UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Individual differences in processes and strategies in analogical reasoning Wilson, Nancy Louise 1980

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1980_A8 W54_6.pdf [ 5.68MB ]
Metadata
JSON: 831-1.0094854.json
JSON-LD: 831-1.0094854-ld.json
RDF/XML (Pretty): 831-1.0094854-rdf.xml
RDF/JSON: 831-1.0094854-rdf.json
Turtle: 831-1.0094854-turtle.txt
N-Triples: 831-1.0094854-rdf-ntriples.txt
Original Record: 831-1.0094854-source.json
Full Text
831-1.0094854-fulltext.txt
Citation
831-1.0094854.ris

Full Text

INDIVIDUAL DIFFERENCES IN PROCESSES AND STRATEGIES IN ANALOGICAL REASONING by /NANCY LOUISE WILSON B.Ed., M c G i l l U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS xn THE FACULTY OF GRADUATE STUDIES Department of Ed u c a t i o n a l Psychology and S p e c i a l Education 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 August 1980 ^jT)Nancy Louise Wilson, 1980 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb ia , I a g ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f Educational Psychology and S p e c i a l Education The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date August, 1980 ABSTRACT The need was presented for further research of the quantitative and q u a l i t a t i v e nature of i n d i v i d u a l differences i n achievement a b i l i t y . The componential theory of analogical reasoning was used to i d e n t i f y differences i n processes and strategies used to solve p i c t o r i a l anal-ogies by students of low, average, and high achievement a b i l i t y . Subjects were 60 boys and g i r l s from nine grade four classes i n four schools:in the Lower Mainland. One t h i r d of the group were high i n achievement a b i l i t y , one t h i r d were average, and one t h i r d were low. The c r i t e r i o n used to determine achievement a b i l i t y was the Canadian Test of Basic S k i l l s . The average age i n the low group was 9 years, 9 months, i n the average group 9 years, 8 months, and i n the high group 9 years, 8 months. These subjects performed a series of forced-choice p i c t o r i a l anal-ogy tasks of the standard form A i s to B as C i s to or D2. The analogies were presented i n booklets. Each booklet contained 16 anal-ogies, four per page. Subjects were given 64 seconds to work on each booklet. The booklets were administered over two sessions. T o t a l time spent on an analogy booklet was decomposed into e s t i -mates of the time spent on each component (process) used i n s o l u t i o n . Response times f or number of items correct and number of items completed f o r each booklet were predicted from independent v a r i a b l e s representing v a r i a t i o n s i n the complexity of analogy items over the 24 booklets. i i Seven models were f i t t e d to the 24 booklet scores at each a b i l i t y l e v e l . The models d i f f e r e d i n the components hypothesized to be used i n s o l u t i o n and i n the mode of component execution, exhaustive, or s e l f -t e r m i n a t i n g . The model which best accounted f o r the va r i a n c e i n the data was designated as the p r e f e r r e d model. M u l t i p l e r e g r e s s i o n r e s u l t s suggested that there were q u a l i t a t i v e d i f f e r e n c e s i n analogy s o l u t i o n f o r the three groups. The same model was p r e f e r r e d by the high and average groups, but a more exhaustive mode of execution was p r e f e r r e d i n the low group. S i g n i f i c a n t q u a n t i t a t i v e group d i f f e r e n c e s were found i n a u n i -v a r i a t e a n a l y s i s of varia n c e which i n d i c a t e d that the high a b i l i t y group had s i g n i f i c a n t l y s h o r t e r l a t e n c i e s c o r r e c t than d i d the average and low groups. The average group had lower l a t e n c i e s c o r r e c t than d i d the low group, but t h i s d i f f e r e n c e was not s i g n i f i c a n t . These r e s u l t s were subject to c e r t a i n l i m i t a t i o n s i n that there was evidence, e s p e c i a l l y i n the low group, that the p r e f e r r e d models were not n e c e s s a r i l y the complete models, and that a d d i t i o n a l f a c t o r s such as non l i n e a r p r o c e s s i n g , speed, f l o o r , and c e i l i n g e f f e c t s may have a f f e c t e d the r e s u l t s . Findings were discussed i n terms of the above l i m i t a t i o n s and Sternberg's theory of a n a l o g i c a l reasoning. I m p l i c a t i o n s of these r e s u l t s f o r f u t u r e research i n i n d i v i d u a l d i f f e r e n c e s were drawn. i i i TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS . v i i i Chapter I INTRODUCTION 1 I I REVIEW OF LITERATURE 7 H i s t o r i c a l Antecedents 7 Factor A n a l y s i s 8 Experimental Psychology 9 C a l l f o r U n i f i c a t i o n 11 D i s s a t i s f a c t i o n w i t h E x i s t i n g Methods 11 The New Wave 13 New Wave Research 15 Componential A n a l y s i s 20 Or i g i n s of Componential A n a l y s i s 21 In t e n s i v e Task A n a l y s i s : I n t e r n a l V a l i d a t i o n . . . 22 Theory 22 Components 23 Component Execution 26 Models 27 Component Est i m a t i o n 33 In t e n s i v e Task A n a l y s i s : E x t e r n a l V a l i d a t i o n . . . 34 Extensive Task A n a l y s i s 34 Testi n g the Componential Model 35 Componential A n a l y s i s and Developmental Research . 39 Summary 43 I I I PROBLEM 45 Statement of the Problem 45 Ra t i o n a l e 45 Research Questions and Hypotheses 49 Theory L e v e l 49 Model L e v e l 50 Component L e v e l . 51 i v IV METHOD 52 Subj ects 52 Formation of Subgroups . 52 Instruments 54 Schematic P i c t u r e Analogies 54 Procedure 55 P i l o t Study: I n i t i a l Procedure . . . . . . . . . 55 P i l o t Study: Revised Procedure . 57 Main Data C o l l e c t i o n 58 Design 59 Dependent V a r i a b l e s 59 Parameter E s t i m a t i o n and Models 61 V RESULTS 70 P r e l i m i n a r y A n a l y s i s 70 Regression A n a l y s i s 72 Determination of Model Preference . . . . . . . . 72 C r i t e r i o n V a r i a b l e 1: Latency Correct 75 Assessment of Equivalence of R 2 Values . . . . . . 82 Component Latencies f o r C r i t e r i o n V a r i a b l e 1 . . . 84 C r i t e r i o n V a r i a b l e 2: Latency Completed 87 Residua l A n a l y s i s 87 Dependent V a r i a b l e 1 90 VI DISCUSSION 92 L i m i t a t i o n s of the Study 93 A n a l o g i c a l Reasoning and Achievement A b i l i t y . . . . 96 Componential A n a l y s i s 103 I m p l i c a t i o n s f o r Future Research . . . . . 104 REFERENCE NOTE 106 REFERENCES . . . . . 107 APPENDIX A: Schematic P i c t u r e Analogy Booklet . 112 APPENDIX B: Answer Sheet f o r Schematic P i c t u r e Analogy Booklet 117 APPENDIX C: Model F i t s f o r A b i l i t y Groups: C r i t e r i o n V a r i a b l e 2 119 v LIST OF TABLES Table 1 Models 1, 2, 3, 4 . . 28 2 Models 1M, 2-3M, 4M 32 3 D e s c r i p t i v e S t a t i s t i c s : NGE Scores . . 54 4 Models f o r Regression 62 5 Data M a t r i x Used to C a l c u l a t e C r i t e r i o n V a r i a b l e Scores 63 6 P r e d i c t o r V a r i a b l e s f o r Regression . 65 7 D e s c r i p t i v e S t a t i s t i c s : C r i t e r i o n V a r i a b l e . 71 8 Models f o r Regression 73 9 Model F i t s f o r Low A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 76 10 Model F i t s f o r Average A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 78 11 Model F i t s f o r High A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 . . 81 12 Composite and Component Latencies f o r Correct Responses • • . . . . . . . . • • • 85 13 R e l i a b i l i t i e s of Residuals from P r e f e r r e d Models . . . 89 14 D e s c r i p t i v e S t a t i s t i c s : Mean Latency Correct 91 v i LIST OF FIGURES Figure 1 Schematic P i c t u r e Analogy . . . . . 24 2 People P i e c e Analogy 29 3 Composite and Component Latencies f o r Correct Responses on Model 4M 86 v i i ACKNOWLEDGEMENT S In the execution of t h i s study and the p r e p a r t i o n of t h i s t h e s i s I was a s s i s t e d by many people. I thank a l l those who c o n t r i b u t e d f o r t h e i r support and guidance. I am e s p e c i a l l y indebted to the committee members: my major a d v i s o r , Dr. Ron Jarman, and Dr. Todd Rogers and Dr. Nancy Suzuki. Their expert and d e t a i l e d comments and suggestions c o n t r i b u t e d immeasur-ably to the t h e s i s . I g r a t e f u l l y acknowledge Dr. Robert Sternberg f o r permission to use the Schematic P i c t u r e Analogies; the Educational Research I n s t i t u t e of B r i t i s h Columbia f o r support through the D i s c r e t i o n a r y Grant Program; Dr. Gary Holmes f o r preparing Figure 3; Mrs. Nina Thurston f o r her expert t y p i n g ; and the school board o f f i c i a l s , p r i n c i p a l s , teachers, and students f o r p a r t i c i p a t i n g i n the study. The l o v e and encouragement I have received from my parents, D a r r e l and Teresa Wilson, and from my f r i e n d s , e s p e c i a l l y Frank, i s e a s i l y acknowledged but my g r a t i t u d e f o r t h e i r constant support f a r exceeds these words of thanks. v i i i CHAPTER I INTRODUCTION The nature of mental a b i l i t y has been the subject of p s y c h o l o g i c a l i n v e s t i g a t i o n s throughout t h i s century. A number of research paradigms have been employed over the years i n c l u d i n g f a c t o r a n a l y t i c and e x p e r i -mental methods. Recently Robert Sternberg (1977b) proposed the method of componential a n a l y s i s as an a l t e r n a t i v e to f a c t o r - a n a l y t i c and c l a s s i c a l experimental methods f o r research on the nature of i n t e l l i g e n c e . With t h i s method, i t i s p o s s i b l e to i d e n t i f y processes and s t r a t e g i e s used by i n d i v i d u a l s i n s o l v i n g a v a r i e t y of t a s k s , although the method appears to be- more s u i t e d f o r use w i t h a n a l o g i c a l reasoning problems. Factor a n a l y s t s during the f i r s t h a l f of the century made important c o n t r i b u t i o n s to t e s t theory and proposed t h e o r i e s d e t a i l i n g the s t r u c -ture of mental a b i l i t i e s . U n f o r t u n a t e l y , they were able to de s c r i b e , but not e x p l a i n , i n d i v i d u a l d i f f e r e n c e s i n i n t e l l i g e n c e . Indeed, there was a l a c k of consensus among c o r r e l a t i o n a l p s y c h o l o g i s t s as to the f a c t o r i a l s t r u c t u r e of mental a b i l i t i e s . Misuse and l i m i t a t i o n s of the f a c t o r -a n a l y t i c method l e d to a p r o l i f e r a t i o n of f a c t o r t h e o r i e s , and l a c k of process explanations. Experimental p s y c h o l o g i s t s , o r i g i n a l l y unconcerned w i t h i n d i v i d u a l v a r i a t i o n , attempted to i d e n t i f y u n i v e r s a l stimulus-response laws of l e a r n i n g . L a t e r , i n f o r m a t i o n processing and c o g n i t i v e research developed, w i t h a renewed emphasis on c o g n i t i v e processing. Again, 1 2 methodological problems l i m i t e d these i n v e s t i g a t i o n s . Task s p e c i f i c process t h e o r i e s lacked g e n e r a l i z a b i l i t y , and t h e o r e t i c a l s t r u c t u r e s were unparsimonious. E v e n t u a l l y , due to d i s s a t i s f a c t i o n w i t h both methods, a u n i f i c a t i o n of d i f f e r e n t i a l and experimental psychology i n the study of i n d i v i d u a l d i f f e r e n c e s was suggested (Cronbaeh, 1957). During the s i x t i e s many d i s i l l u s i o n e d researchers c a l l e d f o r process i n v e s t i g a t i o n s of mental a b i l i t i e s as a means of understanding the nature of a b i l i t y f a c t o r s beyond a s u p e r f i c i a l l e v e l (MeNemar, 1964;. Messiek, 1972). In the s e v e n t i e s , a consensus was reached that new methods should combine the d i f f e r e n t i a l and experimental approaches i n i s o l a t i n g sources of i n d i v i d u a l d i f f e r e n c e s i n performance. A number of i n v e s t i g a t o r s attempted to address these concerns. D i s t i n c t i o n s were made between cap a c i t y ( s t r u c t u r a l ) and st r a t e g y (process) components of i n t e l l i g e n c e (Campione & Brown, 1978; Hunt & Lansman, 1975). D i s t r i b u t i v e memory models were proposed and adopted (Hunt, Frost & Lunneborg, 1973). Research focused on c o r r e l a t i n g i n d i v i d u a l d i f f e r e n c e s as measured by standardized t e s t s w i t h b a s i c information-processing performance. Factors were c h a r a c t e r i z e d according to c o g n i t i v e process models (e.g., C a r r o l l , 1974). A s e r i e s of i n s t r u c t i o n a l s t u d i e s on retarded and normal subjects focused on the use of s t r a t e g i e s and the t r a i n i n g of those s t r a t e g i e s (Campione & Brown, 1978). While i t was hoped that the new breed of experimental s t u d i e s of f a c t o r s would s u c c e s s f u l l y e x p l a i n the nature of a b i l i t y d i f f e r e n c e s , t h i s approach lacked explanatory power due to the t a s k - s p e c i f i c nature of the f i n d i n g s which lacked g e n e r a l i z a b i l i t y . An o v e r a l l framework was needed. 3 Sternberg (1977b) o u t l i n e d a new method s u i t e d to the new era i n i n t e l l i g e n c e research. The method, componential a n a l y s i s , incorporated the views of d i f f e r e n t i a l and c o g n i t i v e psychology. Rather than attempt-i n g to understand i n t e l l i g e n c e through i n t e r c o r r e l a t i o n s among many t a s k s , or through task manipulations, t h i s method focused on i n d i v i d u a l d i f f e r -ences w i t h i n a s i n g l e task. This method had a number of advantages that were l a c k i n g i n previous methods. Sources of var i a n c e that were confounded i n other methods were i d e n t i f i a b l e i n the componential method. R o t a t i o n a l d e c i s i o n s , a weak-ness of the f a c t o r a n a l y t i c method, were not required i n componential a n a l y s i s , r e s u l t i n g i n increased i n f e r e n t i a l power. Data i n componential a n a l y s i s were i n t r a i n d i v i d u a l and not i n t e r i n d i v i d u a l as i n f a c t o r a n a l -y s i s , thus p e r m i t t i n g more exact i n t e r p r e t a t i o n s of i n d i v i d u a l d i f f e r e n c e s . The nature of the technique permitted study of i n d i v i d u a l d i f f e r e n c e s at a number of l e v e l s , r a t h e r than study of d i f f e r e n c e s on o v e r a l l scores or f a c t o r l o a d i n g s . The model or theory was s p e c i f i e d a p r i o r i and not post hoc as i n most f a c t o r analyses, and provided a framework which was absent i n many experimental s t u d i e s . Tasks were chosen which were of t h e o r e t i c a l i n t e r e s t and were expected to c o r r e l a t e w i t h other tasks and a b i l i t y measures, thus avoiding the t r i v i a l i t y of some i n f o r m a t i o n pro-cessing approaches. E s s e n t i a l l y , componential a n a l y s i s accomplishes these improvements through the general method of r e g r e s s i o n a n a l y s i s . A task i s chosen which i s of t h e o r e t i c a l i n t e r e s t . Next, models which s p e c i f y the com-ponents (or i n f o r m a t i o n processes) i n v o l v e d i n analogy task s o l u t i o n are hypothesized. These models a l s o s p e c i f y the order and mode of component execution. The tasks are administered to s u b j e c t s . Then the models 4 are used to decompose o v e r a l l s o l u t i o n l a t e n c y (or e r r o r r a t e ) i n t o estimates of time spent on each component operation. This i s accom-p l i s h e d through m u l t i p l e l i n e a r r e g r e s s i o n f o r each of the hypothesized models using the complete l e a s t squares approach. The proposed models are then evaluated as to t h e i r a b i l i t y to account f o r the v a r i a n c e i n the o v e r a l l score f o r the analogy problem. Thus the mental processes i n v o l v e d i n task execution are hypothesized and t e s t e d , and s u b j e c t s ' scores can be compared not only on the b a s i s of t o t a l score, but a l s o at more elementary subtask l e v e l s , a l l o w i n g m u l t i - l e v e l i s o l a t i o n of i n d i -v i d u a l d i f f e r e n c e s . I n d i v i d u a l s or groups could d i f f e r i n l a t e n c y or d i f f i c u l t y of components, i n s t r a t e g i e s used to combine components ( i . e . , mode and sequence of combinations) and i n the degree of ' f i t ' of t h e i r scores to the p r e d i c t e d scores ( a l l subjects would not n e c e s s a r i l y use a l l of the component processes hypothesized by the t h e o r y ) . This procedure i s e s s e n t i a l l y one of e s t a b l i s h i n g i n t e r n a l v a l i d i t y f o r the task. Regression a n a l y s i s a l s o allows the researcher to e s t a b l i s h e x t e r n a l v a l i d i t y f o r the t a s k s . This i s accomplished through c o r r e l a t i o n of the s u b j e c t s ' scores (both t o t a l and component scores) w i t h 'reference a b i l -i t y ' t e s t s . Subjects' task scores should p r e d i c t scores on a b i l i t y t e s t s which are supposed to measure the same t h i n g as the task i s measuring. I f they do, t h i s provides evidence f o r convergent v a l i d i t y . S i m i l a r l y , task scores should not p r e d i c t ( i . e . , have low c o r r e l a t i o n s ) scores on reference a b i l i t y t e s t s which are supposed to measure something d i f f e r e n t from what the task i s measuring. I f p r e d i c t i o n s are poor i n t h i s case, evidence f o r d i s c r i m i n a n t v a l i d i t y i s provided. Thus, componential a n a l y s i s appears to be a powerful a l t e r n a t i v e to e x i s t i n g methodologies f o r process and s t r a t e g y research on i n d i v i d -u a l d i f f e r e n c e s . One a p p l i c a t i o n of componential a n a l y s i s was Sternberg's componen t i a l theory of a n a l o g i c a l reasoning (1977b). A p i c t o r i a l analogy task was broken down i n t o f i v e hypothesized components: encoding, i n f e r e n c e mapping, a p p l i c a t i o n , and response (Sternberg & R i f k i n , 1979). The r u l e hypothesized f o r the combination of components was a d d i t i v e ; response time f o r s o l u t i o n of the analogy equaled the sum of the time spent on each component. Models, or s t r a t e g i e s , f o r combining compon-ents were developed which s p e c i f i e d the order and mode of component execution. The theory was v a l i d a t e d both i n t e r n a l l y and e x t e r n a l l y (Sternberg & R i f k i n , 1979). The theory was s u c c e s s f u l l y employed to i d e n t i f y s t r a t e g y as w e l l as component and theory d i f f e r e n c e s between the subjects who were second, f o u r t h , and s i x t h grade students, and a d u l t s . Other tasks have al s o been decomposed through componential a n a l y s i s (Sternberg, 1977b, 1978c, 1979f), i n c l u d i n g s y l l o g i s m s and s e r i e s completion problems. In the present study, the r e l a t i o n s h i p between a b i l i t y l e v e l as measured by standardized t e s t s and reasoning a b i l i t y as measured by p i c t o r i a l analogies was i n v e s t i g a t e d i n order to i d e n t i f y the u n d e r l y i n sources of d i f f e r e n c e s measured by the standardized a b i l i t y t e s t s . To t h i s date, no previous study had examined the use of componential a n a l -y s i s as a means f o r i n v e s t i g a t i n g t h i s r e l a t i o n s h i p . Students i n the f o u r t h grade were chosen to p a r t i c i p a t e and were c l a s s i f i e d as h i g h , average, or low a b i l i t y on the b a s i s of t h e i r performance on a 6 standardized achievement b a t t e r y . These students were asked to complete the p i c t o r i a l analogy tasks i n order to i d e n t i f y u n d e r l y i n g sources f o r t h e i r v a r i a t i o n i n a b i l i t y . CHAPTER I I REVIEW OF LITERATURE H i s t o r i c a l Antecedents What do i n t e l l i g e n c e t e s t s measure? Since the advent of standard-i z e d i n t e l l i g e n c e t e s t s , p s y c h o l o g i s t s have attempted to answer t h i s question. Throughout the f i r s t h a l f of t h i s century the dominant paradigm f o r the enquiry was f a c t o r a n a l y s i s . Despite concerted e f f o r t by d i f f e r e n t i a l p s y c h o l o g i s t s over the years, we seem no c l o s e r to an understanding of the nature of mental a b i l i t i e s than was Boring i n 1923 (Boring, 1923/1961): I f we agree, then, to de f i n e i n t e l l i g e n c e as what the t e s t s of i n t e l l i g e n c e t e s t , there i s a good deal that we can say about i t . We can say everything that has been experimentally observed. We can say that i t i s a "common f a c t o r " i n many a b i l i t i e s , that i t i s something l i k e power, that i t can be measured roughly although not very f i n e l y , that i t i s only one f a c t o r among many i n the mental l i f e , that i t develops mostly i n childhood, that i t develops l i t t l e or not at a l l i n adu l t l i f e , and that i t i s l a r g e l y predetermined at f i v e years of age. Only w i t h more observation and l e s s i n f e r e n c e s h a l l we e v e n t u a l l y know much more about both i n t e l l i g e n c e and the s p e c i a l a b i l i t i e s . (Boring, 1923/1961, p. 214) The concept of i n t e l l i g e n c e as po p u l a r i z e d by B i n e t , i n the form of the mental t e s t , was f i r s t r e c e i v e d w i t h enthusiasm, followed by skep-t i c i s m and general disagreement among p s y c h o l o g i s t s (Spearman, 1927/1961). The o r i g i n a l enthusiasm was l a r g e l y due to the hope that i n d i v i d u a l s could be o b j e c t i v e l y c h a r a c t e r i z e d on the b a s i s of these t e s t s . This 7 8 c o l l e c t i v e enthusiasm had degenerated by the e a r l y twenties i n t o d i s -agreement as to what e x a c t l y was being measured by the t e s t s (Estes, 1975; Resnick, 1976a; Spearman, 1927/1961; Sternberg, 1977b). Factor A n a l y s i s Despite conceptual disagreements, f a c t o r a n a l y t i c views of i n t e l -l i g e n c e played an important r o l e i n the f i r s t h a l f of the century. Although t h i s l i n e of research, was unsuccessful i n e x p l a i n i n g i n d i v i d u a l d i f f e r e n c e s i n mental a b i l i t i e s (Jarman & Das, 1977) , i t d i d provide a t o o l f o r i n v e s t i g a t i n g mental a b i l i t i e s at a time when experimental and b e h a v i o r a l p s y c h o l o g i s t s were occupied w i t h o v e r t , non-mental behavior (Sternberg, 1977b). Most of a l l , f a c t o r a n a l y s i s l e d to the develop-ment of a set of h i g h l y p r e d i c t i v e t e s t s of i n t e l l i g e n c e , long considered one of the most important of the products, of p s y c h o l o g i c a l research. L i m i t a t i o n s of f a c t o r a n a l y s i s . One of the b a s i c weaknesses of f a c t o r a n a l y s i s was that i t d i d not lead to a unique s o l u t i o n i n the d e s c r i p t i o n of i n t e l l i g e n c e . As there was disagreement on the d e f i n i t i o n of i n t e l l i g e n c e so was there disagreement on the f a c t o r i a l s t r u c t u r e of mental a b i l i t i e s . Through the years a v a r i e t y of t h e o r i e s were i n vogue at d i f f e r e n t times, i n c l u d i n g Spearman's (1927/1961) two-factor theory, Thurstone's theory of seven primary mental a b i l i t i e s (Sternberg, 1977b), Burt, and then Vernon's, h i e r a r c h i c a l model (Jensen, 1970), and G u i l -ford's cube c o n s i s t i n g of 120 independent f a c t o r s ( C a r r o l l , 1968; Sternberg, 1977b). Sternberg (1977b) i d e n t i f i e d many sources of d i f f e r e n c e among the various f a c t o r i a l t h e o r i e s of i n t e l l i g e n c e . He a l s o i d e n t i f i e d the weak-nesses that r e s t r i c t e d the explanatory concepts a v a i l a b l e through t h i s method. D i f f e r e n c e s stemmed both from misuse of the method and from 9 inherent l i m i t a t i o n s of the method. For example, the choice of a model i n most f a c t o r a n a l y t i c theories-was dependent-"on the ' f o l l o w i n g - d e c i s i o n s : the number of f a c t o r s to e x t r a c t , t e s t s e l e c t i o n f o r a n a l y s i s , choice of s u b j e c t s , and p s y c h o l o g i c a l d e f i n i t i o n of the obtained f a c t o r s . A l l of these c o n t r i b u t e d to d i f f e r e n t i n t e r p r e t a t i o n s of i n t e l l i g e n c e . Other f a c t o r s c i t e d by Sternberg (1977b) i n the eventual f a i l u r e of the method included the l a c k of s p e c i f i c a t i o n of a p r i o r i models, and non-unique r o t a t i o n of axes. Most im p o r t a n t l y , mental processes of i n t e l l i g e n c e , imbedded i n i n t r a i t e m data, were not e l u c i d a t e d s i n c e f a c t o r a n a l y s i s r e l i e d on i n t e r i t e m data. The components of i n t e l l i g e n c e are i n t r a - i n d i v i d u a l — t h e y e x i s t w i t h i n i n d i v i d u a l s u b j e c t s . Factor a n a l y s i s , however, i s g e n e r a l l y i n t e r i n d i v i d u a l — i t analyzes patterns of i n d i v i d u a l d i f f e r e n c e s across s u b j e c t s . Since i n d i v i d u a l d i f f e r e n c e s are meaningless i n the context of one i n d i v i d u a l , i t i s not c l e a r how f a c t o r a n a l y s i s could enable us to d i s cover what the components w i t h i n an i n d i v i d u a l are. (Sternberg, 1977b, p. 33) Experimental Psychology Factor a n a l y s i s was not the only method to f a i l to e x p l a i n i n d i v i d -u a l d i f f e r e n c e s . During the years when f a c t o r a n a l y s i s dominated d i f f e r -e n t i a l psychology, a d i f f e r e n t paradigm was c e n t r a l to the experimental p s y c h o l o g i s t . T r a d i t i o n a l l y , experimental p s y c h o l o g i s t s were concerned w i t h u n i v e r s a l laws of l e a r n i n g and not w i t h i n d i v i d u a l v a r i a t i o n (Resnick, 1976a). The stimulus-response (S-R) models i n vogue from 1920 to 1960 were r e f l e c t i o n s of t h i s a t t i t u d e . In response to the o v e r s i m p l i f i c a t i o n of the S-R models, a new computer-based model of i n f o r m a t i o n processing was developed i n the e a r l y s i x t i e s (Sternberg, 1979d). An i n f l u e n t i a l book by M i l l e r , Galanter, and Pribram (1960) served to spark an i n t e r e s t i n computer s i m u l a t i o n s of human mental processing. Another s e r i e s of s t u d i e s based on the d i s t r i b u t i v e memory 10 model (Hunt, F r o s t , &Lunneborg, 1973) were c h a r a c t e r i s t i c of the renewed emphasis on mental processing which gave r i s e to the d i s c i p l i n e of c o g n i t i v e psychology. These new methods avoided some of the weaknesses of most'previous f a c t o r ^analyses. The model was u s u a l l y s p e c i f i e d a p r i o r i , and not subject to post-hoc determination. Rotations were not r e q u i r e d , pro-cesses were d e l i n e a t e d , and the data base was i n t r a i n d i v i d u a l (Estes, 1975; Sternberg, 1977b). L i m i t a t i o n s of experimental psychology. Despite these advances, the methods of the experimental p s y c h o l o g i s t s i n the s i x t i e s were not without l i m i t a t i o n s . The computer t h e o r i e s were complex and lacked parsimony. Sternberg (1977b) pointed out another major weakness: Information-processing methodology does not provide a means f o r s y s t e m a t i c a l l y studying c o r r e l a t e s of i n d i v i d u a l d i f f e r e n c e s i n performance. I f one wants to examine e i t h e r c o n s i s t e n c i e s i n patterns of i n d i v i d u a l d i f f e r e n c e s across d i f f e r e n t task para-meters, or between task parameters and e x t e r n a l measures of performance, the c o r r e l a t i o n a l methods of d i f f e r e n t i a l p s y c h o l -ogy are needed to accomplish t h i s g o a l . (pp. 60-61) The v e r b a l l e a r n i n g i n v e s t i g a t i o n s of the s i x t i e s and seventies attempted to d i s t i n g u i s h between process and c a p a c i t y (or s t r u c t u r e ) by e i t h e r c o n t r o l l i n g f o r the cap a c i t y v a r i a b l e s and measuring the e f f e c t s of the process v a r i a b l e s , or v i c e v e r s a . These approaches were reviewed by Campione and Brown (1978): One i s to devise extremely simple tasks i n which there i s l i t t l e room f o r LTM v a r i a t i o n to be important (e.g., to attempt to guaran-tee that the inf o r m a t i o n i s e q u a l l y f a m i l i a r to a l l s u b j e c t s ) , a second i s to experiment i n such a way that s t r a t e g i e s are l i k e l y to be e i t h e r d i f f i c u l t to implement or u n l i k e l y to be of h e l p , and a t h i r d i s to develop a p r e c i s e mathematical model of the task i n question i n which s p e c i f i c parameters r e f l e c t i n g d i f f e r e n t pro-cesses can be r e a d i l y estimated. (pp. 284-285) At l e a s t one serious drawback to these c l a s s i c a l main e f f e c t or i n t e r a c t i o n experiments, wherein one v a r i a b l e was manipulated, was the concomitant l i m i t a t i o n of g e n e r a l i z a b i l i t y . The r e s u l t s were o v e r l y s p e c i f i c c o n c l u s i o n s . Furthermore, without a t h e o r e t i c a l framework, the choice of independent v a r i a b l e s to be manipulated became a problem. "In many cases i t i s not c l e a r where t r a i n i n g attempts should be aimed, because we do not know e x a c t l y how to s p e c i f y the problem we are t r y i n g to remediate" (Campione & Brown, 1978, p. 294). Man i p u l a t i o n of one or two v a r i a b l e s was an inadequate approach to the problem of i s o l a t i n g m u l t i l e v e l sources of i n d i v i d u a l d i f f e r e n c e s . C a l l f o r U n i f i c a t i o n Cronbach, as e a r l y as 1957, saw the need f o r a u n i f i c a t i o n of the i n c r e a s i n g l y divergent d i f f e r e n t i a l and experimental d i s c i p l i n e s i n the study of i n d i v i d u a l d i f f e r e n c e s ; an attempt to r i g h t each other's wrongs. " I n d i v i d u a l d i f f e r e n c e s have been an annoyance ra t h e r than a challenge to the experimenter" (Cronbach, 1957, p. 674). On f a c t o r a n a l y s t s , " h i s s o p h i s t i c a t i o n i n data a n a l y s i s has not been matched by s o p h i s t i c a t i o n i n theory. The c o r r e l a t i o n a l p s y c h o l o g i s t was l e d i n t o temptation by h i s own success, l o s i n g himself f i r s t i n p r a c t i c a l p r e d i c -t i o n , then i n a n a r c i s s i s t i c program of studying h i s t e s t s as an end i n themselves" (Cronbach, 1957, p. 675). D i s s a t i s f a c t i o n w i t h E x i s t i n g Methods Cronbach's suggestions d i d not r e s u l t i n an immediate confluence of op i n i o n . S t i l l , many t h e o r i s t s during the s i x t i e s and e a r l y seventies echoed h i s remarks i n v o i c i n g t h e i r d i s s a t i s f a c t i o n w i t h e x i s t i n g methodologies. Humphreys (1962b) c r i t i c i z e d the p r o l i f e r a t i o n of f a c t o r s as w e l l as the p r a c t i c e of i n t e r p r e t i n g f a c t o r s as b a s i c and primary no matter how narrow they might be. He proposed a h i e r a r c h i c a l f a c t o r model along 12 the l i n e s of Vernon's theory (Jensen, 1970) and saw f a c t o r a n a l y s i s more as a means f o r hypothesis f o r m u l a t i o n than f o r hypothesis t e s t i n g . He advocated a " f a c e t theory" i n v o l v i n g task a n a l y s i s of the format and content of t e s t s , and the development of a p r i o r i models f o r f a c t o r a n a l y s i s , to guide i n task s e l e c t i o n . McNemar (1964), i n d i s c u s s i n g the d e c l i n e of "g" (general i n t e l l i -gence) as a u s e f u l t h e o r e t i c a l concept, concluded that w h i l e "g" was s t i l l important i n psychology, i t s nature was s t i l l not understood i n s p i t e of years of i n v e s t i g a t i o n . He described two types of i n d i v i d u a l d i f f e r e n c e s t u d i e s . The f i r s t type ( f a c t o r a n a l y t i c ) had to do x^ith s t u d i e s which assumed that patterns of i n t e r c o r r e l a t i o n s among t e s t s represented the s t r u c t u r e of the i n t e l l e c t . The second type (experimental) searched f o r nontest c o r r e l a t e s of t e s t performance. Both types of s t u d i e s c e r t a i n l y f o r c e one to s t r e s s the over-whelming d i v e r s i t y e x h i b i t e d among the organisms. But these s t u d i e s of i n d i v i d u a l d i f f e r e n c e s never come to g r i p s w i t h the process, or op e r a t i o n , by which a given organism achieves an i n t e l l e c t u a l response. Indeed, i t i s d i f f i c u l t to see how the a v a i l a b l e i n d i v i d u a l d i f f e r e n c e data can be used even as a s t a r t i n g point f o r generating a theory as to the process nature of general i n t e l l i g e n c e or of any other s p e c i f i e d a b i l i t y . (McNemar, 1964, p. 881) Messick (1972) j o i n e d the others i n advocating an augmentation of f a c t o r a n a l y t i c techniques w i t h experimental and o b s e r v a t i o n a l techniques to d e r i v e f u n c t i o n a l r e l a t i o n s h i p s among the c o n s t r u c t s of f a c t o r a n a l -y s i s , and as a means f o r understanding the nature of f a c t o r s beyond a s u p e r f i c i a l l e v e l . He suggested the f o l l o w i n g : C o n c e p t u a l i z a t i o n s of complex l e a r n i n g processes . . . i n c l u d e not only components of information-processing a b i l i t i e s but a l s o higher-order information-processing h e u r i s t i c s such as plans and s t r a t e g i e s , which i n t u r n may i m p l i c a t e v a r i a b l e s of p e r s o n a l i t y and c o g n i t i v e s t y l e . One important p o s s i b i l i t y i n t h i s regard i s t hat higher-order t r a i t s may enter i n t o sequences not only as components (a simple s e q u e n t i a l model) but as organizers of components (a h i e r a r c h i c a l p e r s o n a l i t y model). (Messick, 1972, p. 369). 13 Estes (1974) f e l t that i n t e l l i g e n c e should not be c h a r a c t e r i z e d i n terms of a sampling of item and subscale performances (the c o r r e l a t i o n a l approach), but i n terms of l e a r n i n g processes. This would a l l o w f o r i d e n t i f i c a t i o n of the processes that 'cause' i n t e l l e c t . Learning process theory would provide a f i r m e r ground on which to base i n t e r v e n -t i o n and remediation programs, although i t would not n e c e s s a r i l y improve on the p r e d i c t i v e powers of e x i s t i n g t e s t b a t t e r i e s . As an example of t h i s procedure, Estes (1974) i d e n t i f i e d processes hypothesized to under-l i e subtests such as the d i g i t span and vocabulary t e s t s , w i t h the goal of improving on the d i a g n o s t i c power of current t e s t b a t t e r i e s . In a l a t e r paper (Estes, 1976) he emphasized the need to combine experimental and t h e o r e t i c a l techniques i n order to e x p l a i n the co m p l e x i t i e s of prob-lem s o l v i n g and development. :The New Wave In the mid-seventies, i n t e l l i g e n c e was s t i l l very much a major concern of p s y c h o l o g i s t s . The v o i c e s of d i s s a t i s f a c t i o n of the s i x t i e s mushroomed i n t o symposia and papers c a l l i n g f o r process r a t h e r than s t r u c t u r a l i n t e r p r e t a t i o n s of i n t e l l i g e n c e and advocating the u n i f i c a t i o n of experimental and d i f f e r e n t i a l psychology (Campione& Brown, 1978; C a r r o l l , 1978; C a r r o l l & Maxwell, 1979; Estes, 1976; Glaser & P e l l e g r i n o , 1978; Hunt & Lansman, 1975; Resnick, 1976b; Snow, 1978; Sternberg, 1978b). There seems to be widespread concurrence among t h e o r e t i c i a n s and methodologists a l i k e that new approaches to studying i n t e l l i g e n c e should somehow combine the d i f f e r e n t i a l and c o g n i t i v e ( i n f o r m a t i o n -processing) approaches that have been used i n the past, and that the combination should somehow enable the i n v e s t i g a t o r to i s o l a t e components of i n t e l l i g e n c e that are elementary (at some l e v e l of a n a l y s i s ) . (Sternberg, 1978b, p. 196) 14 The need to i s o l a t e a v a r i e t y of sources of i n d i v i d u a l d ifferences both at general and more elementary l e v e l s of processing was recognized by the "New Wave" i n t e l l i g e n c e researchers. This new approach reaffirmed the need to explain as well as to predict i n d i v i d u a l differences i n performance. E x i s t i n g d i f f e r e n t i a l and cognitive methodologies for research were not considered appropriate for the in-depth task analyses necessary to i s o l a t e elementary processes and sources of differences. Factor theories had focused on the structure of mental a b i l i t i e s and ignored the under-l y i n g processes whereas information processing approaches had demonstrated process e f f e c t s without incorporating the processes into a t h e o r e t i c a l framework or structure (Sternberg, 1979c). The former approach resulted i n theories lacking explanatory power, while the l a t t e r approach spawned a p r o l i f e r a t i o n of task s p e c i f i c processes, not connected to any o v e r a l l theory and hence with l i m i t e d p r e d i c t i v e power. The new wave researchers r e i t e r a t e d the pleas from the s i x t i e s , but also took steps to embody these concerns i n t h e i r research. A s t a r t on the problem was made i n suggesting necessary conceptual d i s t i n c t i o n s . Campione and Brown (1978) s p e c i f i e d four l e v e l s f o r sources of i n d i v i d u a l differences on any task. The f i r s t term, architecture, was used to r e f e r to the hardware, or the major stores, including short-term memory, intermediate, and long-term memory. Properties of the a r c h i t e c t u r e , including capacity, d u r a b i l i t y , and e f f i c i e n c y were also defined. Capacity r e f e r r e d to units of storage space, d u r a b i l i t y r e f e r r e d to the degree of retention of stored information, and e f f i c i e n c y r e f e r r e d to speed of manipulation of stored information. The other l e v e l s involved the contents of memory rather than the 15 a r c h i t e c t u r e , and were thus l e s s f i x e d . F i r s t we use the term knowledge base to r e f e r to the e x i s t i n g semantic networks and data s t r u c t u r e s , the i n d i v i d u a l ' s organized knowledge of the world. The term scheme i s used to r e f e r to P i a g e t i a n r u l e s of t h i n k i n g , both f i g u r a t i v e and oper a t i v e . F i n a l l y , we use c o n t r o l processes to mean the r u l e s and s t r a t e g i e s a v a i l a b l e to the t h i n k e r f o r memorizing, understanding, s o l v i n g problems, e t c . (Campione & Brown, 1978, p. 284) Hunt and Lansman (1975) made s i m i l a r d i s t i n c t i o n s between a r c h i t e c -t u r e and c o n t r o l processes such as r u l e s and s t r a t e g i e s . New Wave Research Hunt, F r o s t , and Lunneborg (1973) were among the f i r s t to put i n t o p r a c t i c e these recommendations. The i n d i v i d u a l d i f f e r e n c e s assessed by an i n t e l l i g e n c e t e s t provide u s e f u l r e f l e c t i o n s of c u l t u r a l and b i o l o g i c d i f f e r e n c e s among men, but the development of those t e s t s has taught us l i t t l e about the nature of these d i f f e r e n c e s . As a r e s u l t , i n t e l l e c t u a l assessment i s a l l too oft e n d e s c r i p t i v e r a t h e r than p r e s c r i p t i v e . (Hunt, F r o s t , "& Lunneborg, 1973, p. 89). Their goals were two-fold: to demonstrate a s u b s t a n t i a l r e l a t i o n -ship between t h e i r d i s t r i b u t e d memory model and c o g n i t i v e t a s k s , and to prove that i n d i v i d u a l d i f f e r e n c e s i n task performance were not due to measurement e r r o r (as p r e v i o u s l y assumed), but due to r e l i a b l e i n d i v i d u a l c h a r a c t e r i s t i c s . These hypotheses were supported. Subjects, c l a s s i f i e d on the b a s i s of v e r b a l and performance a b i l i t y s c a l e s , d i f f e r e d r e l i a b l y i n task performance. Q u a l i t a t i v e d i f f e r e n c e s as w e l l as q u a n t i t a t i v e d i f f e r e n c e s were evident; there was some i n d i c a t i o n that subjects o b t a i n i n g equivalent r e s u l t s were doing so on the b a s i s of d i f f e r e n t s t r a t e g i e s . Hunt begins w i t h t h e o r i e s of memory and then attempts to deduce s i t u a t i o n s i n which i n d i v i d u a l d i f f e r e n c e s i n performance should be observed. His a n a l y s i s leads, f o r example, to the demonstration of l a r g e i n d i v i d u a l d i f f e r e n c e s i n a simple comparison task. The next step i s to show that these d i f f e r -ences are r e l a t e d to scores on standard t e s t s of v e r b a l i n t e l -l i g e n c e . This . . . sets the stage f o r research which i s now needed i n order to c l o s e the gap and show through what . . . sequence of processes, i n d i v i d u a l d i f f e r e n c e s i n simple tasks that were p r e d i c t e d on the b a s i s of c o g n i t i v e theory come to be r e f l e c t e d a l s o i n t e s t performance. (Estes, 1976, p. 297) In the same v e i n , C a r r o l l (1974) o u t l i n e d a d e t a i l e d procedure f o r c h a r a c t e r i z i n g f a c t o r s according to a model of c o g n i t i v e processes. He b e l i e v e d that h i s new " s t r u c t u r e of i n t e l l e c t " model would provide a b e t t e r d e f i n i t i o n of what the t e s t s were t e s t i n g . Adopting a modified v e r s i o n of Hunt's d i s t r i b u t i v e memory model (Hunt et a l . , 1973) he analyzed 48 t e s t s from the K i t of Reference Tests f o r C o g n i t i v e F a c t o r s . Each t e s t was c a t e g o r i z e d according to a number of dimensions, i n c l u d i n g the f o l l o w i n g : the type of memory demands, the modality or contents of memory i n v o l v e d , the operations or s t r a t e g i e s employed i n a ' c e n t r a l processor' and the p o t e n t i a l ranges of i n d i v i d u a l d i f f e r e n c e s on the task. A number of researchers entered the new era i n i n d i v i d u a l d i f f e r -ence research by i n v e s t i g a t i n g processes of i n t e l l i g e n c e i n retarded sub-j e c t s . This research aimed to i d e n t i f y the processes of i n t e l l i g e n c e , study the remediation of r e t a r d a t e d e f i c i t s , and to i n v e s t i g a t e the developmental aspects of i n t e l l i g e n c e . Of the two schools of research, f a c t o r a n a l y s i s and experimental, the experimental p s y c h o l o g i s t s have shown more i n t e r e s t i n the study of d i f f e r e n c e s between normal and retarded subjects of equal c h r o n o l o g i c a l age. These researchers con-centrated on mental processes and s t r a t e g i e s r a t h e r than mental c a p a c i t y . Processes and s t r a t e g i e s were viewed as more amenable to remediation and i n s t r u c t i o n than the r e l a t i v e l y f i x e d a r c h i t e c t u r e . The i d e n t i f i c a t i o n and t r a i n i n g of d i f f e r e n c e s i n s t r a t e g i e s f o r task s o l u t i o n was emphasized (Belmont & B u t t e r f i e l d , 1971; Brown, 1974, 1975; Brown & B a r c l a y , 1976; Brown & Campione, 1977; Brown & Lawton, 1977; K a i l , 1979; Rohwer, 1973). The m a j o r i t y of these s t r a t e g y d e f i c i t s i d e n t i f i e d i n retarded subjects were a t t r i b u t a b l e to p roduction, and not mediation d e f i c i e n c i e s ( F l a v e l l , 1970). In other words, the retarded s u b j e c t s , w h i l e u n l i k e l y to produce s t r a t e g i e s spontaneously, were induced to use the s t r a t e g i e s w i t h prompting or i n s t r u c t i o n s . Thus recent s t u d i e s have emphasized not only t r a i n i n g of s t r a t e g i e s , but a l s o t r a n s f e r of the t r a i n i n g to other tasks (Brown & DeLoache, 1978). Campione and Brown (1978) adopted the view that by t r a i n i n g s p e c i f i c s t r a t e g i e s , improvement i n executive c o n t r o l processes, and thus t r a n s f e r , would r e s u l t . They were able to induce t r a n s f e r of t r a i n i n g i n only one s t r a t e g y . So, despite much research (Brown & Campione, 1977; Brown, Campione, Bray, & Wilcox, 1973; Brown & Lawton, 1977) , d u r a b i l i t y and g e n e r a l i z a b i l i t y of s t r a t e g y t r a i n i n g have remained e l u s i v e goals f o r t h i s group of i n v e s t i g a t o r s . Belmont and B u t t e r f i e l d (1971) attempted to induce t r a n s f e r of s t r a t e g y t r a i n i n g through t r a i n i n g of executive processes. They a l s o f a i l e d to f i n d d u r a b i l i t y or g e n e r a l i z a b i l i t y of t r a i n i n g . Sternberg (1979a) concluded that d u r a b i l i t y and t r a n s f e r of t r a i n i n g was p o s s i b l e , but i n order to have long-term changes, the i n t e r a c t i v e e f f e c t s of performance components would have to be taken i n t o account. Despite a l a r g e degree of research a c t i v i t y attempting to under-stand the processes of i n t e l l i g e n c e , and r e c o g n i t i o n of the flaws i n e a r l i e r attempts, t h i s new body of research was not e n t i r e l y f a u l t l e s s . 18 C a r r o l l (1978) o u t l i n e d a number of problems i n c o g n i t i v e r e s e a r c h , i n c l u d i n g the problems p a r t i c u l a r to m u l t i p l e r e g r e s s i o n a n a l y s i s such as c o l l i n e a r i t y among p r e d i c t o r v a r i a b l e s making r e g r e s s i o n weights d i f f i -c u l t to i n t e r p r e t . He a l s o i d e n t i f i e d more general problems such as processes i d e n t i f i e d being t a s k - s p e c i f i c , the l a c k of d i s t i n c t i o n between o p t i o n a l and r e q u i r e d processes, and the problem of c i r c u l a r i t y , meaning that the processes i d e n t i f i e d were dependent on the t h e o r e t i c a l model proposed. Despite these caveats, C a r r o l l (1978) remained o p t i m i s t i c about i n d i v i d u a l d i f f e r e n c e research i n the c o g n i t i v e f i e l d : Even i f i n d i v i d u a l d i f f e r e n c e s are i n e x t r i c a b l y l i n k e d w i t h pro-cesses, i n d i v i d u a l d i f f e r e n c e methodologies should enable us to narrow down the kinds of processes a s s o c i a t e d w i t h p a r t i c u l a r t a s k s , and to i n v e s t i g a t e the g e n e r a l i t y of those processes over d i f f e r e n t t a s k s . ( C a r r o l l , 1978, p. 110) In a l a t e r paper ( C a r r o l l & Maxwell, 1979) t h i s view was r e i t e r a t e d i n the hope that experimental s t u d i e s might help to determine the nature and developmental c h a r a c t e r i s t i c s of primary a b i l i t i e s . A f u r t h e r i s s u e i n the recent l i t e r a t u r e was the d i s t i n c t i o n between q u a l i t a t i v e and q u a n t i t a t i v e d i f f e r e n c e s i n i n t e l l i g e n c e (Jarman, 1980). There was at l e a s t suggestive evidence that the same task may measure d i f f e r e n t c o g n i t i v e processes or s t r a t e g i e s at d i f f e r e n t develop-mental and c o g n i t i v e l e v e l s (Jarman & Das, 1977). Others have a l s o found d i f f e r e n t f a c t o r loadings f o r groups v a r y i n g on a b i l i t y (Humphreys & Taber, 1973; Stevenson, Parker, W i l k i n s o n , Hegion, & F i s h , 1976). In the c l a s s i c a l psychometric and l e a r n i n g s t u d i e s , q u a n t i t a t i v e changes were assumed, but q u a l i t a t i v e changes were g e n e r a l l y ignored (Jarman, 1980). Snow (1978) i n d i c a t e d that f u t u r e research must i d e n t i f y i n d i v i d u a l 19 d i f f e r e n c e s from a v a r i e t y of sources i n c l u d i n g process d i f f e r e n c e s , s t r a t e g y d i f f e r e n c e s and d i f f e r e n c e s i n the sequencing of processes. In summary, an emphasis was noted on not only i d e n t i f y i n g c o g n i t i v e processes, but a l s o i d e n t i f y i n g how these processes were organized i n t o s p e c i f i c s t r a t e g i e s (Estes, 1975, 1976). These recent trends i n i n t e l l i -gence research underlined the need f o r research focused on elementary processes of i n t e l l i g e n c e and m u l t i p l e sources of i n d i v i d u a l d i f f e r e n c e s i n c l u d i n g c a p a c i t y , content, and s t r a t e g y . I t was hoped that these new trends would give r i s e to new conceptions of i n t e l l i g e n c e which " w i l l f o s t e r the development of educational p o s s i b i l i t i e s that increase i n d i v i d u a l accomplishments" ( Glaser & P e l l e g r i n o , 1978, p. 318). While accumulated evidence i n d i c a t e d that s t r a t e g i e s and processes i n task performance were important components of human a b i l i t y , most of the recent research was i n the experimental t r a d i t i o n i n which only a few v a r i a b l e s were manipulated at any time. T y p i c a l l y , i f s t r a t e g y was being i n v e s t i g a t e d , then c a p a c i t y components were c o n t r o l l e d f o r r a t h e r than included i n the a n a l y s i s . Task by subject i n t e r a c t i o n s were o f t e n ignored. Hunt and MacLeod ('1978) warned that when one p a r t i c u l a r s t r a t e g y model was hypothesized, the parameter estimates became model-s p e c i f i c . Because of these and other l i m i t a t i o n s , recent experimental research was not much more s u c c e s s f u l than were the e a r l i e r experimental and f a c t o r - a n a l y t i c attempts i n i d e n t i f y i n g the nature o f i n t e l l i g e n c e and i n i d e n t i f y i n g m u l t i l e v e l sources of process and s t r a t e g y d i f f e r -ences. In-depth task analyses w i t h i n a t h e o r e t i c a l framework, and m u l t i v a r i a t e methodologies were advocated f o r f u t u r e research. 20 Componential A n a l y s i s P e l l e g r i n o and Glaser (1979) summarized p o t e n t i a l methodologies s u i t e d to the new era i n i n t e l l i g e n c e research. Among s e v e r a l sug-gested methods, one of the most promising was componential a n a l y s i s , developed by Robert Sternberg (1977b) f o r the a n a l y s i s of a n a l o g i c a l reasoning. The o v e r a l l purpose of componential a n a l y s i s i s to i d e n t i f y the component mental operations underlying a s e r i e s of r e l a t e d information-processing tasks and to di s c o v e r the o r g a n i z a t i o n of these component operations i n terms of t h e i r r e l a t i o n s h i p s both to each other and to higher order c o n s t e l l a t i o n s of mental a c t i v i t i e s . (Sternberg, 1977b, p. 93) This method incorporated the views of d i f f e r e n t i a l psychology by p r o v i d i n g a method f o r e l a b o r a t i n g the underlying t r a i t s of i n t e l l i g e n c e t e s t s i n terms of mental operations (processes). The views of cog-n i t i v e psychology were incorporated by p r o v i d i n g a method f o r d i s c o v e r i n g elementary inform a t i o n processes and t h e i r o r g a n i z a t i o n i n i n t e l l i g e n t behavior and r e l a t i n g these processes to reference a b i l i t i e s . Sternberg (1977b) provided a d e t a i l e d account of the method of componential a n a l y s i s and i t s use i n c o n s t r u c t i n g and v a l i d a t i n g a theory of a n a l o g i c a l reasoning. The method was s u c c e s s f u l l y v a l i d a t e d on a v a r i e t y of reasoning t a s k s , i n c l u d i n g v e r b a l , p i c t o r i a l , geometric, and animal-name analogies (Sternberg, 1977b) , l i n e a r , c a t e g o r i c a l , and c o n d i t i o n a l s y l l o g i s m s , and c l a s s i f i c a t i o n and s e r i e s completion prob-lems (Sternberg, 1978c). The f o l l o w i n g summary of the theory and method i s l i m i t e d i t o the a n a l y s i s of analogies of the standard form, A i s to B, as C i s to D (A:B::C:D). C r i t e r i a f o r task s e l e c t i o n and methods f o r task decomposition were o u t l i n e d i n Sternberg (1978c, 1979f). 