 7 II.8 9 3 3 6 .2 9 36.52 39-24 39-53 58.40 55.34 40.89 5 6 .8 5 i t 2 1 .2 5 2 0 .0 9 35.04 2 1 .9 8 2 0 .2 7 22.69 1 4 .8 0 1 6.84 5 36.50 37.25 42.68 4 0 .5 9 4 7 .6 2 5 2 .2 7 34.66 35-10 6 69-46 2 1 .5 4 71,92 2 0 .1 6 6 8 .0 0 71.31 2 2 .0 6 2 0 .8 0 5 1 6 0 .9 6 49.73 1 8. o4 2 6 .6 2 6 6 .5 5 6 0 .9 6 1 5 .8 8 2 1 .2 1 2 92.42 77-98 1 2 .0 8 2 5.65 97-35 8 9 .7 8 4 .1 5 14.82 3 58.56 5 6.ll 4 0 .5 5 39.45 54.60 50.63 5 2 .0 8 37.04 i t 9-39 58.46 1 2 .1 1 2 5 .2 1 8 .7 9 23.49 6 .5 0 1 5 .6 2 5 57-33 58.4l 5 9 .8 0 4 0 .1 9 55.85 55.18 2 7 .5 7 5 4 .8 9 6 62.63 73-24 2 1 .7 8 19.84 6 5 .9 6 69.42 2 0 .8 2 25.95 *Selected category. **N onselected category. 135 APPENDIX VI.C M E A N S AND STA N D A R D DEVIATIONS FOR STEP 3 Sub ject Vari able SAT1 SAT2 Mean Std. Dev. Mean Std. Dev. Gp. A* Gp. B** Gp. A Gp. B Gp. A Gp. B Gp. A Gp. B 1 1 49.43 46.18 13.25 2 1 .6 9 6 0 .1 2 5 1 .2 0 2 0 .2 9 24.46 2 93-02 79.42 11.79 2 2 .6 6 91.58 86.04 1 0 .6 6 1 7 .8 6 3 3 1 .8 2 29.45 44.58 42.94 25.44 2 8 .6 0 40.23 4 1 .3 1 4 1 5 .6 8 35.94 19.76 2 1 .8 8 15.56 31.39 1 6 .1 3 2 2 .9 2 5 30.98 2 6 .9 1 43.55 4o.l6 15.18 2 2 .7 1 25.95 3 5 .8 0 6 75.45 71.77 23.73 24.14 6 1 .3 0 7 2 .0 6 26.47 2 5 .0 9 2 1 46.37 46.94 12.54 2 2 .3 6 57.50 5 1 .8 0 14.96 2 4 .7 4 2 94.52 77.42 9 -8 0 2 3 .1 2 92.46 8 2 .1 7 12.63 2 0 .5 1 3 2 9 .8 1 3 0 .6 9 42.31 42.02 3 2 .0 0 3 0 .6 0 46.03 4 3 .5 3 4 1 3 .2 7 37.09 20.97 2 1 .7 4 1 2 .5 2 36.24 11.32 2 1 .0 2 5 2 9 .7 9 2 7 .9 2 42.28 3 8 .7 6 2 1 .9 6 24.52 34.15 37.60 6 68.77 74.55 2 5 .2 7 24.20 6 2 .8 8 7 0 .9 2 21.54 25.44 3 1 4 9 .2 8 47.24 1 2 .6 7 21.84 5 2 .2 0 52.37 15.40 25.34 2 93.40 78.85 1 0 .2 9 2 1 .7 3 9 4 .1 6 8 3 .6 8 8 .1 8 1 8 .8 0 3 38.30 24.86 46.87 4 0 .7 0 2 3 .4 7 2 9 .1 7 38.33 42.16 4 1 1 .1 7 37-82 17.39 2 1 .2 3 1 5 .2 0 33.71 14.57 22.74 5 33-21 2 1 .7 1 41.70 3 6 .4 5 19.65 34.01 3 6 .1 0 6 74.47 7 2 .2 5 2 4 .8 9 24.22 6 9 .3 3 6 7 .8 6 2 1 .9 8 2 7 .0 2 4 1 51.46 4 7 .4 9 1 5 .2 8 2 3.ll 59.76 4 7 .3 5 2 0 .6 3 2 1 .8 3 2 93.82 7 6 .8 6 11-93 23.89 96.52 8 6 .5 0 3.91 1 6.64 3 2 3 .0 8 23.42 42.68 42.48 35.13 2 8 .3 1 41.61 39.13 4 21.85 .37.44 1 7 .6 2 2 2 .3 4 2 1 .9 8 3 1 .9 9 16.33 2 0 .6 7 5 2 1 .2 8 1 8 .6 7 39.95 35.78 2 5 .8 