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Information seeking behavior among students of educational administration : a Bayesian normed study Angus, Fred 1978

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INFORMATION SEEKING BEHAVIOR AMONG STUDENTS OF EDUCATIONAL ADMINISTRATION: A BAYESIAN NORMED STUDY by FREDERICK GARNET ANGUS B.Sc. Mount A l l i s o n U n i v e r s i t y , 1971 B.Ed. Mount A l l i s o n U n i v e r s i t y , 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Department of Education A d m i n i s t r a t i o n ) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA February, 19 78 (c) F r e d e r i c k Garnet Angus, 19 78 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thesis fo r f i nanc ia l gain sha l l not be allowed without my writ ten pe rm i ss i on . Department of Friuratinnal flriministratinn The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 ABSTRACT The i n f o r m a t i o n seeking behaviour o f d e c i s i o n makers i s an important aspect o f the r a t i o n a l d e c i s i o n making pro c e s s . T h i s study examined the i n f o r m a t i o n seeking behaviour o f students o f e d u c a t i o n a l a d m i n i s t r a t i o n i n an attempt t o more f u l l y understand the d e c i s i o n making process and thus p r o v i d e a b a s i s f o r improving r a t i o n a l d e c i s i o n making. A s t a t i s t i c a l d e c i s i o n game was de v i s e d which u t i l i z e d a Bayesian norm. The value o f i n f o r m a t i o n to a d e c i s i o n maker was c a l c u l a t e d from the game and then compared to the value d e f i n e d by the Bayesian norm. The sample c o n s i s t e d o f twenty-nine p a r t - t i m e students e n r o l l e d i n w i n t e r s e s s i o n courses i n the U n i v e r s i t y o f B r i -t i s h Columbia (U.B.C.) Department o f E d u c a t i o n a l A d m i n i s t r a -t i o n . T h i s sample i n c l u d e d students with v a r i o u s amounts o f completed c l a s s work and e d u c a t i o n a l a d m i n i s t r a t i v e e x p e r i e n c e . Three independent v a r i a b l e s were d e f i n e d . The f i r s t v a r i a b l e , a d m i n i s t r a t i v e experience had two l e v e l s . One l e v e l c o n s i s t e d o f those with a t l e a s t one year o f a d m i n i s t r a t i v e experience, the other c o n s i s t e d o f those w i t h no a d m i n i s t r a -t i v e experience. The second v a r i a b l e , graduate l e v e l t r a i n i n g , had two l e v e l s . One l e v e l c o n s i s t e d o f those who had completed a t l e a s t t hree u n i t s o f graduate l e v e l course work i n educa-t i o n a l a d m i n i s t r a t i o n . The other c o n s i s t e d o f those who had not completed any coursework. The t h i r d v a r i a b l e , c o n s i s t e d o f three d i v i s i o n s with two l e v e l s each and i n t r o d u c e d v a r i a -t i o n a c r o s s the e i g h t games. The dependent v a r i a b l e , i n f o r m a t i o n seeking b i a s , was d e f i n e d as the d i f f e r e n c e between the q u a n t i f i e d value of i n -formation to the d e c i s i o n maker and t h a t v a l u e a s c r i b e d by the Bayesian norm. The sample was t e s t e d i n separate groups ranging i n s i z e from three to s i x . Each person i n a group viewed the same sequence o f e i g h t games, corresponding to the e i g h t treatment l e v e l s of f a c t o r C; however, each group had a d i f f e r e n t r a n -domly determined sequence of games. The f o l l o w i n g f i v e r e s e a r c h q u e s t i o n s were examined: (1) Do students o f e d u c a t i o n a l a d m i n i s t r a t i o n tend to seek the same amount o f i n f o r m a t i o n as p u r e l y Bayesian p l a y e r s i n a programmable d e c i s i o n s i t u a t i o n ? (2) Do students o f e d u c a t i o n a l a d m i n i s t r a t i o n w i t h adminis-t r a t i v e experience behave d i f f e r e n t l y than students w i t h no a d m i n i s t r a t i v e experience i n t h e i r tendency to seek informa-t i o n ? (3) Do students of e d u c a t i o n a l a d m i n i s t r a t i o n who have com-p l e t e d t h r e e o r more u n i t s o f graduate l e v e l t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n behave d i f f e r e n t l y than students with no t r a i n i n g i n t h e i r tendency to seek i n f o r m a t i o n ? (4) Among students o f e d u c a t i o n a l a d m i n i s t r a t i o n does v a r y i n g the p r i o r p r o b a b i l i t i e s and p a y o f f parameters i n the s t a t i s t i -c a l d e c i s i o n game e f f e c t the tendency to seek i n f o r m a t i o n ? i v (5) Does i n f o r m a t i o n seeking b i a s change over the sequence o f games? Does l e a r n i n g take place? The experimental design was based on Winer's (1971) three f a c t o r i a l repeated measure design (case I I ) . In r e -search q u e s t i o n f o u r a S c h e f f e T e s t was to be employed i f the p r e v i o u s a n a l y s i s i n d i c a t e d c e r t a i n combinations o f treatment l e v e l s i n f a c t o r C had r e s u l t e d i n s i g n i f i c a n t f i n d i n g s . Re-search q u e s t i o n f i v e was analyzed by graphing the i n f o r m a t i o n seeking b i a s f o r the v a r i o u s s u b j e c t groups over the sequence of games. I t was found t h a t the group as a whole showed a s t r o n g tendency to seek more i n f o r m a t i o n than the Bayesian o p t i m a l . The hypothesis t h a t the mean i n f o r m a t i o n seeking b i a s between the two l e v e l s of experience and t r a i n i n g was the same c o u l d not be r e j e c t e d . However, the i n t e r a c t i o n e f f e c t s between f a c t o r s A (experience) and C (repeated measures) and between f a c t o r s B ( t r a i n i n g ) and C were found to be s i g n i f i c a n t a t the .10 l e v e l . F i n a l l y , s t r o n g l e a r n i n g curves were noted f o r a l l s u b j e c t groups. As the sequence of games progressed, the mean i n f o r m a t i o n seeking b i a s f o r a l l s u b j e c t groups more c l o s e l y approximated the Bayesian o p t i m a l s t r a t e g y . I t was noted, however, t h a t experienced a d m i n i s t r a t o r s tended to approach the Bayesian optimal s t r a t e g y a t a f a s t e r r a t e than the non-experienced group. The study concluded by recommending t h a t programme de-v e l o p e r s i n e d u c a t i o n a l a d m i n i s t r a t i o n should a t t e n d to V (1) the previous t r a i n i n g and administrative experience of students and (2) the conditions under which decisions are made, when planning for future programs on decision making. v i TABLE OF CONTENTS Page LIST OF TABLES .' i x LIST OF FIGURES x CHAPTER 1. INTRODUCTION 1 DEFINITION OF CONCEPTS 2 THE RATIONAL PROCESS 5 REVIEW OF RESEARCH 7 A n a l y s i s of Closed System Decisions 8 The Bayesian Approach 9 Information i n R a t i o n a l D ecision Making.... 11 STATEMENT OF THE PROBLEM 12 General Problem Statement 13 Expected Outcomes 13 2. DESIGN AND METHODOLOGY 16 THE SAMPLE 16 DEFINITION OF VARIABLES 18 The Independent V a r i a b l e s 18 Grouping f a c t o r A (experience) 18 Grouping f a c t o r B (academic course work) 19 Repeated measures f a c t o r C 20 The Dependent V a r i a b l e 21 v i i EXPERIMENTAL PROCEDURES .. 26 Design o f the Study 29 Dimensions o f f a c t o r C 29 Procedures 31 T r a i n i n g o f Umpires 33 A d m i n i s t r a t i o n o f Game 34 RESEARCH QUESTIONS AND ANALYSIS 35 Research Question Number One. 35 Research Question Number Two 36 Research Question Number Three 38 Research Question Number Four 38 Research Question Number F i v e 39 3. RESULTS 41 Research Question Number One 41 Research Question Number Two 41 Research Question Number Three 4 4 Research Question Number Four 4 4 Research Question Number F i v e 50 4. INTERPRETATION OF RESULTS 55 LIMITATION OF THE STUDY 55 DISCUSSION OF RESULTS 56 Research Question Number One 57 Research Question Numbers.'Two and Three. . ^  59 Research Question Number Four; 60 Research Question Number F i v e 6 3 v i i i 5. SUMMARY AND IMPLICATIONS OF THE STUDY 65 SUMMARY OF EXPERIMENTAL PROCEDURES, RE-SEARCH QUESTIONS AND FINDINGS..... 65 IMPLICATIONS FOR THEORY, FUTURE RESEARCH AND PRACTICE. 70 BIBLIOGRAPHY 74 APPENDIXES 78 A. GAME INSTRUCTIONS AND RESPONSE FORMS 78 B. DERIVATION AND DISCUSSION OF BAYES 1 THEOREM.. 86 C. TRUE STATES FOR EACH CONDITION 88 D. SUMMARY NOTES FOR UMPIRES 89 E. SUMMARY OF GAT-IE PROCEDURES 91 i x LIST OF TABLES Table Page I . S i x Categories f o r Research Questions on Decision Making 3 I I . Sample Research Questions on the Behavior of Decision Makers 5 I I I . Payoff M a t r i x f o r Game Si m u l a t i o n : E n t r i e s i n D o l l a r s per P u p i l 22 IV. Dimension Levels of Factor C 30 V. Dimension Combination Display 30 VI. Experimental Payoff M a t r i x by Condition 32 V I I . Mean Information Seeking Bias f o r A l l P o s s i b l e Combinations of Factor A (Experience) w i t h Factor B (Training) 42 V I I I . A n a l y s i s of Variance f o r the Dependent V a r i a b l e , Information Seeking Bias 43 IX. Results of the A p p l i c a t i o n of the Scheffe Test to the Two-way I n t e r a c t i o n Between Levels of Both Factors A (Experience) and B (Training) under S p e c i f i e d Combina-t i o n s of Factor C 49 X LIST OF FIGURES Figure Page 1. Tree Diagram w i t h Choice P r o b a b i l i t i e s f o r Payoff M a t r i x i n Table Three: Given P e r f e c t Information 25 2. Mean Information Seeking B i a s over the Treatment Levels of Factor C at Factor A (Experience) 46 3. Mean Information Seeking Bias over the Treatment Levels of Factor C at Factor B (Training) -4 7 4. Mean Information Seeking Bias over a l l Subjects over the Sequence i n which the Games were Presented 51 5. Mean Information Seeking Bias f o r Groups at Levels 1 and 2 of Factor B (Training) over the Sequence i n which the Games were Presented 52 6. Mean Information Seeking Bias f o r Groups at Levels 1 and 2 of Factor A (Experience) over the Sequence i n which the Games were Presented. 53 x i ACKNOWLEDGEMENTS The author g r a t e f u l l y r e c o g n i z e s the support, c o n s t r u c -t i v e c r i t i c i s m and c o o p e r a t i o n r e c e i v e d from the f a c u l t y and students w i t h i n the U.B.C. Department o f Ed u c a t i o n A d m i n i s t r a -t i o n . The study would not have been p o s s i b l e without the support o f the students i n the f i r s t year d o c t o r a l seminare who acted as umpires f o r the game, the f a c u l t y members who allowed t h e i r c l a s s time t o be used f o r t e s t i n g purposes and the students who v o l u n t e e r e d to p a r t i c i p a t e i n the study. A s p e c i a l word o f a p p r e c i a t i o n i s due to the t h e s i s committee members, Dr. Jean H i l l s (Chairman), Dr. Graham Kelsey and Dr. Todd Rogers. I t was i n one o f Dr. H i l l ' s courses t h a t the i d e a f o r the study was born and through many i n f o r m a l meetings was shaped i n t o i t s present format. Dr. Kelsey's continued support o f t e n went beyond t h a t o f simply a d v i s i n g . During the data g a t h e r i n g he allowed c l a s s time, as w e l l as h i s own time, to be used f o r t r a i n i n g umpires and f o r a d m i n i s t e r i n g the game. Dr. Roger's suggestions as to a p p r o p r i a t e methodology made a d i r e c t c o n t r i b u t i o n to the exten t o f the study's f i n d i n g s . CHAPTER 1 INTRODUCTION In B r i t i s h Columbia, as i n most provinces, there i s an i n c r e a s i n g emphasis being placed on the masters degree q u a l i -f i c a t i o n as a p r e - r e q u i s i t e , -or at l e a s t a c o - r e q u i s i t e , to an a d m i n i s t r a t i v e p o s i t i o n i n the p u b l i c school system. Most u n i v e r s i t i e s are aware of t h i s trend and have endeavoured, at l e a s t i n p a r t , to provide programs which w i l l eguiperstudents of e d u c a t i o n a l a d m i n i s t r a t i o n w i t h the necessary p r a c t i c a l s k i l l s . H i l l s (19 77) , i n h i s i n f o r m a l a n a l y s i s of the Univer-s i t y of B r i t i s h Columbia (U.B.C.) Department of Ed u c a t i o n a l A d m i n i s t r a t i o n , recognized t h a t despite the lack of e x p l i c i t goals f o r the department there was at l e a s t a p a r t i a l commit-ment to the goal of t r a i n i n g f o r p r a c t i c e . One aspect of the p r a c t i c i n g a d m i n i s t r a t o r ' s behaviour which has been the subject of much i n t e r e s t ( S i n g l e t o n , 1972; Hoan, 1974; McCordic, 1974; Pedersen, 1975) i s tha t of d e c i -sion making. This i s an extremely complex process, For t h i s reason, researchers i n the f i e l d have found i t u s e f u l to cat e g o r i z e s t u d i e s of d e c i s i o n making i n t o s p e c i f i c areas of i n t e r e s t . Thus studies i n edu c a t i o n a l a d m i n i s t r a t i v e d e c i -sion making may f a l l under various academic d i s c i p l i n e s , most notably, the s o c i a l sciences and mathematics. In view of the importance of d e c i s i o n making behaviour i n p r a c t i c i n g a d m i n i s t r a t o r s , the goal of t r a i n i n g f o r prac-t i c e might be expected to in c l u d e a commitment to t r a i n edu-c a t i o n a l a d m i n i s t r a t o r s i n d e c i s i o n making. In the case of 2 e i t h e r an e x p l i c i t or i m p l i c i t commitment i t i s important to understand the f a c t o r s i n f l u e n c i n g d e c i s i o n making be-h a v i o u r , as w e l l as the impact of p r e s e n t programs on such behaviour. By drawing on r e s e a r c h techniques and f i n d i n g s from o t h e r d i s c i p l i n e s , t h i s study examined one aspect of d e c i s i o n making, s p e c i f i c a l l y , i n f o r m a t i o n seeking behaviour among students of e d u c a t i o n a l a d m i n i s t r a t i o n . DEFINITION OF CONCEPTS For the purpose o f t h i s study d e c i s i o n making was d e f i n e d as the process of choosing among two or more a l t e r n a t i v e s . The l i t e r a t u r e on the s u b j e c t tends to concentrate i n three areas; the d e c i s i o n i t s e l f , the d e c i s i o n maker, and the d e c i -s i o n p r o c e s s . Rubenstein and Hoberstroh (1966) p o i n t out t h a t t h i s l i t e r a t u r e has b a s i c a l l y two o r i e n t a t i o n s , normative and d e s c r i p t i v e . Normative s t u d i e s assume c e r t a i n c r i t e r i a r e -l a t i n g to the d e c i s i o n process and then u s i n g these c r i t e r i a d e f i n e what ought to occur. Having d e f i n e d the norm, compari-son with the a c t u a l processes can be made. D e s c r i p t i v e s t u -d i e s do not make any normative assumptions about the p r o c e s s , but r a t h e r , attempt to d e s c r i b e i n an o b j e c t i v e f a s h i o n what a c t u a l l y does take p l a c e . Thus most r e s e a r c h q u e s t i o n s on d e c i s i o n making can be p l a c e d i n t o one of the s i x c a t e g o r i e s d i s p l a y e d i n Table 1. The p r e s e n t study focused on r e s e a r c h q u e s t i o n s which f e l l w i t h i n category 3. 