21 O r i g i n s of Componential A n a l y s i s Componential a n a l y s i s was developed as an answer to the concerns being r a i s e d i n i n d i v i d u a l d i f f e r e n c e research. Sternberg reviewed the e x i s t i n g methodologies f o r research on i n t e l l i g e n c e and found them l a c k i n g i n ways mentioned i n e a r l i e r s e c t i o n s of t h i s review (Sternberg, 1977b, 1979d). The goal of componential a n a l y s i s was to develop a research method that would i s o l a t e i n d i v i d u a l d i f f e r e n c e s at a number of l e v e l s , mainly i n t r a i n d i v i d u a l l y , and to avoid the predeterminism of f a c t o r a n a l y t i c methods, as w e l l as the s p e c i f i c i t y of i n f o r m a t i o n processing paradigms. Sternberg, i n choosing a n a l o g i c a l reasoning as the domain of tasks f o r i n v e s t i g a t i o n , was i n f l u e n c e d by the u b i q u i t y of analogy items on a v a r i e t y of a b i l i t y r t e s t s , a s s w e l l a s i l n everyday.use. Reasoning by analogy i s pervasive i n everyday experience and would seem to be an important part of what we commonly r e f e r to as i n t e l l i g e n c e . . . . A n a l o g i c a l reasoning i s of the utmost importance i n a v a r i e t y of i n t e l l e c t u a l d i s c i p l i n e s . . . . A n a l o g i c a l reasoning a l s o plays an important part i n the law, where i t may be c a l l e d reasoning by example. . . . A n a l o g i c a l reasoning has been the subject of a r e l a t i v e l y s m a l l amount of p s y c h o l o g i c a l research. (Sternberg, 1977b, pp. 99-100) Whitely and Dawis (1974) a l s o commented on the c e n t r a l i t y of analogy items i n the measurement of general i n t e l l i g e n c e . Sternberg (1977b) reviewed a number of c o g n i t i v e and d i f f e r e n t i a l t h e o r i e s d e a l i n g w i t h a n a l o g i c a l reasoning (Spearman, 1923; Johnson, 1962; Rumelhart & Abrahamson, 1973). He concluded that most of the e x i s t i n g t h e o r i e s of a n a l o g i c a l reasoning were incomplete, accounting f o r l i m i t e d p o r t i o n s of a n a l o g i c a l reasoning. They had i n s u f f i c i e n t data bases, lacked g e n e r a l i t y , and none adequately accounted f o r i n d i -v i d u a l d i f f e r e n c e s i n processing. To remedy some of these weaknesses, 22 Sternberg borrowed from the strengths of the e a r l i e r d i f f e r e n t i a l and experimental approaches. The componential theory of a n a l o g i c a l reasoning s p e c i f i e d d e t a i l e d process models f o r the steps i n a n a l o g i c a l reasoning. The theory was s p e c i f i c i n d e s c r i b i n g components, or processes, but a l s o general i n that i t was a p p l i c a b l e to v a r i o u s types of analogy problems. The method of componential a n a l y s i s was a l s o u s e f u l i n a n a l y z i n g a f a i r l y wide v a r i e t y of tasks (Sternberg, 1978c). I t was parsimonious i n that only " p s y c h o l o g i c a l l y s i g n i f i c a n t o p e r a t i o n s " (Sternberg, 1977b, p. 146) were s p e c i f i e d , avoiding t r i v i a l i t y . The theory was f a i r l y w i d e l y t e s t e d and had a s u b s t a n t i a l data base. Componential i n v e s t i g a t i o n s were not l i m i t e d to a n a l o g i c a l reason-i n g ; however, only the theory of a n a l o g i c a l reasoning w i l l be t r e a t e d i n t h i s review. From a psychometric point of view, componential a n a l y s i s may be viewed as a d e t a i l e d a l g o r i t h m f o r construct v a l i d a t i o n . . . from an i n f o r m a t i o n processing point of view, componential a n a l -y s i s may be viewed as a set of procedures f o r d i s c o v e r i n g the i d e n t i t y and o r g a n i z a t i o n of a set of elementary i n f o r m a t i o n processes. (Sternberg, 1978a, p. 277) A component, the b a s i c u n i t of a n a l y s i s , was defined as "an elemen-t a r y i n f o r m a t i o n process that operates upon i n t e r n a l r e p r e s e n t a t i o n s of objects or symbols" (Sternberg, 1977b, p. 93). A component was a non-o p t i o n a l process i n most cases. I n t e n s i v e Task A n a l y s i s : I n t e r n a l V a l i d a t i o n Theory The f i r s t step i n the c o n s t r u c t i o n of a componential theory i n v o l v e d the s e l e c t i o n of a task f o r a n a l y s i s . The task to be analyzed i n t h i s review c o n s i s t e d of a p i c t o r i a l analogy c a l l e d a Schematic P i c t u r e Analogy of the standard form, A i s to B as C i s to D (A:B::C:D). The 23 analogy item i n Figure 1 i s an example of a Schematic P i c t u r e Analogy which w i l l be r e f e r r e d to throughout t h i s d i s c u s s i o n . These schematic p i c t u r e analogies were developed by Sternberg and R i f k i n (1979). The goal was to choose the answer option (Dj. or D2) which c o r r e c t l y completed the analogy. The f i r s t two terms, or f i g u r e s , of the analogy ( l a b e l l e d A and B) e s t a b l i s h e d the r e l a t i o n s h i p to be completed. The next step, at the theory l e v e l , i n v o l v e d decomposition of the task i n t o the components (processes) b e l i e v e d to be necessary i n s o l u t i o n . F i v e components were hypothesized f o r the s o l u t i o n of schematic p i c t u r e a n a l o g i e s : encoding, i n f e r e n c e , mapping, a p p l i c a t i o n , and response. While other components may be i n v o l v e d , f o r parsimony and i n t e r p r e t a b i l i t y only components of t h e o r e t i c a l i n t e r e s t were included i n a theory. The t h i r d step i n the componential theory was s p e c i f i c a t i o n of a r u l e (or algorithm) f o r combining the components. This r u l e was e i t h e r an a d d i t i v e one, m u l t i p l i c a t i v e , or a combination thereof. In the p i c t o r i a l analogy theory, the components were hypothesized to be combined according to a l i n e a r , a d d i t i v e model. Thus the t o t a l l a t e n c y f o r s o l u t i o n of the analogy was equal to the sum of the time spent on each component (see Figure 1). The time spent on each component was a func-t i o n of the number of times the component was executed, m u l t i p l i e d by the d u r a t i o n of the component (an estimated parameter). The theory a l s o s p e c i f i e d that components were a n a l y t i c a l l y executed and t h e r e f o r e separable. Components Encoding. Encoding i n v o l v e d storage i n short term memory of a l l of the p o s s i b l e r e l e v a n t a t t r i b u t e s of the analogy terms as w e l l as storage of a value ([from Sternberg & R i f k i n , 1979) Components 1. Encoding: A t t r i b u t e s hat c o l o r s u i t p a t t e r n footwear handgear Values (black, white) ( s t r i p e d , dotted) (shoes, boots) ( s u i t c a s e , umbrella) Inference: (A-B r e l a t i o n ) 3. Mapping: (A-C r e l a t i o n ) 4. A p p l i c a t i o n : hat c o l o r (black to w h i t e ) , s u i t (no change) footwear (boots to shoes), handgear ( s u i t c a s e to umbrella) hat c o l o r (no change), s u i t (dotted to s t r i p e d ) footwear (no change), handgear (no change) C-Di : hat (black to w h i t e ) , s u i t (no change) footwear (boots to shoes), handgear ( s u i t -case to umbrella) C-D2 : hat (black to w h i t e ) , s u i t ( s t r i p e d to dotted), footwear (no change), handgear ( s u i t c a s e to umbrella) 5. Response: w r i t t e n answer on response sheet Basic Rule f o r Component Combination T o t a l Time = encoding time + i n f e r e n c e time + mapping time + a p p l i c a t i o n time + response time Figure 1. Schematic P i c t u r e Analogy 25 corresponding to each a t t r i b u t e . In the schematic p i c t u r e analogies (e.g., Figure 1) each term (or f i g u r e ) had four a t t r i b u t e s w i t h two values each. These were, hat c o l o r (black or w h i t e ) , s u i t p a t t e r n ( s t r i p e d or polka-d o t t e d ) , footwear (shoes or bo o t s ) , and handgear ( s u i t c a s e or umbrella). Inference. The inf e r e n c e component i n v o l v e d d i s c o v e r i n g and s t o r i n g the r e l a t i o n between the A and B terms of the analogy. I n the sample item, the A to B r e l a t i o n f o r a l l four a t t r i b u t e s was: hat c o l o r (black to w h i t e ) , s u i t p a t t e r n (no change), footwear (boots to shoes), and handgear ( s u i t c a s e to umbrella). Mapping. The mapping component i n v o l v e d d i s c o v e r i n g and s t o r i n g the r e l a t i o n between the A and G terms of the analogy. The f i r s t h a l f of the analogy was thus l i n k e d to the second h a l f . The f u l l mapping r e l a t i o n f o r the sample item i n Figure 1 was: hat c o l o r (no change), s u i t p a t t e r n (polka^dotted to s t r i p e d ) , footwear (no change), and hand-gear (no change). A p p l i c a t i o n . The f o u r t h component, a p p l i c a t i o n , i n v o l v e d applying a r e l a t i o n analogous to the i n f e r r e d A to B r e l a t i o n from the C term to the answer options. In the sample item the r e l a t i o n from C to was: hat c o l o r (black to w h i t e ) , s u i t p a t t e r n (no change), footwear (boots to shoes), and handgear ( s u i t c a s e to umbrella). The r e l a t i o n from C to D2 was: hat c o l o r (black to w h i t e ) , s u i t p a t t e r n ( s t r i p e d to po l k a - d o t t e d ) , footwear (no change), and handgear ( s u i t c a s e to umb r e l l a ) . Therefore when the A to B in f e r e n c e r e l a t i o n was a p p l i e d from C to D^and C to D2, o p t i o n 1 was c o r r e c t as i t permitted the C to D term r e l a t i o n to be analogous to the i n f e r r e d A to B r e l a t i o n . Response. The f i n a l component, response, i n v o l v e d communication 26 of the chosen op t i o n . Thus the analogy task was decomposed. Component Execution Components could be executed i n an exhaustive or s e l f - t e r m i n a t i n g f a s h i o n . I f processing i s exhaustive, then whenever a component i s used i n s o l u t i o n of an item, i t i s executed the maximum p o s s i b l e number of times f o r that item type. I f . p r o c e s s i n g i s s e l f -t e r m i n a t i n g , the component need not be executed the maximum p o s s i b l e number of times. (Sternberg, 1978a, p. 283) For example, i f encoding was exhaustive, the subject would s t o r e a l l of the r e l e v a n t a t t r i b u t e s and values f o r a l l f i v e analogy terms i n the sample item. I f encoding was s e l f - t e r m i n a t i n g , the subject would perceive and s t o r e a t t r i b u t e s and values f o r the terms as they were needed. Thus on the in f e r e n c e step, only the A and B terms need be encoded. When working on mapping, only the A and C terms need be encoded. Exhaustive i n f e r e n c e , mapping, and a p p l i c a t i o n components were described i n the component s e c t i o n of t h i s review. When each component was defined, the r e l a t i o n was completed f o r a l l four a t t r i b u t e s at once. In s e l f - t e r m i n a t i n g execution a t t r i b u t e values were executed one by one u n t i l a unique s o l u t i o n was found. Order of s e l e c t i o n of a t t r i -butes was assumed to be random. Consider the case where a subject executed the i n f e r e n c e , mapping, and a p p l i c a t i o n components i n a s e l f - t e r m i n a t i n g f a s h i o n . I f the subject i n f e r r e d the r e l a t i o n f o r hat c o l o r f i r s t , the in f e r e n c e r e l a t i o n (A to B), would be simply: hat c o l o r (black to w h i t e ) . Next'the mapping r e l a t i o n (A to C), f o r hat c o l o r would be determined: hat c o l o r (no change). The A to B r e l a t i o n f o r hat c o l o r would then be a p p l i e d from C to Di and C to D2 r e l a t i o n s . Unfortunately the c o r r e c t o p t i o n would 27 be i n d i s t i n g u i s h a b l e because the A to B r e l a t i o n f o r hat c o l o r (black to white) a p p l i e s c o r r e c t l y to C to and C to D2. The subject would then have to r e t u r n to the in f e r e n c e step, choose another a t t r i b u t e (e.g., footwear), and proceed through the i n f e r e n c e , mapping, and a p p l i c a t i o n components again. Thus components could be executed from one to four times i n the s e l f - t e r m i n a t i n g mode, whereas w i t h exhaustive component execution the components would be executed once. The number of times a s e l f -t e r m i n a t i n g component was executed was a f u n c t i o n of the number of a t t r i -butes that had the same values i n the two answer options. Models Seven p l a u s i b l e models f o r s o l u t i o n of p i c t o r i a l analogies were hypothesized by Sternberg and R i f k i n (1979). These models s p e c i f i e d the mode and order of component execution: exhaustive or s e l f - t e r m i n a t -i n g . The components were assumed to be combined according to the l i n e a r a d d i t i v e r u l e and a s e r i a l mode of processing was assumed i n a l l seven models. The four models o u t l i n e d i n Table 1 were developed by Sternberg and R i f k i n (1979) to e x p l a i n s o l u t i o n of People Piece Analogies. Figure 2 i l l u s t r a t e s a t y p i c a l people piece analogy. These a n a l o g i e s , l i k e the schematic p i c t u r e a n a l o g i e s , had four a t t r i b u t e s w i t h two values each: height, weight, garment c o l o r , and sex. These are known as i n t e g r a l a t t r i b u t e a nalogies. Sternberg and Rifkin.(1979) defined i n t e g r a l a t t r i b u t e s t i m u l i as those i n which a t t r i b u t e s cannot be n u l l i f i e d without d e s t r o y i n g the i n t a c t n e s s of the f i g u r e . "For example, to por-t r a y the sex of a person (or p i c t u r e of a person), the person must be drawn at some height and at some weight . . . s i m i l a r l y shading i n 28 Table 1 Models 1, 2, 3, 4 Model Components 1 = encoding + in f e r e n c e + mapping + a p p l i c a t i o n + response (exhaustive) (exhaustive) (exhaustive) (exhaustive) 2 = encoding + in f e r e n c e + mapping + a p p l i c a t i o n + response (exhaustive) (exhaustive) (exhaustive) ( s e l f -t erminating) 3 = encoding + in f e r e n c e + mapping + a p p l i c a t i o n + response (exhaustive) (exhaustive) ( s e l f - ( s e l f -terminating) terminating) 4 = encoding + in f e r e n c e + mapping + a p p l i c a t i o n + response (exhaustive) ( s e l f - ( s e l f - ( s e l f -terminating) terminating) terminating) 29 D2 Components 1. Encoding: Attributes height weight garment color sex (from Sternberg & Rifkin, 1979) Values (short, t a l l ) (fat, thin) (black, white) (male, female) Inference: height (short to t a l l ) , weight (thin to fat), (A-B relation) garment color (white to black), sex (no change) height (no change), weight (no change), garment 3. Mapping: (A-C relation) (no change), sex (female to male) 4. Application: 5. Response: C-Di: height (short to t a l l ) , weight (thin to f a t ) , garment color (white to black), sex (no change) C-D2: height (no change), weight (no change), garment color (no change), sex (male to female) record answer Basic Rule for Component Combination Total time = encoding time + inference time + mapping time + application time + response time Figure 2. People Piece Analogy c l o t h i n g can only be shown i f the person wearing the c l o t h i n g has both height and weight" (Sternberg & R i f k i n , 1979, p. 199). In c o n t r a s t , schematic p i c t u r e analogies (Figure 1) had separable a t t r i b u t e s . Separable a t t r i b u t e s t i m u l i are those i n which a t t r i b u t e s may be n u l l i f i e d without d e s t r o y i n g the i n t a c t n e s s of the s t i m u l i . The f i r s t four models a l l hypothesized exhaustive encoding (Table 1) , but d i f f e r e d i n the mode of execution f o r the remaining icomponents.. . Model 1. In Model 1, a l l of the component operations are exhaus-t i v e . The subject encodes the terms of the analogy e x h a u s t i v e l y ( i . e . , a l l a t t r i b u t e s and t h e i r values are s t o r e d ) . Inference, mapping, and a p p l i c a t i o n are a l s o exhaustive. The subject i n f e r s a l l p o s s i b l e r e l a t i o n s between encoded a t t r i b u t e s of the f i r s t two terms of the analogy; next the subject maps a l l p o s s i b l e r e l a t i o n s between encoded a t t r i -butes of the f i r s t and t h i r d analogy terms. F i n a l l y , the subject a p p l i e s a l l p o s s i b l e r e l a t i o n s between the t h i r d term and each o p t i o n . (Sternberg & R i f k i n , 1979, p. 201) The processes would be executed as i l l u s t r a t e d i n the e a r l i e r component s e c t i o n of t h i s review. Model 2. In Model 2, the same steps are followed up to the a p p l i c a t i o n procedure, that i s , encoding, i n f e r e n c e , and mapping are exhaustive and thus executed/once. A p p l i c a t i o n i s s e l f - t e r m i n a t i n g . "The subject only a p p l i e s as many a t t r i b u t e values as are needed to choose a unique answer. . . . we assume that order of s e l e c t i o n of a t t r i b u t e s i s random" (Sternberg & R i f k i n , 1979, p. 201). For example, i f the subjects chose hat c o l o r as the f i r s t a t t r i b u t e f o r a p p l i c a t i o n i n the schematic p i c t u r e item i n Figure 1, they would apply the r e l a t i o n hat c o l o r (black to white) from C to Di and C to D2, but would not be able to d i s t i n g u i s h the c o r r e c t o p t i o n because both options permit the 31 analogy f o r hat c o l o r to be completed. Another a t t r i b u t e must be chosen and the a p p l i c a t i o n component re-executed, u n t i l a unique s o l u t i o n i s found. Thus the a p p l i c a t i o n component may be executed from one to four times i n Model 2, dependent upon which a t t r i b u t e i s chosen f o r a p p l i c a -t i o n . Model 3. Encoding and i n f e r e n c e components are exhaustive i n Model 3. Mapping and a p p l i c a t i o n are s e l f - t e r m i n a t i n g . He or she maps one a t t r i b u t e value from A to C and then a p p l i e s the corresponding a t t r i b u t e value from C to D. I f the chosen a t t r i b u t e i s s u f f i c i e n t to d i s t i n g u i s h between the c o r r e c t and i n c o r r e c t answer o p t i o n s , the subject responds. Otherwise, the subject maps and then a p p l i e s another a t t r i b u t e , again t r y i n g to s e l e c t a unique response. (Sternberg & R i f k i n , 1979, p. 202) For example, i f the subjects chose to map the footwear a t t r i b u t e f i r s t , they found that the A to C r e l a t i o n f o r footwear was (no change). Knowing that the A to B r e l a t i o n f o r footwear was (boots to shoes), and the C to 1 and C to 2 r e l a t i o n s f o r footwear were (boots to shoes), and (no change), r e s p e c t i v e l y , they could d i s t i n g u i s h the c o r r e c t o p t i o n as op t i o n 1. Thus mapping and a p p l i c a t i o n were executed once i n t h i s example. Had the handgear a t t r i b u t e been s e l e c t e d f i r s t f o r mapping, the c o r r e c t o p t i o n would have been i n d i s t i n g u i s h a b l e and the components would have been executed more than once. Model:.4. Encoding i s exhaustive, but i n f e r e n c e , mapping, and a p p l i c a t i o n are s e l f - t e r m i n a t i n g i n Model 4. The subject f i r s t i n f e r s one a t t r i b u t e value from A to B, then maps the corresponding a t t r i b u t e v a l u e from A to C, and f i n a l l y a p p l i e s the a t t r i b u t e value from C to each answer o p t i o n . I f the subject i s able to d i s t i n g u i s h the c o r r e c t from the i n c o r -r e c t answer op t i o n on t h i s b a s i s , the subject responds. (Sternberg & R i f k i n , 1979, p. 202) Thus the repeat loop now leads a l l the way back to the i n f e r e n c e com-ponent i f the c o r r e c t o p t i o n i s not d i s t i n g u i s h a b l e . 32 Each model, then, d i f f e r e d i n the number of times a component oper-a t i o n was executed. Sternberg and R i f k i n (1979) proposed three a d d i t i o n a l models (Table 2) to describe component execution f o r the schematic p i c t u r e analogies i n Figure 1. Because of the nature of the schematic p i c t u r e a n a l o g i e s , Sternberg and R i f k i n (1979) hypothesized that the mapping component (as i l l u s t r a t e d i n Models 1-4) could be by-passed. They f e l t that stimulus a t t r i b u t e s were e a s i l y i d e n t i f i a b l e and thus e a s i l y manipulated, removing the n e c e s s i t y f o r e s t a b l i s h i n g the higher-order A to C r e l a t i o n which l i n k e d the domain to the range of the analogy. Subjects would proceed d i r e c t l y from i n f e r e n c e to a p p l i c a t i o n . Table 2 Models 1M, 2-3M, 4M Model Components 1M = : encoding + i n f e r e n c e + a p p l i c a t i o n + response (exhaustive) (exhaustive) (exhaustive) 2-3M = encoding + i n f e r e n c e + a p p l i c a t i o n + response (exhaustive f o r A,B (exhaustive) ( s e l f terms; s e l f - terminating) t e r m i n a t i n g f o r C,D terms) 4M = encoding + i n f e r e n c e + a p p l i c a t i o n + response ( s e l f - t e r m i n a t i n g ) ( s e l f - ( s e l f -terminating) terminating) The models were l a b e l l e d 1M, 2-3M and 4M to d i s t i n g u i s h them from the f i r s t f our models. In a d d i t i o n to the absence of the mapping com-ponent, these models d i f f e r e d from the f i r s t four i n that encoding was not always exhaustive. The combination r u l e remained the l i n e a r 33 a d d i t i v e one. Model 1M. Model 1M d i f f e r s from Model 1 only i n that i t l a c k s a mapping component. Encoding, i n f e r e n c e , and a p p l i c a t i o n are exhaustive. Model 2-3M. Model 2-3M i n v o l v e s exhaustive i n f e r e n c e w i t h s e l f -t e r m i n a t i n g a p p l i c a t i o n . The A and B terms of the analogy are exhaus-t i v e l y encoded (because in f e r e n c e i s exhaustive) but the C term and D term are encoded i n a s e l f - t e r m i n a t i n g mode. Models 2 and 3 were com-bined i n t h i s model because mapping, the d i s t i n g u i s h i n g element between Model 2 and 3 ( s e l f - t e r m i n a t i n g i n 3 and exhaustive i n 2 ) , was absent i n the modified models. Model 4M. Model 4M i n v o l v e s s e l f - t e r m i n a t i n g i n f e r e n c e and a p p l i c a t i o n and a l l of the terms are encoded i n a s e l f - t e r m i n a t i n g f a s h i o n . Component Es t i m a t i o n The f i n a l step i n the theory i n v o l v e d e s t i m a t i n g the l a t e n c i e s and d i f f i c u l t i e s of the i n d i v i d u a l components. This w i l l be described i n d e t a i l i n the methodology s e c t i o n , but, i n general, In order to make these estimates, the i n v e s t i g a t o r must q u a n t i f y the i n f o r m a t i o n processing model or models, p r e d i c t i n g s u b j e c t s ' l a t e n c i e s and e r r o r r a t e s from a set of independent v a r i a b l e s . Corresponding to each independent v a r i a b l e i s an estimated parameter that represents the la t e n c y or d i f f i c u l t y of a s i n g l e component process. (Sternberg, 1978a, p. 284) This completes the i n t e r n a l v a l i d a t i o n phase of the i n t e n s i v e task a n a l y s i s : s p e c i f i c a t i o n of the theory, models, components, combination r u l e , and parameter e s t i m a t i o n . 34 Int e n s i v e Task A n a l y s i s : E x t e r n a l V a l i d a t i o n The second phase of i n t e n s i v e task a n a l y s i s i n v o l v e d e x t e r n a l v a l i d a t i o n , or determining how the hypothesized components r e l a t e d to i n d i v i d u a l d i f f e r e n c e patterns i n performance on reference a b i l i t y t e s t s , or other e x t e r n a l tasks. This was a process of demonstrating general-i z a t i o n of the e f f e c t s of components to other t a s k s . Subjects' component scores were c o r r e l a t e d w i t h t h e i r scores on reference a b i l i t y t e s t s which were hypothesized to measure the same t h i n g as the component scores (e.g., i n d u c t i v e reasoning t e s t s ) . A high c o r r e l a t i o n i n d i c a t e d convergent v a l i d i t y . S i m i l a r l y , d i s c r i m i n a n t v a l i d i t y was demonstrated by showing low c o r r e l a t i o n s between component scores and unrelated t e s t s , f o r example, perceptual speed t e s t s (Sternberg, 1978a). Extensive Task A n a l y s i s F i n a l l y , i n extensive a n a l y s i s , the goal " i s to i n t e g r a t e the f i n d i n g s of a s e r i e s of i n t e r r e l a t e d i n t e n s i v e analyses. In p a r t i c u l a r , i t i s designed to demonstrate the p s y c h o l o g i c a l r e a l i t y and g e n e r a l i z a b i l -i t y of the i d e n t i f i e d components" (Sternberg, 1977b, p. 71). In summary, according to Sternberg (1979f), componential a n a l y s i s allows f o r an understanding of the determinants of performance, impossible i n l i s t i n g s of tasks and scores (e.g., f a c t o r a n a l y s i s and i n f o r m a t i o n processing methods) and provides a framework f o r i n v e s t i g a t i n g the content and s t r u c t u r e of mental a b i l i t i e s and f o r an a l y z i n g d i f f e r e n c e s w i t h i n and across age l e v e l s . This framework f o r task a n a l y s i s could encompass i n d i v i d u a l d i f f e r e n c e s at s e v e r a l d i f f e r e n t l e v e l s . At the theory l e v e l , there could be i n d i v i d u a l d i f f e r e n c e s i n the components people use i n performing a task, or i n the way component parameters are combined. At the model l e v e l , i n d i v i d u a l d i f f e r e n c e s i n the sequence of components or i n t h e i r mode of operation are p o s s i b l e . And at the component l e v e l , i n d i v i d u a l d i f f e r e n c e s 35 i n the speed or power of each component could occur. A major v i r t u e of Sternberg's method i s that i t allows one to attend to a l l of these l e v e l s at the same time. ( P e l l e g r i n o & Lyon, 1979, p. 170) Testing the Componential Model Sternberg (1977b) presented a comprehensive d i s c u s s i o n of componen-t i a l a n a l y s i s , i n c l u d i n g the theory, a review of r e l a t e d l i t e r a t u r e , and four s t u d i e s supporting the theory. More r e c e n t l y (Sternberg, 1979bje):.:he extended the theory of a n a l o g i c a l reasoning to one of general i n t e l l i g e n c e , c l a s s i f y i n g types of components according to t h e i r f u n c t i o n and l e v e l of g e n e r a l i t y . The more general a p p l i c a t i o n of the theory w i l l not be d i s -cussed i n t h i s review. The i n i t i a l v a l i d a t i o n of the componential theory of a n a l o g i c a l reasoning c o n s i s t e d of a s e r i e s of experiments on c o l l e g e age s u b j e c t s . Type of analogy and p r e s e n t a t i o n format v a r i e d i n each experiment. Each of the experiments c o n s i s t e d of an i n t e n s i v e task a n a l y s i s phase i n c l u d i n g i n t e r n a l and e x t e r n a l v a l i d a t i o n . Four models were te s t e d (Sternberg, 1977a, b ) . Four types of analogies were used, one i n each experiment; people piece analogies ( p i c t o r i a l ) , v e r b a l and geo-metric a n a l o g i e s , and animal-name analogies. In most cases the a n a l -ogies were presented v i a tachistoscope using the precueing method (Sternberg, 1978c, 1979c) to a l l o w e s t i m a t i o n of component parameters and l a t e n c i e s . Analogies d i f f e r e d i n the amount of i n f o r m a t i o n given (precueing). In some cases subjects viewed the A, B, C, and D terms simultaneously. In some they previewed the A, B, and C terms, or the A and B terms, or only the A term, before being presented w i t h the f u l l analogy. Some analogies i n v o l v e d true or f a l s e responses and others i n v o l v e d a choice between two options. The primary dependent v a r i a b l e s were s o l u t i o n times and the 36 primary independent v a r i a b l e was item d i f f i c u l t y , defined as the number of a t t r i b u t e value transformations from the A to B terms, A to C terms, and C to answer terms. Parameters f o r each component were estimated by f i t -t i n g l i n e a r r e g r e s s i o n equations to the s o l u t i o n times f o r d i f f e r e n t items under the d i f f e r e n t precueing c o n d i t i o n s (Reed, 1977). Reasoning, perceptual speed, and vocabulary a b i l i t y t e s t s were admin-i s t e r e d as reference a b i l i t y t e s t s to the subjects i n the people piece and v e r b a l analogy experiments and to h a l f of the subjects i n the animal name experiment. Subjects i n the geometric analogy experiment and h a l f of those i n the animal name experiment received the Card Rotations Test from the French K i t , and a word grouping t e s t . Twelve subjects who scored between the f i f t h and t w e n t y - f i f t h p e r c e n t i l e s and 12 