3 2 6 .3 1 32.43 3 7 .6 6 6 74.13 71.87 23.99 2 2 .8 7 67.07 6 9 .6 3 25.50 2 5 .8 8 5 1 4 7 .3 7 44.45 1 2 .2 3 2 1 .3 9 6 0.4o 5 1 .5 9 20.55 25.75 2 9 2 .0 8 79.90 1 7 .1 6 21.49 9 7 .0 0 8 2 .3 9 3.30 1 9 .6 2 3 28.43 24.47 40.32 37.10 41.67 2 7 .9 8 48.74 43.69 1 2 .7 6 37-51 2 0 .8 0 2 1 .2 9 1 1 .1 5 3 5 .8 3 9.64 2 0 .4 7 5 2 6 .1 2 25.27 37.71 38.59 34.62 2 0 .9 5 42.75 35.58 6 7 2 .0 6 73.74 19.50 24.44 6 1 .6 5 6 5 .4 3 2 2 .7 5 2 6.4o *Selected category. **N on seleeted ca teg o ry . 136 Sub j e c t 1 2 3 4 APPENDIX V I. D M EANS AND STANDARD DEVIATION FOR SATELLITE 3 STEP 1 STEP 2 o r i o le Mean S td . D ev. Mean S td . D ev. Gp. A* Gp. B** Gp. A Gp. B Gp. A Gp. B Gp. A Gp. B 1 8 1 .9 3 6 8 .0 1 6 .4 4 2 2 .9 3 5 5 .8 3 5 4 .3 0 2 7 .4 9 2 6 .4 7 2 9 7 -5 2 8 9 .8 6 2 .0 5 1 3 .2 9 9 0 .9 0 8 4 .7 1 8 -7 9 1 5 .9 7 3 6 3 .3 8 6 6 .2 3 1 3 .5 6 2 3 .7 2 7 3 -1 4 5 0 .6 0 2 8 .0 0 3 3 -6 6 4 1 6 .0 3 4 2 .2 8 7 .5 6 3 0 .3 6 2 8 .8 6 3 7 .9 4 1 5 .0 8 1 7 .4 9 5 4 l . 4 8 5 5 .3 6 1 0 .4 2 2 1 -7 3 5 3 .3 8 3 9 .6 9 2 7 .0 7 3 3 -2 6 6 6 0 .2 4 6 8 .3 9 1 3 .3 3 2 8 .9 5 6 2 .6 6 6 6 .2 3 2 3 .4 3 2 1 .9 4 1 7 8 .5 5 6 8 .4 9 1 1 .9 4 2 2 .8 8 6 1 .2 6 5 0 .6 1 1 7 .8 0 2 5 .8 5 2 9 5 .7 1 9 0 .0 5 3 .2 8 1 3 .4 9 9 0 .6 8 8 5 .4 3 1 1 .7 1 1 6 .0 9 3 6 9 .8 1 6 5 .3 1 1 4 .9 5 2 3 .5 7 7 1 .9 5 5 1 .5 5 2 9 .8 2 3 2 .8 1 1 * 2 1 .9 4 4 1 .4 4 1 2 .4 8 3 0 .7 7 1 6 .1 3 3 5 .4 4 1 2 .8 2 1 9 .0 8 5 4 7 .9 4 5 4 .4 4 9 .8 9 2 2 .1 9 4 5 .3 2 4 3 .7 2 2 6 .3 1 3 4 .3 1 6 7 3 -1 6 6 6 .5 5 2 1 .5 5 2 8 .2 9 5 1 .7 4 6 4 .5 3 2 7 .8 2 2 3 .8 2 1 6 9 .0 0 6 9 .8 6 0 2 3 .5 8 7 1 .8 0 4 9 .3 1 1 5 .0 2 2 4 .0 1 2 9 6 .3 3 9 0 .0 8 3 .5 1 1 3 .2 7 8 9 .7 7 8 3 .7 9 8 .0 8 1 6 .2 6 3 7 1 .0 0 6 5 .1 4 0 2 4 .1 8 6 4 .7 7 5 2 .9 7 1 9 .7 5 3 4 .9 8 1 6 .0 0 4 2 .2 9 0 3 0 .4 9 2 6 .0 0 3 0 .8 8 8 .1 0 1 8 .5 9 5 5 5 .0 0 5 3 .4 3 0 2 2 .6 1 4 1 .8 3 4 4 .4 1 2 8 .7 6 3 2 .8 1 6 8 4 .0 0 6 5 .0 0 0 2 8 .7 3 7 4 .2 3 5 7 -1 2 2 8 .5 6 2 5 .9 9 l 7 9 -7 1 6 8 .3 3 8 .7 3 2 3 .0 2 6 7 .7 9 4 8 .1 3 1 7 .4 7 2 4 .4 7 2 9 7 .8 3 8 9 .8 6 2 .2 6 1 3 .1 9 8 8 .0 4 8 4 .2 4 1 2 .8 5 1 9 .8 0 3 8 9 .2 5 6 2 .5 4 1 9 .0 2 2 1 .2 2 4 9 .3 8 5 1 .9 6 3 0 .8 8 3 4 .3 0 if 1 0 .2 1 4 3 . l l 1 6 .6 0 2 9 .0 4 2 9 .4 2 3 4 .3 4 1 4 .1 7 2 1 .9 3 5 5 9 -7 5 5 2 .7 5 1 4 .2 6 2 1 .8 6 3 0 .5 4 4 2 .3 1 2 4 .5 6 3 4 .9 5 6 4 7 .7 9 7 0 .1 7 2 0 .7 2 2 7 .3 8 6 4 .3 8 6 2 .9 5 2 4 .7 3 2 4 .1 9 1 7 6 .2 6 6 8 .8 2 1 .4 4 2 3 .4 2 5 0 .6 1 5 0 .2 2 1 2 .4 5 2 5 .1 2 2 9 8 .7 4 8 9 .6 1 0 .6 3 1 3 .3 1 8 8 .0 0 8 4 .8 2 1 8 .4 7 1 8 .9 9 3 9 8 .6 1 6 1 .2 0 7 .7 2 2 0 .1 3 8 3 .2 6 4 8 .7 5 2 9 .0 0 3 1 .8 4 if 0 .5 2 4 4 .5 0 2 .8 7 2 7 .7 9 1 1 .3 2 3 5 .8 2 9 .9 1 1 9 .0 1 5 6 7 .9 4 5 1 .5 8 5-93 2 1 .7 5 5 7 .0 0 4 2 .1 2 3 0 .2 9 3 4 .8 0 6 4 0 .5 2 7 1 .2 1 2 .8 7 2 7 .4 1 4 9 .2 9 6 4 .1 8 3 0 .1 9 2 2 .6 0 137 APPENDIX V I .D - - C o n t in u e d MEANS AND STANDARD DEVIATION EOE SATELLITE 3 Sub- Vari- ject able STEP Mean 3 Std. Dev. Gp. A* Gp. B** Gp. A Gp. B 1 1 if8.83 5 0 .8 0 8 .9 8 24.74 2 9 2 .6 2 8 3 .0 5 11.74 14.37 3 lf2.33 2 9 .1 0 48.38 41.70 4 7.71 39.if2 8 .2 2 2 2 .2 2 5 2 9 .6 7 2 2 .7 6 37.80 34.20 6 54.21 8 0 .0 8 2 4 .9 7 24.50 2 1 4 5 .9 7 4 5.44 1 2 .9 0 23.94 2 95.53 8 2. 6i f 6.55 17.85 3 60.53 3 8 .8 7 44.31 44 .2 0 4 1 7. i f 7 ifO .1 7 1 6 .9 5 2 1 .2 3 C > 44.03 2 9 .1 9 3 6 .1 0 3 6 .6 7 6 6 3 .3 0 75.27 2 2 .1 0 25 .4 5 3 1 i + 2 .6 9 i f 6 .5 0 9.69 2 1 .7 1 2 ■ 9 2 .5 0 81.73 13.84 1 8 .6 3 3 7 6 .9 2 45-53 35.30 4 7 .4 8 4 1 5 .0 8 5^.28 1 6 .9 8 2 4 .9 6 5 57.23 3 2 .2 0 34.72 37.32 6 i f i f . 08 65.38 2 4 .4 3 2 7 .3 4 4 l 5 8 .8 6 i f 1. i f 7 2 0 .1 0 2 0 .9 7 2 9 2. i f 3 85 -if3 7.76 1 5 .9 9 3 50.76 3 9 .6 0 5 0 .1 2 48.14 i f 2 9 .5 7 36.74 27.13 23.51 5 2 2 .9 5 23.54 30.24 34.87 6 7 3 .1 0 7 8 .9 1 22.35 2 5 .2 6 5 l 5 1 .0 3 42.01 11.94 18.44 2 8 9 .2 9 8 1 .6 2 14.51 1 8 .5 8 3 i f 6 .77 24.82 48.19 37.29 i f lif. 71 3 3 .7 6 1 8 .5 1 2 0 .6 6 5 56.8if 2 1 .5 2 37-73 33-24 6 8 2 .1 6 84.95 23.39 19.65 *Selected category. ■ ^ N o n s e le c t e d c a t e g o r y . 1 3 8 APPENDIX V I I RANK ORDER OF COEFFICIENTS V ariable 1 2 S u bjects 3 4 5 1 Step 2 3 1 Step 2 3 1 Step 2 3 1 Step 2 3 1 Step 2 3 1 l 1 4 2 4 4 1 4 5 1 1 4 1 4 4 2 4 5 l 4 5 l 3 5 3 2 3 2 4 5 2 1 — 1 Eh 3 . 