3 Table I S i x C a t e g o r i e s f o r Research Questions on D e c i s i o n Making Normative D e s c r i p t i v e D e c i s i o n 1 2 D e c i s i o n Maker 3 4 D e c i s i o n Process 5 6 S t u d i e s which examine the behaviour o f d e c i s i o n makers must a l s o c o n s i d e r the nature o f the d e c i s i o n and the d e c i s i o n process (Kast and Rosenzweig, 1970). The con t e x t i n which the d e c i s i o n maker operates can vary along a continuum from a r e l a t i v e l y c l o s e d system to an open system. By seeking i n -formation i n p u t s from v a r i o u s sources the d e c i s i o n maker tends to move the process towards the open end o f the continuum. For example i f an e d u c a t i o n a l a d m i n i s t r a t o r i s t r y i n g to de-termine s c h o o l p o l i c y he/she c o u l d move the process towards the open end o f the continuun by seeking i n f o r m a t i o n from a number of sources, such as, pa r e n t s , teachers and students. I f the d e c i s i o n maker does not seek f u r t h e r i n f o r m a t i o n , he/she tends to move the process towards the c l o s e d end o f the continuum. In t h i s case there i s l i t t l e o r no i n t e r a c t i o n w i t h the environment. An e d u c a t i o n a l a d m i n i s t r a t o r who pro-duces the t e a c h i n g t i m e t a b l e by t a k i n g o n l y the l e g a l r e q u i r e -ments i n t o c o n s i d e r a t i o n would be making d e c i s i o n s i n a 4 r e l a t i v e l y c l o s e d system. Because the amount o f i n t e r a c t i o n i s s m a l l , d e c i s i o n s which are made i n c l o s e d systems tend to be r e p e t i t i v e and r o u t i n e . The procedures f o r d e a l i n g with a d e c i s i o n have u s u a l l y been v / e l l worked out and are s a i d t o be programmable. As the c o n t e x t u a l system becomes i n c r e a s i n g l y open, the d e c i s i o n process becomes i n c r e a s i n g l y non-programmable. Thus the programmable - nonprogrammable continuum tends t o p a r a l l e l the c l o s e d - open continuum. Th i s d i s t i n c t i o n between c l o s e d and open system d e c i s i o n processes and between programmable and non-programmable d e c i -s i o n s w i l l , g iven the p a r a l l e l i s m between the c o n t i n u a , add one new dimension with two l e v e l s to the s i x c a t e g o r i e s of r e s e a r c h q u e s t i o n s d e a l i n g w i t h the d e c i s i o n maker. Table 2 prese n t s f o u r sample r e s e a r c h q u e s t i o n s f o r v a r i o u s d e c i s i o n s and d e c i s i o n p r o c e s s e s . The q u e s t i o n s correspond to c e l l s 3 and 4 i n Table 1. The prese n t study compared c l o s e d - programmable d e c i s i o n making behaviour w i t h a p r e d e f i n e d norm i n an e f f o r t t o des-c r i b e i n f o r m a t i o n seeking behaviour. T h e r e f o r e , although the u l t i m a t e purpose o f the study was to d e s c r i b e one aspect of d e c i s i o n making behaviour, the methodology employed would r e -q u i r e t h a t the study be p l a c e d i n the category normative-closed-programmable. 5 TABLE TI Sample Research Questions on the Behaviour of Decision Makers Normative D e s c r i p t i v e Open Closed Open Closed Nonpro- Pro- Nonpro- Pro-gramable gramable gramable gramable How can an How should a Do younger Is there a cor-Educational r a t i o n a l edu- a d m i n i s t r a t o r s r e l a t i o n be-A d m i n i s t r a t o r c a t i o n a l seek wider tween the per-be most e f - a d m i n i s t r a t o r p a r t i c i p a t i o n sonal charac-f e c t i v e i n deal w i t h rou- i n d e c i s i o n t e r i s t i c s of p a r t i c i p a t o r y t i n e problems? making than the e d u c a t i o n a l d e c i s i o n o l d e r edu- a d m i n i s t r a t o r making? c a t i o n a l and the number ad m i n i s t r a - :. ' of r o u t i n e de-t o r s ? c i s i o n s made d a i l y ? THE RATIONAL PROCESS The category of normative s t u d i e s on d e c i s i o n making be-haviour i n closed-programable s i t u a t i o n s has r e c e i v e d much a t t e n t i o n , p a r t i c u l a r l y i n the l a s t f o r t y years. The problem of d e f i n i n g standards has been approached i n v a r i o u s ways (Kast and Rosenzweig, 19 70). The approach most g e n e r a l l y accepted today i s the adoption of the " s c i e n t i f i c method" or the r a -t i o n a l model. This model was f i r s t made e x p l i c i t by Dewey (1910) and l a t e r expanded by Simon (1960). Today, the r a t i o n a l d e c i s i o n making model i s g e n e r a l l y c h a r a c t e r i z e d by f i v e sim-p l i f i e d steps. 6 1. R e c o g n i t i o n t h a t a problem e x i s t s . 2. D e f i n i t i o n o f a l t e r n a t i v e s . 3. An understanding of the probable e f f e c t s of each a l t e r n a t i v e . 4. " A p p l i c a t i o n o f some value f u n c t i o n which produces a p r e f e r e n c e o r d e r i n g of the a l t e r n a t i v e s . 5. The a c t u a l c h o i c e . The d e c i s i o n making process i s much more complicated than i s i n d i c a t e d by the above f i v e s t e ps. Simon (1957), i n h i s study o f the a d m i n i s t r a t i v e d e c i s i o n making p r o c e s s , de-f i n e d the r a t i o n a l process and then s t a t e s t h a t i t was impos-s i b l e f o r an i n d i v i d u a l t o reach any h i g h degree of r a t i o n a l -i t y . The r a t i o n a l process r e q u i r e s the g e n e r a t i o n o f such a l a r g e number of a l t e r n a t i v e s and the p r o c e s s i n g o f such huge amounts o f i n f o r m a t i o n t h a t i t i s d i f f i c u l t to c o n c e i v e of anyone even approximating i t . The r e s u l t , a c c o r d i n g to Simon, i s a form o f "bounded r a t i o n a l i t y " i n which the d e c i -s i o n maker attempts to make the b e s t c h o i c e p o s s i b l e g i v e n the l i m i t s to r a t i o n a l i t y . Despite t h i s problem, i n c l o s e d system d e c i s i o n s i t u a -t i o n s , the concept of p u r e l y r a t i o n a l behaviour can be c l o s e l y approximated. The l i t e r a t u r e d e a l i n g w i t h c l o s e d system de-c i s i o n making i s e x t e n s i v e and demonstrates t h a t the r a t i o n a l model has been s u c c e s s f u l l y employed i n normative s t u d i e s (Ugalde, 1973; M o r r i s , 1964; Dawes and C o r r i g a n , 1974). 7 The p r e s e n t study w i l l d e f i n e both a c l o s e d system de-c i s i o n s i t u a t i o n and a corresponding norm f o r r a t i o n a l de-c i s i o n making behaviour. T h i s design w i l l then be used to examine one dimension o f d e c i s i o n making behaviour, namely, the manner i n which i n f o r m a t i o n i s accomodated. Information f o r the purposes o f t h i s study i s d e f i n e d t o mean knowledge ( f a c t s understood by the d e c i s i o n maker) deemed to be r e l e v a n t to the d e c i s i o n under c o n s i d e r a t i o n . I t has been p o i n t e d out t h a t by not seeking i n f o r m a t i o n , a d e c i s i o n maker c l o s e s the c o n t e x t u a l system i n which he/she operates. Because the r e s e a r c h q u e s t i o n s and a n a l y t i c t e c h -niques employed i n s t u d y i n g d e c i s i o n making depend on the system i n which the d e c i s i o n i s made, i t i s important to understand the i n f o r m a t i o n seeking behaviour o f the d e c i s i o n maker. Hence the p r e s e n t study w i l l examine the tendency o f the d e c i s i o n maker to seek i n f o r m a t i o n , t h a t i s , open the c o n t e x t u a l system i n a c o n t r i v e d c l o s e d system d e c i s i o n s i t u a t i o n . REVIEW OF RESEARCH The l i t e r a t u r e r e l e v a n t to t h i s study w i l l be reviewed under t h r e e g e n e r a l headings: (1) s t u d i e s on c l o s e d system d e c i s i o n making, (2) use o f Bayesian s t a t i s t i c s i n d e f i n i n g a r a t i o n a l norm, and (3) s t u d i e s examining i n f o r m a t i o n i n d e c i s i o n making. 8 This s e c t i o n begins w i t h a b r i e f o u t l i n e of the develop-ment of the s t a t i c model i n s t a t i s t i c a l d e c i s i o n theory. The e v o l u t i o n of the r a t h e r l i m i t e d s t a t i c model i n t o the more r e a l i s t i c and u s e f u l dynamic model w i l l then be shown to have r e s u l t e d from the a p p l i c a t i o n of Bayesian s t a t i s t i -c a l techniques to the s t a t i c model. F i n a l l y , a number of stu d i e s w i l l be discussed which have s u c c e s s f u l l y employed the dynamic model i n examining i n f o r m a t i o n seeking behaviour i n d e c i s i o n s i t u a t i o n s . A n a l y s i s of Closed System Decisions Various techniques have been developed to s i m p l i f y and analyze c l o s e d system d e c i s i o n making (Kast and Rosenzweig, 1970) . Few, i f any, r e a l - l i f e d e c i s i o n s can be handled by any one of these techniques, however, of these models the payoff matrix i n s t a t i s t i c a l d e c i s i o n theory has proved to be p a r t i c u l a r l y u s e f u l . I t s usefulness stems from three sources. F i r s t , i t i s a p p l i c a b l e to a wide range of manage-r i a l and a d m i n i s t r a t i v e d e c i s i o n s (Green e t a l . , 1967; M o r r i s , 1974). Second, the concepts of s t a t i s t i c a l d e c i s i o n theory are based on the r a t i o n a l d e c i s i o n making model (McGee, 1971) . T h i r d , the payoff matrix can be e a s i l y incorporated i n t o dynamic models of d e c i s i o n making (Edwards, 1962). 9 A p a y o f f matrix p r e s e n t s the d e c i s i o n maker wit h a choice between at l e a s t two a l t e r n a t i v e s . The p a y o f f assoc-i a t e d w i t h each a l t e r n a t i v e i s dependent upon the s t a t e o f c o n d i t i o n s i n f l u e n c i n g the d e c i s i o n s i t u a t i o n . Each s t a t e may be a s s i g n e d an o b j e c t i v e p r o b a b l i l i t y of occurance, (an example of a p a y o f f matrix i s given i n Table 3, page 18, and w i l l be d e s c r i b e d i n g r e a t e r d e t a i l i n Chapter 2). iOnce the d e c i s i o n maker makes h i s / h e r c h o i c e the d e c i s i o n process ends. T h i s use of the p a y o f f matrix i s r e f e r r e d t o as the s t a t i c model because there i s no o p p o r t u n i t y f o r r e v i s i n g d e c i s i o n s t r a t e g i e s i n the l i g h t o f p a s t d e c i s i o n s or a c q u i r -ed i n f o r m a t i o n . The Bayesian Approach For many years the s t a t i c model, a p p l i e d under v e r y narrowly d e f i n e d c o n d i t i o n s , was the o n l y one a v a i l a b l e . The complicated mathematics i n v o l v e d i n extending the model to account f o r s t r a t e g y changes as new i n f o r m a t i o n became a v a i l a b l e i n the d e c i s i o n making s i t u a t i o n , p r o v i d e d an e f f e c t i v e b a r r i e r t o f u r t h e r , more meaningful, s t u d i e s . In the 1940's experimenters r e d i s c o v e r e d the work of Thomas Bayes, an e i g h t e e n t h century mathematician. They found t h a t by a p p l y i n g Bayes' theorem to the s t a t i c model i t was p o s s i b l e to extend the process to a l l o w f o r p o s s i b l e changes i n s t r a t -egy as a r e s u l t of a c q u i r e d i n f o r m a t i o n (Edwards 1962). Thus 10 the s t a t i c model was transformed i n t o a dynamic model. Be-cause o f the c l o s e r correspondence w i t h r e a l l i f e d e c i s i o n making, the Bayesian-normed dynamic model was found t o be a much more accurate r e p r e s e n t a t i o n o f the way r a t i o n a l people behave when faced with programable d e c i s i o n s . In h i s review of the development o f Bayesian s t a t i s t i c s , Anascombe (1964) r e p o r t e d the f i n d i n g s of 'man-in-the-street' s t u d i e s which i n d i c a t e d t h a t man does not behave r a t i o n a l l y , p a r t i c u l a r l y i n gambling s i t u a t i o n s . He goes on to say t h a t these r e s u l t s should not d e t e r experimenters who are i n t e r e s t -ed i n understanding the d e c i s i o n making behaviour o f a s c i e n t i f i c a l l y minded a d m i n i s t r a t o r . A theory o f c o n s i s t e n t p r e f e r e n c e s , as d e f i n e d by Bayesian s t a t i s t i c s , should be thought o f as a means f o r s p e c i f y i n g r a t i o n a l behaviour. Edwards (1962) i n h i s taxonomy o f d e c i s i o n t a s k s a l s o s t r e s s e s the dynamic d e c i s i o n model as a normative instrument. Confidence i n Bayes" theorem as a normative instrument r e s t s on i t s b a s i s i n the s c i e n t i f i c method and the r a t i o n a l process mentioned e a r l i e r . Using j u s t f o u r c r i t e r i a : unam-b i g u i t y , u n i v e r s a l c o m p a r a b i l i t y , c o n s i s t e n c y , and c o r r e s -pondence wi t h common sense, McGee (1971) developed a model f o r p l a u s i b l e reasoning which i s unique, comprehensive and f l e x i b l e . That model i s , i n e f f e c t , an a d a p t a t i o n o f Bayes 1 theorem and consequently McGee r e f e r s to i t as the Bayesian approach. T h i s approach has proved p a r t i c u l a r l y u s e f u l i n st u d y i n g i n f o r m a t i o n seeking behaviour among d e c i s i o n makers (Green e t a l . , 1967). Information i n R a t i o n a l D e c i s i o n Making 11 Information p l a y s a c e n t r a l r o l e i n the r a t i o n a l d e c i - o s i o n making process ( A l l i s o n , 1971; David, 1961; Thurston, 0, 1962; Ott e t a l . , 1973). A r a t i o n a l d e c i s i o n maker may seek i n f o r m a t i o n a t s e v e r a l stages i n Simon's model. He/She may seek i n f o r m a t i o n w h i l e r e c o g n i z i n g t h a t a problem e x i s t s , i n d e f i n i n g a l t e r n a t i v e s , and i n understanding the probable a f f e c t s o f each a l t e r n a t i v e . In attempting to accound f o r t h i s i n f o r m a t i o n seeking behaviour i n d e c i s i o n making i t was found t h a t dynamic d e c i s i o n models were p a r t i c u l a r l y u s e f u l (Green e t a l . , 1964 and 1967; M o r r i s , 1974). These models allowed f o r the r e s u l t s o f p r e v i o u s d e c i s i o n s and a c q u i r e d i n f o r m a t i o n t o be c o n s i d e r e d i n each subsequent a n a l y s i s . By keeping o t h e r dimensions as constant as p o s s i -b l e and then v a r y i n g the c o s t or r e l i a b i l i t y o f the r e l e v a n t i n f o r m a t i o n , the i n f o r m a t i o n seeking behaviour o f d e c i s i o n makers c o u l d be s t u d i e d . Edwards (1962) o u t l i n e d t h r e e advantages i n u s i n g dyna-mic d e c i s i o n models to study i n f o r m a t i o n seeking behaviour. F i r s t , d e c i s i o n making does i n v o l v e the concept o f bounded r a t i o n a l i t y , whereby i n c o n s i s t a n t v a l u e s . a r e traded* of f a c c o r d i n g to some value f u n c t i o n . Second, people, e i t h e r c o n s c i o u s l y o r not, do a s c r i b e p r o b a b i l i t i e s to events. T h i r d , the mathematical concept of expected value does r e -p r e s e n t , to some exten t , the way i n which people combine p r o b a b i l i t i e s and p a y o f f s . 12 As a r e s u l t of Shannon's (1949) work i n Communication Theory, information has become a q u a n t i f i a b l e item. Several researchers (Taylor 1975; Green, et a l . , 1967; M o r r i s , 1974) studying d e c i s i o n making have q u a n t i f i e d i n f o r m a t i o n i n terms of the s u b j e c t i v e value placed upon i t by the d e c i s i o n maker. Edwards (1962) recognized the importance of dynamic d e c i s i o n models as a means by which s u b j e c t i v e value may be a s c r i b e d to s p e c i f i c i n f o r m a t i o n , or as i t i s more commonly termed, c a l c u l a t i o n of information seeking b i a s . To c a l c u l a t e i n f o r m a t i o n seeking b i a s i t i s f i r s t nec-essary to define a norm. In the present study a Bayesian norm was employed. This norm represents the value to the purely r a t i o n a l d e c i s i o n maker of the informa t i o n presented. Then, through experimental techniques, the value of the information to the r e a l d e c i s i o n maker can be determined. The d i f f e r e n c e between the value placed on the informa t i o n by the r e a l d e c i s i o n maker and the value a s c r i b e d by the norm i s termed the informa t i o n seeking b i a s . This measure may be p o s i t i v e or negative. A negative number would r e -present a tendency to seek l e s s information and a p o s i t i v e number would represent a tendency to seek more informat i o n r e l a t i v e to the defined norm. 13 STATEMENT OF THE PROBLEM E d u c a t i o n a l a d m i n i s t r a t o r s are d e c i s i o n makers who work i n a r e l a t i v e l y open system. However, not a l l o f the d e c i -s i o n s d e a l t w i t h are nonprogrammable (Hoan, 1974), as the e d u c a t i o n a l a d m i n i s t r a t o r o f t e n has the o p t i o n to open the d e c i s i o n p r o c e s s . T h i s o p t i o n i n t u r n r e s u l t s i n what Simon r e f e r s to as "Greshams Law of P l a n n i n g " whereby programmed a c t i v i t y tends to d r i v e out nonprogrammed a c t i v i t y when both are p r e s e n t i n an a d m i n i s t r a t i v e p o s i t i o n . Thus the p r a c -t i c i n g e d u c a t i o n a l a d m i n i s t r a t o r i s o f t e n i n v o l v e d w i t h c l o s e d system programmable d e c i s i o n making. The tendency to open o r c l o s e the d e c i s i o n process has been shown above to depend upon the e d u c a t i o n a l a d m i n i s t r a -t o r ' s tendency to seek i n f o r m a t i o n . That tendency to seek i n f o r m a t i o n i s measured by the i n f o r m a t i o n seeking b i a s . T h e r e f o r e , i n t r y i n g t o understand d e c i s i o n making behaviour among e d u c a t i o n a l a d m i n i s t r a t o r s i t i s important to study i n f o r m a t i o n seeking b i a s . S i m i l a r l y , i f programs of i n s t r u c -t i o n i n e d u c a t i o n a l a d m i n i s t r a t i o n are based upon a committ-ment to t r a i n f o r p r a c t i c e then the i n f o r m a t i o n seeking be-h a v i o u r of students o f e d u c a t i o n a l a d m i n i s t r a t i o n might use-f u l l y be s t u d i e d by those o f f e r i n g such programs. 