who scored between the s e v e n t y - f i f t h and n i n e t y - f i f t h p e r c e n t i l e s on word grouping were s e l e c t e d f o r the geometric analogy study. Subjects who took the reasoning and perceptual speed t e s t s were c l a s s i f i e d i n t o four groups and four subjects were s e l e c t e d from each group, f o r a t o t a l of s i x t e e n . Group 1 con s i s t e d of subjects s c o r i n g above the e i g h t i e t h p e r c e n t i l e on reasoning and perceptual speed. Group 2 subjects scored high (above e i g h t i e t h p e r c e n t i l e ) on reasoning and low (between the tenth and t h i r t i e t h p e r c e n t i l e s ) on perceptual speed. Subjects i n group 3 were low on reasoning and high on speed, and subjects i n group 4 were low on both measures. The models hypothesized f o r component execution were s i m i l a r , although not i d e n t i c a l to those i n Table 1. The theory hypothesized that s i x components were necessary i n s o l u t i o n : encoding, i n f e r e n c e , mapping, a p p l i c a t i o n , j u s t i f i c a t i o n , and response, and that the combin-a t i o n r u l e was l i n e a r and a d d i t i v e . The a d d i t i o n a l component, j u s t i -f i c a t i o n , was used when an exact s o l u t i o n was not a v a i l a b l e . J u s t i f i c a t i o n permits comparison of the options. The o p t i o n which per-mits the c l o s e s t approximation ( d i f f e r i n g i n the fewest elements) to the A to B r e l a t i o n i s chosen. This process was unnecessary i n the people piece and schematic p i c t u r e analogies as there was always an exact s o l u -t i o n a v a i l a b l e . The componential theory of a n a l o g i c a l reasoning was supported across the four experiments. The combination r u l e f o r components was a d d i t i v e and s i x components were used to s o l v e analogies (although the j u s t i f i c a t i o n component was o p t i o n a l ) . Model 3 was the p r e f e r r e d model f o r component execution on a l l dependent measures f o r v e r b a l analogies f o r both high and low reasoners. Model 3 combined exhaustive encoding and i n f e r e n c e , w i t h s e l f - t e r m i n a t i n g mapping and a p p l i c a t i o n . On some types of analogies both Model 3 and 4 f i t the data, but Model 3 was designated as p r e f e r r e d . Response times were g e n e r a l l y constant across analogy types but absolute times spent on the other components v a r i e d . R e l a t i v e times a l s o v a r i e d across a n a l o g i e s , w i t h encoding always t a k i n g the most time and a p p l i c a t i o n the l e a s t . E r r o r r a t e data were l e s s c o n c l u s i v e but s i m i l a r to the l a t e n c y data. There was no evidence for' i n d i v i d u a l d i f f e r e n c e s i n model choice across these experiments, but the response component l a t e n c i e s were h i g h l y c o r r e l a t e d w i t h reasoning a b i l i t y . Longer encoding time on v e r b a l analogies was a s s o c i a t e d w i t h lower response l a t e n c y and w i t h success on the reasoning t e s t . This was i n t e r p r e t e d as evidence that slower and more thorough encoding may pay o f f i n increased a b i l i t y to compare a t t r i -butes r a p i d l y or to perform e f f i c i e n t l y the numerous book-keeping operations i n v o l v e d i n problem s o l u t i o n . (Sternberg, 1977b, p. 253) 38 Consistency i n st r a t e g y use (be t t e r model f i t s ) was as s o c i a t e d w i t h higher a b i l i t y scores on the v e r b a l analogies. These c o r r e l a t i o n s suggested that subjects higher i n reasoning a b i l i t y tend to be more systematic i n t h e i r s o l u t i o n of analogy problems and the system they use i s that s p e c i f i e d by the com-p o n e n t i a l theory. (Sternberg, 1977b, p. 253) In analogies where discovery of r e l e v a n t a t t r i b u t e s was d i f f i c u l t , the i n f e r e n c e , mapping, a p p l i c a t i o n , and j u s t i f i c a t i o n component l a t e n c i e s were p o s i t i v e l y r e l a t e d to scores on the general a b i l i t y t e s t s . Evidence suggesting that reasoning was a good measure of general i n t e l l i g e n c e (Sternberg, 1977b), i n c l u d e d : the c o r r e l a t i o n of the response component w i t h reference a b i l i t y t e s t s ; the o c c a s i o n a l r e l a t i o n of i n f e r e n c e , mapping, and a p p l i c a t i o n to the reference t e s t s ; the r e l a t i o n s h i p between encoding and the other operations; and the r e l a t i o n -ship between model f i t s and reasoning scores. Other s t u d i e s have followed these i n i t i a l attempts to v a l i d a t e the theory. Many have i n v o l v e d other types of reasoning, p a r t i c u l a r l y deductive reasoning a b i l i t y as represented i n : l i n e a r s y l l o g i s m s , c l a s s i f i c a t i o n s , s e r i e s completion, c a t e g o r i c a l , and c o n d i t i o n a l s y l l o -gisms (Sternberg, 1978c, 1979f). The method has been used i n con s t r u c t v a l i d a t i o n of a p t i t u d e t e s t s (Sternberg, 1979d). The componential theory of i n t e l l i g e n c e was a l s o a p p l i e d to the t r a i n i n g of i n t e l l i g e n c e i n the retarded (Sternberg, 1979a). Sternberg concluded that i t was p o s s i b l e to t r a i n aspects of i n t e l l i g e n c e i n the retarded, and suggested a greater focus on d u r a b i l -i t y and g e n e r a l i z a b i l i t y i n the t r a i n i n g of s t r a t e g i e s as w e l l as emphasis on the m o t i v a t i o n a l and i n t e r a c t i v e aspects of behavior. 39 Componential A n a l y s i s and Developmental Research Sternberg extended the componential theory to developmental as w e l l as i n d i v i d u a l d i f f e r e n c e research. In an i n v e s t i g a t i o n of the develop-ment of l i n e a r s y l l o g i s t i c reasoning (Sternberg, 1980) no evidence was found f o r a change i n s t r a t e g y w i t h age, as the same model was p r e f e r r e d by subjects i n grades 3, 5, 7, 9, and 11. There was evidence that con-s i s t e n c y i n st r a t e g y use increased w i t h age as the model f i t s improved w i t h age. Sternberg and Nigro (1980) s t u d i e d developmental patt e r n s i n the s o l u t i o n of v e r b a l analogies. Twenty subjects i n each age group, grades 3, 6, 9, and c o l l e g e , were i n v o l v e d . A s t r a t e g y s h i f t was i n d i c a t e d i n that the t h i r d and s i x t h grade subjects were incomplete reasoners and tended to use word a s s o c i a t i o n to solve v e r b a l a n a l o g i e s . The n i n t h grade and c o l l e g e subjects d i d not r e l y on v e r b a l a s s o c i a t i o n , but on v e r b a l reasoning. Subjects increased exhaustive processing and had l e s s s e l f - t e r m i n a t i n g processing w i t h i n c r e a s i n g age. Another developmental study (Sternberg & R i f k i n , 1979) i n v e s t i -gated the g e n e r a l i z a b i l i t y of the componential theory to second, f o u r t h , s i x t h grade students, and college-age students. Two experiments were described, one i n v o l v i n g people piece a n a l o g i e s , and one i n which sub-j e c t s solved schematic p i c t u r e analogies during three sessions. The models described i n Table 1 and Table 2 were developed to account f o r the data. Developmental d i f f e r e n c e s were p r e d i c t e d at three l e v e l s : theory, model, and component l e v e l s . At the theory l e v e l i t was hypothesized that a) subjects might d i f f e r i n the a v a i l a b i l i t y of component opera-t i o n s , s p e c i f i c a l l y that the mapping component might be acquired l a t e r 40 than the other components, and b) subjects might d i f f e r i n the combina-t i o n r u l e employed, s p e c i f i c a l l y that older c h i l d r e n and a d u l t s might use s e r i a l ' p r o c e s s i n g and the a d d i t i v e r u l e , w h i l e younger c h i l d r e n might process h o l i s t i c a l l y . At the model l e v e l , d i f f e r e n c e s were p r e d i c t e d i n a) choice of model; older c h i l d r e n and a d u l t s would choose models that required fewer r e p e t i t i o n s of the component processes ( i . e . , Models 3 and 4 ) , w h i l e younger c h i l d r e n would f o l l o w more r e p e t i t i v e models ( i . e . , Model 1 ) , and b) consistency i n use of model; younger c h i l d r e n might use a d i f f e r -ent model f o r each problem i n s t e a d of using a general s t r a t e g y or model. At the component l e v e l , i t was hypothesized that subjects would d i f f e r i n speed of component operations; older c h i l d r e n would be f a s t e r . Subjects would a l s o d i f f e r i n e r r o r r a t e ; younger subjects would be l e s s accurate. Results supported the p r e d i c t i o n of d i f f e r e n c e s i n use of compon-ents. Subjects i n grade 2 d i d not use a mapping component on e i t h e r analogy type. Subjects i n grades 4 and 6 and a d u l t s d i d not use the mapping component i n s o l v i n g separable a t t r i b u t e problems, but d i d use mapping on i n t e g r a l a t t r i b u t e s o l u t i o n s . Subjects showed no d i f f e r e n c e s i n combination r u l e . A l l subjects processed s e r i a l l y and conformed to the a d d i t i v e algorithm. Sternberg (1980) suggested that the absence of the mapping compon-ent w i t h separable a t t r i b u t e s t i m u l i was due to the nature of the s t i m u l i . With separable a t t r i b u t e s t i m u l i i t was not necessary to e x t r a c t the a t t r i b u t e s one by one. There was some evidence that t h i s component was u n a v a i l a b l e to younger c h i l d r e n . Mapping r e q u i r e d r e c o g n i t i o n of a second order r e l a t i o n s h i p , a c a p a c i t y not w e l l developed u n t i l the age 41 of 11 or 12. At the model l e v e l , d i f f e r e n c e s were found both w i t h age and type of analogy. In analogies w i t h separable a t t r i b u t e s , Model 4M was pre-f e r r e d by a l l age groups. For i n t e g r a l a t t r i b u t e a n a l o g i e s , subjects i n grade 2 p r e f e r r e d Model 4M, grade 4 students p r e f e r r e d Model 4, and grade 6 students and a d u l t s p r e f e r r e d Model 3. Thus r e s u l t s from the e a r l i e r study (Sternberg, 1977b) p r e d i c t i n g Model 3 as the p r e f e r r e d s t r a t e g y were g e n e r a l i z a b l e only to grade 6 subjects and a d u l t s . Young c h i l d r e n p r e f e r r e d models w i t h more s e l f - t e r m i n a t i n g than exhaus-t i v e operations. Evidence a l s o i n d i c a t e d an increase i n consistency of s t r a t e g y choice w i t h age. Brown and DeLoache (1978) have suggested that although exhaustive processing minimized e r r o r s , increased use of exhaustive i n f o r m a t i o n processing was a general c h a r a c t e r i s t i c of c o g n i t i v e development. F i n a l l y , w i t h respect to component operation l a t e n c i e s and e r r o r r a t e s , e r r o r r a t e s decreased across age l e v e l s as d i d most component l a t e n c i e s , w i t h the exception of the encoding l a t e n c y . Encoding times decreased from grade 2 to grade 4, then increased from grade 4 to grade 6 and from grade 6 to adulthood. As f o r separable and i n t e g r a l analogy problems, d i f f e r e n c e s i n s o l u t i o n algorithms were found. D i f f e r e n c e s were a t t r i b u t e d to d i f f e r -ences i n encoding s t r a t e g y . Subjects were b e l i e v e d to employ s e l f -t e r m i nating encoding f o r the separable a t t r i b u t e items and exhaustive encoding f o r the i n t e g r a l a t t r i b u t e items. Older subjects were l e s s w i l l i n g to trade o f f accuracy f o r speed. "The more s o p h i s t i c a t e d s t r a t e g y , then, i s to lengthen one's encoding lat e n c y i n order to shorten one's comparison l a t e n c y " (Sternberg & R i f k i n , 42 1979, p. 230). While evidence has been presented to support the v a l i d i t y of com-p o n e n t i a l a n a l y s i s f o r s t r a t e g y and. process research, r e s u l t s on younger populations showed that consistency i n use of st r a t e g y and choice of strat e g y was not as unequivocal as research on c o l l e g e age subjects i n d i c a t e d . Developmental d i f f e r e n c e s were found at the theory, model, and component l e v e l s . P e l l e g r i n o and Lyon (1979) suggested that although Sternberg (1977b) found l i t t l e evidence f o r i n d i v i d u a l d i f f e r e n c e s at the model (strategy) l e v e l i n c o l l e g e students, research aimed at a wider range of item d i f f i c u l t y and subject a b i l i t y may r e f l e c t greater v a r i a n c e at the model l e v e l . We wonder how much of reasoning a b i l i t y over i t s e n t i r e range might be due to d i f f e r e n c e s i n the a b i l i t y to assemble and monitor h i g h l y complex algorithms such as those embodied i n Sternberg's models. I t seems reason-able that many Stanford undergraduates already have a v a i l a b l e to them such an al g o r i t h m and thus i n d i v i d u a l d i f f e r e n c e s at t h i s l e v e l of a b i l i t y may not r e s t i n the sheer speed of processing m a t e r i a l s . However, other i n d i v i d u a l s w i t h lower measured a b i l i t i e s and those at an e a r l i e r m a t u r a t i o n a l l e v e l may manifest d i f f e r e n c e s not so much i n the speed of executing each process, but i n the l i k e l i h o o d that the program to execute the task can be assembled given meager amounts of p r a c t i s e i n the task. ( P e l l e g r i n o & Lyon, 1979, p. 183) Thus the method of componential a n a l y s i s appears'to be a promising t o o l , when compared to previous methods, f o r i n v e s t i g a t i n g d i f f e r e n c e s i n processes and s t r a t e g i e s . 43 Summary A v a r i e t y of methods and approaches to the study of i n t e l l i g e n c e have been reviewed. During the f i r s t h a l f of the twentieth century f a c t o r a n a l y t i c views predominated, but were unsuccessful i n determining the processes underlying the s t r u c t u r e of mental a b i l i t i e s . A number of reasons f o r the f a i l u r e of t h i s method were o u t l i n e d , i n c l u d i n g r o t a t i o n dilemmas, problems i n t e s t s e l e c t i o n , and the l a c k of i n t r a i t e m a n a l y s i s . Experimental p s y c h o l o g i s t s during the s i x t i e s and seventies attempted the study of i n d i v i d u a l d i f f e r e n c e s p r i m a r i l y through i n f o r m a t i o n process-ing models. This approach was a l s o l e s s than s a t i s f a c t o r y , r e s u l t i n g i n t a s k - s p e c i f i c conclusions l a c k i n g e x t e r n a l v a l i d i t y . A s o l u t i o n to the problem was suggested as e a r l y as 1957 by Gronbach through the u n i f i c a t i o n of d i f f e r e n t i a l and experimental d i s c i -p l i n e s . D i s s a t i s f a c t i o n w i t h e x i s t i n g methods grew during the s i x t i e s and by the mid-seventies the consensus was that process explanations of i n d i v i d u a l d i f f e r e n c e s were necessary and obtainable through a combina-t i o n of the experimental and f a c t o r i a l viewpoints. E a r l y attempts at convergence included those of Brown (1974, 1975), Campione and Brown (1978), C a r r o l l (1974), and Hunt et a l . (1973). C o g n i t i v e processes and s t r a t e g i e s f o r o r g a n i z i n g the processes were the focus of a t t e n t i o n . One of the most thorough and promising methods f o r u n i t i n g f a c t o r -i a l and experimental approaches was that of Sternberg (1977b). This approach, componential a n a l y s i s , allowed f o r m u l t i - l e v e l i n v e s t i g a t i o n s of i n d i v i d u a l d i f f e r e n c e s , and avoided the weaknesses of f a c t o r a n a l y t i c and i n f o r m a t i o n processing paradigms by r e l y i n g on r e g r e s s i o n a n a l y s i s i n v a l i d a t i n g d e t a i l e d t h e o r i e s . The d i s c u s s i o n of componential a n a l y s i s focused on the componential theory of a n a l o g i c a l reasoning. A d e t a i l e d d e s c r i p t i o n of the steps i n v o l v e d i n componential a n a l y s i s f o l l o w e d . A task was chosen, and broken down i n t o a set of components which comprised the theory f o r that task. A r u l e was s p e c i f i e d f o r the combination of the components and models were developed which s p e c i f i e d the mode and sequence f o r component execution. I n t e r n a l v a l i d a t i o n of the theory c o n s i s t e d of p r e d i c t i n g the t o t a l score from the su b j e c t s ' estimated component scores. External, v a l i d a t i o n c o n s i s t e d of determining how the components r e l a t e d to i n d i v i d u a l d i f f e r e n c e s i n performance on reference a b i l i t y t e s t s . These steps were i l l u s t r a t e d by the decom-p o s i t i o n of two types of p i c t o r i a l a nalogies. Evidence to support the componential theory of a n a l o g i c a l reasoning was presented, based on a c o l l e g e sample and a l s o a developmental study of younger s u b j e c t s . In the ol d e r sample, q u a n t i t a t i v e d i f f e r e n c e s i n laten c y and e r r o r r a t e s were found. Subjects d i d not d i f f e r i n model preference but d i d d i f f e r i n consistency of model use. Some component scores and model f i t s were r e l a t e d to reasoning a b i l i t y as measured by the reference t e s t . In the developmental study i n d i v i d u a l d i f f e r e n c e s were found at the theory, model, and component l e v e l s , i n cont r a s t to r e l a t i v e l y fewer d i f f e r e n c e s i n the c o l l e g e sample. It. was concluded that f o r the purposes of t h i s study, componential a n a l y s i s would be the most appropriate i n v e s t i g a t i v e t o o l , e s p e c i a l l y f o r d e a l i n g w i t h i n d i v i d u a l d i f f e r e n c e s i n processes and s t r a t e g i e s as measured by standardized achievement t e s t s . CHAPTER I I I PROBLEM Statement of the Problem The review of the l i t e r a t u r e i l l u s t r a t e d the need f o r f u r t h e r research on the nature of i n d i v i d u a l d i f f e r e n c e s i n a b i l i t y i n elemen-t a r y school c h i l d r e n . The method of componential a n a l y s i s (Sternberg, 1977b) was chosen i n order to i s o l a t e sources of i n d i v i d u a l d i f f e r e n c e s i n performance on Schematic P i c t u r e Analogies. With t h i s method i t was p o s s i b l e to i d e n t i f y the processes and s t r a t e g i e s used by i n d i v i d u a l s i n problem s o l u t i o n . The problem addressed i n t h i s study centred around the i d e n t i f i c a -t i o n of processes and s t r a t e g i e s u n d erlying d i f f e r e n c e s i n achievement a b i l i t y . More s p e c i f i c a l l y the f o l l o w i n g questions were asked: Do students of d i f f e r e n t a b i l i t y l e v e l s use d i f f e r e n t processes (components) i n p i c t o r i a l analogy task s o l u t i o n ? Do students of d i f f e r e n t a b i l i t y l e v e l s d i f f e r i n the mode of process execution and process combination ( i . e . , s t r ategy) used i n p i c t o r i a l analogy s o l u t i o n ? Do students who d i f f e r i n a b i l i t y l e v e l a l s o d i f f e r i n consistency of st r a t e g y use? R a t i o n a l e Major advances i n education may w e l l have to wait upon our achievement of deeper understanding of the c o g n i t i v e processes which the c h i l d b r i n g s to bear on the t a s k s , and the way i n which these processes come to be organized as a f u n c t i o n of d i f f e r e n t kinds of experience. (Estes, 1975, p. 13) 45 46 In recent years i n d i v i d u a l d i f f e r e n c e s have, more o f t e n than not, been viewed w i t h i n a framework of process, and p a r t i c u l a r l y of s t r a t e g i c d i f f e r e n c e s . Hunt and Lansman (1975) proposed that the a b i l i t y to produce and use s t r a t e g i e s was an important and s t a b l e subject charac-t e r i s t i c , and might have some r e l a t i o n t o degree of s c h o o l i n g . Brown (1975) and her colleagues long emphasized the importance of s t r a t e g i c d i f f e r e n c e s as a source of v a r i a t i o n . i n the performance of normal and retarded s u b j e c t s . Jarman and Das. (1977), d e s p i t e small sample s i z e and r e s t r i c t i o n of range on IQ, found evidence f o r s t r a t e g y d i f f e r e n c e s i n i n f o r m a t i o n processing between a high IQ group and the low and aver-age groups. While a l l the subjects seemed to use simultaneous and successive modes of processing there were q u a l i t a t i v e group d i f f e r e n c e s i n the methods used to solve the same task. Thus there was evidence suggesting the r e l a t i o n s h i p between processes and the a b i l i t y to combine the processes i n t o a s t r a t e g y , or p l a n , and i n d i v i d u a l d i f f e r e n c e s as measured by general i n t e l l i g e n c e t e s t s . I t was decided to f u r t h e r i n v e s t i g a t e t h i s r e l a t i o n s h i p through the method of componential a n a l y s i s (Sternberg, 1977b) of p i c t o r i a l analogy tasks. Analogy s o l u t i o n was chosen as the task f o r i n v e s t i g a t i o n f o r a number of reasons. The componential theory of a n a l o g i c a l reasoning was the most complete and well-documented a p p l i c a t i o n of the general method of componential a n a l y s i s , a r e l a t i v e l y new technique. Furthermore, the method was powerful i n i d e n t i f y i n g u n d erlying sources of i n d i v i d u a l d i f f e r e n c e s on a task at more than one l e v e l (e.g., theory, model, and component l e v e l d i f f e r e n c e s were i s o l a t e d ) . In a d d i t i o n to the q u a l i t i e s of the a n a l y s i s i t s e l f , analogies have a long h i s t o r y of important-roles i n p s y c h o l o g i c a l t h e o r i e s of 47 i n t e l l i g e n c e (e.g., Spearman, 1923). As pointed out by Sternberg (1977b), reasoning by analogy i s pervasive i n everyday l i f e . The measurement of a n a l o g i c a l reasoning i s a major component i n many standardized i n t e l l i -gence and achievement measures i n c l u d i n g the Standard P r o g r e s s i v e M a t r i c e s , M i l l e r Analogies Test, Lorge-Thorndike I n t e l l i g e n c e Test, and the Graduate Record Examination. A b e t t e r understanding of what these and other t e s t s measured was to be gained through an in-depth a n a l y s i s of the processes and s t r a t e g i e s of a n a l o g i c a l reasoning. Because scores on standardized group achievement t e s t s were more common measures of i n d i v i d u a l d i f f e r e n c e s i n elementary schools than were standardized i n t e l l i g e n c e t e s t s , t h i s study adopted a group achievement t e s t as a c r i t e r i o n measure f o r c a t e g o r i z i n g students i n terms of a b i l i t y . Group achievement t e s t s were .in wide use i n elementary schools' f o r a v a r i -ety of purposes i n c l u d i n g diagnosis f o r remediation and enrichment, and grade placement. Despite t h i s widespread'use, r e l a t i v e l y l i t t l e was /• known about the nature of academic achievement as measured by these t e s t s . This study attempted to provide a d d i t i o n a l i n f o r m a t i o n as to the nature of achievement as measured by standardized t e s t s . One disadvantage to the use of an achievement r a t h e r than i n t e l l i -gence measure as the c r i t e r i o n f o r s e l e c t i o n was that achievement measures tend to be r e l a t e d more to school l e a r n i n g than to general reasoning a b i l i t y . Thus the r e l a t i o n s h i p between scores on the analogy task and group membership on the a b i l i t y f a c t o r could be expected to be somewhat more attenuated than i f a measure of general i n t e l l i g e n c e and reasoning a b i l i t y (e.g., Standard P r o g r e s s i v e M a t r i c e s ) were used as the c r i t e r i o n . On the other hand, t h i s disadvantage may be an advantage; because 48 achievement t e s t s tap school l e a r n i n g more than i n t e l l i g e n c e t e s t s , the r e s u l t s based on an achievement t e s t c r i t e r i o n w i l l a l s o be more c l o s e l y t i e d to the e d ucational process w i t h c l e a r e r i m p l i c a t i o n s f o r teaching and remediation (Humphreys, 1962a). Across.a number of l o n g i t u d i n a l s t u d i e s , the c o r r e l a t i o n between achievement and i n t e l l i g e n c e t e s t s has been assessed. Bloom (1964) reported an average c o r r e l a t i o n of + .85. T y l e r (1974) reported c o r r e -l a t i o n s ranging from .40 to .60.. Some f a c t o r s a t t e n u a t i n g the c o r r e l a -t i o n s included r e s t r i c t i o n of range, long range p r e d i c t i o n s , and s u i t -a b i l i t y of the t e s t s f o r d i f f e r e n t age groups ( T y l e r , 1965). Most researchers assume a c o n s i s t e n t , moderate but dependable r e l a t i o n s h i p between i n t e l l i g e n c e and achievement scores ( T y l e r , 1965; Vernon, 1970). Humphreys (1962a) found no evidence that achievement d i f f e r e d from i n t e l l i g e n c e and equated:the two. He found that scores on IQ and achievement t e s t s c o r r e l a t e d as h i g h l y as scores on two d i f -f e r e n t IQ t e s t s . Thus i t was acknowledged that i n v e s t i g a t i o n of the r e l a t i o n s h i p between achievement and a n a l o g i c a l reasoning would tap one important f a c t o r , but not other f a c t o r s i n v o l v e d , such as m o t i v a t i o n , language, SES, and e t h n i c background. With these l i m i t a t i o n s i n mind, f o u r t h grade students, a p p r o x i -mately 10 years of age, were chosen to p a r t i c i p a t e i n the study. D i f f e r e n t p a t t e r n s of s t r a t e g i e s and processes were f e l t to be c l e a r and f a i r l y s t a b l e at t h i s age, w h i l e these patterns were s t i l l i n a period of f l u x i n younger students i n grades 1 and 2. Furthermore, both i n t e l l i g e n c e and achievement t e s t scores become i n c r e a s i n g l y s t a b l e w i t h age and by the f o u r t h grade, the scores are r e l i a b l e i n p r e d i c t i n g 49 f u t u r e scores (Bloom, 1964; T y l e r , 1974). Research Questions and Hypotheses F i v e research questions were posed. There was s u f f i c i e n t informa-t i o n to s t a t e hypotheses associated w i t h the l a s t two questions. Given the ambiguity i n the l i t e r a t u r e surrounding the f i r s t three questions, they were not s t a t e d as formal hypotheses, but as questions of an e x p l o r -atory nature. Theory L e v e l Question 1. -Do h i g h , low and average a b i l i t y students use the f i v e components (encoding, i n f e r e n c e , mapping, a p p l i c a t i o n , and response), hypothesized by the componential theory of a n a l o g i c a l reasoning i n s o l v i n g separable a t t r i b u t e analogy items? Sternberg and R i f k i n ' s (1979) i n v e s t i g a t i o n i n d i c a t e d that students i n grades 2, 4, and 6, and a d u l t s d i d not use mapping on schematic p i c -t u r e a n a l o g i e s , but they d i d use the remaining components: encoding, i n f e r e n c e , a p p l i c a t i o n , and response. While t h e i r study showed no e v i -dence of developmental d i f f e r e n c e s i n the components (processes) used, given the evidence i n other s t u d i e s f o r i n d i v i d u a l d i f f e r e n c e s i n s t r a t -egies used i n task s o l u t i o n (Brown, 1975), i t i s p o s s i b l e that Sternberg and R i f k i n ' s (1979) r e s u l t s were sample s p e c i f i c . a n d that students i n the present study w i l l d i f f e r i n the components used i n s o l u t i o n . Question 2. Do the h i g h , average, and low a b i l i t y groups d i f f e r i n the extent to which the l i n e a r a d d i t i v e combination r u l e accounts f o r t h e i r performance i n schematic p i c t u r e analogy s o l u t i o n ? In the previous s t u d i e s using p i c t o r i a l analogies (Sternberg, 1977b; Sternberg & R i f k i n , 1979), a l l subjects used the a d d i t i v e combination r u l e and processed i n an a n a l y t i c a l r a t h e r than h o l i s t i c f a s h i o n . 