5 4 3 3 3 2 6 3 1 5 6 6 5 1 1 $ 4 6 6 6 6 6 6 ' 5 6 6 6 5 5 6 6 6 5 2 3 5 1 1 3 2 2 4 3 2 1 2 2 5 6 3 2 2 3 2 5 4 1 2 4 4 3 3 3 3 1 4 4 1 5 4 2 5 4 5 4 l 3 5 2 3 2 2 3 3 2 3 4 3 3 2 6 2 1 2 3 4 CVI EH 3 5 l 2 1 1 l 4 2 4 1 4 2 1 5 2 % 6 6 6 6 5 6 6 6 6 5 3 5 6 6 6 5 3 5 5 4 6 5 2 5 3 3 6 6 4 1 5 6 1 2 4 3 2 3 1 1 1 2 5 4 3 4 1 1 2 5 2 2 3 4 2 1 6 6 1 1 6 3 4 2 4 2 3 4 5 2 4 4 2 3 3 2 3 3 3 EH 3 6 1 1 6 l 5 6 6 1 l 6 4 1 1 5 S i 4 5 6 6 5 6 6 5 5 5 2 5 6 5 6 6 5 1 4 4 1 4 I l 2 4 5 2 3 2 4 1 6 3 3 5 3 2 3 3 3 3 4 4 5 4 2 2 v 1 3 9 APPENDIX V I I I .A AGREEMENT OP Ss' CHOICES ON SAT3 WITH DERIVED DISCRIMINANT FUNCTION ( SAT3) S u b jects Choice Order ; ------------- Step of Model 1 2 3 ^ 5 1 23 13 30 16 30 2 k 9 0 2 0 3 0 3 0 0 0 - 1 + 0 k 0 2 1 5 2 1 0 3 0 6 1 1 0 10 7 0 0 0 0 0 8 0 0 0 0 0 • Total 30 31 30 2k 31 - 1 9 2 7 3 3 2 k 6 5 1 6 2 7 l Total 29 16 20 11 23 7 5 5 0 1+ 5 k 0 1 0 3 1 3 0 0 7 0 0 1 0 0 0 0 0 31 30 2k 31 1 16 16 22 13 22 2 5 8 2 4 5 3 2 5 1 2 0 k 1 1 0 1 1 5 0 0 1 1 3 6 0 0 0 0 0 Total 2 k 30 26 21 31 i4o APPENDIX V I I I . B AGREEMENT OF Ss’ CHOICES ON SAT3 WITH ASSIGNED DISCRIMINANT FUNCTION (FROM SAT1-SAT2) Step Choice Order o f Model Subjects 1 2 3 . 4 5 1 12 1 30 8 30 2 17 13 0 11 0 3 1 9 0 2 1 1 4 0 2 0 0 0 5 0 4 0 2 0 6 0 2 0 1 0 7 0 0 0 0 0 8 0 0 0 0 0 Total 30 3. 1 30 24 31 1 14 10 6 11 26 2 3 l4 7 7 0 3 4 3 4 0 0 2 4 5 3 12 4 5 5 0 0 1 l 0 6 1 l 0 l 0 7 2 0 0 0 0 Total 29 31 30 24 31 1 14 11 14 7 20 2 6 11 1 7 6 2. 3 2 6 8 2 0 J 4 2 0 0 3 2 5 0 1 2 2 0 6 0 1 1 0 3 Total 24 30 26 2 1 31

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Creator Wong, Wilson (author)

Core Title The Discriminant Function As A Model For Diagnostic Problem-Solving

Degree Doctor of Philosophy

Degree Program Psychology

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

Tag OAI-PMH Harvest,psychology, experimental

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Davis, Daniel J. (committee chair), Priest, Robert F. (committee member), Wolbers, Harry L. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-654125

Unique identifier UC11361206

Identifier 6905076.pdf (filename),usctheses-c18-654125 (legacy record id)

Legacy Identifier 6905076.pdf

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Document Type Dissertation

Rights Wong, Wilson

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...

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