14 General Problem Statement T h i s study used the dynamic Bayesian approach as a model of r a t i o n a l d e c i s i o n making. Then by u s i n g t h i s model as a norm, the d e c i s i o n s t r a t e g i e s o f students o f e d u c a t i o n a l a d m i n i s t r a t i o n who were c o n f r o n t e d w i t h programable d e c i s i o n s were compared. The g e n e r a l q u e s t i o n r a i s e d e a r l i e r may now be formu-l a t e d i n t o the more s p e c i f i c q u e s t i o n s : 1. Do p a r t - t i m e masters students o f E d u c a t i o n a l A d m i n i s t r a t i o n behave as Bayesians i n t h e i r search f o r i n f o r m a t i o n i n c l o s e d system de-c i s i o n s i t u a t i o n s ? 2. Are there d i f f e r e n c e s i n i n f o r m a t i o n seeking b i a s between groups wi t h v a r y i n g amounts o f formal t r a i n i n g i n E d u c a t i o n a l A d m i n i s t r a t i o n . 3. Are there d i f f e r e n c e s i n i n f o r m a t i o n seeking b i a s between groups wi t h v a r y i n g amounts of E d u c a t i o n a l A d m i n i s t r a t i v e experience? 4. What i s the e f f e c t o f v a r y i n g p a y o f f parameters and p r i o r p r o b a b i l i t i e s on the amount o f i n f o r -mation purchased? Expected Outcomes St u d i e s u s i n g Bayesian experimental games to examine i n -formation seeking b i a s e s have tended t o show c o n s i s t a n t r e -s u l t s (Edwards, 1962; Green e t a l . , 1964 and 1967; M o r r i s , 19 74). Based on these p r e v i o u s s t u d i e s i t was expected t h a t s u b j e c t s would g e n e r a l l y tend to overvalue i n f o r m a t i o n , r e -l a t i v e to a Bayesian norm. A l s o i t was expected t h a t i n f o r -15 mation seeking bias would be sensitive to differences i n pr i o r p r o b a b i l i t i e s but not to v a r i a t i o n i n payoffs. F i n a l l y the study reported by Green et a l . (1967) suggested that ad-ministrative experience would be found to be a determining factor i n information seeking behavior. 16 CHAPTER 2 DESIGN AND METHODOLOGY The design and methodology used i n t h i s study to answer the q u e s t i o n s posed a t the end of the pr e v i o u s chapter w i l l be d i s c u s s e d under the f o l l o w i n g major headings, (1) The Sample, (2) D e f i n i t i o n o f V a r i a b l e s (3) Experimental Pro-cedures and (4) Research Questions and A n a l y s i s . THE SAMPLE The p o p u l a t i o n f o r t h i s study c o n s i s t e d o f a l l students e n r o l l e d on the masters program i n the U.B.C. Department o f E d u c a t i o n a l A d m i n i s t r a t i o n d u r i n g the academic year 1977 — 1978. At t h a t time there were approximately 180 f u l l - t i m e and p a r t - t i m e masters c a n d i t a t e s , w i t h the gre a t m a j o r i t y , approximately n i n e t y - f i v e p e r c e n t , e n r o l l e d on the p a r t - t i m e program. For pa r t - t i m e students a t l e a s t t hree years i s i s u s u a l l y r e q u i r e d t o complete the f i f t e e n u n i t s and major paper necessary f o r gr a d u a t i o n . Most f u l l - t i m e students com-p l e t e the program i n one cale n d a r year. From t h i s p o p u l a t i o n a sample o f twenty-nine students was obtained. T h i s sample c o n s i s t e d e n t i r e l y o f pa r t - t i m e students. I t was f e l t t h a t f u l l - t i m e students, many o f whom had given up the s e c u r i t y o f a tenured t e a c h i n g p o s i t i o n and 17 the f i n a n c i a l s e c u r i t y o f a r e g u l a r income, would be more prone to r i s k t a k i n g . For t h i s reason the p o p u l a t i o n f o r the study was changed t o i n c l u d e a l l students e n r o l l e d i n the p a r t - t i m e masters program. A l l p a r t - t i m e students r e g i s t e r e d i n w i n t e r s e s s i o n evening courses were approached i n c l a s s and asked t o p a r t i -c i p a t e i n the study. In c l a s s e s which had both f u l l - t i m e and par t - t i m e s t u d e n t s , both groups were asked t o p a r t i c i p a t e . T h i s was done i n an e f f o r t to s i m p l i f y data g a t h e r i n g proce-dures and i n the event o f i n s u f f i c i e n t response by p a r t - t i m e students, to p r o v i d e a p o s s i b l e a l t e r n a t e sample group. F o r t y - t h r e e students were t e s t e d . T h i r t e e n students were not co n s i d e r e d i n the a n a l y s i s because they were e i t h e r f u l l - t i m e students o r they were not r e g i s t e r e d i n the Department o f E d u c a t i o n a l A d m i n i s t r a t i o n . One pa r t - t i m e student was r e j e c -t ed because he i n d i c a t e d t h a t he was f a m i l i a r w i t h s t a t i s t i c a l d e c i s i o n theory and i t was f e l t t h a t t h i s would i n f l u e n c e h i s p l a y i n g s t r a t e g y . The sample c o n s i s t e d o f twenty-one males and e i g h t females w i t h a mean of 6.0 years t e a c h i n g e x p e r i e n c e . E l e v e n of the su b j e c t s were experienced a d m i n i s t r a t o r s with a mean of 3.4 years i n e d u c a t i o n a l a d m i n i s t r a t i v e p o s i t i o n s . Nine of the students had completed a t l e a s t t hree u n i t s o f course work w i t h i n the U.B.C. Department of E d u c a t i o n a l A d m i n i s t r a t i o n , the mean f o r the nine students being 8.3 u n i t s . No one i n the sample i n d i c a t e d t h a t they had completed graduate l e v e l course work i n e d u c a t i o n a l a d m i n i s t r a t i o n a t a U n i v e r s i t y 18 other than the U n i v e r s i t y of B r i t i s h Columbia. DEFINITION OF VARIABLES The Independent V a r i a b l e s T h i s study employed three independent v a r i a b l e s . Two of the v a r i a b l e s were grouping f a c t o r s w i t h two l e v e l s each. The t h i r d f a c t o r i n v o l v e d repeated measures wi t h e i g h t t r e a t ment l e v e l s . Thus the study may be c l a s s i f i e d as a 2 x 2 x f a c t o r i a l experiment w i t h repeated measures on the l a s t f a c -t o r . T h i s design was s i m i l a r to t h a t d e f i n e d by Winer (19 71 559) as "a repeated measures three f a c t o r experiment, case I I " . Grouping f a c t o r A ( e x p e r i e n c e ) . T a y l o r (1975:79) i n h i study of managerial d e c i s i o n making found t h a t , "the amount of experience i n making d e c i s i o n s was p o s i t i v e l y r e l a t e d to accuracy i n j u d g i n g the value of i n f o r m a t i o n " . T h i s would appear to i n d i c a t e t h a t d i f f e r e n c e s i n i n f o r m a t i o n seeking b i a s would a l s o be found between s u b j e c t groups w i t h educa-t i o n a l a d m i n i s t r a t i v e experience and those without such experience. A l s o because p r a c t i c a l experience i s an impor-t a n t c o n s i d e r a t i o n i n h i r i n g p r a c t i c e s , i t would be u s e f u l to a s c e r t a i n through e m p i r i c a l study the i n f l u e n c e o f ex-p e r i e n c e on t h i s aspect o f the e d u c a t i o n a l a d m i n i s t r a t o r s job. 19 For the purpose of t h i s study, e d u c a t i o n a l a d m i n i s t r a -t i v e experience was d e f i n e d as a t l e a s t one year as a p r a c -t i c i n g a d m i n i s t r a t o r a t the department head l e v e l o r above. T h i s i n c l u d e d , s c h o o l board or department of educ a t i o n o f f i c i a l s , as w e l l as, v i c e - p r i n c i p a l s , p r i n c i p a l s , d e p a r t - :i ment heads and program c o - o r d i n a t o r s . As the r e s p o n s i b i l i -t i e s o f department heads and program c o - o r d i n a t o r s v a r i e d g r e a t l y , job d e s c r i p t i o n s , presented by the students, were examined t o ensure t h a t the job t h a t they were doing was i n f a c t a d m i n i s t r a t i v e . Evidence of a d m i n i s t r a t i v e experience would be, f o r example, budget a l l o c a t i o n , time t a b e l l i n g and program development. Two l e v e l s were d e f i n e d under f a c t o r A. L e v e l one i n -cluded those with a t l e a s t one year o f e d u c a t i o n a l adminis-t r a t i v e experience and l e v e l two i n c l u d e d those w i t h no edu-c a t i o n a l a d m i n i s t r a t i v e experience. Grouping f a c t o r B (academic course work) Many s t u d i e s (Husen, 1972; Averch e t a l . , 1972; Hyman e t a l . , 1975) have been conducted to determine the e f f e c t s o f s c h o o l i n g on p u p i l achievement. Because of the l a r g e number of i n t e r f e r i n g v a r i a b l e s and problems with data c o l l e c t i o n , the r e s u l t s o f such s t u d i e s have o f t e n been c o n t r a d i c t o r y . The Gross and H e r r i o t (1965) study i n t o the "Executive P r o f e s s i o n a l Leader-s h i p " (E.P.L.) of e d u c a t i o n a l a d m i n i s t r a t o r s d e a l t , i n p a r t , with the e f f e c t s o f graduate s t u d i e s i n e d u c a t i o n a l adminis-t r a t i o n . They found t h a t the g r e a t e r the number o f semester 20 hours of graduate s t u d i e s i n e d u c a t i o n a l a d m i n i s t r a t i o n the lower the a d m i n i s t r a t o r ' s EPL s c o r e s . Leadership i s one dimension of a d m i n i s t r a t i o n , d e c i s i o n making i s another. An e x t e n s i v e review o f the l i t e r a t u r e has i n d i c a t e d t h a t to date, no r e s e a r c h i n t o the p o s s i b l e e f f e c t s o f graduate t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n on d e c i s i o n making behaviour has been undertaken. For the purpose of t h i s study, t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n was d e f i n e d as the completion o f a t l e a s t three u n i t s of graduate l e v e l course work i n the department of e d u c a t i o n a l a d m i n i s t r a t i o n a t U.B.C. The course E d u c a t i o n 460, I n t r o d u c t i o n t o E d u c a t i o n a l A d m i n i s t r a t i o n , was c o n s i d -ered as a graduate l e v e l course, i f i t was taken as a p r e -r e q u i s i t e f o r f u r t h e r study w i t h i n the Department of Educa-t i o n a l A d m i n i s t r a t i o n and not merely as a f i n a l year under-graduate e l e c t i v e . There were two l e v e l s i n the sample d e f i n e d under f a c -t o r B. L e v e l one i n c l u d e d students with a t l e a s t 3 u n i t s o f course work i n e d u c a t i o n a l a d m i n i s t r a t i o n and l e v e l two i n -cluded students with no graduate l e v e l t r a i n i n g . Repeated measures, f a c t o r C. The repeated measures f a c -t o r f o r t h i s study was based upon t h a t used by Green e t a l . (1967) i n t h e i r study of p e r f e c t i n f o r m a t i o n as a f u n c t i o n o f p r i o r p r o b a b i l i t i e s and p a y o f f parameters. In the p r e s e n t study f a c t o r C was c o n s i d e r e d to have three dimensions. The f i r s t dimension was concerned w i t h the p r i o r p r o b a b i l i t i e s . The second and t h i r d dimensions were concerned wi t h the pay-21 o f f parameters and rep r e s e n t e d two ways, namely, m u l t i p l i c a -t i v e and a d d i t i v e c o n s t a n t s , by which the p a y o f f s were v a r i e d . As the treatment l e v e l s o f t h i s f a c t o r depend upon the nature o f the s i m u l a t i o n game, f u r t h e r d i s c u s s i o n o f t h i s independ-ent v a r i a b l e w i l l be d e f e r r e d u n t i l a f t e r a d i s c u s s i o n o f the s i m u l a t i o n game and dependent v a r i a b l e (see page 2 8)• The Dependent V a r i a b l e The dependent v a r i a b l e , i n f o r m a t i o n seeking b i a s , was d e f i n e d as the d i f f e r e n c e between the value p l a c e d on i n f o r -mation by a d e c i s i o n maker and the val u e a s c r i b e d by a pre -determined norm. T h i s study employed a Bayesian norm and u t i l i z e d a p a y o f f matrix to a s c r i b e v a l u e to a s p e c i f i c u n i t of i n f o r m a t i o n . An example w i l l be used to i l l u s t r a t e the Bayesian approach as employed i n t h i s experimental game. Each p a r t i c i p a n t i n t h i s experiment was asked t o pre -tend t h a t he/she was the p r i n c i p a l o f a l a r g e p u b l i c s c h o o l and r e s p o n s i b l e f o r d e c i d i n g which of two academic programs was to be implemented. The p l a y e r s o b j e c t i v e was to maxi-mize the per p u p i l budget a l l o t m e n t from the S e c r e t a r y -T r e a s u r e r . T h i s a l l o t m e n t was dependent on which of two s t a t e s p r e v a i l e d i n the o f f i c e o f the S e c r e t a r y - T r e a s u r e r . Each s t a t e c o n s i s t e d o f a l l the f a c t o r s which c o u l d i n f l u e n c e the S e c r e t a r y - T r e a s u r e r i n h i s d e c i s i o n to fund the program. For example there may be p o l i t i c a l and economic f a c t o r s , as w e l l as, p e r s o n a l i t y f a c t o r s . Each s t a t e represented a d i f f e r e n t combination of f a c t o r s . Each s t a t e was assigned a p r o b a b i l i t y or l i k e l i h o o d of occuri n g . A d e t a i l e d explana-t i o n of the experimental game i s to be found i n 'Game I n -s t r u c t i o n s and Response Forms' i n Appendix A. An example of a s i m u l a t i o n s i t u a t i o n i s i l l u s t r a t e d i n Table I I I . Table I I I Payoff M a t r i x f o r Game Simu l a t i o n : E n t r i e s i n D o l l a r s per P u p i l Program (Act) 1 Program (Act) 2 P r o b a b i l i t y of s t a t e State 1 State 2 450 100 310 200 .8 .2 To help s i m p l i f y the d i s c u s s i o n , the f o l l o w i n g n o t a t i o n w i l l be employed. Let: th A^ denote the i act on program ( i = 1,2) S_. denote the j t h s t a t e (j = 1,2) O^j denote the outcome of the i t h act and the j t h s t a t e Pj denote the p r o b a b i l i t y of the occurance of the .th . . j s t a t e Z^ j denote t h a t the r e s u l t s of the study conducted i n d i c a t e d that s t a t e j w i l l p r e v a i l P (Sj/Z_^) denote the p r o b a b i l i t y ( p o s t e r i o r ) of s t a t e J occuring given t h a t the study i n d i c a t o r s t a t e i w i l l occur E (.) denote mathematical expectation I f the p l a y e r chose program 1 and s t a t e 1 was.found ,to p r e v a i l , the average student subsidy would be $450, wh i l e i f s t a t e 2 had occured the average student subsidy would be $100. State 1 i s assigned a p r o b a b i l i t y of .8 and s t a t e 2 a p r o b a b i l -i t y of .2. The experiment as described thus f a r i s a s t a t i c , s t a -t i s t i c a l d e c i s i o n problem. In order to determine the long term payoff of choosing a p a r t i c u l a r a c t , the expected value (E(A^) i s c a l c u l a t e d . The expected value i n v o l v e s the weighting of the payoff from each s t a t e by the p r o b a b i l i t y of the occurance of that s t a t e . For example: E(A.) = ^ P (S . ) .0.. E(A 1) = P(S 1).0 l l s,+ P(S 2) •  . 0 1 2 = .8 X 450 + .2 X 100 = 380 E(A 2) = P ( S 2 ) . 0 _ 2 1 + P ( S 2 ) . 0 _ 2 2 = . 