50 Despite these f i n d i n g s , Sternberg and R i f k i n (1979) acknowledged that p a r a l l e l processing or non l i n e a r component combination r u l e s were pos-s i b l e i n these analogy t a s k s , thus i t i s p o s s i b l e that the groups w i l l d i f f e r i n the degree to which the l i n e a r a d d i t i v e combination r u l e accounts f o r the data. Model L e v e l Question 3. Do h i g h , average, and low a b i l i t y students d i f f e r i n the r u l e they use f o r combining m u l t i p l e executions of the same component ( i . e . , i n p r e f e r r e d model choice)? Components were assumed to be s e r i a l l y executed i f the combination r u l e was l i n e a r and a d d i t i v e (Question 2 ) , but the mode of execution w i t h i n components may d i f f e r . Mode ( s e l f - t e r m i n a t i n g versus exhaustive) of execution was s p e c i f i e d i n the seven hypothesized models (Tables 1, 2). Sternberg and Nigro (1980), and Sternberg and R i f k i n (1979), found that younger students tended to use more s e l f - t e r m i n a t i n g and l e s s exhaustive operations than d i d o l d e r subjects on people piece analogies. Brown and DeLoache (1978) suggested that i n c r e a s i n g use of exhaustive processing was a general developmental c h a r a c t e r i s t i c . Thus i f low a b i l i t y students are assumed to be developmentally immature as compared wi t h equal CA average and high a b i l i t y students, they may use fewer exhaustive opera t i o n s , on some ta s k s . However, i n Sternberg and R i f k i n (1979) a l l subjects used only s e l f - t e r m i n a t i n g operations (Model 4M) on the schematic p i c t u r e a n a l o g i e s , thus no d i f f e r e n c e s i n component execu-t i o n may be evident on these p a r t i c u l a r t a s k s . Question 4. Does consistency i n s t r a t e g y use vary as a f u n c t i o n of~ l e v e l of a b i l i t y on separable a t t r i b u t e analogy tasks? In previous i n v e s t i g a t i o n s o l d e r subjects were found to be more systematic than younger subjects i n s t r a t e g y use (Sternberg, 1980; Sternberg & Nigro, 1980; Sternberg & R i f k i n , 1979) and high reasoners were more c o n s i s t e n t i n choice of s t r a t e g y than low reasoners (Stern-berg, 1977b). Hypothesis 4.1. Consistency i n model choice w i l l i n c r e a s e as a f u n c t i o n of l e v e l of a b i l i t y . Component Le v e l Question 5. Do component l a t e n c i e s and e r r o r r a t e s vary as a f u n c t i o n of l e v e l of a b i l i t y ? Jarman and Das (1977) suggested that speed of c e n t r a l processing may vary w i t h age and covary w i t h i n t e l l i g e n c e l e v e l (among other v a r i -ables) . In Sternberg and R i f k i n (1979) o l d e r c h i l d r e n and a d u l t s had fewer e r r o r s than d i d younger c h i l d r e n . Older subjects executed most component operations more r a p i d l y than d i d younger students. Hypothesis 5.1. E r r o r r a t e s and l a t e n c y scores f o r components and o v e r a l l task on separable a t t r i b u t e analogies w i l l vary as a func-t i o n of a b i l i t y l e v e l . An a d d i t i o n a l area of i n t e r e s t , w h i l e not t e s t e d d i r e c t l y i n hypothesis form was the degree of correspondence between f o u r t h grade students' performance i n t h i s study, and the performance of f o u r t h grade students i n a s i m i l a r study by Sternberg and R i f k i n (1979). CHAPTER IV METHOD Subj ects The sample pool c o n s i s t e d of 155 f o u r t h grade students from nine c l a s s e s i n four elementary schools. The schools were a l l w i t h i n the same school d i s t r i c t l o c a t e d i n a metropolitan area i n south western B.C. The students i n the schools represented a range of socio-economic l e v e l s and came from a v a r i e t y of et h n i c backgrounds. Formation of Subgroups From t h i s sample of 155 students, three equal s i z e groups were s e l e c t e d : students of high achievement, average achievement, and low achievement. The students were s e l e c t e d on the b a s i s of t h e i r e x i s t i n g scores on the Canadian Test of Basic S k i l l s (King, 1976), a group admin-i s t e r e d standardized achievement t e s t . The Canadian Test of Basic S k i l l s (CTBS) had been administered to the students by classroom teachers the previous year, w h i l e the- students'werewin 1 grade three. The CTBS, i n wide use across Canada, i s e s s e n t i a l l y a Canadian adaptation of the Iowa Test of Basic S k i l l s . Students are t e s t e d on vocabulary, reading comprehension, language s k i l l s , work-study s k i l l s , and mathematics s k i l l s . The t e s t measures general i z e d academic s k i l l s r a t h e r than achievement i n s p e c i f i c content areas. The t e s t provides grade e q u i v a l e n t , p e r c e n t i l e rank, and stanine subtest and composite scores. 52 53 The CTBS was standardized i n 1973 on a s t r a t i f i e d random sample of E n g l i s h schools across Canada (King, 1976). The t e s t manual reported the f o l l o w i n g s p l i t - h a l f r e l i a b i l i t y estimate f o r the grade 3 l e v e l composite scores, r = .98. I n t e r c o r r e l a t i o n s among subtests and between subtests and composite scores ranged from r = .49 to r = .93 f o r the t h i r d grade sample. S t a b i l i t y data were not presented. V a l i d i t y data were not a v a i l a b l e i n published t e s t m a t e r i a l s . Of the 155 f o u r t h grade boys and g i r l s , 27 e i t h e r had no e x i s t i n g CTBS scores, or were absent during the experimental s e s s i o n s , thus reducing the p o t e n t i a l sample pool to 128 students. The sampling pool was f u r t h e r reduced to 124 when 4 students were dropped from one se s s i o n a f t e r c r e a t i n g a disturbance. The remaining 124 students had grade-equivalent CTBS scores. Because the t e s t s had been administered i n d i f f e r e n t months of the year i n the four schools, these grade-equivalent CTBS scores were converted to p e r c e n t i l e scores (King, 1977). The p e r c e n t i l e scores were i n t u r n con-verted to Normal Curve Equivalent (NCE) scores (Tallmadge & Wood, 1976). The NCE i s a "normalized standard score that has been l i n e a r l y t r a n s -formed to match the p e r c e n t i l e d i s t r i b u t i o n at values of 1, 50, and 99" (Tallmadge & Wood, 1976, p. 2). The scores range from 1.00 to 99.00, w i t h a mean of 50.00 and a standard d e v i a t i o n of 21.06. The s c a l e i s assumed to be equal i n t e r v a l , and thus permits numerical c a l c u l a t i o n s , i n c ontrast to p e r c e n t i l e s . Table 3 summarizes the means, standard d e v i a t i o n s , and range f o r the sample of 60 students at three a b i l i t y l e v e l s . Twenty students (12 male, 8 female) had scores between one and three standard d e v i a t i o n s below the sample mean and were c l a s s i f i e d as the low achievement group. Twenty students (9 male, 11 female) who had scores between one and three 54 Table 3 D e s c r i p t i v e S t a t i s t i c s : NCE Scores Group n Mean SD Range Mean Age Low 20 36. 51 7 .68 17.30-44. 10 9 y r s 9 mbs Average 20 60. 92 9 .46 44.70-78. 20 9 yrs 8 mos High 20 89. 66 7 .71 79.60-99. 00 9 y r s 8 mos standard d e v i a t i o n s above the sample mean were c l a s s i f i e d as a high achievement group. The remaining 84 students, who had scores between one standard d e v i a t i o n above or below the sample mean, were c l a s s i f i e d as the average achievement group. Twenty students (9 male, 11 female) were drawn from the average group to maintain equal sample s i z e s at each a b i l i t y l e v e l . The average range of the NCE scores was d i v i d e d i n t o four equal i n t e r v a l s and students drawn randomly but p r o p o r t i o n a t e l y from each i n t e r -v a l to y i e l d the d e s i r e d sample of s i z e 20. The standard d e v i a t i o n i n the average group was higher than i n : t h e low and high groups, but s i n c e the data a n a l y s i s was group o r i e n t e d , t h i s d i f f e r e n c e should not i n f l u e n c e the r e s u l t s . Instruments Schematic P i c t u r e Analogies The Schematic P i c t u r e Analogies (Figure 1) were of the form A i s to B as C i s to Di or D2. Each term of the analogy v a r i e d on four separable a t t r i b u t e s . Separable a t t r i b u t e s are those which can be n u l l i f i e d without d e s t r o y i n g the i n t a c t n e s s of the stim u l u s . Each a t t r i b u t e had two pos-s i b l e v a l u e s : hat c o l o r (black or w h i t e ) , s u i t p a t t e r n . ( s t r i p e d or p o l k a -d o t t e d ) , handgear ( s u i t c a s e or umbre l l a ) , and footwear (shoes or boo t s ) . The analogies were presented i n 24 b o o k l e t s , each of which contained 55 16 a n a l o g i e s , 4 per page (see Appendix A). Subjects were given 64 seconds to complete each booklet. The 16 items w i t h i n each booklet were homogen-eous i n the number of a t t r i b u t e values transformed from the A to B terms, A to C terms, and to D 2 terms. For example, i n Figure 1 there were three a t t r i b u t e value transformations between the A and B terms: hat c o l o r , footwear, and handgear. One a t t r i b u t e value was transformed be-tween the A and C terms: s u i t p a t t e r n . The two transformations between the T>i and D 2 terms were s u i t p a t t e r n , and footwear. Thus, i f t h i s analogy item was i n a booklet of 16 items, a l l the items i n that booklet would have three a t t r i b u t e value transformations" between A and B, one between A and C and two transformations between and D2. The i d e n t i t y of the a t t r i b u t e values transformed v a r i e d across items w i t h i n a b o o k l e t , but the number of transformations was constant. Students recorded the 16 responses f o r each booklet on a separate answer sheet (see Appendix B). Sets of 24 booklets were numbered, and contained i n separate f o l d -e r s . Order of pages w i t h i n each booklet and order of booklets w i t h i n each set of .24 were random, as a c o n t r o l f o r p r a c t i c e and s e s s i o n e f f e c t s . Procedure A p i l o t a d m i n i s t r a t i o n of the procedure was performed, followed by the main data c o l l e c t i o n . P i l o t Study: I n i t i a l Procedure An i n i t i a l t e s t a d m i n i s t r a t i o n procedure, adapted from the procedure developed by Sternberg and R i f k i n (1979) was p i l o t - t e s t e d w i t h a group of 35 f o u r t h grade students. The students were asked to p a r t i c i p a t e i n a research p r o j e c t and were reassured that t h e i r performance would not a f f e c t t h e i r school grades. The students were then introduced to the Schematic P i c t u r e 56 Analogy problem. Sample sheets of four schematic p i c t u r e items were d i s t r i b u t e d and presented simultaneously on an overhead p r o j e c t o r . The four relevant a t t r i b u t e s and t h e i r values were i d e n t i f i e d by the students i n response to the experimenter's question "How are these clowns a l i k e ? In what ways are they d i f f e r e n t ? " Once the students were f a m i l i a r w i t h the a t t r i b u t e s and v a l u e s , the goal of the analogy problem was explained. The students were t o l d to choose the answer o p t i o n (Dj or D 2) that was the same as and d i f f e r e n t from C i n the same ways that A was the same as and d i f f e r e n t from B. They were a l s o t o l d to use the four a t t r i b u t e s and t h e i r values to guide them i n t h e i r answer choice f o r the f i r s t sample item. A f t e r the students had recorded t h e i r responses on the answer sheet, the c o r r e c t o p t i o n was i n d i c a t e d and students were t o l d that the o p t i o n was c o r r e c t because i t was the same as and d i f f e r e n t from the t h i r d analogy term as the second term was from the f i r s t . The students were then asked to s o l v e the three remaining sample a n a l o g i e s ; feedback was provided and questions were answered f o r the sample items. The 24 analogy booklets were then administered. .Students were reminded that they were not expected to complete a l l of the a n a l -o g i e s , but to work as w e l l as they could w i t h i n the a l l o t t e d time of 64 seconds. The s e s s i o n was to take approximately 1 hour. No feedback was given f o r the b o o k l e t s . Despite the success of t h i s p i l o t procedure w i t h other c h i l d r e n i n grades 2, 4, and 6 reported by Sternberg and R i f k i n (1979), the l a c k of understanding and confusion observed i n the group of 35 students d i c -tated a r e v i s i o n of the procedure. 57 A number of problems were i d e n t i f i e d : 1. Students d i d not understand the goal of the task even a f t e r comple-t i o n of the sample items.; 2. students found the answer sheets confusing; 3. one hour was i n s u f f i c i e n t time to complete a l l 24 b o o k l e t s . Only ten were completed i n the f i r s t s e s s i o n ; 4. the group was too l a r g e to permit the experimenter to deal w i t h questions i n d i v i d u a l l y ; and 5. the group was too l a r g e f o r : the experimenter to monitor behavior and prevent d i s r u p t i o n s . In order to reduce the task r e l a t e d confusion, the t r a i n i n g , or p r a c t i c e s e s s i o n i n the f i r s t hour was augmented, to in c r e a s e f a m i l i a r -i z a t i o n w i t h the task and m a t e r i a l s . The time problem was solved by a l l o t t i n g two 1-hour sessions f o r completion of the 24 bo o k l e t s . Group s i z e was reduced to al l o w f o r more i n d i v i d u a l a t t e n t i o n to questions and to permit b e t t e r management of the students. And, to reduce the memory demands of the task, the a t t r i b u t e s and t h e i r values were l i s t e d on the classroom blackboard. P i l o t Study: Revised Procedure The f i r s t s e s s ion of the r e v i s e d procedure was p i l o t - t e s t e d on a second group of 15 f o u r t h grade students. Since the procedure f o r se s s i o n 2 was very s i m i l a r to se s s i o n 1, i t was not p i l o t - t e s t e d . Again, the students were asked to p a r t i c i p a t e i n a research p r o j e c t which was an attempt to f i n d out how c h i l d r e n l e a r n at school and were reassured that the a c t i v i t i e s were not i n any way r e l a t e d to t h e i r school grades. They were then t o l d the a c t i v i t i e s i n v o l v e d cartoon f i g u r e s (Schematic P i c t u r e A n a l o g i e s ) , but before beginning they 58 had to l e a r n how to do the a c t i v i t i e s . Each student was given two sample analogy booklets numbered 1 and 2, answer sheets, and a p e n c i l . The sample items were a l s o d i s p l a y e d on the overhead p r o j e c t o r . The l i s t of r e l e v a n t a t t r i b u t e s and t h e i r values were e l i c i t e d through questioning and w r i t t e n on the board where i t remained i n view f o r the d u r a t i o n of the s e s s i o n . Next the goal of the analogy was introduced, to choose the c o r r e c t o p t i o n to complete the analogy. Students were t o l d : "Look at the f i r s t two clowns. How are they the same? How are they d i f f e r e n t ? Now look at the t h i r d clown, t h i s one. You must choose a partner f o r t h i s clown. But h i s partner must be the same as and d i f f e r e n t from him (clown 3) i n the same ways as the f i r s t two clowns were the same and d i f f e r e n t . " Next, the students were shown how to record t h e i r chosen op t i o n on the answer sheets. Feedback was given. The f i r s t three pages of booklet 1 were completed i n t h i s manner, and the experimenter d e a l t w i t h any confusion r e l a t e d to the task and ensured that students were re c o r d -ing t h e i r responses p r o p e r l y . The second sample booklet was used to introduce the timed nature of the task. Students were t o l d they had 64 seconds to work on a book-l e t but that accuracy, and not speed, was important. F o l l o w i n g the com-p l e t i o n of booklet 2, any f u r t h e r questions were d e a l t w i t h . The p r a c t i c e s e s s i o n took approximately 25 minutes. The students then worked on the f i r s t nine analogy booklets i n t h e i r set f o r the remainder of the hour. No problems were observed using these r e v i s e d procedures. Main Data C o l l e c t i o n Data were c o l l e c t e d from nine c l a s s e s . Classes were u s u a l l y d i v i d e d i n t o two groups f o r t e s t i n g . The smallest group t e s t e d 59 co n s i s t e d of 11 students and the l a r g e s t group had 22 students. The sessions were conducted i n the school l i b r a r y , an empty classroom, or the s t a f f room. Teachers were not present during e i t h e r s e s s i o n . The f i r s t s e s s i o n , which l a s t e d f o r 1 hour, c o n s i s t e d of an i n t r o -d u c t i o n to the m a t e r i a l s and task followed by a d m i n i s t r a t i o n of 9 of the 24 timed analogy booklets. Timing was done by the experimenter w i t h a stopwatch. The second s e s s i o n , which l a s t e d approximately 40 minutes, con-s i s t e d of a b r i e f review of the a t t r i b u t e s and values which were again l i s t e d on the board. Next the goal of the ta s k , task i n s t r u c t i o n s , and response format were reviewed. Then the students completed the remain-ing 15 b o o k l e t s . Design Dependent V a r i a b l e s Scoring. Each analogy item was scored 1 i f c o r r e c t , 0 i f i n c o r r e c t . Items not attempted were not scored. The c o r r e c t o p t i o n was that which completed the second h a l f of the analogy so that the A to B term r e l a t i o n was the same as the C to D r e l a t i o n , and i n the same d i r e c t i o n . Three scores were then derived f o r each of the 24 analogy b o o k l e t s : number of items answered c o r r e c t l y i n a booklet (maximum = 16); number of items completed i n a boo k l e t , both c o r r e c t and i n c o r r e c t (maximum = 16); and number of items i n c o r r e c t (maximum = 16). These three scores were used to c a l c u l a t e two lat e n c y scores and an e r r o r r a t e score f o r each subject on each booklet. Dependent v a r i a b l e 1: l a t e n c y c o r r e c t . The score f o r number of items answered c o r r e c t l y i n a booklet was used to c a l c u l a t e the f i r s t dependent v a r i a b l e , s o l u t i o n l a t e n c y f o r c o r r e c t l y answered items. The 60 time a l l o t t e d f o r a boo k l e t , 64 seconds, was d i v i d e d by the number of c o r r e c t items on a booklet. Any student w i t h a score of 0 f o r number of c o r r e c t items on a booklet was a u t o m a t i c a l l y assigned a score of 1, to permit d i v i s i o n . In many s t u d i e s , students w i t h worse than chance per-formance are dropped. In t h i s study, a major emphasis was the i n v e s t i -g a t i o n of the performance of the low a b i l i t y students, thus d i s c a r d i n g these subjects w i t h 0 c o r r e c t scores was u n j u s t i f i e d . In l i e u of dropping the students, the c o r r e c t i o n was made. This c o r r e c t i o n was only necessary f o r three students and only on dependent v a r i a b l e 1. 64 Thus, the maximum late n c y f o r c o r r e c t items was - j - = 64 seconds per 64 c o r r e c t item. The minimum lat e n c y was -77- = 4 seconds per c o r r e c t lb item., Dependent v a r i a b l e 2; l a t e n c y completed. The second raw score was the number of items completed i n a b o o k l e t , both c o r r e c t and i n c o r -r e c t . This score'was used to c a l c u l a t e the second dependent v a r i a b l e , s o l u t i o n l a t e n c y f o r a l l answered items. This score was c a l c u l a t e d by d i v i d i n g 64 seconds by the t o t a l number of completed items. As f o r s o l u t i o n l a t e n c y f o r c o r r e c t items, the maximum l a t e n c y f o r completed 64 items was — = 64 seconds per completed item and the minimum l a t e n c y 64 f o r completed items was -j^r = 4 seconds per completed item. Dependent v a r i a b l e 3: e r r o r r a t e . The t h i r d raw. score was the number of items i n c o r r e c t i n a booklet. This score was used to c a l c u -l a t e the t h i r d dependent v a r i a b l e , e r r o r r a t e . This v a r i a b l e was com-puted by d i v i d i n g the number of i n c o r r e c t items by the t o t a l number of items completed i n a booklet. The maximum score was 1.00 and the m i n i -mum score was 0.00. 61 Parameter E s t i m a t i o n and Models The next step i n the a n a l y s i s c o n s i s t e d of d e r i v i n g component scores from the booklet scores. Component scores were derived by decomposing t o t a l time spent on an analogy item i n t o estimates of the time spent on each component. This was accomplished through m u l t i p l e l i n e a r r e g r e s s i o n using the complete l e a s t squares approach. Seven models were hypothesized by Sternberg and R i f k i n (1979) to account f o r performance on p i c t o r i a l analogy problems (Tables.1, 2). Table 4 represents the components i n the seven models f o r which l a t e n c y and e r r o r estimates were der i v e d . Some of the component estimates were confounded due to the nature of the task m a t e r i a l s (see pp. 66-68). Encoding and response component estimates were confounded i n Models 1 to 4 and Model 1M. Inference and a p p l i c a t i o n component estimates were con-founded i n Models, 1, 4, 1M, and 4M. The b a s i s of the componential method of a n a l y s i s was that response times (or e r r o r r a t e s ) f o r each bo o k l e t , i . e . , the c r i t e r i o n s c o r e s , were p r e d i c t e d from independent v a r i a b l e s r e p r e s e n t i n g v a r i a t i o n s i n the com-p l e x i t y of analogy items i n the 24 b o o k l e t s . C r i t e r i o n v a r i a b l e s : booklet scores. The c r i t e r i o n scores were generated by c o l l a p s i n g booklet scores on a dependent, v a r i a b l e across subjects at each a b i l i t y l e v e l . The data frame used i s summarized i n Table 5. There were 20 students i n each group. Each of those students had 24 l a t e n c y c o r r e c t scores, 24 l a t e n c y completed scores, and 24 e r r o r r a t e scores; a score f o r each of 24 booklets on the 3 dependent v a r i -a bles. The c r i t e r i o n scores f o r the regressions were not s u b j e c t s ' scores,^but booklet scores. The 20 subjects w i t h i n each group served as r e p l i c a t i o n s to ensure the r e l i a b i l i t y of each booklet score. Scores 62 Table 4 Models f o r Regression Model Components 1M 2-3M 4M *encoding-response Y = bo *encoding-response Y = b 0 *encoding-response Y = bo *encoding-response Y = b 0 *encoding-response Y = b 0 response Y = b 0 response *exhaustive i n f e r e n c e -a p p l i c a t i o n + b i X i exhaustive exhaustive i n f e r e n c e mapping exhaustive mapping + b2X2 s e l f - t e r m i n a t i n g a p p l i c a t i o n •+ b i X i + b2X2 exhaustive s e l f - t e r m i n a t i n g i n f e r e n c e mapping + b i X i + b2X2 * s e l f - t e r m i n a t i n g i n f e r e n c e -a p p l i c a t i o n + b i X i ^exhaustive i n f e r e n c e -a p p l i c a t i o n + b ^ i exhaustive s e l f - t e r m i n a t i n g i n f e r e n c e a p p l i c a t i o n + b 3 X 3 s e l f - t e r m i n a t i n g a p p l i c a t i o n + b 3 X 3 s e l f - t e r m i n a t i n g mapping + b2X2 + b i X i + b 3 X 3 Y = b 0 * s e l f - t e r m i n a t i n g i n f e r e n c e -a p p l i c a t i o n + b i X i s e l f - t e r m i n a t i n g encoding s e l f - t e r m i n a t i n g encoding + b^Xtt * = confounded components 63 Table 5 Data M a t r i x Used to C a l c u l a t e C r i t e r i o n V a r i a b l e Scores Booklet 1 Booklet 2 ... Booklet 24 Group Subject DVX DV 2 DV 3 DV]. DV 2 DV 3 DVX DV 2 DV 3 1 2 Low 20 20 20 20 Sum EDVi EDV2 EDV3 n=l n=l n=l Mean EDVx EDV2 EDV3 ( C r i t e r i o n V a r i a b l e ) 20 20 20 Mean Mean Mean lat e n c y l a t e n c y e r r o r c o r r e c t completed r a t e 1 2 Average 20 Sum Mean ( C r i t e r i o n V a r i a b l e ) 1 2 High ' 20 Sum Mean ( C r i t e r i o n V a r i a b l e ) on each booklet were averaged across subjects w i t h i n a b i l i t y l e v e l f o r each dependent v a r i a b l e , to y i e l d three sets ,of 24 mean booklet scores: mean la t e n c y c o r r e c t scores f o r booklets 1 to 24, mean la t e n c y com-p l e t e d scores f o r booklets 1 to 24, and mean e r r o r r a t e scores f o r book-l e t s 1 to 24. P r e d i c t o r v a r i a b l e s . Each of the 24 booklets was s t r u c t u r e d so that the complexity (defined as the number of a t t r i b u t e - v a l u e t r a n s -formations between r e l e v a n t analogy terms) v a r i e d s y s t e m a t i c a l l y across the b o o k l e t s , as shown i n Table 6. Each column represents the number of a t t r i b u t e value transformations across the 24 analogy booklets f o r p a r t i c u l a r terms. V a r i a t i o n i n complexity of these columns, when entered as a p r e d i c t o r v a r i a b l e i n the r e g r e s s i o n , should p r e d i c t v a r i -a t i o n i n the o v e r a l l booklet score i f that component was used i n s o l u -t i o n . For example, the numbers i n column 1 of Table 6 represent the 'distances' (numbers of transformations) between the A and B terms of the 24 analogy b o o k l e t s . The values range from one to three. This column was used as the p r e d i c t o r v a r i a b l e to estimate exhaustive i n f e r e n c e l a t e n c i e s and error, r a t e . Thus i n f e r e n c e l a t e n c y and d i f f i c u l t y , and consequently t o t a l l a t e n c y and d i f f i c u l t y should i n c r e a s e as the number of A to B values transformed i n c r e a s e s , i f exhaustive i n f e r e n c e i s used i n s o l u t i o n . There are two v a r i e t i e s of estimates, those f o r e x h a u s t i v e l y executed components and those f o r components executed i n a s e l f -t e r m i nating mode. Exhaustive