University of Southern California Dissertations and Theses

A Factor-Analytic Study Of Problem-Solving Abilities

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A Factor-Analytic Study Of Problem-Solving Abilities

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Content FACTOR-ANALYTIC STUDY OF PROBLEM-SOLVING ABILITIES by Philip Ralph Merrifield A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Psychology) June 1959 UNIVERSITY O F S O U T H E R N C A L IF O R N IA c. ■ I: A U U A T i. S C H O O L U N I V E R S I T Y PA RK L O S A N G E L E S 7 C A L I F O R N I A T h is d is s e r t a t i o n , n'ritten by Phi l ip. RaXp.U Marr iflald u n d e r thi' d i r e c t i on o f /i.is D i ssertnfion C o m ini/tee, a n d a p p r o v e d b y a ll its m e m b e r s , has been p r e s e n t e d to a n d a e e e p t e d b \ the (I rad uat e S c h o o l , ut p a r t i a l j u lfillm e n t of lo g n ir e m eats f o r the d e g r e e of D O C T O R O F P H I L O S O P H Y Dean Date June, 19r. 9 I) ISSERT ATI ON COMMITTi: E ii Acknowledgements To Dr. J. P. Guilford, the writer Is much Indebted for his constant encouragement and advice during the course of this study. In the early stages of the theoretical de velopment and design of tests, Dr. P. R. Christensen and Dr. J. W. Prick contributed helpful criticism and m«ny ideas. The writer appreciates the contributions of the Project team: Mrs. Anna Deutsch, Mr. Henry Bedard, Mr. Sheldon Gardner, and Mr. Arthur Gershon. Without their assistance, this research would still be "in progress." The writer is especially grateful to his wife, Kathryn, for her equanimity, patience, and support. Ill TABLE OF CONTENTS CHAPTER PAGE I. THE PROBLEM...................................... 1 II. BACKGROUND OF THE STUDY........................ 3 Theories of Problem Solving . . 3 Factor-analytic Basis of Constructs ......... 5 The Structure of Intellect Nomenclature . . . 6 III. HYPOTHESES AND SELECTION OF TESTS................11 A Modified Theoretical Framework................ 11 Design of the Study..............................15 Hypotheses and Description of Tests ......... 20 IV. TEST ADMINISTRATION AND TREATMENT OF THE DATA . 1 + 1 + The Administration and Sample.................. 1 * 1 + Treatment of Test Scores.........................1*5 The Factor Analysis............................. 1*8 V. INTERPRETATION OF THE FACTORS.................... 55 VI. DISCUSSION...........................................65 VII. COMMENTS ON CERTAIN METHODOLOGICAL ASPECTS. . . 71 Scores From Alternate Forms .................. 71 Group Indicator..................................72 Random Variable.............................* • 72 VIII. SUMMARY............................................. 71* REFERENCES..................................................79 iv LIST OF TABLES TABLE PAGE 1. Means, Standard Deviations, and Reliabilities of Scores......................................... 1+7 2. 'Hie Correlation Matrix.............................. 1+9” 51 3. Centroid Matrix of Aptitude Measures.............. 53 1*. Rotated Factor Matrix of Aptitude Measures. . * 51+ 5. Fate of the Hypotheses...............................66 6. Factor Content of Criterion Tests ............... 69 ChArT&K I TfLh PttO iiLiiPi Problem-solving is a continuing human activity. The description of its processes remains a challenge to psychologists. The intent of this study is to explore the possibility of describing, adult problem-solving processes in terms of factor dimensions of human intellect. A problem situation is one in which certain initial information is given, and some goal is specified, but the relationships between the given and the goal are not ap parent . A factor dimension of intellect is a psychological construct, deduced from considerations regarding the nature of thinking, and deriving empirical support from the sta tistical technique of factor-analy3i3. Organization of the Dissertation Chapter II contains a brief review of theories and experimentation In the area of problem solving, and a 1 summary of the work on factor* dimensions carried out by Guilford and his associates. In Chapter III appear a mod ified theory of problem solving, hypotheses and alterna tives, and descriptions of tests used in tnis ana lysis. Chapter IV deals with the administration of tae test bat tery and the processing of the data. Obtained factors are interpreted in Chapter V. Tae discussion in Chapter VI concerns the evaluation of the hypotheses and the conclu sions based upon the analysis. A brief comment on method ology appears In Chapter VII. A summary appears in Chapter VIII. The present study is one of the series carried out by the Project on Aptitudes of High Level Personnel, De partment of Psychology, University of Southern California. J. P. Guilford Is principal investigator. C H A P T T ’R I I BACKSROUIhJ OF THE 3TU0Y This chapter includes : i brief discussion of the background of theory pertinent to this study, an account of the development of a system of constructs tnrough trie tech nique of factor-analysis, and the nomenclature for factor dimensions to be used in this report. Theories of Problem-Solving The scientific approach to the psychology of thought may be said to have begun with Wundt. However, his relatively rigid classifications and his emphasis upon in trospection as the preferred method of investigation led to several reactions, the most pertinent of which was the es tablishment of the Wurzburg school, led by Kiilpe and Sels. Their emphasis on analysis of the goal resulted in the idea of an anticipatory schema, or directing tendency, as a critical aspect of problem solving. Fuller discussions of the work of this group may be found in Johnson (30) and Murphy (32). 