8 X 310 + .2 X 200 = 288 In the absence of any f u r t h e r i n f o r m a t i o n the d e c i s i o n maker, who wished to maximize the payoff, would choose the program (act) w i t h the highest mathematical expectation. In the above example i t would be program 1. More r e a l i s t i c a l l y the d e c i s i o n maker may decide to delay implementing the program i n order to allow a study of the p r e v a i l i n g s t a t e i n the o f f i c e of the S e c r e t a r y - T r e a s u r e r to be conducted. The r e l i a b i l i t y , o r degree to which the i n f o r m a t i o n given i n t h i s study may be accepted as t r u e , c o u l d vary from zero percent to one hundred pe r c e n t . For t h i s t h e s i s the r e l i a b i l i t y o f the study was assumed to be one hundred percent, t h a t i s , the study i n d i c a t e d w i t h c e r -t a i n t y which s t a t e would p r e v a i l . However, by conducting the study, the implementation of the program would be delayed r e s u l t i n g i n a r e d u c t i o n i n the average student subsidy. In the above example, suppose t h a t conducting the survey r e s u l t e d i n a r e d u c t i o n of $27 i n the per p u p i l subsidy. T h i s c o u l d be s a i d t o r e p r e s e n t the 'cost of the i n f o r m a t i o n ' . The p l a y e r s must now decide whether the i n f o r m a t i o n as to which s t a t e w i l l p r e v a i l i s worth purchas-i n g . In o r d e r to determine how the p u r e l y r a t i o n a l d e c i s i o n maker would choose, i t i s necessary to determine the proba-b i l i t i e s o f each s t a t e o c c u r i n g , g i v e n the r e s u l t s o f the study. These p r o b a b i l i t i e s are known as p o s t e r i o r p r o b a b i l i -t i e s and can be c a l c u l a t e d u s i n g Bayes' Theorem. For a b r i e f d i s c u s s i o n of Bayes' theorem, which can be employed r e g a r d l e s s o f the r e l i a b i l i t y of the study, r e f e r t o Appendix B. Because the i n f o r m a t i o n i s assumed to be one hundred p e r c e n t r e l i a b l e , the d e r i v a t i o n o f the Bayesian norm i s con-s i d e r a b l y s i m p l i f i e d . Suppose t h a t the study i n d i c a t e d t h a t s t a t e 1 would p r e v a i l . Then PfS^/Z^) = 1 and PfS^/Z^) = 0. The mathematical e x p e c t a t i o n can now be c a l c u l a t e d u s i n g p o s t e r i o r p r o b a b i l i t i e s . E(A 1) =• P f S j / Z ^ . 0±1 + PCS^/Z^). 0 =--450 X 1 + 100 X:0 = 450 E(A 2) = P (Sj/Z^) . 0_21 + P(S 2/Z^ 1). 0_22= 310 X 1 + 200 X 0 = 310 The Bayesian d e c i s i o n maker would choose the a c t wit h the g r e a t e s t expected v a l u e . Max E (A. ) = Max 21 P (S ./Z . ) . 0 . . = 450 i - i 1 3 - 3 - 1 -13 N o t i c e t h a t i n t h i s s p e c i a l case o f a p e r f e c t study: Max E(A ) = Max 0 ., j = 1. i —1 1 —13 The same procedure may be f o l l o w e d assuming t h a t s t a t e 2 w i l l p r e v a i l . F i g u r e 1 summarizes the r e s u l t s . But each s t a t e i s assig n e d a p r i o r p r o b a b i l i t y . That i s , s t a t e 1 c o u l d have occured w i t h p r o b a b i l i t y .8, s t a t e 2 wit h p r o b a b i l i t y .2. The mathematical e x p e c t a t i o n E 1 (.) can now be a p p l i e d to the r e s u l t s o f the above a n a l y s i s . E1= <T- Max E (A. ) .P . 1 1 - 1 3 = ^S" [Max 0.. ] P. s u b s t i t u t i n g Max 0 .. = Max E(A ) J—. L 1 - ; L 3 J 3 1 ~ 13 1 - i = .8 X 450 + .2 X 200 = 360 + 40 = 400 The process o f choosing a t e r m i n a l a c t on the b a s i s of p r i o r p r o b a b i l i t i e s and experimental information, vcombined by the use o f Bayes' theorem, i s known as p o s t e r i o r a n a l y s i s . P r i o r a n a l y s i s r e f e r s to the process o f choosing a f i n a l a c t on the b a s i s o f the p r i o r p r o b a b i l i t i e s alone. The subjec-t i v e value o f the i n f o r m a t i o n can be computed by s u b t r a c t i n g 26 P r o b a b i l i t y o f S t a t e F i g u r e 1 Tree Diagram wi t h Choice P r o b a b i l i t i e s For P a y o f f M a t r i x i n Table 3: Given P e r f e c t Information 27 the expected p a y o f f a s s o c i a t e d w i t h the p r i o r a n a l y s i s from the p a y o f f expected from the p o s t e r i o r a n a l y s i s . The expec-t e d value o f the p e r f e c t i n f o r m a t i o n (EVPI) can be expressed: EVPI = E 1 - Max E(A.) (max 0..). P. - max 21 p 0 j x - i j j l j j - i j = 400 - 380 = 20 The Bayesian d e c i s i o n maker would be expected to pay up to $20 f o r the p e r f e c t i n f o r m a t i o n . T h i s r e p r e s e n t s the value o f the i n f o r m a t i o n to the d e c i s i o n maker, or s i m i l a r l y , the c o s t o f p r i o r u n c e r t a i n t y . Thus i f the p l a y e r had p a i d $27 f o r the p e r f e c t i n f o r m a t i o n , f o r which the Bayesian p l a y e r would have p a i d no more than $20, the i n f o r m a t i o n seeking b i a s would be $27 - $20=$7. EXPERIMENTAL PROCEDURES Each s u b j e c t was presented with e i g h t unique games s i m i -l a r to the one d e s c r i b e d above. For each game the p l a y e r was presented w i t h s i x d i f f e r e n t s t u d i e s ranging i n c o s t from $1 to $210. The study c o s t s were chosen such t h a t (a) h a l f o f the surveys would c o s t more than the EVPI, and h a l f l e s s , and (b) a wide d i s p e r s i o n o f c o s t s was e f f e c t e d . For odd num-bered c o n d i t i o n s the EVPI=20. The study c o s t s f o r a l l the odd numbered c o n d i t i o n s were as f o l l o w s : 28 1, 5, 13, 27, 70, 200 They were presented t o the s u b j e c t s i n the random se-quence : 200, 5, 27, 13, 70, 1 For even numbered c o n d i t i o n s , the EVPI = 30. The study c o s t s f o r a l l the even numbered c o n d i t i o n s were as f o l l o w s : 10, 15, 23, 37, 80, 210 They were presented to the students i n the random se-quence : 210, 15, 37, 23, 80, 10 The p l a y e r had to decide which s t u d i e s to purchase and having made th a t d e c i s i o n the p l a y e r then had to choose one of the two programs f o r each s i t u a t i o n . The game was a d m i n i s t e r e d i n sma l l groups ranging i n s i z e from three to s i x s u b j e c t s under the s u p e r v i s i o n of one umpire. Members o f the c l a s s being sampled were randomly assign e d to a group. Umpires were s p e c i a l l y t r a i n e d students from the d o c t o r a l program i n e d u c a t i o n a l a d m i n i s t r a t i o n (see page 3 3). Each person i n the group worked on the same se-quence of games, so t h a t a f t e r each game the p l a y e r s c o u l d compare t h e i r scores and the person with the h i g h e s t score was d e c l a r e d the winner o f t h a t game. T h i s i n i t i a t e d compe-t i t i o n and s t i m u l a t e d i n t e r e s t i n the game. A f t e r the completion of a l l e i g h t games, one p l a y e r was chosen a t ramdom and asked, i n p r i v a t e , t o d e s c r i b e how he/ she "came to decide which surveys were worth p u r c h a s i n g i n games one, two, and s i x . " The comments were recorded by the umpires. In o r d e r to i n t r o d u c e v a r i e t y a c r o s s the e i g h t games, v a r i o u s parameters i n the p a y o f f matrix were a d j u s t e d . T h i s was done s y s t e m a t i c a l l y and represented the repeated measures of f a c t o r C. Design o f the Study Dimensions of f a c t o r C. There were three dimensions under f a c t o r C. Each dimension was d i v i d e d i n t o two l e v e l s 3 r e s u l t i n g i n 2 or e i g h t unique treatment l e v e l s . Dimension re p r e s e n t e d the p r i o r p r o b a b i l i t i e s and was d i v i d e d i n t o two l e v e l s . At l e v e l one, the p r i o r p r o b a b i l i -t i e s were (.8, .2) and a t l e v e l two they were (.5, .5). Dimension B r e p r e s e n t e d the constant by which the p a y o f f s were m u l t i p l i e d . At l e v e l one the constant was one, a t l e v e l two i t was 1.5. T h i s p a r t i c u l a r m u l t i p l i c a t i v e constant was chosen be-cause i t p r o v i d e d v a r i a t i o n i n the EVPI without i n d u c i n g e x c e s s i v e l y wide v a r i a t i o n i n the game p a y o f f s . The o n l y c r i t e r i o n f o r choosing these dimension l e v e l s was t h a t there was a d i s t i n c t v a r i a t i o n between the two l e v e l s . Dimension re p r e s e n t e d the constant to which the p a y o f f s were added. At l e v e l one the constant was zero, a t l e v e l two i t was 300. 30 Table IV summarizes the dimensions of f a c t o r C. Table V d i s p l a y s a l l the p o s s i b l e combinations of the t h r e e dimen-si o n s o f f a c t o r C. Table IV Dimension L e v e l s of F a c t o r C Dimension I d e n t i f i c a t i o n L e v e l 1 L e v e l 2 a P r i o r p r o b a b i l i t i e s a-^=.8, .2 c t 2 = - 5 , .5 3 M u l t i p l i c a t i v e constant B i = l B2="^" ^  y A d d i t i v e Constant Yj_ = 0 Y2 =3°0 Table V Dimension Combination D i s p l a y = 5 a2 • => , .5 B = 1 B = 1.5 B = 1 B = 1.5 C o n d i t i o n 1 C o n d i t i o n 2 C o n d i t i o n 3 C o n d i t i o n 4 Y2=300 C o n d i t i o n 5 C o n d i t i o n 6 C o n d i t i o n 7 C o n d i t i o n 8 There were two base p a y o f f m a t r i c i e s , one f o r each o f the two l e v e l s i n dimension a . The p a y o f f s i n each o f these two base m a t r i c i e s , c o n d i t i o n s 2 and 3 i n Table V, were ad-j u s t e d so t h a t the EVPI was equal to twenty. Thus c o n d i t i o n s conditions 1 and 3, given i n Table V, would have an EVPI of twenty, even though the actual payoffs i n each matrix were quite d i f f e r e n t . Table 6 displays the eight conditions used i n t h i s study. Note that conditions 1 and 3 are the base matricies, a l l the others can be obtained from them by applying the appropriate dimension l e v e l operations indicated i n Table V. Procedures. Each group received a d i f f e r e n t sequence of conditions. Each condition was i n the f i r s t p o s i t i o n (e.g., Game 1) at lea s t once. Once game 1 was fixed the sequence i n which the remaining conditions were presented was deter-mined from a sequence of random numbers. For a description of how the true states were chosen, as well as, a l i s t of those states for each condition refer to Appendix D. As was mentioned above, the payoffs i n conditions 1 and 3 were adjusted so that the EVPI was the same regardless of pr i o r p r o b a b i l i t i e s . An additive constant, such as Y 2 ' W 1 H not a f f e c t the EVPI; however, a m u l t i p l i c a t i v e constant, such as B 2 = 1.5, w i l l increase the EVPI by a factor of .5. Thus: EVPI (for conditions 1, 3, 5, 7) = 20 EVPI (for conditions 2, 4, 6, 8) = 30 A Bayesian player would be expected to: 1. Conduct a l l studies which cost less than $20 on odd num-bered conditions and less than $30 on even numbered condi-tions . Table VI Experimental Payoff M a t r i x by Condition C o n d i t i o n 1 Condition 2 Condition 3 C o n d i t i o n 4 P(S i) P(S i) A, p ( s i ) p ( s i ) "1 450 310 . 8 675 465 . 8 450 270 .5 675 405 .5 "2 100 200 .2 150 300 .2 100 140 .5 150 210 .5 Condition 5 Condition 6 Condition 7 Condition 8 A, P(S i) P(S i) P(s i) A, P(S ±) "1 750 610 .8 975 765 .8 750 570 .5 975 705 .5 "2 400 500 .2 450 600 .2 400 440 .5 450 510 .5 2. Choose program 1 i f the study i s not conducted. Program 1 always maximizes the expected payoff. 3. Choose program 1 i f the study indicates state 1 w i l l p r e v a i l and choose program 2 i f the study indicates state 2 w i l l p r e v a i l . Training of Umpires During July, 1977 a p i l o t study for t h i s experiment was administered to four f u l l - t i m e and part-time masters candi-dates at the U.B.C. Department of Educational Administration. As a re s u l t of t h i s p i l o t study a number of changes were i n -dicated. I t was discovered that the maximum group size under one umpire should not exceed six. Confusing portions of the game instructions were reworded. Response forms were rede-signed to f a c i l i t a t e c a l c u l a t i o n of scores. The game proce-dures were revised s l i g h t l y i n an e f f o r t to increase player p a r t i c i p a t i o n . F i n a l l y , a number of minor administrative re-commendations were made which f a c i l i t a t e d the playing of the game. Some of the classes approached held over t h i r t y students Therefore, i n order to maintain the small group size recom-mended by the p i l o t study, i t was decided that the experi-menter would t r a i n umpires i n administering the simulation game. In t h i s way, an entire class could be sampled at one time. The procedure had three advantages, (1) there was a 34 minimum of d i s r u p t i o n i n r e g u l a r academic classwork, (2) there was no p o s s i b i l i t y o f contamination o f the sample by the i n t e r a c t i o n o f an un t e s t e d group with a group t h a t had a l r e a d y p l a y e d the game, and (3) the s h o r t t e s t i n g p e r i o d , e a r l y i n the w i n t e r s e s s i o n , minimized the i n f l u e n c e o f p r e s e n t course work on grouping f a c t o r B ( t r a i n i n g ) . The c l a s s i n s t r u c t o r and seven members o f the U.B.C. department of e d u c a t i o n a l a d m i n i s t r a t i o n f i r s t year d o c t o r a l seminar were t r a i n e d as umpires. T r a i n i n g took p l a c e d u r i n g a r e g u l a r l y scheduled three hour c l a s s s e s s i o n . T r a i n e e s were asked t o p l a y the game, then q u e s t i o n s concerning the a d m i n i s t r a t i o n o f the game were d i s c u s s e d . F i n a l l y , the t r a i n e e s were broken i n t o groups and asked to a d m i n i s t e r the game to each o t h e r . As a f u r t h e r c o n t r o l , p r i o r t o each t e s t i n g s e s s i o n , the experimenter reviewed the game proce-dures w i t h the umpires. Each umpire r e c e i v e d a copy o f summary notes (Appendix D) and a summary o f the game proce-dures (Appendix E) as w e l l as, the m a t e r i a l s presented t o the s u b j e c t s . A d m i n i s t r a t i o n o f Game T e s t i n g took p l a c e between September 2 8 and October 4, 1977. Nine groups from three c l a s s e s were t e s t e d . Students i n each c l a s s were randomly assi g n e d to a group. No i n f o r -mation concerning the nature o f the study was giv e n to the 35 students other than t h e i r being asked to p a r t i c i p a t e i n a study which would involve them i n playing a game. Each group, ranging i n size from three to s i x , was tested i n a separate room. During the administration of the game the experimenter moved from group to group to ensure that proper and uniform test procedures were maintained. RESEARCH QUESTIONS AND ANALYSIS The following i s a s p e c i f i c a t i o n of the general research questions outlined e a r l i e r , with a description of the analysis procedures employed. Research Question Number One Do U.B.C. students of educational administration tend to seek the same amount of information as a purely Bayesian player, i n a programable decision situation? The BMD: P2V - repeated measures analysis of variance with covariates - Program of the Health Sciences Computing F a c i l i t y , University of C a l i f o r n i a was used to analyze the data. This computer program was based upon the analysis of the repeated measures three factor experiment (case II) per-formed by Winer (1971). A repeated measures design was em-ployed because of the rather small sample and the uneven c e l l sizes. Winer (1971:517) has pointed out that i n the repeated measures d e s i g n , "by having each s u b j e c t serve as h i s own c o n t r o l , the experimenter attempts t o work with a s m a l l e r sample s i z e . " The grand mean, over a l l s u b j e c t s and a l l c o n d i t i o n s , was taken as a measure o f the informa-t i o n seeking b i a s of the sample as a whole. In an attempt to r e l a t e numerical response p a t t e r n s w i t h u n d e r l y i n g s t r a t e g i e s , a post-game i n t e r v i e w was con-ducted with one randomly chosen member o f each group. During the i n t e r v i e w , the s u b j e c t was asked t o d e s c r i b e how he/she, came to decide which surveys were worth p u r c h a s i n g i n game 1, game 2, and game 6". The responses were recorded i n as much d e t a i l as p o s s i b l e . No prec o n c e i v e d framework f o r c a t e g o r i -z i n g the s t r a t e g i e s was employed. The i n f o r m a t i o n o b t a i n e d was intended to be d e s c r i p t i v e , and to a i d i n the i n t e r p r e -t a t i o n o f the study r e s u l t s . Research Question Number Two Do U.B.C. students o f e d u c a t i o n a l a d m i n i s t r a t i o n w i t h e d u c a t i o n a l a d m i n i s t r a t i v e experience behave d i f f e r e n t l y than students with no a d m i n i s t r a t i v e experience i n t h e i r tendency to seek i n f o r m a t i o n ? Using the BMD: P2V program the main e f f e c t o f the two l e v e l s o f grouping f a c t o r A (experience) was t e s t e d . T h i s problem may a l s o be expressed i n the form o f the s t a t i s t i c a l h y p o t h e s i s : Where i i s t h a t p o r t i o n o f the p l a y e r s score a t t