component estimates were based on the o b j e c t i v e numbers of a t t r i b u t e value transformations. For example, exhaustive i n f e r e n c e l a t e n c y and d i f f i c u l t y were defined as a f u n c t i o n 65 Table 6 P r e d i c t o r V a r i a b l e s f o r Regression A p p l i c a - D = Analogy Inference Mapping t i o n UT M u l t i -Book A-B A-C C- DT Encoding Encoding D F p l i e r 1 2 3 4 5 6 7 8 9 10 11 12 e St e St e St e St e* st+ (h) q 20-4h 1 1 .25 3 .75 1 .25 5 1.25 3 .75 0 5/20 2 1 .63 2 1.25 1 .63 5 3.13 3 1.88 3 5/8 3 1 .25 1 .25 1 .25 5 1.25 3 .75 0 5/20 4 1 .63 3 1.88 1 .63 5 3.13 3 1.88 3 5/8 5 1 .63 1 .63 1 .63 5 3.13 3 1.88 3 5/8 6 1 .42 1 .42 1 .42 5 2.08 3 1.25 2 5/12 7 1 .42 2 .83 1 .42 5 2.08 3 1.25 2 5/12 8 1 .25 2 .50 1 .25 5 1.25 3 .75 0 5/20 9 1 .31 2 .63 1 .31 5 1.56 3 .94 1 5/16 10 1 .42 3 1.25 1 .42 5 2.08 3 1.25 2 5/12 11 1 .31 1 .31 1 .31 5 1.56 3 .94 1 5/16 12 1 .31 3 .94 1 .31 5 1.56 3 .94 1 5/16 13 2 .83 1 .42 2 .83 5 2.08 3 1.25 2 5/12 14 2 .50 1 .25 2 .50 5 1.25 3 .75 0 5/20 15 2 .63 1 .31 2 .63 5 1.56 3 .94 1 5/16 16 2 .50 2 .50 2 .50 5 1.25 3 .75 0 5/20 17 2 1.25 2 1.25 2 1.25 5 3.13 3 1.88 3 5/8 18 2 1.25 1 . .63 2 1.25 5 3.13 3 1.88 3 5/8 19 2 .83 2 .83 2 .83 5 2.08 3 1.25 2 5/12 20 2 .63 2 .63 2 .63 5 1.56 3 .94 1 5/16 21 3 .75 1 .25 3 .75 5 1.25 3 .75 0 5/20 22 3 1.88 1 .63 3 1.88 5 3.13 3 1.88 3 5/8 23 3 .94 1 .31 3 .94 5 1.56 3 .94 1 5/16 24 3 1.25 1 .42 3 1.25 5 2.08 3 1.25 2 5/12 Mean 1.6.7 , r67 1.67.';.67. • 1.67 .67 5 2.01 3 1.21 * p a r t i a l l y exhaustive t p a r t i a l l y s e l f - t e r m i n a t i n g Note: e = exhaustive execution st = s e l f - t e r m i n a t i n g execution of the number of a t t r i b u t e values transformed from the A to B analogy terms. These values f o r the 24 booklets are l i s t e d i n column 1 of Table 6, and ranged from one to three. Column 1 was the p r e d i c t o r v a r i -able f o r exhaustive i n f e r e n c e estimates i n a l l seven models. Exhaustive mapping lat e n c y and d i f f i c u l t y were defined as a func-t i o n of the number of a t t r i b u t e values transformed from A to C analogy terms. These values f o r each bo o k l e t , l i s t e d i n column 3 of Table 6, ranged from one to three. Column 3 was the p r e d i c t o r v a r i a b l e f o r exhaustive mapping component estimates i n a l l seven models. Exhaustive a p p l i c a t i o n l a t e n c y and d i f f i c u l t y were defined as a f u n c t i o n of the number of a t t r i b u t e values transformed between the C and E>True terms (always equal to the A to B d i s t a n c e ) . Column 5 of Table 6, summarizes these transformations across the 24 b o o k l e t s . The number of a t t r i b u t e values transformed from C to the c o r r e c t answer o p t i o n had to be equal to the number of values transformed from A to B, to permit cor-r e c t completion of the analogy. Thus columns 1 and 5 of Table 6 are i d e n t i c a l . Encoding was defined as the number of analogy terms ( f i g u r e s ) to be encoded. Since i n exhaustive encoding a l l of the.terms are encoded, column 7 of Table 6 represents the values f o r the p r e d i c t o r v a r i a b l e f o r exhaustive encoding. The value i s f i v e f o r a l l 24 b o o k l e t s . In order f o r a component to be independently estimated, i t must be represented by a p r e d i c t o r v a r i a b l e which v a r i e s across b o o k l e t s . Therefore exhaustive encoding and response (which i s a l s o constant across booklets) components were confounded and estimated as the r e g r e s s i o n constant i n Models 1 to 4 and i n Model 1M (see Table 4 ) . Independent or p r e d i c t o r v a r i a b l e s f o r s e l f - t e r m i n a t i n g components are a l s o based on the number of a t t r i b u t e - v a l u e transformations but i n a d d i t i o n they are a. f u n c t i o n of the d i s t a n c e between the two answer op t i o n s , D and D . The fewer values the options have i n common, the e a s i e r i t i s to d i s t i n g u i s h the c o r r e c t o p t i o n when i n a s e l f - t e r m i n a t i n g mode. Columns i n Table 6 rep r e s e n t i n g p r e d i c t o r v a r i a b l e s f o r s e l f -t e r m inating components were derived by m u l t i p l y i n g the p r e d i c t o r values f o r the corresponding exhaustive component by the f o l l o w i n g m u l t i p l i e r (see column 12, Table 6): N + 1 [N(N - h + 1)] ' where N = the number of a t t r i b u t e s that could be encoded (always f o u r ) , and h = the number of D„ values that were the same as D 'values (column r I 11). Thus the p r e d i c t o r v a r i a b l e (column 2) f o r s e l f - t e r m i n a t i n g i n f e r -ence was derived by m u l t i p l y i n g column 1 by column 12. S e l f - t e r m i n a t i n g mapping was estimated by using column 4 as a p r e d i c t o r v a r i a b l e , and s e l f - t e r m i n a t i n g a p p l i c a t i o n estimates were based on column 6, which was i d e n t i c a l to column 2. When encoding was s e l f - t e r m i n a t i n g (Models 2-3M and 4M, Table 4 ) , i t was p o s s i b l e to d e r i v e separate estimates f o r encoding l a t e n c y and d i f f i c u l t y . In Model 4M, encoding was s e l f - t e r m i n a t i n g f o r a l l f i v e terms of the analogy, thus column 8 i n Table 6, the p r e d i c t o r v a r i a b l e f o r s e l f - t e r m i n a t i n g encoding, was generated b y . m u l t i p l y i n g column 7 by column 12. This created v a r i a t i o n across booklets whereas column 7 had no such v a r i a t i o n . In Model 2-3M, encoding was hypothesized to be exhaustive f o r the 68 f i r s t terms and s e l f - t e r m i n a t i n g f o r the l a s t three terms. The f i r s t two terms were thus confounded w i t h the response component, but the p r e d i c t o r v a r i a b l e f o r encoding f o r the l a s t three terms was column 10 of Table 6, computed by m u l t i p l y i n g column 9 by the s e l f - t e r m i n a t i n g m u l t i p l i e r , column 12. Because the p r e d i c t o r v a r i a b l e s f o r exhaustive i n f e r e n c e and exhaustive a p p l i c a t i o n were i d e n t i c a l (columns 1 and 5 i n Table 6 ) , when a model hypothesized both exhaustive i n f e r e n c e and a p p l i c a t i o n , the component estimates were confounded. Model 1 and 1M i n Table 4, are examples of t h i s confounding. S i m i l a r l y , the p r e d i c t o r v a r i a b l e s f o r s e l f - t e r m i n a t i n g i n f e r e n c e and a p p l i c a t i o n were i d e n t i c a l (columns 2 and 6 of Table 6), so that s e l f - t e r m i n a t i n g i n f e r e n c e and a p p l i c a t i o n e s t i -mates were confounded i n Model 4 and Model 4M i n Table 4. Thus the m u l t i p l e regressions f o r each model i n Table 4 c o n s i s t e d of the c r i t e r i o n scores (mean booklet l a t e n c i e s , and e r r o r r a t e s , see Table 5 ) , and the re l e v a n t p r e d i c t o r v a r i a b l e s from Table 6. What were estimated i n t h i s r e g r e s s i o n procedure were the component c o e f f i c i e n t s . These can be i n t e r p r e t e d as estimates of component l a t e n -c i e s and d i f f i c u l t y . This d i f f e r e d from the usual r e g r e s s i o n case i n that task v a r i a t i o n , and not subject v a r i a t i o n was being p r e d i c t e d . In summary, a b i l i t y , a.three.Mevel f a c t o r (high, average, low) was crossed w i t h task m a t e r i a l s , a repeated measures f a c t o r c o n s i s t i n g of 24 schematic p i c t u r e analogy booklets (see Table 5). At each of three a b i l i t y l e v e l s (low, average, h i g h ) , three sets of'24 c r i t e r i o n scores were derived by c o l l a p s i n g booklet scores across the 20 subjects w i t h i n each a b i l i t y l e v e l . These sets of 24 c r i t e r i o n scores f o r each group were entered i n t o seven r e g r e s s i o n s , one f o r each hypothesized model f o r 69 a t o t a l of 3 x 3 x 7 = 63 regressions ( a b i l i t y x set of c r i t e r i o n scores x models = 63). Once each model was f i t t e d to the data, the model which best accounted f o r task variance was determined f o r each a b i l i t y l e v e l on a l l three c r i t e r i o n v a r i a b l e s . The c r i t e r i a f o r s e l e c t i o n of the best model w i l l be discussed i n the next chapter together w i t h the presenta-t i o n of the r e s u l t s . The program used i n the r e g r e s s i o n analyses was UBC TRP (Le & T e n i s c i , 1978), and was run on the Amdahl 470 V/6, Model I I computer under the Michigan Terminal System (MTS). CHAPTER V RESULTS P r e l i m i n a r y A n a l y s i s Before beginning the r e g r e s s i o n analyses, the c r i t e r i o n v a r i a b l e s described i n Chapter IV, Table 5, were evaluated to decide whether or not a l l three c r i t e r i o n v a r i a b l e s should be included i n subsequent analyses. The f i r s t step was to ensure that the data were an a l y z a b l e ; that i s , to determine whether there was s u f f i c i e n t v a r i a n c e across the mean booklet scores to permit r e g r e s s i o n a n a l y s i s . The second step i n v o l v e d examina-t i o n of the variance-covariance matrices of the c r i t e r i o n v a r i a b l e s f o r each a b i l i t y group. I f the covariances of the three v a r i a b l e s were s i m i l a r , then there would be no need to analyze a l l three c r i t e r i o n v a r i a b l e s i n a group. Subsequent analyses would t h e r e f o r e be performed on only one of the three c r i t e r i o n v a r i a b l e s . The three c r i t e r i o n v a r i -ables at each a b i l i t y l e v e l were c a l c u l a t e d as described i n Chapter IV, (see Table 5). The three sets of scores were: mean la t e n c y c o r r e c t , mean la t e n c y completed, and mean e r r o r r a t e scores f o r the 24 analogy booklets at each a b i l i t y l e v e l . The means, standard d e v i a t i o n s , ranges, and variance of the three c r i t e r i o n v a r i a b l e s at each a b i l i t y l e v e l are summarized i n Table 7. Insp e c t i o n of c r i t e r i o n v a r i a b l e 3, mean e r r o r r a t e , revealed that i n 70 Table 7 D e s c r i p t i v e S t a t i s t i c s : C r i t e r i o n V a r i a b l e Group C r i t e r i o n V a r i a b l e Mean SD V a r i -ance Range Low 1 14.51 3.52 12.39 9.58-23.71 2 8.45 1.73 2.99 6.74-13.73 3 .34 .07 .00 .22- .48 Average 1 10.51 2.83 8.01 6.41-18.43 2 7.44 1.18 1.39 5.76- 9.44 3 .17 .07 .00 .08- .33 High 1 7.71 1.57 2.46 5.49-11.88 2 7.42 1.35 1.82 5.34-10.71 3 .03 .02 .00 .00- .08 Note: These values were rounded to two decimal pl a c e s . Values of .00 were r e s u l t s of rounding. 72 a l l three a b i l i t y groups there was i n s u f f i c i e n t v a r i a n c e to permit subse-quent analyses to be c a r r i e d out. The remaining c r i t e r i o n v a r i a b l e s , mean l a t e n c y c o r r e c t and mean lat e n c y completed, were included i n r e g r e s s i o n analyses f o r a l l three a b i l i t y groups. The second step i n the p r e l i m i n a r y a n a l y s i s , examination of the variance-covariance m a t r i c e s , was not necessary, given the d e c i s i o n to drop v a r i a b l e 3 i n subsequent analyses. Regression A n a l y s i s The r e s u l t s of the r e g r e s s i o n analyses conducted f o r each model and which were used to determine model preference and values f o r component l a t e n c y estimates are presented separately f o r each a b i l i t y group and each c r i t e r i o n v a r i a b l e which was analyzed. Determination of Model Preference The seven models hypothesized by Sternberg and R i f k i n (1979) f o r the s o l u t i o n of p i c t o r i a l analogies were evaluated i n two phases. The models described i n Table 4 are reproduced i n Table 8 f o r reference. The f i r s t phase i n v o l v e d the e v a l u a t i o n of the two sets of models, models 1 to 4 and 1M to 4M. These two sets of models d i f f e r e d i n that a) mapping components were included i n Models 1 to 4, but not 1M to 4M, and b) encoding was exhaustive i n Models 1 to 4, but could be s e l f -t e r m i nating i n Models 1M to 4M. Thus, i f mapping estimates were not s i g n i f i c a n t i n Models 1 to 4, the models were r e j e c t e d , f o r unless a component occupied n o n - t r i v i a l time, i t was assumed that i t was not used i n s o l u t i o n . Further evidence f o r the r e j e c t i o n of Models 1 to 4 would be the s i g n i f i c a n c e of s e l f - t e r m i n a t i n g encoding estimates i n the second set of models. Table 8 Models f o r Regression Model Components 1M *encoding-response Y = bu *encoding-response Y = b 0 *encoding-response Y = bo *encoding-response Y = bo *encoding-response Y = b 0 2-3M response Y = bo 4M response *exhaustive i n f e r e n c e -a p p l i c a t i o n + bi X i exhaustive exhaustive in f e r e n c e mapping exhaustive mapping + b 2 X 2 s e l f - t e r m i n a t i n g a p p l i c a t i o n + b i X i + b z X 2 exhaustive s e l f - t e r m i n a t i n g i n f e r e n c e mapping + b i X i + b2X2 * s e l f - t e r m i n a t i n g i n f e r e n c e -a p p l i c a t i o n + b i X i ^exhaustive i n f e r e n c e -a p p l i c a t i o n + b i X i exhaustive s e l f - t e r m i n a t i n g i n f e r e n c e a p p l i c a t i o n + b 3 X 3 s e l f - t e r m i n a t i n g a p p l i c a t i o n + b 3 X 3 s e l f - t e r m i n a t i n g mapping + b2X2 + b i X i b 3 X 3 * s e l f - t e r m i n a t i n g i n f e r e n c e -a p p l i c a t i o n s e l f - t e r m i n a t i n g encoding s e l f - t e r m i n a t i n g encoding Y = b 0 + b i x i + bi+Xit * = confounded components 74 In the second phase, the remaining models were evaluated i n terms of the f o l l o w i n g s i x interdependent c r i t e r i a : a) Values of R 2 i n competing models. b) S i g n i f i c a n c e of i n c r e a s e i n R 2. Because some models hypothesized one more component than a competing model, the s i g n i f i c a n c e of the increase i n R due to the a d d i t i o n a l component was evaluated. I f the increase was not s i g n i f i c a n t , then the a d d i t i o n a l component was considered not necessary, and the more parsimonious model was pre^ f e r r e d . c) S i g n i f i c a n c e of r e g r e s s i o n c o e f f i c i e n t s . d) Values of r e g r e s s i o n F f o r the competing models. The F r a t i o takes i n t o account the number of p r e d i c t o r v a r i a b l e s , i n an equation. I f an a d d i t i o n a l p r e d i c t o r v a r i a b l e increased the value of F t h i s i n d i -cated support f o r that model. I f the a d d i t i o n a l p r e d i c t o r v a r i a b l e i n a model decreased the value of F, then the more parsimonious model was p r e f e r r e d . e) The p r o p o r t i o n of decrease i n the standard e r r o r of estimate due to an a d d i t i o n a l component i n competing models. I f the decrease was s m a l l , the a d d i t i o n a l parameter was considered unwarranted and the parsimonious model was given p r i o r i t y . f ) The nature of the component estimates. I f a c o e f f i c i e n t was negative, but small and not s t a t i s t i c a l l y s i g n i f i c a n t , the negative value was a t t r i b u t e d to sampling e r r o r and i n t e r p r e t e d as n o n s i g n i f -i c a n t . I f a negative c o e f f i c i e n t was l a r g e and/or s t a t i s t i c a l l y s i g n i f i c a n t , the models were r e j e c t e d as t h i s was a s i g n that the assumption of s e r i a l processing and the l i n e a r r u l e f o r component combination may have been v i o l a t e d . 75 C r i t e r i o n V a r i a b l e 1: Latency Correct Low a b i l i t y . The raw r e g r e s s i o n c o e f f i c i e n t s and i n d i c e s of model f i t f o r the seven models on lat e n c y c o r r e c t scores f o r the low a b i l i t y students are summarized i n Table 9. Using the phase 1 c r i t e r i a discussed above, Models 1 to 4 were r e j e c t e d . F i r s t , none of the map-ping l a t e n c y estimates d i f f e r e d s i g n i f i c a n t l y from zero i n Models 1 to 4. Second, the s e l f - t e r m i n a t i n g encoding latency estimate i n Model 2-3M was s i g n i f i c a n t (p < .01). Models 1M, 2-3M, and 4M were then evaluated using the phase 2. c r i t e r i a . The f i r s t c r i t e r i o n was the values of R 2 i n competing models. Model 2-3M accounted f o r the l a r g e s t p r o p o r t i o n of var i a n c e (R 2 = .54), followed by Model 4M (R 2 = .34), and Model 1M (R 2 = .28). The second c r i t e r i o n i n v o l v e d the s i g n i f i c a n c e of the increase i n R 2 due to an a d d i t i o n a l parameter i n one of the two models evaluated. Since i n f e r e n c e and a p p l i c a t i o n were unconfounded i n Model 2-3M, but were confounded i n Model 4M, i t was p o s s i b l e to evaluate the change i n R between Model 2-3M and Model. 4M. The d i f f e r e n c e was s i g n i f i c a n t (^1,20 = 9.33, p < .01), thus the a d d i t i o n a l component i n Model 2-3M was warranted. Model 4M had an a d d i t i o n a l component over Model 1M because encoding and response estimates i n Model 4M were unconfounded. The change i n R 2 between Model 4M and 1M was not s i g n i f i c a n t ( F i ^ l = 2.00, p > .05), thus Model 1M and 2-3M were favored on t h i s c r i t e r i o n . The t h i r d c r i t e r i o n , the s i g n i f i c a n c e of the r e g r e s s i o n parameters, i n d i c a t e d Model 1M and 4M were p r e f e r r e d over Model 2-3M. Inference-a p p l i c a t i o n and encoding-response c o e f f i c i e n t s were s i g n i f i c a n t i n Model 1M. Inference and s e l f - t e r m i n a t i n g encoding c o e f f i c i e n t s were s i g n i f -i c a n t i n Model 2-3M but a p p l i c a t i o n and response c o e f f i c i e n t s were not. 76 Table 9 Model F i t s f o r Low A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 Component Estimates I n f . - E n c -Model Inf . Appl. Appl. Map. Enc. Resp. Resp. R 2 F a est 1 2.47* .08 10.27** .28 4.12* 3.14 2 1.00 3.67 .08 10.26** .35 3.55* 3.04 3 1.85 2.33 1.77 8.68** .38 4.10* 2.98 4 5.01** .35 10.92** .34 5.48* 3.01 1M 2.43** 10.46** .28 8.48** 3.07 2-3M 6.19** -9.39 8.68** 0.01 .54 7.96** 2.56 4M 4.34* .63 10.33** .34 5.48* 2.99 Note: Estimates are i n terms of seconds spent on a component per analogy item. * = p < .05 ** = p < .01 77 F i n a l l y , i n f e r e n c e - a p p l i c a t i o n and response c o e f f i c i e n t s were s i g n i f i c a n t i n Model 4M but s e l f - t e r m i n a t i n g encoding was not. The f o u r t h c r i t e r i o n was the value f o r the r e g r e s s i o n F. In t h i s case, the F f o r Model 2-3M (F = 7.96) was higher than that f o r Model 4M (F = 5.48). The F f o r Model 1M (F =8.48), was higher than that f o r Model 2-3M or 4M. Despite these d i f f e r e n c e s , a l l three F r a t i o s were s i g n i f -i c a n t (p < .01), so no model was designated as p r e f e r r e d on t h i s c r i t e r i o n . The p r o p o r t i o n of decrease i n the standard e r r o r of estimate (a est) from Model 4M to Model 2-3M was .15, and the decrease from Model 1M to 4M was .03. Neither decrease was.considered s u f f i c i e n t to warrant the a d d i t i o n a l component, t h e r e f o r e Models 1M and 4M were p r e f e r r e d . F i n a l l y , Model 2-3M had a negative c o e f f i c i e n t f o r the s e l f - t e r m i n -a t i n g a p p l i c a t i o n component, but t h i s c o e f f i c i e n t was not s i g n i f i c a n t and thus was a t t r i b u t e d to random e r r o r . Neither Model 1M nor Model 4M had negative component c o e f f i c i e n t s . Model 2-3M was r e j e c t e d a f t e r being evaluated on the preceding c r i t e r i a . Model 1M was designated as m a r g i n a l l y p r e f e r r e d over Model 4M f o r the l a t e n c y c o r r e c t data f o r low a b i l i t y students. However, i n subsequent analyses of c r i t e r i o n v a r i a b l e 1, both Model 1M: and 4M were evaluated wherever p o s s i b l e due to the equivocal nature of the l a t e n c y c o r r e c t data i n t h i s group. In two of the subsequent analyses Model 4M was used as the p r e f e r r e d model to maintain c o m p a r a b i l i t y across the groups. This was only f o r convenience of those two analyses, and was no i n d i c a t i o n that Model 4M was a b e t t e r model than 1M f o r e x p l a i n i n g the low group's la t e n c y c o r r e c t data. Average a b i l i t y . The same c r i t e r i a were a p p l i e d to the l a t e n c y cor-r e c t data f o r average a b i l i t y students, presented i n Table 10. Models 78 Table 10 Model F i t s f o r Average A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 Component Estimates I n f . - E n c -Model Inf . Appl. Appl. Map. Enc. Resp. Resp. R 2 F a est 1 2.04* -.37 7.74** .37 6.17** 2.36 2 .43 4.01* -.37 7.74** .51 6.94** 2.13 3 .69 3.89 .15 6.65** .50 6.68** 2.14 4 4.90** -.38 7.49** .49 10.21** 2.11 1M 2.22** 6.81** .36 12.41** 2.32 2-3M 2.67 -1.11 3.40 2.71 .55 8.13** 2.05 4M 4.81** .07 7.16** .49 10.21** 2.12 Note: Estimates are i n terms of seconds spent on a component per analogy item. * = p < .05 ** = p < .01 79 1 to 4 were again r e j e c t e d as estimates f o r the mapping component were not s i g n i f i c a n t i n any model. In terms of values of R , the f i r s t c r i t e r i o n , Model 2-3M was p r e f e r r e d (R 2 = .55), followed by Model 4M (R 2 = .49), and Model 1M (R 2 =.36). The d i f f e r e n c e i n R 2 between Models 2-3M and 4M was not s i g n i f i c a n t , i n d i c a t i n g the a d d i t i o n a l parameter i n Model 2-3M was unwarranted (Fl,20 = 2.67, p > .05). In comparing the d i f f e r e n c e i n R between Models 4M and 1M, the a d d i t i o n a l parameter was warranted due to the s i g n i f i c a n t d i f f e r e n c e i n R 2 ( F i 21 = 5.42, p < .05). Model 4M was p r e f e r r e d t h e r e f o r e , on the second c r i t e r i o n . In terms of the t h i r d c r i t e r i o n , the s i g n i f i c a n c e of the regres-s i o n c o e f f i c i e n t s , Model 1M was the p r e f e r r e d model. None of the com-ponent estimates were s i g n i f i c a n t i n Model 2-3M. The i n f e r e n c e -a p p l i c a t i o n and response c o e f f i c i e n t s were s i g n i f i c a n t i n Model 4M, but s e l f - t e r m i n a t i n g encoding was not. A l l of the component estimates were s i g n i f i c a n t i n Model 1M. The f o u r t h c r i t e r i o n was the values of r e g r e s s i o n F. Again, a l l three F r a t i o s were s i g n i f i c a n t , so the models were equivalent on t h i s c r i t e r i o n . The f i f t h c r i t e r i o n , p r o p o r t i o n of decrease i n the standard e r r o r of estimate, i n d i c a t e d that Model 1M was p r e f e r r e d . While the propor-t i o n of decrease from Model 4M to Model 2-3M (.04) i n d i c a t e d the a d d i -t i o n a l parameter i n Model 2-3M was unnecessary, the p r o p o r t i o n of decrease from Model 1M to 4M (.09) i n d i c a t e d the a d d i t i o n a l parameter i n Model 4M was a l s o unnecessary. However, s i n c e Model 4M was p r e f e r r e d on c r i t e r i o n 2 which was a more o b j e c t i v e measure of the value of the 80 a d d i t i o n a l parameter than was c r i t e r i o n 5, the preference of Model 1M on c r i t e r i o n 5 was outweighed by the preference of Model 4M on c r i t e r i o n 2. In terms of the nature of the r e g r e s s i o n c o e f f i c i e n t s , none of the estimates i n Models 1M or 4M were negative. Model 2-3M had a negative estimate ( s e l f - t e r m i n a t i n g a p p l i c a t i o n = -1.11) but the estimate was s m a l l , and a t t r i b u t e d to sampling e r r o r , thus no model was p r e f e r r e d over the others on t h i s c r i t e r i o n . Model 4M and 1M were s i m i l a r on most of the c r i t e r i a , but the i n c r e a s e i n the value of R 2 of Model 4M over 1M was s i g n i f i c a n t . Model 4M thus was designated the p r e f e r r e d model f o r l a t e n c y c o r r e c t data i n the average a b i l i t y group. High a b i l i t y . The l a t e n c y c o r r e c t r e s u l t s f o r high a b i l i t y s t u -dents are summarized i n Table 11. Models 1 to 4 were r e j e c t e d s i n c e only one of the four mapping estimates was s t a t i s t i c a l l y s i g n i f i c a n t , whereas s e l f - t e r m i n a t i n g encoding estimates were s i g n i f i c a n t i n both Models 2-3M and 4M. Model lMwas a l s o r e j e c t e d as i t accounted f o r only 7% of the v a r i a n c e i n the data. Model 2-3M had a higher R 2 than Model 4M (.90 and .89 r e s p e c t i v e l y ) , however t h i s d i f f e r e n c e i n the R 2 values was not s i g n i f i c a n t ( F i ^ O = 2.00, p > .05), so Model 4M was p r e f e r r e d on t h i s c r i t e r i o n . A l l of the r e g r e s s i o n c o e f f i c i e n t s were s i g n i f i c a n t i n Model 4M. The i n f e r e n c e estimate was not s i g n i f i c a n t i n Model 2-3M, thus Model 4M was p r e f e r r e d on the t h i r d c r i t e r i o n . The o v e r a l l r e g r e s s i o n F value was l a r g e r i n Model 4M than i n Model 2-3M, but both F values were s i g n i f i c a n t at the .01 l e v e l , thus no model preference was e s t a b l i s h e d by t h i s c r i t e r i o n . The p r o p o r t i o n of decrease i n the standard e r r o r of estimate from 81 Table 11 Model F i t s f o r High A b i l i t y Group: C r i t e r i o n V a r i a b l e 1 Component Estimates I n f . - Enc.-Model I n f . Appl. Appl. Map. Enc. Resp. Resp. R 2 F o est 1 .53 -.05 6.92** .07 .80 1.59 2 -1.59** 5.28** -.05 6.91** .87 44.62** .61 3 -1.41** 5.05** .31 6.48** .87 44.62** .60 4 3.00** 1.40** 4.77** .75 31.25** .82 1M .55 6.80** .07 1.67 1.55 2-3M -.60 2.88* 1.60* 4.86** .90 60.00** .53 4M 1.54** 1.41** 3.86** .89 89.00** .54 Note: Estimates .are i n terms of seconds spent on a component per analogy item. * = p < .05 ** = p < .01 82 Model 4M to Model 2-3M was .02. This was not s u f f i c i e n t to warrant the a d d i t i o n a l parameter i n Model 2-3M so Model 4M was p r e f e r r e d on t h i s c r i t e r i o n . The nature of the r e g r e s s i o n c o e f f i c i e n t s d i d not lead to any model preference. A l l of the c o e f f i c i e n t s were p o s i t i v e i n Model 4M. Inference was negative i n Model 2-3M but was small (-.60) and thus i n t e r -preted as n o n s i g n i f i c a n t . Model 4M was designated the p r e f e r r e d model f o r the f i r s t c r i t e r i o n v a r i a b l e , l a t e n c y c o r r e c t , f o r high a b i l i t y students. In summary, Model 4M was the p r e f e r r e d model f o r average and high a b i l i t y groups f o r l a t e n c y c o r r e c t data. Model 1M was m a r g i n a l l y pre-f e r r e d over Model 4M i n the low a b i l i t y group. The d e c i s i o n s regarding model preference on t h i s v a r i a b l e were made w i t h greater confidence i n the h i g h a b i l i t y group than i n the low and average a b i l i t y groups. This corresponded w i t h higher values f o r the standard e r r o r of estimate i n the low and average groups than i n the high a b i l i t y group. The r e g r e s s i o n weights estimated i n the p r e f e r r e d models were i n t e r -preted as estimates of the l a t e n c y of a s i n g l e execution of a component f o r one analogy item. For example, i n the average a b i l i t y group, a s i n g l e execution of s e l f - t e r m i n a t i n g i n f e r e n c e - a p p l i c a t i o n component was estimated to take 4.81 seconds of the t o t a l time spent on an item. The s e l f - t e r m i n a t i n g encoding estimate, .07 seconds, i n d i c a t e d that r e l a t i v e l y l i t t l e of the time spent on an item was spent on encoding i n the average group. Assessment of Equivalence of R Values Once the p r e f e r r e d model f o r each a b i l i t y group was designated f o r a p a r t i c u l a r ...criterion measure, the values of R 2 f o r the p r e f e r r e d model 83 were compared across a b i l i t y groups f o l l o w i n g a procedure o u t l i n e d by H a k s t i a n (1978). The procedure t e s t e d the s i g n i f i c a n c e of the d i f f e r -ences i n values of R 2 f o r the three a b i l i t y groups. k The t e s t s t a t i s t i c M = E W (6 - 6 0) k=l k k 2 was d i s t r i b u t e d as a x 2 w i t h k - 1 degrees of freedom, where k = number of groups. 