3 4 Under the impact of behaviorism, the psychology of thought was neglected, especially in this country, until relatively recent years. In Kurope, Clapar^de and Duncker continued their work in the area. Duncker (3) carried for ward the ideas of the lAfiirzburg school, using the concept of a search model to elucidate his descriptions of the prob lem-solving behavior of his experimental subjects. In the United States, theories of problera-sojving in other than behavioristLc terms have regained the atten tion of psychologists during the past decade. Buracn: (2 ) analyzed protocols of problem-solving behavior and con cluded that the selection of a crucial aspect of the prob lem was of primary importance In achieving a solution. Guilford (7) suggested that problem-solving ability is not a unitary trait, but rather* varies with the nature of the problem, and urged the use of factorial dimensions as ex planatory constructs in in\estlgations of this area of thinking. Meanwhile, experimental studies of problem-solving, many related to hypotheses traceable to the Wurzburg school or to Gestalt psychology, were being conducted. The names of Harlow, Maler, Thorndike, Wertheimer, and others are to be remembered. The reader is referred to Johnson (3^)» Taylor and McNemar (3b), and Gagne (b) for fuller discus sions of experimental results in this area. Ray (3^1) 5 presents an excellent summary of apparatus tests for use in problem-solving experiments. In recent theoretical developments, Polya (33)» a mathematician, has listed four steps toward the solution of a problem: understanding the problem, working out connec tions between known and unknown and deriving a plan of so lution, carrying out the plan, and examining, the solution. In a more elaborate representation, Ray (35) considers as intervening variables such components of "skill" as prece dent cognitions, cognitive operations, and activating hy potheses, and such other influences as previous learning, the problem materials, and a directing tendency, meaning by the last term motivation and channelisation toward a de sired situation. Factor-analytic Basis of Constructs In his discussion of creative thought, Johnson (30) suggests that the success of Guilford and his associates in identifying factors of creativity may hinge on their empha sis on psychological operations, rather than on tests as such. The writer's own experience attests to the emphasis on kind of operation required, although recent theoretical developments place an almost equivalent emphasis on the kind of content used and the kind of product resulting. It Is helpful to recall that the progress of factor 6 analysis as a technique has been primarily a facet of the testing movement, in that the practical objective was to reduce the number and superficial variety of test3 devel oped to predict success in academic work and in various occupations. For a time it appeared that the proliferation of factors based on different tests would lead to the same disregard of the principles of parsimony that was charac teristic of the old faculty psychology and the overexten sion of McDougall's system of instincts. The first major attempt at the cross-identification of thinking factors was made by French (4) in 1951* He was able to systematize the results of 69 factor-analytic stud ies in terms of 36 factors that can be subsumed under the term "intellectual,” plus a number of others in the cate gories of psychomotor abilities, biodata, and non-aptitude aspects of personality. During the eight years since French's monograph, factor-analytic studies have in general confirmed his identifications, and have evinced a greater concern for experimental design. As a result, several of French's factor have been shown to be composites of two, or sometimes more, separable traits in the intellectual cate gory. The Structure of Intellect Nomenclature In 1966, Guilford (10, 11) formulated a system of known intellectual factors tnat described tnese constructs in terms of psychological process or operation, kind of context or content, and kind of result or product. Later developments have resulted in a cubic model in which kinds of products are parallel for all combinations of content and operation, kinds of contents are parallel for all com binations of product and operation, and kinds of operations are parallel for all combinations of content and product. Five kinds of psychological operations are differ entiated: cognition, memory, divergent production, conver gent production, and evaluation. The structure embraces three kinds of content: semantic, having to do with verbal meanings or concepts; figural, characterized by such prop erties as form, size, and texture; and symbolic, dealing with arbitrary signs having little or no intrinsic meaning outside their own system, such as letters and numerals. The third class ificatory emphasis is on the kind of prod uct: units, classes, relations, systems, transformations, and implications. Sixteen factors from the structure of intellect are referred to in this analysis. Their descriptions appear below, grouped initially by operations. All involve seman tic content. Within the operations groupings, the listings are parallel by products. In parentheses after each factor name appears the previous name of the factor and biblio- tt graphic references to studies by the Project on Aptitudes of High-Level Personnel in which the factor vas identified by the tests used in the present analysis. The three- letter code designation preceding each factor name will be used occasionally in subsequent chapters. CMU cognition of semantic units {verbal comprehension, lj, lk, 17, 22, 2k) awareness of the meanings of words or ideas CMC cognition of semantic classes (conceptual classiiication, 2k) awareness of categories of word meanings or ideas CMR cognition of semantic relations (eduction of conceptual relations, 13, 1®, 19, 214) awareness of relations between meanings of words or ideas CMS cognition of semantic systems (general reasoning, li7, 17, 22, 2k) awareness of interrelatedness among components CMT cognition of semantic transformations (penetration, 2k) awareness of possible changes, neither immediate nor obvious, in meanings CMI cognition of semantic implications (conceptual