r i b u t -able to the main e f f e c t s o f grouping f a c t o r A. Due to the complexity o f s t a t i n g the s t a t i s t i c a l h y p o t h e s i s f o r the i n t e r a c t i o n e f f e c t s u s i n g t h i s n o t a t i o n , Winer's (1971:561) e q u i v a l e n t n o t a t i o n w i l l be adopted i n t h i s study. Thus the s t a t i s t i c a l h ypothesis f o r Research Questions Two, Three and Four may be s t a t e d as> f o l l o w s : 1. Main e f f e c t s o f f a c t o r A (experience) V 6 a 2 = 0 H r 6 a 2 > 0 2. Main e f f e c t s o f f a c t o r B ( t r a i n i n g ) H : 6 ft 2 = 0 o p H±: 6 g 2 > 0 3. Main e f f e c t o f f a c t o r C ( c o n d i t i o n s ) 2 H : 6 v = 0 o Y H 1: 6 y 2 > 0 4. I n t e r a c t i o n e f f e c t between f a c t o r s A and C 2 H o : 6 a y = 0 H l : 6 ay2 >: 0 5. I n t e r a c t i o n e f f e c t between f a c t o r s B and C 2 H Q: 6 3 y = 0 H r 6 B Y 2 * 0 Where 6 a r e p r e s e n t s t h a t p o r t i o n o f the v a r i a n c e a t t r i b u t a b l e to grouping f a c t o r A. To t e s t these h y p o t h e s i s a 2 x 2 x 8 (experience x t r a i n i n g x c o n d i t i o n s ) a n a l y s i s o f v a r i a n c e w i t h repeated measures was performed. Research Question Number Three Do U.B.C. students o f e d u c a t i o n a l a d m i n i s t r a t i o n , who have completed t h r e e o r mqre u n i t s o f graduate l e v e l t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n behave d i f f e r e n t l y than students with no t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n , i n t h e i r t e n -dency to seek i n f o r m a t i o n ? Using the BMD: P2V program the main e f f e c t o f the two l e v e l s o f grouping f a c t o r B ( t r a i n i n g ) was t e s t e d . Research Question Number Four Among U.B.C. students o f e d u c a t i o n a l a d m i n i s t r a t i o n , does v a r y i n g the p r i o r p r o b a b i l i t i e s and p a y o f f parameters i n the s t a t i s t i c a l d e c i s i o n game, e f f e c t the tendency t o seek in f o r m a t i o n ? Using the BMD: P2V program the main e f f e c t o f f a c t o r C, as w e l l as, the i n t e r a c t i o n e f f e c t s o f f a c t o r s A and B wit h C were t e s t e d . An omnibus F s t a t i s t i c was c a l c u l a t e d to t e s t f o r a d i f f e r e n c e i n i n f o r m a t i o n seeking b i a s among a l l p o s s i -b l e combinations o f the treatment l e v e l s o f f a c t o r C. A l s o omnibus F s t a t i s t i c s were c a l c u l a t e d to t e s t f o r d i f f e r e n c e s 39 i n i n f o r m a t i o n seeking b i a s between the two l e v e l s o f group-i n g f a c t o r s A and B and a l l p o s s i b l e combinations o f t r e a t -ment l e v e l s o f f a c t o r C. I f the a n a l y s i s o f v a r i a n c e r e v e a l e d s i g n i f i c a n t d i f f e r -ences then the S c h e f f e procedure f o r m u l t i p l e comparisons was to be performed to a s c e r t a i n the p a r t i c u l a r combinations o f the f a c t o r l e v e l s l e a d i n g to s i g n i f i c a n c e where the num-ber of combinations was g r e a t e r than two. The Scheffe" t e s t was chosen because of the c o n s e r v a t i v e nature o f the t e s t .. and because non-pairwise combinations o f treatment l e v e l s were of p a r t i c u l a r i n t e r e s t . As w e l l , s i g n i f i c a n t i n t e r a c -t i o n s were graphed t o a i d i n i n t e r p r e t i n g such i n t e r a c t i o n s . Research Question Number F i v e 1 " Does i n f o r m a t i o n seeking b i a s change over the sequence of games? Does l e a r n i n g take p l a c e ? Each o f the nine groups r e c e i v e d a d i f f e r e n t randomly ordered sequence of games with each of the e i g h t c o n d i t i o n s i n the f i r s t p l a c e ( i e . game 1) a t l e a s t once. For each l e v e l o f the two grouping f a c t o r s the mean i n f o r m a t i o n seek-i n g b i a s was graphed over the sequence of games. For example, 1. T h i s q u e s t i o n , although not mentioned under the g e n e r a l problem statement, was i n c l u d e d because o f the repeated measures r e s e a r c h design adopted and the p o s s i b i l i t y t h a t l e a r n i n g c o u l d occur over the sequence o f games. 40 the mean information seeking bias for game one included sub-ject responses over a ramdon sample, with replacement, of a l l eight conditions. Trends i n information seeking bias over the sequence of games were observed from the graphs. 41 CHAPTER 3 RESULTS The r e s u l t s of the a n a l y s i s w i l l be d i s c u s s e d s e p a r a t e l y under each r e s e a r c h q u e s t i o n . Research Question Number One Table VII summarizes marginal means f o r a l l f o u r p o s s i b l e combinations of experience and t r a i n i n g . A complete l i s t i n g of the c e l l means, marginal means and standard d e v i a t i o n s f o r each treatment l e v e l o f f a c t o r C i s pres e n t e d i n Appendix F. Over a l l s u b j e c t s and a l l games the mean i n f o r m a t i o n seeking b i a s o f the sample group was 43.86, while the Bayesian o p t i m a l was 0. T h i s i n d i c a t e d a p o s i t i v e i n f o r m a t i o n seeking b i a s . S e l e c t e d r e s u l t s of the post game i n t e r v i e w w i l l be r e -f e r r e d to d u r i n g the d i s c u s s i o n of the study f i n d i n g s i n Chapter 4. Research Question Number Two Table V I I I summarizes the a n a l y s i s of v a r i a n c e produced by the computer program BMD: P2V. 42 Table VII Mean Information Seeking B i a s f o r A l l P o s s i b l e Combinations o f F a c t o r A (Experience) w i t h F a c t o r B (Training) F a c t o r A F a c t o r B Mean Information Seeking B i a s A d m i n i s t r a t i v e Experience ( l e v e l 1) Graduate L e v e l T r a i n i n g ( l e v e l 1) 36.44 No Graduate L e v e l T r a i n i n g ( l e v e l 2) 38.64 No A d m i n i s t r a t i v e Experience Graduate T r a i n i n g ( l e v e l 1) 56.88 ( l e v e l 2) No Graduate L e v e l T r a i n i n g ( l e v e l 2) 41.19 Grand Mean 43. 86 Table V I I I A n a l y s i s o f Va r i a n c e f o r the Dependent Variable, Information Seeking B i a s Source Sum o f Squares Degrees of Freedom(df) Mean Square F P r o b a b i l i t y o f F Exceeded Mean 283865.563 1 283865.56 47. 551 0.000 Experience(A) 5005.437 1 5005.437 838 .369 T r a i n i n g ( B ) 1720.625 1 1720.625 288 .596 AxB 3028.188 1 3028.188 . 507 .483 E r r o r 149244.188 25 5969.766 Game Parameters(c) 47990.563 7 6855.793 1. 608 .136 CxA 61260.063 7 8751.438 2. 053 .051 CxB 65240.688 7 9320.098 2. 186 .038 CxAxB 50741.250 7 7248.750 1. 701 .112 E r r o r 745969.313 175 4262.680 P < .10 The portion of the analysis testing the relationship between the two levels of factor A (experience) resulted i n an F s t a t i s t i c of .84. The pr o b a b i l i t y of obtaining that number or greater was .37. Therefore the hypothesis that there was no difference i n the mean information seeking bias between the two level s of factor A (experience) could not be rejected. Research Question Number Three The portion of the analysis testing the relationship be-tween the two levels of factor B (training) ^resulted in: the F s t a t i s t i c .29, (see Table 8). The pr o b a b i l i t y of obtaining that number or greater was .596. Therefore the contention that there was no difference i n the mean information seeking bias between the two levels of factor B could not be rejected. Research Question Number Four The portion of the analysis testing the relationship of the mean information seeking bias over a l l subjects and i n a l l possible combinations of the treatment l e v e l s of factor C re-sulted i n the F s t a t i s t i c 1.61. The pr o b a b i l i t y of obtaining that number or greater was .136. Therefore the hypothesis that there was no difference i n the mean information seeking bias over a l l subjects for various combinations of game para-45 meters ( f a c t o r C) c o u l d not be r e j e c t e d . The t e s t o f i n t e r a c t i o n e f f e c t s between each of the two l e v e l s o f grouping f a c t o r s A and B wit h the treatment l e v e l s o f f a c t o r C r e s u l t e d i n F s t a t i s t i c s o f 2.05 and 2.19 respec-t i v e l y . The p r o b a b i l i t y o f o b t a i n i n g 2.05 o r g r e a t e r was .051. And the p r o b a b i l i t y o f o b t a i n i n g 2.19 o r g r e a t e r was .038. Therefore the hypothesis t h a t there was no d i f f e r e n c e i n mean i n f o r m a t i o n seeking b i a s between each o f the two l e v e l s of f a c t o r s A and B and s p e c i f i c combinations o f t r e a t -ment l e v e l s i n f a c t o r C c o u l d be r e j e c t e d a t p .10. F i g u r e 2 prese n t s a g r a p h i c a l r e p r e s e n t a t i o n of the mean i n f o r m a t i o n seeking b i a s over the e i g h t treatment l e v e l s o f f a c t o r C, a t each l e v e l o f f a c t o r A. In F i g u r e 2 th e r e i s a n o t i c e a b l e d i f f e r e n c e i n i n f o r m a t i o n seeking b i a s between the l e v e l s o f f a c t o r A a t s p e c i f i c treatment l e v e l s o f f a c t o r C. Fi g u r e 3 presents the same i n f o r m a t i o n f o r f a c t o r B. In f i g u r e 3 there i s a l s o a very n o t i c e a b l e d i f f e r e n c e i n i n f o r -mation seeking b i a s between the l e v e l s o f f a c t o r B a t s p e c i f i c treatment l e v e l s o f f a c t o r C. For example, i n F i g u r e 3, the group a t l e v e l 1, those w i t h t r a i n i n g i n e d u c a t i o n a l adminis-t r a t i o n , tended to seek l e s s i n f o r m a t i o n under those c o n d i -t i o n s i n which the group a t l e v e l 2, those with no t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n , tended to seek more informa-t i o n . The r e l a t i o n s h i p s i d e n t i f i e d i n F i g u r e s 2 and 3 i n d i c a t e d t h a t an a p o s t e r i o r i a p p l i c a t i o n o f the Sc h e f f e t e s t to 46 15C 14C_ 13C_ 12 C, 11C 100-90-80-70. 60. 50r-40-3d 2d I d -Mean Information Seeking B i a s A Comparison of L e v e l 1 (Experienced) and L e v e l 2 (Not Experienced) of F a c t o r A ( A d m i n i s t r a t i v e Experience) L e v e l 2 Not Experienc 3 4 C o n d i t i o n s F i g u r e 2 Mean Information Seeking B i a s Over the Treatment L e v e l s of F a c t o r C at F a c t o r A (Experience) 47 Mean Information Seeking B i a s 70 60 50 40 30 20 10-A Comparison of L e v e l 1 (Trained and L e v e l 2 (Not Trained) o f F a c t o r B ( T r a i n i n g i n E d u c a t i o n a l A d m i n i s t r a t i o n ) /'Level // ( N o t T r a i n e -» — i 1 i _ i 4 5 6 7 8 C o n d i t i o n s F i g u r e 3 Mean Information Seeking B i a s over the Treatment L e v e l s of F a c t o r C a t F a c t o r B (Training) 48 s p e c i f i c combinations o f f a c t o r C ( c o n d i t i o n s ) c o u l d prove u s e f u l . Table IX summarizes the r e s u l t s of t h i s a n a l y s i s f o r grouping f a c t o r s A and B. The r e s u l t s i n d i c a t e d t h a t none of the p a i r w i s e compari-sons between l e v e l s o f f a c t o r A under s i n g u l a r c o n d i t i o n s r e -s u l t e d i n s i g n i f i c a n t F s t a t i s t i c s . However, s i g n i f i c a n t d i f f e r e n c e s were noted f o r c e r t a i n combinations o f c o n d i t i o n s . S i g n i f i c a n t d i f f e r e n c e s i n the mean i n f o r m a t i o n seeking b i a s between l e v e l s 1 and 2, of those with a d m i n i s t r a t i v e e x p e r i -ence and those without, o f f a c t o r A occured when (1) the EVPI was low and the study c o s t s were low, i e . , c o n d i t i o n s 1, 3, 5, 7,; (2) the p r i o r p r o b a b i l i t i e s were d i v e r s e (.8, .2), i e . , c o n d i t i o n s 1, 2, 5, 6 and (3) the p a y o f f s were low not having been i n c r e a s e d by the a d d i t i v e constant, i e . , c o n d i t i o n s 1, 2, 3, 4. The r e s u l t s o f the Sc h e f f e T e s t , summarized i n Table IX, a l s o i n d i c a t e d t h a t a s i g n i f i c a n t d i f f e r e n c e i n the mean i n -formation seeking b i a s between l e v e l s 1 and 2 of f a c t o r B occured under c o n d i t i o n s 1 and 8. No common game parameters c o u l d be re c o g n i z e d between c o n d i t i o n s 1 and 8 to e x p l a i n t h i s r e s u l t . However s i g n i f i c a n t d i f f e r e n c e s were a l s o noted f o r c e r t a i n combinations o f c o n d i t i o n s . S i g n i f i c a n t d i f f e r -ences i n mean i n f o r m a t i o n seeking b i a s f o r groups at l e v e l 1 and l e v e l 2 occured when (1) the EVPI was low and the study c o s t s were low, i e . , c o n d i t i o n s 1, 3, 5, 7; (2) the p r i o r p r o b a b i l i t i e s were d i v e r s e (.8, .2), i e . , c o n d i t i o n s 1, 2, 5, Table IX R e s u l t s of the A p p l i c a t i o n of the Scheffe Test to the Two-Way I n t e r a c t i o n Between L e v e l s of Both F a c t o r s A (Experience) and B (Training) Under S p e c i f i e d Combinations of Factor C Combinations o f F a c t o r C F a c t o r A F S t a t i s t i c F a c t o r B F S t a t i s t i c .90 F c r i t i c a l P a i r w i s e C o n d i t i o n 1 2 3 4 5 6 7 8 * Combination 2.21 .08 .05 1. 81 .40 .24 .44 1. 70 2.94' .01 .62 .05 1.11 .82 .81 4.00* 1, 3, 5, 7 25.50 a 34.68 a 2, 4, 6, 8 .24 2.52 1, 2, 5, 6 20.95 a 12.96 3 3, 4, 7, 8 .89 14.78 a 1, 2, 3, 4 21.03 a 1.57 5, 6, 7, 8 . 89 38.37 a 2. 90 12.60 Significant at the .10 level 50 6; (3) the p r i o r p r o b a b i l i t i e s were equal (.5, .5), i e . , c o n d i t i o n s 3, 4, 7,8 and (4) the p a y o f f s were high having been i n c r e a s e d by the a d d i t i v e constant, i e . , c o n d i t i o n s 5, 6, 7, 8. Research Question Number F i v e F i g u r e 4 prese n t s a graph of the mean i n f o r m a t i o n seek-i n g b i a s f o r a l l s u b j e c t s over the sequence of games. As the sequence of games progressed the mean i n f o r m a t i o n seeking b i a s decreased from 90 to 28. The sharpest d e c l i n e i n i n f o r m a t i o n seeking b i a s occured between games one and t h r e e , with a gradu a l r a t h e r uneven d e c l i n e o c c u r i n g a f t e r game t h r e e . F i g u r e 5 presents the mean i n f o r m a t i o n seeking b i a s f o r each l e v e l o f f a c t o r B ( t r a i n i n g ) over the sequence of games. A l e a r n i n g p a t t e r n s i m i l a r to t h a t d e s c r i b e d above was noted f o r both l e v e l s o f f a c t o r B a f t e r game three both groups appeared to adopt s t r a t e g i e s which r e s u l t e d i n s i m i l a r i n f o r -mation seeking behaviour. T h i s was not the case f o r groups a t l e v e l s 1 and 2 of f a c t o r A (experience) graphed i n F i g u r e 6. Although the l e v e l 1 group began the s e r i e s o f games by seeking more i n -formation than the l e v e l 2 group they were, by game s i x , more c l o s e l y approaching the Bayesian o p t i m a l . The l e v e l 2 group began by purchasing l e s s i n f o r m a t i o n than the group i • 1 : l i 1 1 » game game game game game game game game 1 2 3 4 5 6 7 8 Sequence of Games F i g u r e 4 Mean Information Seeking B i a s over a l l Subjects over the Sequence i n Which the Games were Presented 52 Mean Information Seeking B i a s 150 140 -130 -120 " 110 L L e v e l 1 (Trained) 10 h — t 1 i _ J i : 1 1 , game game game game game game game game 1 2 3 4 5 6 7 8 Sequence of Games F i g u r e 5 Mean Information Seeking B i a s f o r Groups a t Le v e l s 1 and 2 o f F a c t o r B (Training) over the Sequence i n which the Games were Presented 53 F i g u r e 6 Mean Information Seeking B i a s f o r Groups a t L e v e l s 1 and 2 of F a c t o r A (Experience) over the Sequence i n which the Games were Presented 54 at l e v e l 1, but maintained a f a i r l y high (approximately 40) tendency to seek information. 