6 = arctanh R*, where R* was an unbiased estimate of the popula-t i o n R, c a l c u l a t e d by R*2 = 1 - [ ( n - l ) / ( n - p ) ] ( l - R 2 ) , where p = number of p r e d i c t o r v a r i a b l e s , and n = sample s i z e . W. = \ where var(6, ) = 7 — o w o ^ o x , and k var(e^) k (n-3)(2n-3p) k E w. e. eo - k E W, k = l k Hakstian's procedure was developed f o r l a r g e sample s i z e s . Since the sample s i z e i n t h i s study was small (n = 20), the r e s u l t s from t h i s a n a l y s i s were i n t e r p r e t e d w i t h c a u t i o n . A second l i m i t a t i o n was r e l a t e d to the choice of model preference i n each group. The p r e f e r r e d models, e s t a b l i s h e d i n the preceding s e c t i o n were: Model 1M m a r g i n a l l y p r e f e r r e d over 4M i n the low group, and Model 4M i n the average and high groups. Model 4M was used as the p r e f e r r e d model f o r the low group i n t h i s a n a l -y s i s to maintain c o m p a r a b i l i t y across groups. The values of R 2 f o r Model 4M on c r i t e r i o n v a r i a b l e 1 were: low a b i l i t y R 2 = .34, average a b i l i t y R 2 = .49, and high a b i l i t y R 2 = .89. The o v e r a l l t e s t s t a t i s t i c was s i g n i f i c a n t (M = 10.78, p < .01). 84 Simultaneous 95% confidence i n t e r v a l s were c a l c u l a t e d about the simple p a i r w i s e c o n t r a s t s according to the procedure o u t l i n e d by Marascuilo (1966) where, i f 9, - 6. ± /^95 x2, -, v^varTC^T^^arTeTT k\ k 2 k-1 kx k 2 spanned zero, the c o n t r a s t was not s i g n i f i c a n t . The p r o p o r t i o n of v a r i a n c e i n l a t e n c y c o r r e c t scores accounted f o r by the p r e f e r r e d model (4M) increased as a b i l i t y increased. The i n c r e a s e i n R values between the low and high groups and between the average and high groups was s i g n i f i c a n t , but the increase between the low and average a b i l i t y groups was not s i g n i f i c a n t . Component Latencies f o r C r i t e r i o n V a r i a b l e 1 The t o t a l amount of time spent by each a b i l i t y group on a component across booklet types was estimated by m u l t i p l y i n g the raw r e g r e s s i o n c o e f f i c i e n t f o r that component i n the p r e f e r r e d model, by the mean of i t s p r e d i c t o r v a r i a b l e as shown i n Table 6, Chapter IV. This mean rep r e -sented the average number o f i t i m e s a component was executed over the 24 booklets. These values f o r the three a b i l i t y groups on c r i t e r i o n v a r i -able 1 are summarized i n Table 12 and shown i n Figure 3. As expected, the composite values in.Table 12 correspond w i t h the means of c r i t e r i o n v a r i a b l e 1, reported i n Table 7. In order to permit comparisons between the groups, Model 4M was again s u b s t i t u t e d f o r Model 1M as the p r e f e r r e d model i n the low a b i l i t y group. The values f o r Model 1M were: i n f e r -e n c e - a p p l i c a t i o n , 4.06 seconds per item, and encoding-response, 10.46 seconds per item f o r a composite of 14.52 seconds per item. Table 12 Composite and Component Latencies f o r Correct Responses Low A b i l i t y Group Average High Encoding 1.27 .14 2.83 I n f e r e n c e - A p p l i c a t i o n 2.91 3.22 1.03 Response 10.33 7.16 3.86 Composite 14.51 10.52 7.72 Note: The u n i t s represent seconds per analogy item. 86 Composite Low Average High ABILITY GROUP Figure 3. Composite and component l a t e n c i e s f o r c o r r e c t responses on Model 4M. 87 As shown i n Figure 3, o v e r a l l latency per item decreased monotonic-a l l y as a b i l i t y i n c r e a s e d , as d i d response l a t e n c y . The response com-ponent took most time at a l l a b i l i t y l e v e l s . Encoding decreased from low to average a b i l i t y groups, while i n f e r e n c e - a p p l i c a t i o n estimates were s i m i l a r f o r these two groups. The high group spent more time encoding than e i t h e r the average or low group and l e s s time on i n f e r e n c e - a p p l i c a -t i o n than the average and low groups. C r i t e r i o n V a r i a b l e 2: Latency Completed P r e l i m i n a r y i n s p e c t i o n of the r e s u l t s f o r the low, average, and high a b i l i t y students on c r i t e r i o n v a r i a b l e 2 revealed that the r e s u l t s were d i f f i c u l t to i n t e r p r e t i n terms of the c r i t e r i a used i n preceding analyses, p o s s i b l y due to the low v a r i a n c e i n these data. The r e s u l t s f o r these groups on c r i t e r i o n v a r i a b l e 2 are presented i n Appendix C, and w i l l not be discussed f u r t h e r . Residual A n a l y s i s An a n a l y s i s of the r e s i d u a l s was conducted to determine whether the var i a n c e unexplained by the p r e f e r r e d models contained a systematic as w e l l as a random component. The p r e f e r r e d model was 4M f o r the average and high groups on c r i t e r i o n v a r i a b l e 1. In view of the ambiguous r e s u l t s i n the low group on c r i t e r i o n v a r i a b l e 1, the r e s i d u a l s of both Model 1M and 4M were analyzed i n t h i s group. The - c r i t e r i o n v a r i a b l e s f o r the r e g r e s s i o n analyses were c a l c u -l a t e d , as shown i n Table 5, by computing the mean booklet scores f o r the 20 students w i t h i n each a b i l i t y l e v e l . For the r e s i d u a l a n a l y s i s , the sample of 20 at each a b i l i t y l e v e l was a r b i t r a r i l y d i v i d e d i n t o two h a l f -samples of 10 students each. Then the c r i t e r i o n v a r i a b l e s were r e c a l -c u l a t e d f o r the h a l f samples i n each group by computing mean booklet scores f o r 10 students w i t h i n each a b i l i t y l e v e l . This y i e l d e d two sets of c r i t e r i o n v a r i a b l e 1 scores at each a b i l i t y l e v e l . The r e s i d u a l a n a l y s i s was not conducted f o r c r i t e r i o n v a r i a b l e s 2 and 3. Once the c r i t e r i o n v a r i a b l e s were c a l c u l a t e d f o r the h a l f samples, the p r e f e r r e d models at each a b i l i t y l e v e l were r e f i t t e d to the data of the h a l f samples. These regressions were c a l c u l a t e d i n order to d e r i v e two sets of r e s i d u a l booklet scores (observed from p r e d i c t e d booklet scores) w i t h i n each a b i l i t y l e v e l . Then these r e s i d u a l s f o r each p a i r of h a l f samples ( w i t h i n a b i l i t y l e v e l ) were c o r r e l a t e d w i t h each other. The r e s i d u a l booklet scores from the h a l f samples should be u n c o r r e l a t e d i f the p r e f e r r e d model i s the 'complete' model, that i s , i f there are no components being used by the students which were u n s p e c i f i e d i n the models. I f the p r e f e r r e d model i s not a complete model, that i s , some systematic f a c t o r u n s p e c i f i e d by the model c o n t r i b u t e s to v a r i a n c e i n the data, then the r e s i d u a l s w i l l be s i g n i f i c a n t l y c o r r e l a t e d because the systematic p o r t i o n s of r e s i d u a l v a r i a n c e i n the h a l f samples w i l l be c o r r e l a t e d . C o r r e l a t i o n s f o r a l l a b i l i t y groups on c r i t e r i o n v a r i a b l e 1 are presented i n Table 13. The only s i g n i f i c a n t c o r r e l a t i o n s were f o r the low a b i l i t y group ( r 1 M = .50, p < .05, r ^ M = .46, p < .05). This sug-gested that one or more a d d i t i o n a l systematic f a c t o r s were c o n t r i b u t i n g to the v a r i a n c e of l a t e n c y c o r r e c t data f o r the low a b i l i t y students, and these f a c t o r s were not tapped by the p r e f e r r e d model 1M, nor the competitive model 4M. In summary, the p r e f e r r e d models were i n d i s t i n g u i s h a b l e from the 'complete' models of performance i n a l l cases, except f o r the l a t e n c y c o r r e c t data i n the low group. These r e s u l t s are subject to the 89 Table 13 R e l i a b i l i t i e s of Residuals from P r e f e r r e d Models Group P r e f e r r e d Model C r i t e r i o n V a r i a b l e 1 Low 1M r = .50* 4M r = .46* Average 4M r = .17 High 4M r = -.13 * = p < .05 90 l i m i t a t i o n that determination of model preference was eq u i v o c a l i n the average and low groups on c r i t e r i o n v a r i a b l e 1. Dependent V a r i a b l e 1 F i n a l l y , the q u a n t i t a t i v e performance of subjects on l a t e n c y c o r r e c t data was evaluated. In Chapter IV, Table 5, mean booklet scores were der i v e d by summing s u b j e c t s ' scores w i t h i n a b i l i t y l e v e l and d i v i d i n g by 20. This was done f o r each booklet on each c r i t e r i o n v a r i a b l e to y i e l d three sets of 24 c r i t e r i o n scores at each a b i l i t y l e v e l . In c o n t r a s t , f o r the present a n a l y s i s , s u b j e c t s ' scores were the focus, not booklet scores. Mean late n c y c o r r e c t scores f o r each subject were c a l c u l a t e d by summing the dependent v a r i a b l e 1 scores on the 24 analogy booklets and d i v i d i n g the sum by 24. Thus each of the 60 subjects had a mean la t e n c y c o r r e c t score. D e s c r i p t i v e s t a t i s t i c s f o r the scores are presented i n Table 14. A one-way a n a l y s i s of vari a n c e i n d i c a t e d that l a t e n c y c o r r e c t scores d i f f e r e d s i g n i f i c a n t l y between the a b i l i t y groups (F(2,57) = 9.88, p < .01). Simple p a i r w i s e comparisons i n d i c a t e d students i n the high and average a b i l i t y groups had s i g n i f i c a n t l y s horter l a t e n c i e s than the low a b i l i t y students (p < .05). The high a b i l i t y group a l s o had sh o r t e r average l a t e n c y c o r r e c t scores than d i d the average group, but t h i s d i f f e r e n c e was not s t a t i s t i c a l l y s i g n i f i c a n t . Table 14 D e s c r i p t i v e S t a t i s t i c s : Mean Latency Correct Group n Mean SD Low 20 14.50 6.91 Average 20 10.51 3.90 High 20 7.71 2.70 T o t a l 60 10.91 5.54 CHAPTER VI DISCUSSION The purpose of t h i s study was to i n v e s t i g a t e the r e l a t i o n s h i p between a n a l o g i c a l reasoning, as measured by Schematic P i c t u r e Analogies, and a b i l i t y , as measured by a standardized achievement t e s t , i n f o u r t h grade boys and g i r l s . The aim was to i d e n t i f y sources of i n d i v i d u a l d i f f e r e n c e s i n a b i l i t y i n terms of both q u a l i t a t i v e and q u a n t i t a t i v e performance d i f f e r e n c e s on an analogy task. Sternberg's componential a n a l y s i s (1977b) was chosen as the methodological and t h e o r e t i c a l paradigm f o r the study. Performance of f o u r t h grade students of low, average, and high a b i l i t y on schematic p i c t u r e analogies was analyzed f o r a b i l i t y - r e l a t e d d i f f e r e n c e s at f i v e l e v e l s : 1. the components (processes) used i n s o l u t i o n of p i c t o r i a l a n a l o g i e s , 2. the r u l e f o r combination of these components, 3. the mode of component execution, 4. consistency i n s t r a t e g y (model) use i n s o l u t i o n , and 5. q u a n t i t a t i v e d i f f e r e n c e s i n component scores. The d i s c u s s i o n focuses on the two main is s u e s i n the study: f i r s t , the u nderlying reasons f o r d i f f e r e n c e s i n achievement, and second, the u t i l i t y of componential a n a l y s i s i n i n d i v i d u a l d i f f e r e n c e research. P r i o r to d i s c u s s i o n of these i s s u e s , the l i m i t a t i o n s of the study are o u t l i n e d . 92 93 L i m i t a t i o n s of the Study The study was designed as a modified v e r s i o n of Sternberg and R i f k i n ' s (1979) developmental study, the main d i f f e r e n c e being subjects v a r i e d i n a b i l i t y r a t h e r than age. U n f o r t u n a t e l y , the procedure adopted by Sternberg and R i f k i n (1979) was unsuccessful w i t h the f o u r t h grade students i n the present study. This f a i l u r e was a t t r i b u t e d p r i m a r i l y to sample d i f f e r e n c e s . Sternberg's subjects were from a high SES Hebrew day s c h o o l , whereas t h i s sample was drawn from an area w i t h a range of economic and ethnic backgrounds. In a d d i t i o n to these sample d i f f e r -ences, the answer format f o r the analogies was d i f f e r e n t i n the current study, which increased the complexity of the analogy task i n the i n i t i a l i n t r o d u c t i o n phase. Thus, the procedure f o r data c o l l e c t i o n described i n Sternberg and R i f k i n (1979) was modified f o r use i n t h i s study. S p e c i f i c a l l y , the i n t r o d u c t o r y phase of the task was augmented. These changes had two e f f e c t s r e l e v a n t to the d i s c u s s i o n . F i r s t , due to the apparent sample d i f f e r e n c e s and the procedural d i f f e r e n c e s between the present study and Sternberg and Rifkin.'s (1979) experiment, cross-study comparisons were sev e r e l y l i m i t e d . A second e f f e c t of the procedural d i f f e r e n c e s was the r i s k of i n f l u e n c i n g the s u b j e c t s ' choice of model or s t r a t e g y i n task s o l u t i o n through augmentation of t r a i n i n g on the .task. O r i g i n a l group d i f f e r e n c e s or s i m i l a r i t i e s i n model preference may have been a f f e c t e d by the e x t r a p r a c t i c e and feedback given i n the present study. A p o s s i b l e confounding v a r i a b l e i n the study was response s t y l e . The task was timed. Although accuracy and not speed was s t r e s s e d i n the i n s t r u c t i o n s , there was no d i r e c t c o n t r o l f o r i n d i v i d u a l d i f f e r e n c e s i n response s t y l e (speed versus accuracy). A n o n t r i v i a l number of students 94 completed a l l 16 items i n some of the bo o k l e t s , and these students may have been those w i t h an impulsive response s t y l e . These students, w h i l e completing more items might have higher e r r o r r a t e s than a more r e f l e c -t i v e , a n a l y t i c respondent. The r e l i a b i l i t y of the data may have been weakened si n c e students who had worse than chance performance were not discarded. Some of the students w i t h worse than chance performance may have been guessing i f they m i s i n t e r p r e t e d the goal of the task as completion of as many items as p o s s i b l e i n the a l l o t t e d time. Since i t was not p o s s i b l e to d i s t i n g u i s h between a ' guesser.' and;a student w i t h low.scores f o r more. sub s t a n t i v e reasons, none of the low scorers were discarded, which may have weakened the r e l i a b i l i t y of the data p a r t i c u l a r l y i n the low a b i l i t y group. While the main goal of t h i s study was to explore the un d e r l y i n g nature of d i f f e r e n c e s i n achievement a b i l i t y , the conclusions were l i m i t e d by the f a c t that only one aspect of achievement, general reason-in g a b i l i t y , was i n v o l v e d . While a n a l o g i c a l reasoning a b i l i t y may be an important f a c t o r i n determining scores on standardized achievement t e s t s , i t i s s t i l l only one of many c o n t r i b u t i n g f a c t o r s , i n c l u d i n g m o t i v a t i o n , SES, e t h n i c background, and v a r i o u s p e r s o n a l i t y f a c t o r s . Thus t h i s study d i d not attempt to e x p l a i n the whole range of r e l a t e d f a c t o r s , but focused on one f a c t o r . Furthermore, any r e l a t i o n s h i p s i d e n t i f i e d between a n a l o g i c a l reasoning performance and achievement a b i l i t y were c o r r e l a t i o n a l and not ca u s a l . F i n a l l y , whenever one samples from the upper and lower ranges of the a b i l i t y spectrum, one may encounter f l o o r or c e i l i n g e f f e c t s i n task performance. The p r e l i m i n a r y a n a l y s i s of c r i t e r i o n v a r i a b l e 3 i n d i c a t e d there was a l a c k of variance i n e r r o r r a t e s across the 24 booklets i n a l l 95 three a b i l i t y groups. S i m i l a r l y the l a c k of i n t e r p r e t a b i l i t y i n c r i t e r -i o n v a r i a b l e 2 model f i t s f o r the three groups was a t t r i b u t e d to a l a c k of v a r i a n c e . I n s p e c t i o n of the data suggested that the l a c k of v a r i a n c e i n the high group was due to a c e i l i n g e f f e c t , as scores were g e n e r a l l y h i g h i n accuracy and students completed a l l 16 items i n a number of b o o k l e t s . Since the p i c t o r i a l analogy task was used s u c c e s s f u l l y w i t h s i x t h grade students and a d u l t s by Sternberg and R i f k i n (1979), i t i s p o s s i b l e that the c e i l i n g e f f e c t observed i n the present data f o r the high a b i l i t y group may be l i n k e d to the augmentation of t r a i n i n g and i n s t r u c t i o n . The l a c k of vari a n c e on the e r r o r r a t e c r i t e r i o n i n the low a b i l i t y group suggested a f l o o r e f f e c t . The v a r i a t i o n i n the complexity of the bo o k l e t s , which was i n s u f f i c i e n t to a f f e c t the performance of the high a b i l i t y students, appeared to be too great to a f f e c t the performance of the low a b i l i t y students. The r a t i o of number of items i n c o r r e c t to number of items completed was even and high across the 24 booklets i n t h i s group. As f o r the average group, the variance was low but d i d not seem to represent a f l o o r or c e i l i n g e f f e c t . The students seemed to complete a s i m i l a r number of items across booklets and the r a t i o of i n c o r r e c t to completed items was a l s o s i m i l a r across types of analogies. Students d i d not have h i g h l y accurate or h i g h l y i n a c c u r a t e performance as i n the high and low groups, but the v a r i a t i o n i n complexity of the task across the booklets was not r e f l e c t e d i n the variance i n booklet scores on c r i t e r i o n v a r i a b l e 2 and 3. C r i t e r i o n v a r i a b l e 1 was a measure of the q u a l i t y , not q u a n t i t y , of s u b j e c t s ' performance and more v a r i a t i o n across the booklets was 96 obtained, although the variance i n the high group was s t i l l r e l a t i v e l y low. Thus the r e s u l t s of the analyses were i n t e r p r e t e d w i t h these l i m i t a -t i o n s i n mind. A n a l o g i c a l Reasoning and Achievement A b i l i t y The r e s u l t s of the model f i t t i n g permit the i s o l a t i o n of achievement r e l a t e d d i f f e r e n c e s i n analogy s o l u t i o n at three l e v e l s , the theory, model, and component l e v e l s . The f i r s t research question, at the theory l e v e l , asked whether s t u -dents of h i g h , average, and low a b i l i t y used the f i v e components hypothe-s i z e d by the componential theory of a n a l o g i c a l r e a s o h i n g i n s o l v i n g the analogy tasks. I f one assumes that the components s p e c i f i e d i n the pre-f e r r e d model are the components used by the group, then according to t h i s c r i t e r i o n , the h i g h , average, and low a b i l i t y students i n t h i s study d i d not d i f f e r i n the components they used to solve schematic p i c t u r e analog-i e s . Model 1M, the m a r g i n a l l y p r e f e r r e d model i n the low a b i l i t y group, hypothesized i n f e r e n c e , a p p l i c a t i o n , encoding, and response components as d i d Model 4M, the p r e f e r r e d model i n the average and high a b i l i t y groups. Mapping was not used by these s u b j e c t s . Sternberg and R i f k i n (1979) a l s o reported that subjects of d i f f e r e n t ages d i d not d i f f e r i n the components used, which were: encoding, i n f e r e n c e , a p p l i c a t i o n , and response. None of the subjects used mapping. Thus, mapping d i d not appear to be neces-sary i n s o l u t i o n of schematic p i c t u r e analogies i n e i t h e r study, and students who v a r i e d i n a b i l i t y and age a l l used encoding, i n f e r e n c e , a p p l i c a t i o n , and response components i n s o l u t i o n , according to t h i s c r i t e r i o n . However, i f one a p p l i e s a more s t r i n g e n t c r i t e r i o n to t h i s q u estion, namely that a component estimate must be s i g n i f i c a n t i f the component i s 97 assumed to be employed i n s o l u t i o n , then the evidence i s weakened. Only i n the high a b i l i t y group were a l l the component estimates s i g n i f i c a n t . According to t h i s c r i t e r i o n , subjects d i f f e r i n g i n a b i l i t y used d i f f e r e n t components i n the s o l u t i o n . o f schematic p i c t u r e a n a l o g i e s . Because the v a l i d i t y of i n d i v i d u a l component estimates were r e l a t i v e to the degree of model f i t and model f i t s were l e s s than p e r f e c t i n the current study, the f i r s t c r i t e r i o n was adopted. Mapping was r u l e d out as a component neces-sary to the s o l u t i o n of schematic p i c t u r e analogies f o r students at the a b i l i t y l e v e l s included i n t h i s study. Mapping i s considered to be neces-sary i n most analogy t a s k s , but not w i t h separable a t t r i b u t e s t i m u l i (Sternberg, 1980), and these r e s u l t s lend f u r t h e r support to that c o n c l u -s i o n . According to the f i r s t c r i t e r i o n , students of d i f f e r i n g a b i l i t y l e v e l s i n t h i s study d i d not d i f f e r i n the components they used i n s o l v -i n g the analogies. These components were: encoding, i n f e r e n c e , a p p l i c a -t i o n , and response. The second research question, a l s o at the theory l e v e l , concerned the appropriateness of the l i n e a r a d d i t i v e r u l e f o r combination of com-ponents. The c r i t e r i o n used to evaluate t h i s question was the amount of va r i a n c e accounted f o r by the p r e f e r r e d models. I f the values of R 2 are h i g h , then the l i n e a r combination r u l e i s supported. The only R 2 v a l u e high enough to warrant support of the l i n e a r a d d i t i v e r u l e was i n the high a b i l i t y group. The low R 2 values i n the average group and low group could be a t t r i b u t e d t o : v i o l a t i o n of the l i n e a r assumption, l a c k of variance i n the data, or missing components i n the models. Since the v a r i a n c e i n the average and low groups was higher than that i n the high group, but the values of R 2 were lower, the l a c k of v a r i a n c e explanation was r u l e d out f o r these two groups. The f a c t that the r e s i d u a l a n a l y s i s of low a b i l i t y group data i n d i c a t e d a systematic p o r t i o n of vari a n c e i n the r e s i d u a l s unaccounted f o r by both Model 1M and 4M suggested that the low values of R 2 i n the low group could be due to the inappropriateness of the hypothesized models f o r t h i s group's performance. One f a c t o r which may have c o n t r i b u t e d to systematic v a r i a n c e i n the r e s i d u a l s was speed, or response s t y l e . Data inspec-t i o n revealed that many students i n the low group who had very few items c o r r e c t had many items completed. The late n c y c o r r e c t c r i t e r i o n v a r i a b l e i s a measure of q u a l i t y , not qu a n t i t y of performance and the model i t s e l f does not hypothesize a speed component, thus i f speed was relevant i n t h i s group's data, i t would e x p l a i n the inappropriateness of the hypothesized models, and thus the poor f i t . In a d d i t i o n to these expla n a t i o n s , the low R could have been due to v i o l a t i o n of the l i n e a r a d d i t i v e assumption. The poor model f i t s i n the average group were not a t t r i b u t e d to a missing component s i n c e the c o r r e l a t i o n of r e s i d u a l s was not s i g n i f -i c a n t f o r t h i s group. The l a c k of varia n c e explanation was r u l e d out. I t appears more l i k e l y that the low R i n t h i s group was due to the v i o l a t i o n of the l i n e a r assumption, or to measurement e r r o r . A r e l a t e d i s s u e i s that of the negative r e g r e s s i o n c o e f f i c i e n t s i n c e r t a i n models. While the sm a l l negative weights were a t t r i b u t e d to measurement e r r o r and dismissed as n o n s i g n i f i c a n t , l a r g e r and s i g n i f i c a n t negative weights, or c o n s i s t e n t patterns of negative weights were l e s s r e a d i l y dismissed. These negative weights may be a f u r t h e r i n d i c a t i o n of v i o l a t i o n of the l i n e a r , a d d i t i v e assumption. A p p l i c a t i o n i n Model 2-3M f o r low a b i l i t y group l a t e n c y c o r r e c t data was l a r g e and negative. This may be an i n d i c a t i o n that components were executed i n a h o l i s t i c r a t h e r than a s e r i a l f a s h i o n , which would i n v a l i d a t e the independent estimates. One p o s s i b l e h o l i s t i c s t r a t e g y i n v o l v e s working backwards through the analogy. When the two answer options share very few a t t r i b u t e s and are obviously d i s c r e p a n t , the student could work backwards, encoding the a t t r i b u t e which d i s t i n g u i s h e d two answer options and then matching that a t t r i b u t e r e l a t i o n i n the A to B terms from C to or D2. Thus only the rel e v a n t d i s t i n g u i s h i n g elements would be encoded and a p p l i e d . In summary, the l i n e a r a d d i t i v e component combination r u l e was sup-ported by the data i n the high group. The appropriate r u l e f o r component combination i n the average and low groups was not c l e a r l y e s t a b l i s h e d and may have been l i n e a r or n o n l i n e a r . These r e s u l t s c o n t r a s t w i t h those i n previous componential s t u d i e s (Sternberg, 1977b; Sternberg & R i f k i n , 1979) i n which the l i n e a r a d d i t i v e combination r u l e was unequivocally supported. The t h i r d question concerned the model preference of the three a b i l i t y groups, or s p e c i f i c a l l y , the p r e f e r r e d mode of component execu-t i o n . Sternberg and R i f k i n (1979) found that students of d i f f e r e n t ages d i d not d i f f e r i n model preference on the schematic p i c t u r