55 CHAPTER 4 INTERPRETATION OF RESULTS Before the r e s u l t s o f t h i s study are d i s c u s s e d , three l i m i t a t i o n s as to the g e n e r a l i z a b i l i t y o f the f i n d i n g s should be noted. LIMITATIONS OF THE STUDY Because of d i f f i c u l t y i n c o n t a c t i n g p a r t - t i m e masters students, the sample s i z e f o r t h i s study was s m a l l . The p o p u l a t i o n f o r the study c o n s i s t e d o f a l l p a r t - t i m e masters students. Most of these students are r e s i d e n t s o u t s i d e the v i c i n i t y of Vancouver and can a t t e n d U.B.C. o n l y d u r i n g the summer s e s s i o n . Had the game s i m u l a t i o n been a d m i n i s t e r e d d u r i n g the summer s e s s i o n a much l a r g e r and more r e p r e s e n t a -t i v e sample of par t - t i m e masters students c o u l d have been obt a i n e d . Second, because o f the smal l sample s i z e , i t was neces-sary to al l o w unequal c e l l s i z e s . In the case of experienced a d m i n i s t r a t o r s who had completed more than three u n i t s o f graduate t r a i n i n g the c e l l s i z e was o n l y two. Although analy-s i s was s t i l l p o s s i b l e w i t h such a s m a l l c e l l s i z e , the p o s s i b i l i t y o f o b t a i n i n g s i g n i f i c a n t r e s u l t s was dimin i s h e d . The repeated measures design employed i n t h i s study p a r t l y compensated f o r the above l i m i t a t i o n s . 56 F i n a l l y , the study r e s u l t s i n d i c a t e d t h a t l e a r n i n g occured over the sequence o f games. As the sequence of con-d i t i o n s was not randomized f o r each i n d i v i d u a l s u b j e c t , but r a t h e r , on a group b a s i s , the p o s s i b i l i t y t h a t l e a r n i n g con-founded the r e s u l t s of the a n a l y s i s of i n f o r m a t i o n seeking b i a s cannot be ignored. Winer (1971:518) warns t h a t a r e -peated measures design i s to be avoided "...where primary i n t e r e s t l i e s i n e v a l u a t i o n of the e f f e c t of i n d i v i d u a l t r e a t -ments i n the absence of p o s s i b l e sequence e f f e c t s . " However, i n the p r e s e n t study each of the e i g h t c o n d i t i o n s was i n the f i r s t p l a c e a t l e a s t once with the remaining p o s i t i o n s ran-domly d i s t r i b u t e d i n each group. As a r e s u l t o f u s i n g t h i s experimental design i t i s b e l i e v e d t h a t the e f f e c t s o f l e a r n i n g over the sequence of games d i d not unduly i n f l u e n c e the mean i n f o r m a t i o n seeking b i a s over a l l s u b j e c t s and sub-j e c t groups. S t u d i e s i n t h i s area should, by means of a p p r o p r i a t e methodology, be separated i n t o those which study i n f o r m a t i o n seeking behaviour and c o n t r o l f o r l e a r n i n g as i n the p r e s e n t study, and those which examine l e a r n i n g p a t t e r n s . DISCUSSION OF RESULTS The r e s u l t s o f the a n a l y s i s w i l l be d i s c u s s e d s e p a r a t e l y f o r each of the i n d i v i d u a l r e s e a r c h q u e s t i o n s . 57 Research Question Number One The a n a l y s i s presented i n Chapter 3 i n d i c a t e d t h a t the s u b j e c t group as a whole showed a p o s i t i v e i n f o r m a t i o n seek-i n g b i a s . T h i s confirmed the f i n d i n g s of p r e v i o u s s t u d i e s (Green, e t a l . , 1967 and Edwards, 1962) i n t o i n f o r m a t i o n seeking b i a s . Green, e t a l . , (1967) r e p o r t e d on two e x p l a n a t i o n s which had been advanced to t r y and e x p l a i n t h i s phenomenon. F i r s t , a number of r e s e a r c h e r s b e l i e v e t h a t m o t i v a t i o n a l , i e . the need-to-be-sure, c o n s i d e r a t i o n s c o u l d be c o n t r i b u t i n g to the p o s i t i v e b i a s . These mo t i v a t o r s are, i n t u r n , rooted i n the i n d i v i d u a l s p e r s o n a l i t y and, to date, s t u d i e s i n the area have g e n e r a l l y been i n c o n c l u s i v e . T h i s e x p l a n a t i o n , t h a t a need-to-be-sure was a m o t i v a t o r . i n seeking i n f o r m a t i o n , was r e - i n f o r c e d d u r i n g the post game i n t e r v i e w s . Comments such as "I looked a t how much I would l o s e " , "I f e l t my l u c k runs i n s t r e a k s " , and " I f there i s a b i g d i f f e r e n c e i n p a y o f f s then the s t u d i e s are worth purchasing" were recorded. These comments seemed to i n d i c a t e an u n d e r l y i n g need f o r c e r t a i n t y which, i n the above cases a t l e a s t , d i d a f f e c t i n f o r m a t i o n seeking behaviour. The second e x p l a n a t i o n maintains t h a t c o g n i t i v e l i m i t a -t i o n s a f f e c t the s u b j e c t s a b i l i t y to perform, e i t h e r i m p l i c i t l y o r e x p l i c i t y , the c a l c u l a t i o n s necessary to a r r i v e a t the Bayesian optimal s o l u t i o n . Each i n d i v i d u a l has a s u b j e c t i v e 58 'cost of thinking' which l i m i t s his/her e f f o r t s to maximize the game score. Post game interviews i n the present study also supported t h i s explanation. Comments such as, "In game one I was just getting the f e e l of the game", and "I just took a chance I had no p a r t i c u l a r strategy" indicated that players were searching for the optimal strategy without attempting to figure i t out according to a preconceived r a t i o n a l plan. Post game interviews were not detailed enough to indicate with certainty the application of p a r t i c u l a r ( i e . , Bayesian) strategies. However, the desire to reduce the expected loss i n a p a r t i c u l a r game appeared to influence the information seeking behaviour of many of those interviewed. Statements such as, "I looked at how much I would lose, what the payoff was as opposed to the cost of the study", "If there i s a big difference i n payoffs the studies are worth purchasing", and "The difference at state B was $ 7 0 therefore why pay $ 6 0 to buy the knowledge of the true state" were common to many of those interviewed. Green et a l . ( 1 9 6 7 : 3 5 ) recognized s i m i l a r strategies stating that players "...were w i l l i n g to pay up to and including the t o t a l regret-loss which could be incurred..." i n choosing the wrong program. As far as could be ascertained from the results of the study, none of those interviewed adopted a consistant Bayesian strategy, although at least one player appeared to have adopted such a strategy by game six. When interviewed, few players c o u l d be s p e c i f i c about t h e i r game s t r a t e g y . Comments such as, "I j u s t bought the cheapest ones ( s t u d i e s ) " , and "I chose these (s t u d i e s ) because the o t h e r s were too expensive", appeared to i n d i c a t e t h a t many p l a y e r s had assumed a s t r a t e g y without being cognizant of the f a c t . Research Questions Numbers Two and Three The repeated measures a n a l y s i s f a i l e d to show any s i g -n i f i c a n t d i f f e r e n c e s i n the i n f o r m a t i o n seeking b i a s between the two l e v e l s of f a c t o r s A ( a d m i n i s t r a t i v e experience) and B (graduate l e v e l t r a i n i n g ) . Green's e t a l . (1967) study of marketing e x e c u t i v e s appeared t o i n d i c a t e t h a t experience was a f a c t o r i n determining i n f o r m a t i o n seeking b i a s . How-ever, Green t e s t e d f o r d i f f e r e n c e s between a group o f e x p e r i -enced e x e c u t i v e s and a group of graduate l e v e l marketing students. He found a s i g n i f i c a n t d i f f e r e n c e i n i n f o r m a t i o n seeking b i a s between the two groups and a t t r i b u t e d t h a t d i f f e r e n c e to experience, i g n o r i n g the p o s s i b i l i t y t h a t t r a i n i n g c o u l d a l s o have been an i n f l u e n c i n g f a c t o r . The present study separated the two f a c t o r s o f t r a i n i n g and ex-p e r i e n c e and analyzed each s e p a r a t e l y , f i n d i n g no s i g n i f i c a n t d i f f e r e n c e i n e i t h e r case. The l a c k of s i g n i f i c a n t r e s u l t s i n the p r e s e n t study c o u l d have been due i n p a r t to the r a t h e r s m a l l sample s i z e . But u n t i l f u r t h e r s t u d i e s c o n f i r m t h a t t r a i n i n g does not i n -60 f l u e n c e i n f o r m a t i o n seeking b i a s , s t u d i e s which examine ot h e r p o s s i b l e determinants o f i n f o r m a t i o n seeking b i a s should i n -sure t h a t t r a i n i n g i s a c o n t r o l l e d v a r i a b l e . Research Question Number Four The a n a l y s i s presented i n Chapter 3 i n d i c a t e d t h a t over a l l s u b j e c t s no p a r t i c u l a r s e n s i t i v i t y i n i n f o r m a t i o n seeking b i a s was noted w i t h r e s p e c t t o p r i o r p r o b a b i l i t y d i f f e r e n c e s i n p a y o f f or the c o s t o f i n f o r m a t i o n i n the d e c i s i o n game. Green (196 7) has noted t h a t i n p a s t experiments, p r i m a r i l y u s i n g students as s u b j e c t s , i n f o r m a t i o n seeking b i a s has shown s e n s i t i v i t y to p r i o r p r o b a b i l i t y but not to d i f f e r e n c e s i n p a y o f f . The r e s u l t s r e p o r t e d i n Green's work can be a p p l i e d t o the presen t study o n l y with g r e a t care, because the p r e s e n t sample c o n s i s t e d of j u s t p a r t - t i m e students and of those sampled, approximately 67 per c e n t had completed no graduate l e v e l courses. The i n t e r a c t i o n e f f e c t s between each o f t r a i n i n g and experience and combinations o f c o n d i t i o n s were found t o be s i g n i f i c a n t . The S c h e f f e t e s t confirmed t h a t c e r t a i n com-b i n a t i o n s o f c o n d i t i o n s f o r both f a c t o r s d i d l e a d to s i g n i f i -cant d i f f e r e n c e s . Under f a c t o r B ( t r a i n i n g ) i t was noted t h a t a s i g n i f i c a n t d i f f e r e n c e i n i n f o r m a t i o n seeking behaviour between l e v e l s d i d occur f o r both d i v e r s e (.8, .2) and equal (.5, .5) p r i o r p r o b a b i l i t i e s . In the case of both d i v e r s e 61 (.8, .2) and equal (.5, .5) p r i o r p r o b a b i l i t i e s those w i t h d i f f e r e n t l e v e l s o f t r a i n i n g tended to have d i f f e r e n t mean i n f o r m a t i o n seeking b i a s e s . Although the groups d i f f e r e d , n e i t h e r group scored c o n s i s t e n t l y h i g h e r or lower than the o t h e r . T h i s r e s u l t emphasized the p o i n t made e a r l i e r t h a t t r a i n i n g must be c o n t r o l l e d i n s t a t i s t i c a l d e c i s i o n s t u d i e s o f i n f o r m a t i o n seeking b i a s . Post-game i n t e r v i e w s i n d i c a t e d t h a t a number of s u b j e c t s d i d c o n s i d e r p a y o f f s and p r i o r p r o b a b i l i t i e s i n t h e i r game p l a y i n g . Whether these were a p p l i e d i n a c o n s i s t a n t manner was not apparent from the study r e s u l t s . For both F a c t o r A (experience) and f a c t o r B ( t r a i n i n g ) s i g n i f i c a n t d i f f e r e n c e s between l e v e l s were found to occur when the EVPI was twenty and the study c o s t s were low. T h i s i n d i c a t e d t h a t both f a c t o r s were s e n s i t i v e t o study c o s t s , t h a t i s , low study c o s t was a good d i s c r i m i n a t o r between the two l e v e l s of both experience and t r a i n i n g . In the case of f a c t o r A (experience) those w i t h no e d u c a t i o n a l a d m i n i s t r a -t i v e experience tended to seek more i n f o r m a t i o n than e x p e r i -enced a d m i n i s t r a t o r s . Under f a c t o r B ( t r a i n i n g ) those w i t h t r a i n i n g i n e d u c a t i o n a l a d m i n i s t r a t i o n tended to seek more i n f o r m a t i o n than those w i t h no such t r a i n i n g . In the case o f t r a i n i n g , h i g h e r p a y o f f was found to be a good d i s c r i m i n a t o r w h i l e f o r the experience f a c t o r lower p a y o f f s was found to be a good d i s c r i m i n a t o r . I t was sus-62 pected t h a t those w i t h e x t e n s i v e t r a i n i n g would have a t e n -dency to seek more i n f o r m a t i o n than those w i t h no t r a i n i n g . T h i s b i a s c o u l d have been c a r r i e d over from the s u b j e c t s course work and the f a c t t h a t the study was conducted d u r i n g a r e g u l a r l y scheduled c l a s s p e r i o d . Thus wi t h the h i g h e r p a y o f f s , i e . , when more was a t stake, the group with more t r a i n i n g would have been more i n c l i n e d t o seek i n f o r m a t i o n . While a t lower p a y o f f s , students may have f e l t l e s s of a need to purchase i n f o r m a t i o n . The g r e a t e s t d i s c r e p a n c y between experienced and non-experien c e d groups occured when the p a y o f f s were lower. T h i s appeared t o i n d i c a t e t h a t when the stakes are hig h e x p e r i e n c e makes l e s s d i f f e r e n c e i n i n f o r m a t i o n seeking behaviour than when p a y o f f s were lower. Experienced a d m i n i s t r a t o r s tended to seek l e s s i n f o r m a t i o n i n low p a y o f f s i t u a t i o n s . Thus ex-p e r i e n c e d a d m i n i s t r a t o r s appeared to be more prone t o r i s k t a k i n g than those with no experience when the p a y o f f s are low; but when the stakes are h i g h , they behave much l i k e the non-experienced group i n t h e i r i n f o r m a t i o n seeking. T h i s r e s u l t p o i n t s out the i n t e r e s t i n g p o s s i b i l i t y t h a t e x p e r i e n c e , as an i n d i c a t o r o f job performance, should not u n i v e r s a l l y be accepted, but r a t h e r , be dependent on the degree of r e s p o n s i -b i l i t y o f the p o s i t i o n . Research Question Number F i v e The graphs of mean i n f o r m a t i o n seeking b i a s over the sequence of games w i l l be r e f e r r e d t o as l e a r n i n g curves. The d e c r e a s i n g shape of t h e l e a r n i n g curve f o r a l l s u b j e c t s i n d i c a t e d t h a t as the games progressed the p l a y e r s were ad-j u s t i n g t h e i r s t r a t e g i e s toward the Bayesian o p t i m a l . On the f i r s t game, s u b j e c t s purchased f a r too much i n f o r m a t i o n ; however by the t h i r d game the mean amount of i n f o r m a t i o n pur-chased had f a l l e n by over 45 perc e n t . A f t e r the t h i r d game there was a grad u a l but uneven approach t o the Bayesian op-t i m a l o f zero b i a s . Post game i n t e r v i e w s confirmed t h i s changing p a t t e r n i n i n f o r m a t i o n seeking. Comments such as "I chose a l l s t u d i e s i n games one and two, they were e x p l o r a t o r y " and "by game 6 (six) I was choosing o n l y the lowest c o s t i n g s t u d i e s " tend to c o n f i r m the p a t t e r n i n d i c a t e d by the l e a r n -i n g curves. Both l e v e l s o f f a c t o r B ( t r a i n i n g ) i n d i c a t e d s i m i l a r l e a r n i n g curves, p a r t i c u l a r l y a f t e r the t h i r d game. T h i s i n -d i c a t e d t h a t graduate l e v e l t r a i n i n g i n e d u c a t i o n a l adminis-t r a t i o n had l i t t l e e f f e c t on l e a r n i n g p a t t e r n s i n t h i s type of experiment. By game three both groups had adopted s i m i l a r s t r a t e g i e s . L e v e l s o f f a c t o r A (experience) d i d d i f f e r i n t h e i r l e a r n -i n g curves. The group wi t h e d u c a t i o n a l a d m i n i s t r a t i v e e x p e r i -ence tended to 'play i t s a f e ' e a r l y i n the experiment but by 64 the f o u r t h game, they began to very q u i c k l y approach the Bayesian o p t i m a l . The group w i t h l i t t l e e xperience was not as c a u t i o u s i n i t i a l l y , but f a i l e d t o approach the Bayesian o p t i m a l as the games progressed. I t appeared t h a t e x p e r i -enced a d m i n i s t r a t o r s , although i n i t i a l l y c a u t i o u s , were s u f f i c i e n t l y attuned to the game t h a t they r e c o g n i z e d , i f only i m p l i c i t l y , the o p t i m i z i n g s t r a t e g y . Perhaps the nature of the a d m i n i s t r a t o r s job r e q u i r e s him/her t o r e c o g n i z e q u i c k l y , o p t i m i z i n g s t r a t e g i e s . For example not wasting money or p u r c h a s i n g unnecessary i n f o r m a t i o n , t h a t i s , p l a y i n g i t s a f e . 65 CHAPTER 5 SUMMARY AND IMPLICATIONS OF THE STUDY Summary o f Experimental Procedures, Research  Questions and F i n d i n g s In r a t i o n a l models of the d e c i s i o n making p r o c e s s , i n -formation r e l e v a n t to the d e c i s i o n under c o n s i d e r a t i o n can be sought by d e c i s i o n makers a t v a r i o u s stages. E d u c a t i o n a l A d m i n i s t r a t o r s are d e c i s i o n makers. T h e r e f o r e , to understand and, h o p e f u l l y , improve r a t i o n a l d e c i s i o n making among educa-t i o n a l a d m i n i s t r a t o r s , i t would be u s e f u l to study t h e i r i n -formation seeking behaviour. In r e c e n t years u n i v e r s i t y departments o f e d u c a t i o n a l a d m i n i s t r a t i o n have been assuming a g r e a t e r p o r t i o n of the task of t r a i n i n g a d m i n i s t r a t o r s f o r p r a c t i s e . Because de-c i s i o n making i s such a c e n t r a l p a r t of the a d m i n i s t r a t o r s f u n c t i o n , i t i s important t h a t t r a i n i n g i n s t i t u t i o n s under-stand a l l aspects of t h i s phenomenon i n an e f f o r t t o advance t h e o r e t i c a l knowledge and prepare a base f o r p r a c t i c a l a p p l i c a t i o n . The p r e s e n t study adopted a technique f o r s t u d y i n g i n -formation seeking behaviour which had been s u c c e s s f u l l y em-p l o y e d i n o t h e r d i s c i p l i n e s . T h i s technique u t i l i z e d a Bayesian norm to d e f i n e p u r e l y r a t i o n a l behaviour i n a s t a t i s -t i c a l d e c i s i o n game. Subjects were asked to p l a y a game which 66 f a c i l i t a t e d the q u a n t i f i c a t i o n o f the va l u e of c e r t a i n i n -formation to the p l a y e r . T h i s amount c o u l d then be compared to the value d e r i v e d from the Bayesian norm. The sample f o r the present study was drawn from the s e t of p a r t - t i m e students e n r o l l e d i n the wi n t e r s e s s i o n courses i n the U.B.C. Department of E d u c a t i o n a l A d m i n i s t r a t i o n . P a r t i c i p a t i o n was on a v o l u n t a r y b a s i s ; twenty-nine students were i n c l u d e d i n the f i n a l a n a l y s i s . Of these, eleven were experienced a d m i n i s t r a t o r s , nine had completed a t l e a s t t h r e e u n i t s o f graduate l e v e l course work wit h the department and the group as a whole had a mean of 6.0 years t e a c h i n g e x p e r i -ence . The p r e s e n t study employed three independent v a r i a b l e s and may be c l a s s e d as a 2 x 2 x 8 ( e x p e r i e n c e - b y - t r a i n i n g - b y -Treatment Design) f a c t o r i a l experiment w i t h repeated measures on the l a s t f a c t o r . L e v e l one of grouping f a c t o r A i n c l u d e d those s u b j e c t s w i t h a t l e a s t one year o f e d u c a t i o n a l a d m i n i s t r a t i v e e x p e r i -ence and l e v e l two i n c l u d e d those w i t h no a d m i n i s t r a t i v e ex-p e r i e n c e . L e v e l one of grouping f a c t o r B i n c l u d e d those sub-j e c t s who had completed a t l e a s t t h r e e u n i t s o f graduate l e v e l coursework i n e d u c a t i o n a l a d m i n i s t r a t i o n and l e v e l two i n c l u d e d those w i t h no graduate l e v e l t r a i n i n g . The f a c t o r C had three dimensions, each of which had two l e v e l s . The thr e e dimensions were (1) p r i o r p r o b a b i l i t i e s (2) an a d d i t i v e constant and a (3) m u l t i p l i c a t i v e constant, t o be a p p l i e d to 67 the game p a y o f f s . T h i s f a c t o r i n t r o d u c e d v a r i a t i o n across the games. The dependent v a r i a b l e , i n f o r m a t i o n seeking b i a s , was d e f i n e d as the d i f f e r e n c e between the a c t u a l q u a n t i f i e d value of c e r t a i n i n f o r m a t i o n t o the d e c i s i o n maker and t h a t v a l u e a s c r i b e d by the Bayesian norm. The s i m u l a t i o n game presented the d e c i s i o n maker wit h a cho i c e bewteen two or more a l t e r n a t i v e s . The p a y o f f a s s o c i -ated with each a l t e r n a t i v e was dependent upon the s t a t e which e x i s t e d a t the time o f the d e c i s i o n . Before choosing one a l t e r n a t i v e the p l a y e r was given the o p p o r t u n i t y to purchase i n f o r m a t i o n as to which s t a t e would occur. By determining the amount of i n f o r m a t i o n purchased under known game c o n d i -t i o n s and comparing t h a t to the Bayesian o p t i m a l , the i n f o r -mation seeking b i a s was determined. The game was adm i n i s t e r e d i n groups r a n g i n g i n s i z e from three t o s i x s u b j e c t s , each under the d i r e c t i o n of a s p e c i a l l y t r a i n e d umpire. Each person i n a group r e c e i v e d the same sequence of e i g h t games corresponding to the e i g h t treatment l e v e l s of f a c t o r C, however, each group had a d i f f e r e n t ran-domly determined sequence of games. The f o l l o w i n g f i v e r e s e a r c h q u e s t i o n s were examined. (1) Do students of e d u c a t i o n a l a d m i n i s t r a t i o n tend to seek the same amount of i n f o r m a t i o n as p u r e l y Bayesian p l a y e r s , i n a programable d e c i s i o n s i t u a t i o n ? 68 (2) Do students of educational administration with ad-ministrative experience behave d i f f e r e n t l y than students with no administrative experience in t h e i r tendency to seek information? (3) Do students of educational administration, who have completed three or more units of graduate l e v e l t r a i n i n g i n educational administration behave d i f f e r e n t l y than students with no t r a i n i n g i n t h e i r tendency to ,seek information? (4) Among students of educational administration does varying the p r i o r p r o b a b i l i t i e s and payoff parameters i n the s t a t i s t i c a l decision game, e f f e c t the tendency to seek information? (5) Does information seeking bias change over the se-quence of games? Does learning take place? The analysis of research questions one through four was performed by the BMD: P2V computer program which was based on Winer's three f a c t o r i a l repeated measures design (case II):. Research question one was examined by using the grand mean, over a l l subjects and a l l conditions, as a measure of the information seeking bias of the sample as a whole. The re-sults of the analysis indicated that the sample showed a strong tendency to seek more information than the r a t i o n a l l y derived Bayesian optimal. To answer research question two the main effects of the two levels of factor A (experience) was tested. The F s t a t i s -69 t i c which was c a l c u l a t e d i n d i c a t e d t h a t a t j? < .10 the n u l l h y p o t h e s i s t h a t t h e r e was no d i f f e r e n c e i n mean i n f o r m a t i o n seeking b i a s between the two l e v e l s o f f a c t o r A c o u l d not be r e j e c t e d . Research q u e s t i o n t h r e e i n v o l v e d t e s t i n g the n u l l hypo-t h e s i s t h a t there was no d i f f e r e n c e i n mean i n f o r m a t i o n seek-i n g b i a s between the two l e v e l s o f f a c t o r B ( t r a i n i n g ) . The F s t a t i s t i c which was c a l c u l a t e d i n d i c a t e d t h a t a t p .10 the n u l l h y p o t h e s i s c o u l d not be r e j e c t e d . Research q u e s t i o n f o u r r e q u i r e d an examination o f the main e f f e c t s o f f a c t o r C, as w e l l as the i n t e r a c t i o n e f f e c t s between f a c t o r s A (experience) and C and between f a c t o r B ( t r a i n i n g ) and C. The F s t a t i s t i c determined from the a n a l y -s i s o f the main e f f e c t s o f f a c t o r C i n d i c a t e d t h a t the hypo-t h e s i s t h a t t h e r e was no d i f f e r e n c e i n the mean i n f o r m a t i o n seeking b i a s over a l l s u b j e c t s f o r v a r i o u s combinations o f game parameters ( f a c t o r C) c o u l d not be r e j e c t e d . However, the i n t e r a c t i o n e f f e c t s between f a c t o r s A and C and between f a c t o r s B and C were found t o be s i g n i f i c a n t a t p .10. To determine what s p e c i f i c combinations o f treatment l e v e l s i n f a c t o r C c o n t r i b u t e d t o the s i g n i f i c a n t r e s u l t s a S c h e f f e t e s t was a p p l i e d . T h i s t e s t i n d i c a t e d t h a t s i g n i f i c a n t d i f f e r e n c e s i n mean i n f o r m a t i o n seeking b i a s between the l e v e l s o f f a c t o r A (experience) occured when, (1) the study c o s t s were low (2) the p r i o r p r o b a b i l i t i e s were d i v e r s e and (3) the game m a t r i x p a y o f f s were low. A l s o s i g n i f i c a n t 70 d i f f e r e n c e s i n mean i n f o r m a t i o n seeking b i a s occured between the l e v e l s o f f a c t o r B ( t r a i n i n g ) when (1) the study c o s t s were low (2) the p r i o r p r o b a b i l i t i e s were d i v e r s e (3) the p r i o r p r o b a b i l i t i e s were equal and (4) the p a y o f f s were high. Research q u e s t i o n f i v e was examined by graphing the mean i n f o r m a t i o n seeking b i a s o f the v a r i o u s s u b j e c t groups over the sequence i n which the c o n d i t i o n s were presented. A s t r o n g l e a r n i n g curve f o r a l l groups was noted. As the games pro-gressed the i n f o r m a t i o n seeking b i a s more c l o s e l y approximated the Bayesian o p t i m a l . The two l e v e l s o f f a c t o r B ( t r a i n i n g ) showed s i m i l a r l e a r n i n g curves, however, under f a c t o r A (ex-perience) experienced a d m i n i s t r a t o r s tended t o approach the Bayesian optimal s t r a t e g y a t a f a s t e r r a t e than the non-ex-p e r i e n c e d group. The i m p l i c a t i o n s o f these r e s u l t s w i l l now be presented. IMPLICATIONS FOR THEORY, FUTURE RESEARCH AND PRACTISE The p r e s e n t study confirms some of the f i n d i n g s o f pre -v i o u s r e s e a r c h and i n d i c a t e s t h e i r a p p l i c a b i l i t y to the study o f e d u c a t i o n a l a d m i n i s t r a t i o n . The f a c t t h a t s i g n i f i c a n t i n t e r a c t i o n e f f e c t s were found between t r a i n i n g and experience p o i n t s out the importance o f c o n t r o l l i n g f o r t r a i n i n g when student groups are used. A l s o the f a c t t h a t s t r o n g l e a r n i n g curves were noted i n d i c a t e s t h a t f u t u r e s t u d i e s should adopt 71 methodologies which e i t h e r c o n t r o l f o r across sequence l e a r n -i n g o r permit i t to occur as a phenomena f o r study. The f a c t t h a t i n t e r a c t i o n e f f e c t s between the grouping f a c t o r s , experience and t r a i n i n g , and v a r i o u s combinations of the repeated measures f a c t o r , game parameters, were found t o be s i g n i f i c a n t i n d i c a t e s t h a t f u t u r e s t u d i e s c o u l d u s e f u l l y examine the e f f e c t s of game parameters on the s u b j e c t group as a whole. T h i s e f f e c t was found t o be not s i g n i f i c a n t i n the pre s e n t study. However, the low F s t a t i s t i c 1.61 wit h a p r o b a b i l i t y o f being exceeded of .14, i n d i c a t e d t h a t perhaps f u t u r e s t u d i e s with l a r g e r sample s i z e s would d i s c o v e r s i g n i f i -cant d i f f e r e n c e s across treatment l e v e l s o f the game para-meters. I t was shown e a r l i e r t h a t under c e r t a i n game c o n d i t i o n s t r a i n i n g and a d m i n i s t r a t i v e experience does have some e f f e c t on i n f o r m a t i o n seeking b i a s . For i n s t a n c e when the study c o s t s were low those w i t h e d u c a t i o n a l a d m i n i s t r a t i v e e x p e r i -ence tended t o seek l e s s i n f o r m a t i o n than those without a d m i n i s t r a t i v e experience has an e f f e c t , under c e r t a i n c o n d i -t i o n s , on the r a t e a t which new s t r a t e g i e s are adopted. For those r e s p o n s i b l e f o r dev e l o p i n g programs and courses i n edu-c a t i o n a l a d m i n i s t r a t i v e d e c i s i o n making, the need f o r con-s i d e r a t i o n of (1) the c o n d i t i o n s under which d e c i s i o n s are made and (2) the experience and t r a i n i n g o f the students has been emphasized. No f i r m recommendations to p r a c t i t i o n e r s w i l l be made on the b a s i s o f t h i s study alone. However, the 72 r e s u l t s of t h i s study c o n f i r m the need f o r f u t u r e r e s e a r c h and a l s o serve as a c a u t i o n to program developers who are tempted to ignore a d m i n i s t r a t i v e experience and pr e v i o u s t r a i n i n g among masters students. As w e l l as having immediate f i n d i n g s , the pr e s e n t study r a i s e s a number of qu e s t i o n s which c o u l d prove worthy of f u t u r e i n v e s t i g a t i o n . In Chapter Four i t was p o s t u l a t e d t h a t the r e d u c t i o n o f u n c e r t a i n t y was a f a c t o r i n the over pur-chasing of i n f o r m a t i o n i n games 1 and 2. Since t h i s i n f o r -mation seeking b i a s d i m i n i s h e d over the sequence of games, the q u e s t i o n a r i s e s as t o the r e l a t i o n s h i p between the r e -d u c t i o n o f u n c e r t a i n t y as a moti v a t o r and the need-to-win or succeed as a mo t i v a t o r . Another q u e s t i o n i s r a i s e d by the f a c t t h a t i n the pre -sent study i t was not p o s s i b l e to s t a t e w i t h c e r t a i n t y t h a t the i n f o r m a t i o n seeking b i a s of the groups approached the Bayesian o p t i m a l . T h i s r a i s e s the p o s s i b i l i t y t h a t the Bayesian model does not give an ac c u r a t e r e p r e s e n t a t i o n of the i n f o r m a t i o n seeking behavior of e d u c a t i o n a l a d m i n i s t r a t i o n . F u r t h e r s t u d i e s which expand the presen t experimental design to i n c l u d e a longer sequence of games would h e l p t o c l a r i f y t h i s p o i n t . I f such s t u d i e s show an approach to some number othe r than the Bayesian o p t i m a l , the q u e s t i o n would then a r i s e as to the reason why t h i s should occur. F i n a l l y , the p o s s i b i l i t y o f expanding the model of r a t i o n a l behavior t o i n c l u d e dimensions r a t i o n a l i t y o t h e r 73 than the purely economic could prove u s e f u l . This would be a d i f f i c u l t task f o r two reasons, f i r s t , the human r e l a t i o n s aspect of an administrators job would be hard to quantify and second, the d e f i n i t i o n of a s u i t a b l e u t i l i t y f u n c t i o n i s most d i f f i c u l t when dealing with human values. 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Gross, Neal and Robert H a r r i o t 1965 S t a f f Leadership i n P u b l i c Schools: A S o c i o l o g i c a l I n q u i r y . Nev/ York: John Wiley and Sons. H i l l s , Jean 1975 "Some Notes on the Methodology of Science f o r Researchers and A d m i n i s t r a t o r s , " i n T h e o r e t i c a l Dimensions o f E d u c a t i o n a l A d m i n i s t r a t i o n , W i l l i a m Monhan, (ed.) New York: MacMillan. 1977 "An A n a l y s i s of the Current S t a t e of the Centre f o r the Study o f A d m i n i s t r a t i o n i n Education." Unpublished paper, U.B.C. Hoen, Robert 1974 P a r t i c i p a t i o n i n School L e v e l D e c i s i o n Making: A Case Study. D o c t o r a l T h e s i s , U.B.C. Husen, T o r s t e n 1972 "Does More Time i n School Make a D i f f e r e n c e ? " Saturday Review, A p r i l 29, pp. 32-35. Hyman, Hubert; C h a r l e s Wright and John Reed. 1975 The Enduring E f f e c t s o f E d u c a t i o n . Chicago: The U n i v e r s i t y o f Chicago P r e s s . 76 Jencks, C h r i s t o p h e r 1972 On E q u a l i t y o f E d u c a t i o n a l Opportunity. New York: Vintage Books. Kant, Fremont and James Rosenzweig 1970 O r g a n i z a t i o n and Management: A Systems Approach. U.S^A.: McGraw-Hill, pp. 356-435. Lindblom, Charles E. 1968 The P o l i c y Making Process. New J e r s e y : P r e n t i c e - H a l l . McCordic, W. J . 1974 "Who's Making the D e c i s i o n s and How?" Education Canada, 12:43-51. McGee, V i c t o r E. 1971 P r i n c i p l e s o f S t a t i s t i c s : T r a d i t i o n a l and Bayesian. New York: Appleton-Century-C r o f t s . Meyer, Donald L. 1964 "A Bayesian School Superintendent." Ameri-can E d u c a t i o n a l Research J o u r n a l , 1:219-228. M o r r i s , P e t e r A. 1974 " D e c i s i o n A n a l y s i s E x p e r t Use." Management Scienc e , 20:1233-1241. O.E.C.D. 19 75 E x t e r n a l Examiners Report on E d u c a t i o n a l P o l i c y i n Canada. Toronto. CAAE. Ott, Jack: S h e i l a F l e t c h e r and Donald Turner. 1973 "Taxonomy o f A d m i n i s t r a t i v e Information Needs: An A i d to E d u c a t i o n a l P l a n n i n g and E v a l u a t i o n . " E d u c a t i o n a l Technology, 13:29-31. Petersen, George. 