e analogies although they d i d d i f f e r i n model choice on other types of analogies. A l l of the subjects p r e f e r r e d model 4M. While determination of model preference was d i f f i c u l t i n the low and average a b i l i t y groups i n the present study, of the seven hypothesized models, 4M was c l e a r l y the p r e f e r r e d model f o r the high group. The pre-f e r r e d model i n the low group was 1M but only m a r g i n a l l y , and i n the average group, 4M. In view of the d i f f i c u l t y of the d e c i s i o n of model preference i n the low and average groups, as w e l l as the question of the appropriateness of the l i n e a r assumption on which the model preferences were based, the nature of the p r e f e r r e d models was i n v e s t i g a t e d . The only model to account f o r l a r g e p o r t i o n s of the variance was Model 4M i n the high a b i l i t y group. Furthermore, the r e s i d u a l a n a l y s i s i n d i c a t e d that the best f i t t i n g models i n the low group, Model 1M and 4M, were incomplete i n that some systematic variance remained i n the r e s i d u a l s , unaccounted f o r by the model. In a d d i t i o n , the l i n e a r a d d i t i v e assump-t i o n may have been v i o l a t e d i n the low and average groups. Thus, i t was concluded that w h i l e the model preferences i n d i c a t e d that low a b i l i t y students may p r e f e r exhaustive component execution, and'the average and high groups p r e f e r r e d a s e l f - t e r m i n a t i n g execution mode, these observa-t i o n s were confounded by the l i m i t a t i o n s p r e v i o u s l y mentioned. Sternberg and R i f k i n (1979) found no age-related d i f f e r e n c e s i n model preference on schematic p i c t u r e a n a l o g i e s , but d i f f e r e n c e s were found on the people piece analogies. The tendency on the people piece analogies was towards i n c r e a s i n g use of exhaustive processing w i t h i n c r e a s i n g age, which i s a general c h a r a c t e r i s t i c of c o g n i t i v e develop-ment according to Brown and DeLoache (1978). I t may be that students a c t u a l l y d i f f e r e d i n the mode of component execution i n the present study, but t h i s r e s u l t may al s o have been an a r t i f a c t of the low v a r i -ance or the inappropriatness of the l i n e a r a d d i t i v e assumption. Hypothesis 4.1 s t a t e d that consistency i n model choice would 101 i n c r e a s e as a f u n c t i o n of a b i l i t y . While the values of R 2 were s i g n i f -i c a n t l y higher i n the high group than i n the average and low groups, the increases were not n e c e s s a r i l y due to an increase i n consistency w i t h a b i l i t y . Other f a c t o r s , discussed i n r e l a t i o n to question 2, which may have i n f l u e n c e d the increase i n c l u d e : 1. v i o l a t i o n of the l i n e a r a d d i t i v e assumption i n the low and average groups, and 2. a missing component i n the low a b i l i t y group (response speed). In view of these confounding f a c t o r s i t was concluded that w h i l e the d i f f e r e n c e s i n R 2's suggested that the consistency w i t h which sub-j e c t s used the p r e f e r r e d s t r a t e g y increased as a f u n c t i o n of a b i l i t y , other f a c t o r s may have i n f l a t e d or d e f l a t e d the R 2's, and thus no con-c l u s i o n s as to the consistency of s t r a t e g y use across a b i l i t y l e v e l s were made. Sternberg and R i f k i n (1979) observed that w h i l e R 2 values f o r the age groups were s i m i l a r , when' the p r e f e r r e d models were f i t t e d to the i n d i v i d u a l subject's l a t e n c i e s , the values of R 2 increased w i t h age, which he i n t e r p r e t e d as a s i g n of increase i n the consistency of s t r a t e g y use. The f i n a l hypothesis, 5.1, s t a t e d . t h a t l a t e n c y and e r r o r r a t e scores would vary as a f u n c t i o n of a b i l i t y . The e r r o r r a t e and l a t e n c y completed data were not analyzed, but the three groups were:found to d i f f e r i n the l a t e n c y f o r number of items completed c o r r e c t l y . The f a c t that the low and average a b i l i t y • s t u d e n t s had fewer c o r r e c t items than the high group may be because they adopted an i n a p p r o p r i a t e s t r a t e g y of responding i m p u l s i v e l y i n order to f i n i s h a l l of the items i n t h e i r book-l e t . Accuracy of response may have been of lower p r i o r i t y to them. 102 Thus q u a n t i t a t i v e d i f f e r e n c e s i n performance were found between the hig h a b i l i t y group and the low and average group. The high group was more accurate than the average and low groups. As f o r group d i f f e r e n c e s i n i n d i v i d u a l component scores, i n view of the low R 2's, and v i o l a t i o n of assumptions, these component estimates may be i n v a l i d and at best must be i n t e r p r e t e d w i t h c a u t i o n . In the present study, composite l a t e n c y and response l a t e n c y decreased as a b i l i t y increased. Sternberg and R i f k i n (1979) found composite and response l a t e n c i e s a l s o decreased as age increased. The three groups spent more time on response than on the other components. Response was always estimated as the r e g r e s s i o n constant; f u t u r e s t u d i e s should attempt to s p e c i f y component processes subsumed under the response component, as i t seems u n l i k e l y that the act of r e c o r d i n g the response would take as much time as i t d i d . I t i s pos-s i b l e that the l a t e n c i e s of more than one process were estimated as a s i n g l e component l a t e n c y . In summary, students of d i f f e r e n t achievement a b i l i t y had q u a n t i -t a t i v e performance d i f f e r e n c e s on an a n a l o g i c a l reasoning task and the data suggested evidence of q u a l i t a t i v e performance d i f f e r e n c e s i n the components used, i n the way the components were combined and executed, and i n the consistency of these executions. This contrasted w i t h Sternberg and R i f k i n ' s (1979) r e s u l t s wherein students of d i f f e r e n t ages d i f f e r e d i n q u a n t i t a t i v e but not q u a l i t a t i v e performance on the analogy task. Their r e s u l t s may have been sample s p e c i f i c , as students of d i f f e r e n t ages d i f f e r e d q u a l i t a t i v e l y on another analogy task reported i n the same study (Sternberg & R i f k i n , 1979). In terms of the u n d e r l y i n g nature of achievement, the evidence 103 presented d i d not c o n t r a d i c t the hypothesis that students of d i f f e r e n t achievement l e v e l s may use d i f f e r e n t processes, and d i f f e r e n t r u l e s or s t r a t e g i e s f o r combining and executing processes, however i t was not p o s s i b l e to show co n c l u s i v e support f o r the hypothesis. The t e n t a t i v e evidence f o r q u a l i t a t i v e d i f f e r e n c e s was s i m i l a r to other research which i n d i c a t e d that i n d i v i d u a l d i f f e r e n c e s were not s o l e l y of a q u a n t i t a t i v e nature. Jarman and Das (1977) al s o suggested that subjects of d i f f e r -ent i n t e l l i g e n c e l e v e l s may use d i f f e r e n t modes of processing on the same task. Brown (1974, 1975) i m p l i c a t e d s t r a t e g y d i f f e r e n c e s as an important source of i n d i v i d u a l d i f f e r e n c e s i n performance. Hunt, F r o s t , and Lunneborg (1973) found that subjects of d i f f e r e n t v e r b a l and per-formance a b i l i t y a l s o had q u a l i t a t i v e and q u a n t i t a t i v e performance d i f f e r -ences on a task. Other supportive evidence included that of Humphreys and Taber, 1973, and Stevenson et a l . , 1976, who found that i n d i v i d u a l d i f f e r e n c e s i n s u b j e c t s ' a b i l i t y were r e f l e c t e d i n d i f f e r e n t f a c t o r loadings f o r the same set of t a s k s . The i n c o n c l u s i v e r e s u l t s of t h i s study r e s t r i c t the d i s c u s s i o n of whether or not students of d i f f e r e n t a b i l i t y use d i f f e r e n t processes and s t r a t e g i e s on t a s k s , but the question remains an important one f o r f u t u r e i n v e s t i g a t i o n s . Componential A n a l y s i s The s t r e n g t h i n the method of componential a n a l y s i s l i e s i n i t s a b i l i t y to d i r e c t l y t e s t hypothesized models of task performance, as w e l l as provide measures of processes used i n the s o l u t i o n of the t a s k s . The method i s s u i t e d to some tasks such as a n a l o g i e s , but would not be a p p l i c a b l e to a l l tasks (e.g., f i g u r e completion). Sternberg o r i g i n a l l y developed the method f o r use i n an i n d i v i d u a l 104 t e s t i n g s i t u a t i o n (1977b), and only l a t e r devised the group administered procedure adapted f o r use i n the present study (Sternberg & R i f k i n , 1979). E v a l u a t i o n of the d i f f i c u l t i e s encountered i n the present study suggested that the i n d i v i d u a l data c o l l e c t i o n method was p r e f e r a b l e to the group a d m i n i s t r a t i o n . Fewer component estimates are confounded using the pre-cueing method ( i n d i v i d u a l l y administered), and i t seems l i k e l y that the r e l i a b i l i t y of the data would be maximized i n an i n d i v i d u a l s i t u a t i o n . In group t e s t i n g s i t u a t i o n s , measurement e r r o r i s l i k e l y more pr e v a l e n t . While i t may be argued that group data c o l l e c t i o n i s a common element of educational research, and that the l o g i s t i c s of i n d i v i d u a l t e s t i n g are p r o h i b i t i v e , the sample s i z e s r e q u i r e d f o r componential analyses are small enough to permit i n d i v i d u a l data c o l l e c t i o n . Thus, the componential approach to i n d i v i d u a l . d i f f e r e n c e s research (Sternberg, 1977b) was implemented w i t h some d i f f i c u l t y i n t h i s study. I t was concluded that w h i l e the componential a n a l y s i s technique i s w e l l -s u i t e d to i s o l a t i n g d i f f e r e n t sources o f : i n d i v i d u a l d i f f e r e n c e s on a task, i t i s more amenable to some tasks, than to o t h e r s , and i t i s more manage-able i n an i n d i v i d u a l , r a t h e r than a group t e s t i n g s i t u a t i o n . I m p l i c a t i o n s f o r Future Research Suggestions f o r f u t u r e research i n i n d i v i d u a l d i f f e r e n c e s developed from t h i s i n v e s t i g a t i o n . The suggestion that students of d i f f e r e n t a b i l i t y l e v e l s may d i f f e r i n t h e i r s t r a t e g i e s f o r component combination and execution should be pursued. This would i n v o l v e the development and t e s t i n g of d i f f e r e n t models to e x p l a i n i n d i v i d u a l d i f f e r e n c e s i n a n a l o g i c a l reasoning. These models should attempt to i d e n t i f y components at a more s p e c i f i c l e v e l than the current models, and a l s o t e s t n o n l i n e a r r u l e s f o r component 105 combination. The task performances should be r e l a t e d back to reference a b i l i t y scores i n order to e s t a b l i s h e x t e r n a l v a l i d i t y . A second concern i s that the current study d i d not attempt to e x p l a i n a l l of the v a r i a n c e i n achievement scores. Future i n v e s t i g a -t i o n s should attempt to c o n t r o l f o r other aspects of achievement a b i l i t y such as response s t y l e and socio-demographic f a c t o r s . Given the evidence f o r s t r a t e g y d i f f e r e n c e s , the question of remedia-t i o n and t r a i n i n g of these s t r a t e g i e s i s important. I t i s necessary not only to determine why c h i l d r e n are d i f f e r e n t , but a l s o to f i n d ways of remediating these d i f f e r e n c e s . The question of the s t a b i l i t y of d e f i c i t s over time i s a l s o of i n t e r e s t . A design i n c o r p o r a t i n g both age and a b i l i t y d i f f e r e n c e s i s needed. Reference Note Hakstian, R. A. I n f e r e n t i a l procedures w i t h m u l t i p l e c o r r e l a t i o n s . Paper presented at the Annual Meeting of The Society of M u l t i v a r i -ate Experimental Psychology, C i n c i n n a t i , Ohio, November 1978. 107 REFERENCES Belmont, J . M. , & B u t t e r f i e l d , E. C. Learning s t r a t e g i e s as determinants of memory d e f i c i e n c i e s . C o g n i t i v e Psychology, 1971, 2^ , 411-420. Bloom, B. S. S t a b i l i t y and change i n human c h a r a c t e r i s t i c s . New York: John Wiley & Sons, Inc., 1964. Boring, E. G. I n t e l l i g e n c e as the t e s t s t e s t i t . In J . J . Jenkins & D. J . Paterson (Eds.), Studies i n i n d i v i d u a l d i f f e r e n c e s : The  search f o r i n t e l l i g e n c e . New York: Appleton Century C r o f t s , 1961. (Reprinted from The New Republic, 1923, June 6.) Brown, A. L. The r o l e of s t r a t e g i c behavior i n r e t a r d a t e memory. In N. R. E l l i s (Ed.), I n t e r n a t i o n a l review Of research i n mental r e t a r d a t i o n ( V o l . 7). New York: Academic P r e s s , 1974. Brown, A. L. The development of memory: Knowing, knowing about knowing, and knowing how to know. In H. W. Reese (Ed.), Advances i n c h i l d  development and behavior ( V o l . 10). New York: Academic Press, 1975. Brown, A. L., & B a r c l a y , C. R. The e f f e c t s of t r a i n i n g s p e c i f i c mnemonics on the metamnemonic e f f i c i e n c y of retarded c h i l d r e n . C h i l d Develop- ment, 1976, 47, 71-80. Brown, A. L., & Campione, J . C. T r a i n i n g s t r a t e g i c study time a p p o r t i o n -ment i n educable retarded c h i l d r e n . I n t e l l i g e n c e , 1977, 1^ , 94-107. Brown, A. L., Campione, J . C., Bray, N. W., & Wilcox, B. L. Keeping t r a c k of changing v a r i a b l e s : E f f e c t s of r e h e a r s a l t r a i n i n g and r e h e a r s a l prevention i n normal and retarded adolescents. J o u r n a l of E x p e r i - mental Psychology, 1973, 101, 123-131. Brown, A. L., & DeLoache, J . S. S k i l l s , p l a n s, and s e l f - r e g u l a t i o n . In R. S i e g l e r (Ed.), C h i l d r e n ' s t h i n k i n g : What develops. H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1978. Brown, A. L., & Lawton, S. C. The f e e l i n g of knowing experience i n educable retarded c h i l d r e n . Developmental Psychology, 1977, 13 (4) , 364-370. Campione, J . C , & Brown, A. L. Toward a theory of i n t e l l i g e n c e : C o n t r i b u t i o n s from research w i t h retarded c h i l d r e n . I n t e l l i g e n c e , 1978, 2, 279-304. C a r r o l l , J . B. Review of The nature of human i n t e l l i g e n c e , by J . P. G u i l f o r d . American Educational Research J o u r n a l , 1968, 5^ , 249-256. C a r r o l l , J . B. Psychometric t e s t s as c o g n i t i v e t a s k s : A new " S t r u c t u r e  of I n t e l l e c t " (Technical Report No. 4). P r i n c e t o n , New Jersey: Educational T e s t i n g S e r v i c e , 1974. 108 C a r r o l l , J . B. How s h a l l we study i n d i v i d u a l d i f f e r e n c e s i n c o g n i t i v e a b i l i t i e s ? — M e t h o d o l o g i c a l and t h e o r e t i c a l p e r s p e c t i v e s . I n t e l l i g e n c e , 1978, 2, 87-115. C a r r o l l , J . B., & Maxwell, S. E. I n d i v i d u a l d i f f e r e n c e s i n c o g n i t i v e a b i l i t i e s . Annual Review of Psychology, 1979, _30, 603-640. Cronbach, L. J . The two d i s c i p l i n e s of s c i e n t i f i c psychology. American P s y c h o l o g i s t , 1957, 12, 671-684. Estes, W. K. Learning theory and i n t e l l i g e n c e . American P s y c h o l o g i s t , 1974, 29, 740-49. Estes, W. K. The s t a t e of the f i e l d : General problems and issues of theory and metatheory. In W. K. Estes (Ed.), Handbook of l e a r n i n g  and c o g n i t i v e processes ( V o l . 1 ). H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1975. Estes, W. K. I n t e l l i g e n c e and c o g n i t i v e psychology. In L. B. Resnick (Ed.), The nature of i n t e l l i g e n c e . H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1976. F l a v e l l , J . H. Developmental s t u d i e s of mediated memory. In H. W. Reese & L. P. L i p p s i t t (Eds.), Advances i n c h i l d development and behavior (Vo l . 5). New York: Academic Press, 1970. Glase r , R., & P e l l e g r i n o , J . ¥. U n i t i n g c o g n i t i v e process theory and d i f f e r e n t i a l psychology: Back home from the wars. I n t e l l i g e n c e , 1978, 2, 305-319. Humphreys, L. G. The nature and o r g a n i z a t i o n of human a b i l i t i e s . In M. Katz (Ed.), The 19th yearbook of the N a t i o n a l C o u n c i l ori Measurement  i n Education. Ames, Iowa: N a t i o n a l C o u n c i l on Measurement i n Educa-t i o n , 1962. (a) Humphreys, L. G. The o r g a n i z a t i o n of human a b i l i t i e s . American P s y c h o l - o g i s t , 1962, 17, 475-483. (b) Humphreys, L. G., & Taber, T. A b i l i t y f a c t o r s as a f u n c t i o n of advantaged and disadvantaged groups. J o u r n a l of Educational Measurement, 1973, 10(2), 107-115. Hunt, E., F r o s t , N., & Lunneborg, C. I n d i v i d u a l d i f f e r e n c e s i n c o g n i t i o n : A new approach to i n t e l l i g e n c e . In G. Bower (Ed.), The psychology of  l e a r n i n g and motivation ( V o l . 7). New York: Academic Press, 1973. Hunt, E., & Lansman, M. Co g n i t i v e theory a p p l i e d to i n d i v i d u a l d i f f e r -ences. In W. K. Estes (Ed.), Handbook of l e a r n i n g and c o g n i t i v e  processes (Vol. 1 ). H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1975. Hunt, E., & MacLeod, C. M. The s e n t e n c e - v e r i f i c a t i o n paradigm: A case study of two c o n f l i c t i n g approaches to i n d i v i d u a l d i f f e r e n c e s . I n t e l l i g e n c e , 1978, 2, 129-144. 109 Jarman, R. F. Comments on John B. C a r r o l l ' s "How s h a l l we study i n d i v i d u a l d i f f e r e n c e s i n c o g n i t i v e a b i l i t i e s ? — M e t h o d o l o g i c a l and t h e o r e t i c a l p e r s p e c t i v e s . " I n t e l l i g e n c e , 1980, 4_, 73-82. Jarman, R. F., & Das, J . P. Simultaneous and successive syntheses and i n t e l l i g e n c e . I n t e l l i g e n c e , 1977, 1, 151-169. Jensen, A. R. H i e r a r c h i c a l t h e o r i e s of mental a b i l i t y . In W. B. D o c k r e l l (Ed.), On i n t e l l i g e n c e . London: Methuen & Co., L t d . , 1970. Johnson, D. M. S e r i a l a n a l y s i s of v e r b a l analogy.problems. J o u r n a l of  Educational Psychology, 1962, _53(2), 86-88. K a i l , R. Use of s t r a t e g i e s and i n d i v i d u a l d i f f e r e n c e s i n c h i l d r e n ' s memory. Developmental Psychology, 1979, 15_(3), 251-255. King, E. M. (Ed.). Canadian t e s t s of b a s i c s k i l l s : , Manual f o r adminis- t r a t o r s , s u p e r v i s o r s , and c o u n s e l l o r s . Don M i l l s , Ontario: Thomas Nelson & Sons (Canada) L i m i t e d , 1976. King, E. M. (Ed.). Canadian t e s t s of b a s i c s k i l l s : Teacher's guide. Don M i l l s , Ontario: Thomas Nelson & Sons (Canada) L i m i t e d , 1977. Le, C., & T e n i s c i , T. UBC TRP: T r i a n g u l a r Regression Package. Vancouver, B r i t i s h Columbia: Computing Centre, U n i v e r s i t y of B r i t i s h Columbia, 1978. M a r a s c u i l o , L. A. Large-sample m u l t i p l e comparisons.. P s y c h o l o g i c a l  B u l l e t i n , 1966, 65(5), 280-290. McNemar, Q. Lost: Our i n t e l l i g e n c e ? Why? American P s y c h o l o g i s t , 1964, 19, 871-882. Messick, S. Beyond s t r u c t u r e : In search of f u n c t i o n a l models of psy c h o l -o g i c a l process. Psychometrika, 1972, 37_, 357-375. M i l l e r , G. A., Galanter, E., & Pribram, K. H. Plans and the s t r u c t u r e of  behavior. New York: Holt Rinehart & Winston, 1960. P e l l e g r i n o , J . W., & Glas e r , R. Co g n i t i v e c o r r e l a t e s and components i n the a n a l y s i s of i n d i v i d u a l d i f f e r e n c e s . I n t e l l i g e n c e , 1979, 3^ , 187-214. P e l l e g r i n o , J . W., & Lyon, D. R. The components of a componential a n a l y s i s . I n t e l l i g e n c e , 1979, 3, 169-186. Reed, S. K. Review of I n t e l l i g e n c e , i n f o r m a t i o n processing and a n a l o g i c a l  reasoning, by R. J . Sternberg. I n t e l l i g e n c e , 1977, 1, 331-334. Resnick, L. B. I n t r o d u c t i o n : Changing conceptions of i n t e l l i g e n c e . In L. B. Resnick (Ed.), The nature of i n t e l l i g e n c e . H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1976. (a) 110 Resnick, L. B. The nature of i n t e l l i g e n c e . H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1976. (b) Rohwer, W. D., J r . E l a b o r a t i o n and l e a r n i n g i n childhood and adolescence. In H. W. Reese (Ed.), Advances i n c h i l d development and behavior ( V o l . 8). New York: Academic Press, 1973. Rumelhart, D. E., & Abrahamson, A. A. A model f o r a n a l o g i c a l reasoning. C o g n i t i v e Psychology, 1973, _5, 1-28. Snow, R. E. Theory and method f o r research on a p t i t u d e processes. I n t e l l i g e n c e , 1978, 2, 225-278. Spearman, C. The nature of " i n t e l l i g e n c e " and the p r i n c i p l e s of c o g n i t i o n . London: MacMillan, 1923. Spearman, C. The a b i l i t i e s of man. In J . J . Je n k i n s , & D. G. Paterson (Eds.), Studies i n i n d i v i d u a l d i f f e r e n c e s : The search f o r i n t e l l i - gence. New York: Appleton Century C r o f t s , 1961. (Reprinted from The A b i l i t i e s of Man, 1927.) Sternberg, R. J . Component processes i n a n a l o g i c a l reasoning. P s y c h o l o g i c a l Review, 1977, 84(4), 353-378. (a) Sternberg, R. J . I n t e l l i g e n c e , i n f o r m a t i o n p r o c e s s i n g , and a n a l o g i c a l reasoning: The componential-analysis,of human a b i l i t i e s . H i l l s d a l e , New Jersey: Lawrence Erlbaum A s s o c i a t e s , 1977. (b) Sternberg, R. J . Componential i n v e s t i g a t i o n s of human i n t e l l i g e n c e . In A. Lesgold, J . P e l l e g r i n o , S. Fokkema, & R. Glaser (Eds.), C o g n i t i v e psychology and i n s t r u c t i o n . New York: Plenum, 1978. (a) Sternberg, R. J . I n t e l l i g e n c e research at the i n t e r f a c e between d i f f e r -e n t i a l and c o g n i t i v e psychology: Prospects and proposals. I n t e l l i g e n c e , 1978, 2, 195-222. (b) Sternberg, R. J . I s o l a t i n g the components of i n t e l l i g e n c e . I n t e l l i g e n c e , 1978, 2, 117-128. (c) Sternberg, R. J . C o g n i t i v e - b e h a v i o r a l approaches to the t r a i n i n g of  i n t e l l i g e n c e i n the retarded ( C o g n i t i v e Development Technic a l Report No. 6). New Haven: Department of Psychology, Yale U n i v e r s i t y , 1979. (a) Sternberg, R. J . Components of human i n t e l l i g e n c e (Technical Report No. 19). New Haven: Department of Psychology, Y a l e U n i v e r s i t y , 1979. (b) Sternberg, R. J . S i x authors i n search of a charac t e r : A play about i n t e l l i g e n c e t e s t s i n the year 2000. I n t e l l i g e n c e , 1979, ^3, 283-293. (c) I l l Sternberg, R. J . The construct v a l i d i t y of a p t i t u d e t e s t s : An informa-t i o n - p r o c e s s i n g assessment (Technical Report No. 20). New Haven: Department of Psychology, Y a l e U n i v e r s i t y , 1979. (d) Sternberg, R. J . The development of human i n t e l l i g e n c e ( C o g n i t i v e Devel-opment Te c h n i c a l Report No. 4). New Haven: Department of Psychology, Yale U n i v e r s i t y , 1979. (e). Sternberg, R. J . The nature of mental a b i l i t i e s . American P s y c h o l o g i s t , 1979,. 34(3), 214-230. ( f ) Sternberg, R. J . The development of l i n e a r s y l l o g i s t i c reasoning. J o u r n a l of Experimental C h i l d Psychology, 1980, 29(2), 340-356. Sternberg, R. J . , & Nigro, G. Developmental patt e r n s i n the s o l u t i o n of v e r b a l analogies. C h i l d Development, 1980, _51_(1) , 27-38. Sternberg, R. J . , & R i f k i n , B. The development of a n a l o g i c a l reasoning processes. J o u r n a l of Experimental C h i l d Psychology, 1979, 2_7, 195-232. Stevenson, H. W., Parker, T., W i l k i n s o n , A., Hegion, A., & F i s h , E. L o n g i t u d i n a l study of i n d i v i d u a l d i f f e r e n c e s i n c o g n i t i v e development and s c h o l a s t i c achievement. J o u r n a l of Educational Psychology, 1976, 68, 377-400. Tallmadge, G. K., & Wood, C. T. User's Guide, ESEA T i t l e I e v a l u a t i o n  and r e p o r t i n g system. Mountain View, C a l i f o r n i a : RMC Research Cor-p o r a t i o n , 1976. T y l e r , L. E. The psychology of human differences.. New York: Appleton-Century-Crofts, 1965. T y l e r , L. E. I n d i v i d u a l d i f f e r e n c e s : A b i l i t i e s arid m o t i v a t i o n a l d i r e c - t i o n s . New York: Appleton-Century-Crofts, 1974. Vernon, P. E. I n t e l l i g e n c e . In W. B. D o c k r e l l (Ed.), On i n t e l l i g e n c e . London: Methuen & Co. L t d . , 1970. Whiteley, S. E., & Dawis, R. V. E f f e c t s of c o g n i t i v e i n t e r v e n t i o n on l a t e n t a b i l i t y measured from analogy items. J o u r n a l of Edu c a t i o n a l  Psychology, 1974, 66(5), 710-717. Appendix A: Schematic P i c t u r e Analogy Booklet 113 114 116 Appendix B: Answer Sheet f o r Schematic P i c t u r e Analogy Booklet Appendix C: Model F i t s f o r A b i l i t y Groups C r i t e r i o n V a r i a b l e 2 120 Model F i t s f o r Low A b i l i t y Group: C r i t e r i o n V a r i a b l e 2 Component Estimates Model Inf . Inf .-Appl. Appl. Map. Enc. E n c -Resp. Resp. R 2 . F o est 1 -.03 -.23 8.88** .01 .11 1.80 2 -1.74* 4.26** -.23 8.87** .44 5.25** 1.39 3 -2.21** 5.14** -1.16 9.47** .48 6.15** 1.34 4 1.94* .54 6.79** .23 3.11 1.59 1M .08 8.31** .001. . .02 1.77 2-3M -1.65 4.31 -.04 8.35** .43 5.02** 1.40 4M .66 1.20* 5.60** .38 6.33** 1.43 Note: Estimates are i n terms of seconds spent on a component per analogy item. * = p < .05 ** = p < .01 121 Model F i t s f o r Average A b i l i t y Group: C r i t e r i o n V a r i a b l e 2 Component Estimates I n f . - Enc.-Model I n f . Appl. Appl. Map. Enc. Resp. Resp. R 2 F a est 1 -.21 -.25 8.21** .02 .32 1.22 2 -1. 60** 3.45** -.25 8.21** .63 11.35** .77 3 -1. 44** 3.41** .06 7.51** .61 10.41** .79 4 1.32* 1.17* 5.77** .38 6.44** .97 1M -.08 7.58** .00 .04 1.21 2-3M -. 12 .09 2.24* 4.88** .72 17.14** .67 4M -.18 1.43** 4.69** .72. 27.69** .. .65 Note: Estimates are i n terms of seconds spent on a component per analogy item. * = p < .05 ** = p < .01 122 Model F i t s f o r High A b i l i t y Group: C r i t e r i o n V a r i a b l e 2 Component Estimates I n f . - E n c -Model I n f . Appl. Appl. Map. Enc. Resp. Resp. R z F a est 1 .42 -.11 6.90** .07 .80 1.36 2 -1.36** 4.44** -.11 6.89** .84 35.00** .58 3 -1.21** 4.30** .19 6.43** .84 35.00** .58 4 2.55** 1.12** 4.96** .72 27.69** .76 1M .48 6.63** .07 1.67 1.33 2-3M -.32 1.97 1.64* 4.65** .88 48.83** .50 4M 1.27** 1.22** 4.12** .88 73.33** .49 Note: Estimates are i n terms of seconds spent on a component per analogy item. * = p «.05 ** = p < .01 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0094854/manifest

Comment

Related Items