1975 " E d u c a t i o n a l D e c i s i o n Making: An I r r a t i o n a l Process." E d u c a t i o n Canada, 2:30-35. Rubenstein, A l b e r t and Chadwick Haberstrokh (eds.) 1966 Some The o r i e s of O r g a n i z a t i o n . Homewood, 111.: The Dorsey P r e s s . Shannon, C E . and W. Weaver 1949 The Mathematical Theory o f Communication. Urbana: U n i v e r s i t y o f I l l i n o i s P r e s s . 77 Simon, Herbert 1957 A d m i n i s t r a t i v e Behavior. New York: The Free P r e s s . 1960 S i n g l e t o n , J . W. 1972 The New Science o f Management. New York: Harper and B r o t h e r s . " D e c i s i o n Making." Educa t i o n Canada, 12:45-50. T a y l o r , Ronald N, 1975 Thurston, P h i l i p H. 1962 Ugalde, Antonio 1973 Winer, B. J . 1971 "Age and Experience as Determinants o f Management Information P r o c e s s i n g and D e c i s i o n Making Performance." Academy of Management J o u r n a l , 18:74-81. "Who Should C o n t r o l Information Systems." Harvard Business Review, 40:135-139. "A D e c i s i o n Model f o r the Study o f P u b l i c B u r e a u c r a c i e s . " P o l i c y S c i e n c e s , 4:75-84. S t a t i s t i c a l P r i n c i p l e s i n Experimental Design (2nd e d i t i o n ) . New York: McGraw-H i l l . 78 APPENDIX A GAME INSTRUCTIONS AND RESPONSE FORM GAME INSTRUCTIONS Your co o p e r a t i o n i s requested on an experiment designed to determine how people value i n f o r m a t i o n . Please read c a r e -f u l l y the f o l l o w i n g game i n s t r u c t i o n s . Assume t h a t you are the p r i n c i p a l o f a l a r g e s c h o o l . You are r e s p o n s i b l e f o r d e c i d i n g which of two academic pro-grams are to be implemented. Your o b j e c t i v e i s to maximize the per p u p i l budget a l l o t m e n t from the S e c r e t a r y - T r e a s u r e r . The Two academic programs are c a l l e d program 1 and pro-gram 2. For each o f these programs there are two p o s s i b l e s t a t e s . Each s t a t e c o n s i s t s o f a l l the f a c t o r s which c o u l d i n f l u e n c e the S e c r e t a r y - T r e a s u r e r i n h i s d e c i s i o n t o fund the program. For example, there may be p o l i t i c a l and economic f a c t o r s , as w e l l as p e r s o n a l i t y f a c t o r s . Each s t a t e r e p r e -sents a d i f f e r e n t combination of f a c t o r s . Although you do not know which s t a t e w i l l p r e v a i l , you are given the pro-b a b i l i t y o r l i k e l i h o o d o f t h a t s t a t e o c c u r r i n g . You, as p r i n c i p a l , may devote time to a s c e r t a i n i n g which s t a t e a c t u a l l y does p r e v a i l . However, the time and g o o d w i l l l o s t i n t h i s process w i l l r e f l e c t i t s e l f i n lower per p u p i l s u b s i d i e s . 79 Here i s an example to help c l a r i f y the problem: EXAMPLE s t a t e A s t a t e B program 1 350 130 program 2 275 190 p r o b a b i l i t y of s t a t e . 8 .2 I f program 1 i s chosen and s t a t e A o c c u r s , then the average subsidy per p u p i l i s $350. However, i f s t a t e B had p r e v a i l e d , then the average student subsidy would be $130. I f program 2 i s chosen and s t a t e A o c c u r s , then the average student subsidy w i l l be $275, w h i l e i f s t a t e B occurs the average student subsidy would be $190. I t i s given t h a t the p r o b a b i l i t y o f s t a t e A o c c u r r i n g i s .8, w h i l e the p r o b a b i l i t y o f s t a t e B o c c u r r i n g i s .2. This means t h a t , i n the long run, s t a t e A w i l l occur 8 times out o f 10 and s t a t e B w i l l occur 2 times out o f 10. Before choosing program 1 or program 2 you may decide t o conduct a survey which w i l l determine with c e r t a i n t y which s t a t e w i l l p r e v a i l . However, t h i s survey w i l l cause d e l a y s i n implementing the program which i n t u r n w i l l r e s u l t i n the lowering o f the average per p u p i l subsidy. T h i s l o w e r i n g or 'cost' w i l l range from $1 to $210. Your problem i s to determine (1) whether you w i l l , o r w i l l not, conduct the study and (2) having made t h a t d e c i s i o n , which program (1 or 2) you w i l l choose. 80 There w i l l be s i x s i t u a t i o n s i n each game and there are e i g h t games. The s i x s i t u a t i o n s r e p r e s e n t s i x independent s t u d i e s . Each study c o s t s a s p e c i f i e d amount. In each study you w i l l r e c e i v e the same i n f o r m a t i o n ; namely, what s t a t e i s going to occur f o r t h a t s i t u a t i o n . Look a t game one on your response sheets. Suppose t h a t conducting the study w i l l r e s u l t i n the lowering of the sub-s i d y by $210, and you decide t h a t i t i s b e t t e r not to conduct the study. I f so, you w i l l check the 'Not Conduct Study' column o f your response sheet. Suppose t h a t you do decide to conduct the study. Check the column headed 'Conduct Study'. When you have i n d i c a t e d on your response sheet which of the s i x s t u d i e s you wish to purchase, r a i s e your hand. The umpire w i l l then come to your seat and w r i t e on your response form, under the column headed . 'True S t a t e " , the r e s u l t s of the s t u d i e s which you have de-c i d e d to conduct. Remember the umpire w i l l t e l l you which s t a t e w i l l p r e v a i l o n l y f o r those s i t u a t i o n s i n which you purchased a study. You then choose program 1 or program 2 f o r each s i t u a t i o n . Remember t h a t i f you decide to conduct the study, the net student subsidy w i l l r e f l e c t the r e d u c t i o n caused by conduct-i n g the study. E n t e r the program you choose P i or P2 under the column headed 'Program'. When everyone has f i n i s h e d the f i r s t game, the umpire w i l l c a l l out the t r u e s t a t e f o r a l l s i x s i t u a t i o n s . You en-81 t e r these under the column headed 'True S t a t e ' . The gross scores can now be determined. The net score f o r those cases where no i n f o r m a t i o n was sought i s the same as the gross s c o r e . The net score f o r those cases where the study was conducted i s ob t a i n e d by s u b t r a c t i n g the c o s t o f the study from the p a y o f f i n d i c a t e d i n the matrix. Bear i n mind t h a t the survey r e s u l t s r e f l e c t the long term p r o b a b i l i t i e s f o r each s t a t e . However, the i n d i v i d u a l r e s u l t s have been chosen from a t a b l e o f random numbers, so i t i s imp o s s i b l e t o p r e d i c t the outcome o f a study from p r e -v i o u s r e s u l t s . A f t e r the net scores have been determined f o r a l l s i x s i t u a t i o n s , you t o t a l t h i s .column t o o b t a i n the t o t a l s c o r e . You w i l l be asked to c a l l out your t o t a l s c o r e . The person i n the group wi t h the h i g h e s t score w i l l be d e c l a r e d the winner f o r t h a t game. The person who wins the most games w i l l be d e c l a r e d the winner o v e r a l l . When you complete game 8, you w i l l be asked to hand i n the game i n s t r u c t i o n s , and response forms, then you w i l l be asked t o f i l l i n a p e r s o n a l i n f o r m a t i o n sheet. Before beginning, the umpire w i l l review, i n step form, the r u l e s and procedures t o be f o l l o w e d . You may now ask any p r o c e d u r a l q u e s t i o n s b e f o r e beginning. 82. PERSONAL RESPONSE FORM Please f i l l i n the p e r s o n a l i n f o r m a t i o n requested below. A l l i n f o r m a t i o n w i l l be c o n f i d e n t i a l and r e p o r t e d o n l y as group s t a t i s t i c s . (1) Name (2) Sex: (3) Teaching E x p e r i e n c e : ' ye a r s . (4) Have you had any p r a c t i c a l experience i n e d u c a t i o n a l a d m i n i s t r a t i o n a t the department head l e v e l o r beyond ( i e . v i c e - p r i n c i p a l , p r i n c i p a l , c e n t r a l o f f i c e p o s i t i o n ) : yes no I f yes, (a) Please g i v e (1) the t i t l e o f the p o s i t i o n ( s ) , (2) number of years occupied and (3) a b r i e f d e s c r i p t i o n -I of the r e s p o n s i b i l i t i e s assumed: (1) Job T i t l e (2) Number of Years Occupied (3) B r i e f  Job D e s c r i p t i o n  (5) How many GRADUATE l e v e l course u n i t s i n the U.B.C. De-partment o f E d u c a t i o n a l A d m i n i s t r a t i o n have you COMPLETED: u n i t s Note: The course Ed. 460 may be i n c l u d e d as a graduate 83. course i f i t was taken as a p r e r e q u i s i t e f o r the masters program; otherwise o n l y 500 l e v e l courses may be i n c l u d e d . How many GRADUATE l e v e l course u n i t s i n e d u c a t i o n a l ad-m i n i s t r a t i o n have you completed a t an i n s t i t u t i o n o t h e r than U.B.C.: ' u n i t s U n i v e r s i t y NOTE: I f courses were not assign e d u n i t s , p l e a s e i n -d i c a t e course weighting ( i e . f u l l - c o u r s e , 2 semesters) :____ ' Have you ever s t u d i e d S t a t i s t i c a l D e c i s i o n Theory: yes no I f yes (a) Please i n d i c a t e a t what l e v e l ( i e . under-graduate, graduate, independent s t u d y ) : (b) B r i e f l y describe the nature of the course (ie. mathematical, applied s t a t i s t i c s , computer science): : SAMPLE GAME RESPONSE FORMS [For Umpire - Cond. 1] GAME STATE A STATE B PROGRAM 1 450 100 PROGRAM 2 310 200 PROBABILITY OF STATE .8 .2 SITUATION COST OF CONDUCT NOT TRUE PROGRAM GROSS COST OF NET CONDUCTING' STUDY CONDUCT STATE SCORES STUDIES SCORES STUDY STUDY PURCHASED 1 200 2 5 3 27 4 13 5 70 6 1 T o t a l Score SAMPLE GAME RESPONSE FORMS [For Umpire - Cond. 2] GAME STATE A STATE B PROGRAM 1 675 150 PROGRAM 2 465 300 PROBABILITY OF STATE .8 .2 SITUATION COST OF CONDUCTING STUDY CONDUCT STUDY NOT CONDUCT STUDY TRUE STATE PROGRAM GROSS SCORES COST OF STUDIES PURCHASED NET SCORES 1 2X0 2 15 3 37 4 23 80 5 6 10 T o t a l Score 86 APPENDIX B DERIVATION AND DISCUSSION OF BAYES THEOREM In t h i s d e r i v a t i o n o f Bayes Theorem the f o l l o w i n g n ota-t i o n w i l l be used. L e t P(A) denote the p r o b a b i l i t y o f event A o c c u r r i n g P(AB) denote the p r o b a b i l i t y o f the j o i n t occurrence of events A and B P(A/B) denote the p r o b a b i l i t y o f event A o c c u r r i n g g i v e n t h a t event B has o c c u r r e d Define: P(A/B) = P(AB) and P(B/A) = P(AB) P(B) P(A) N o t i c e t h a t with these d e f i n i t i o n s , i n the s p e c i a l case where A and B are mutually e x c l u s i v e P(AB) = P(A).P(B) s u b s t i t u t i n g P(A/B) = P(A).P(B) and P(B/A) =P(A).P(B) P(B) P(A) P(A/B) = P(A) and P(B/A) ='P(B) Thus the p r o b a b i l i t y o f event A o c c u r r i n g , g i v e n t h a t event B has o c c u r r e d i s e x a c t l y the same as i f the outcome o f event B was unknown. The d e f i n i n g equations may be rearranged t o g i v e : P(AB) = P(B). P(A/B) and P(AB) = P(A). P(B/A) P(B). P(A/B) = P(A). P(3/A) P(A/B) = P(A). P (B/A) P(B) 87 T h i s l a s t equation i s known as Bayes Theorem. For an example of how t h i s theorem i s o f t e n used by experimenters, l e t event A be some hypothesis HI which i s to be t e s t e d . Before conducting any experiment suppose t h a t the experimenter has decided t h a t the p r o b a b i l i t y o f hypothesis H i being t r u e i s .5, i e . P(H1) = .5. The experiment i s conducted, and data i s gathered. The experimenter wants to know how the data gathered a f f e c t s the p r o b a b i l i t y o f the h y p o t h e s i s , i e . P ( H l / D ) . T h i s can be ob t a i n e d by u s i n g Bayes Theorem. P(H1/D) = P(HI).P ( D/Hl) (McGee, 1971) P(D) P o s t e r i o r = P r i o r L i k e l i h o o d P r o b a b i l i t y P r o b a b i l i t y R a t i o I n the l i k e l i h o o d r a t i o , P(D/H1) r e p r e s e n t s the p r o b a b i l -i t y of o b t a i n i n g the data given t h a t H i i s t r u e , w h i l e P ( D ) r e p r e s e n t s the p r o b a b i l i t y o f g e t t i n g the data anyway. The main c r i t i c i s m o f the Bayesian approach has appeared to c e n t r e on the assignment of p r i o r p r o b a b i l i t i e s . McGee (1971) argues t h a t both Bayesian and t r a d i t i o n a l s t a t i s t i c s make a r b i t r a r y assumptions about the p o p u l a t i o n being s t u d i e d . In the case o f t r a d i t i o n a l s t a t i s t i c s , s t a t i s t i c a l models are presented as adequate r e p r e s e n t a t i o n s o f the r e a l world. McGee goes on to s p e c i f y techniques f o r a s s i g n i n g p r i o r p r o b a b i l i t i e s . In t h i s experiment such techniques were not necessary, as the p r i o r p r o b a b i l i t i e s were a r b i t r a r i l y a s s i g n -ed and c o n s t i t u t e d one f a c t o r i n the experimental d e s i g n . APPENDIX C TRUE STATES FOR EACH CONDITION ANSWER SHEET FOR UMPIRES The e x i s t i n g (true) s t a t e s f o r each c o n d i t i o n are given below: CONDITION SITUATION 1 SITUATION 2 SITUATION 3 SITUATION 4 SITUATION 5 SITUATION 6 1 B A A A A B 2 A A A B B A 3 A B A B B B 4 B B A A B A 5 A A A A B A 6 A A A B A A 7 B A A B A B 8 B B B B A A CO 0 0 89 APPENDIX D SUMMARY NOTES FOR UMPIRES ( 1) I n t r o d u c t i o n s ( 2) Hand out game i n s t r u c t i o n s and response forms to each p l a y e r ( 3) Allow 10 - 15 minutes f o r p l a y e r s to read the game i n s t r u c t i o n s ( 4) Answer any P r o c e d u r a l Questions ( 5) Read through the summary of game i n s t r u c t i o n s ( 6) Answer any p r o c e d u r a l q u e s t i o n s ( 7) Begin game 1 ( 8) Upon completion of game 1 have the p l a y e r s c a l l out t h e i r t o t a l scores ( 9) Acknowledge the winner by s a y i n g 'very good X won t h a t game' (10) Repeat f o r a l l 8 games (11) Declare the o v e r a l l winner, i e . , the person who has won the most games (12) Hand out the p e r s o n a l i n f o r m a t i o n sheet (13) Choose, a t random, one member of the group. From the oth e r s c o l l e c t a l l forms. They may then be d i s m i s s e d . (14) To the remaining p l a y e r ask the f o l l o w i n g q u e s t i o n : "Please d e s c r i b e , as c l e a r l y as p o s s i b l e , how you came to decide which games were worth pu r c h a s i n g i n game 1, game 2, and game 6 ?" 90 (15) Record the answer to the q u e s t i o n i n note (14) i n as much d e t a i l as p o s s i b l e . (16) Return p e r s o n a l i n f o r m a t i o n sheets, game i n s t r u c t i o n s , response forms and the answer t o the d e s c r i p t i v e ques-t i o n t o Fred Angus, Room 16, SSOB. 91 APPENDIX E SUMMARY OF GAME PROCEDURES To be read by umpire a f t e r p l a y e r s have read game i n s t r u c t i o n s ( 1) C a r e f u l l y study the matrix f o r each game. Some games may appear t o be s i m i l a r , but they are a l l d i f f e r e n t . ( 2) Look a t the s i x s i t u a t i o n s f o r each game and the c o s t o f conducting the s i x s t u d i e s . ( 3) Choose which s t u d i e s you f e e l are worth purchasing. ( 4) I n d i c a t e with a check mark on your response sheet which s t u d i e s you w i l l conduct and which you w i l l not conduct. ( 5) Raise your hand, the umpire w i l l i n d i c a t e under the column headed 'true s t a t e ' which s t a t e w i l l occur f o r those s t u d i e s which you have decided t o conduct. ( 6) For each s i t u a t i o n i n d i c a t e which program you wish t o implement. ( 7) When everyone has f i n i s h e d , the umpire w i l l c a l l out the t r u e s t a t e f o r a l l s i x s i t u a t i o n s . E n t e r these under the column headed 'true s t a t e ' . Note t h a t i f you have purchased a survey you a l r e a d y know the t r u e s t a t e f o r t h a t s i t u a t i o n . ( 8) With the program you have chosen and the t r u e s t a t e , f i n d the per p u p i l budget a l l o t m e n t from the game matrix and en t e r i t under the column headed 'gross 92 s c o r e s ' . ( 9) For those s t u d i e s which you purchased, e n t e r the c o s t under the column headed 'cost of s t u d i e s purchased'. (10) C a l c u l a t e the net score by s u b t r a c t i n g the c o s t of s t u d i e s purchased from the gross s c o r e s . (11) T o t a l the net score column t o o b t a i n the ' t o t a l s c o r e ' . (12) The umpire w i l l then ask you to c a l l out your t o t a l s c o r e . The p l a y e r w i t h the h i g h e s t score w i l l win the game. (13) The same procedure i s f o l l o w e d f o r each game u n t i l a l l e i g h t games are completed. You w i l l .then be asked t o hand i n your i n f o r m a t i o n sheet response sheet, and game i n s t r u c t i o n s . 

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