foresight, 13) awareness of antecedents, concurrents, or conse quents of given information DMU divergent production of semantic units (ideational fluency, 13* 1^» 17» 26, 28) the production of many ideas appropriate In meaning to a given idea DMC divergent production of semantic classes {spontaneous flexibility, 17, 28) the production of many categories of ideas appropriate In meaning to a given idea DMR divergent production of semantic relationships (associational fluency, 11|, 2i|, 26, 28) the production of many relationships or associations appropriate in meaning to a given idea DMT divergent production of semantic transformations (originality, l i j . , 2JLp) the production of a number of changes of interpreta tion, neither immediate nor obvious, that are appro priate to a general requirement, NMC convergent production of semantic classes (not previously identified) the production of a required category of meaning NMR convergent production of semantic relationships (eduction of conceptual correlates, 1) 4, 2ip) the production of a unique relationship implied by the 10 conjunction of two or more concepts NMT convergent production of semantic transformations (conceptual redefinition, 21, 2b) the production of a specific change of interpretation, neither immediate nor obvious, that is essential to a specified new requirement. i!MI convergent production of semantic implications (deduction, ) the production of a specific antecedent, concurrent, or consequent from given information EMR evaluation of semantic relations (logical evaluation, 13, 17, 21, 22) deciding on the appropriateness of a relationship on the basis of logical consistency EMI evaluation of semantic implications (sensitivity to problems, 2i f . , 26, 28) deciding on the more crucial antecedents, concurrents, or consequents of given information CHAPTER III HYPOTHESES AND SELECTION OF TESTS This chapter contains a description of a modified theoretical framework for problem-solving, a brief comment on limitations and design of the present study, a statement of the hypotheses and their alternatives, and descriptions of the tests used in the fsctor-analysis. A Modified Theoretical Framework Introduction and Overview The present study envisions the total problem solving process in five stages, similar to those proposed by Johnson (30): preparation, analysis, production of ten tative solutions, verification, and reapplication to the problem. The absence of incubation and illumination, two processes frequently considered central to problem solving, requires comment* Johnson (30) has pointed out that "Incu bation and illumination are fascinating and perhaps myster ious only if one expects that the process of productive 11 12 thought is always open to subjective observation.” In one sense, the testing of the hypotheses to be proposed will further restrict the amount of behavior necessarily ob served subjectively. II' It can be shown that certain abil ities, derived from objective observation and analysis, ac count for a relatively large portion of the variance aris ing from individual differences in solving problems, then the portion of the variance remaining to be explained, by incubation or illumination or similar concepts, will be less. The preparation phase includes the effects of moti vation, social interaction, and previous experience. In both the analysis and production phases, emphasis Is placed on the joint elaboration of both the given data and the de sired situation, producing alternative outcomes from the given data, and alternative antecedents from the desired situation. The choice of a tentative solution is presumed to be based on the comparisons of the alternative outcomes and the necessary antecedents. The verification phases in volves the testing of the tentative solution. If the choice proves to be not acceptable, the process resumes, other alternatives are produced, another choice Is made, and so on. The returning, or reapplication phase, probably Involves motivation and perhaps ego Involvement and other personality traits. 13 Details of the New Framework Preparation This phase includes Ha;; ' s "previouj learning," the "problem materials," and that portion of "precedent cogni tions" which arise primarily from memory (35)- Polya's "understanding the problem" partly overlaps preparation as used here, but is more closely related to the second phase (33). Analysis In this systematization, the analysis phase is pri mer ily concerned with those processes by which the solver becomes familiar both with the data and its attributes and with the goal and its attributes. The behavior assigned to tnl3 phase corresponds to Polya's (33) "understanding the problem," and to Ray*3 (35) "precedent cognitions" and to some extent hia "cognitive operations." The analysis phase culminates in the selection of a method of approach to the problem. Several methods are usually available, such as a synthesis of the given information, the establishment of conditions necessarily antecedent to the desired situation, reasoning by analogy, trial and error manipulations, or combinations of these. The most efficient method Is proba bly a function of the specific problem to be solved. 1U Production Data-based activity. Production encompasses those processes of synthesizing, of determining alternative out comes from combinations of the given items of information, of deducing relationships inherent in the given informa tion, that are based almost entirely on the data. From these processes, a set of possible alternative outcomes is generated. Goal-based activity. In addition, production in cludes the heuristic processes, the working backward, and the derivation of necessary antecedents that are based al most entirely on the analysis of the goal. From these, a search model, or possibly a set of alternative search mod els, is produced. A similar emphasis on the goal is sug gested by Ray’s (35) "directing tendency," and the whole phase of production would seem to correspond to his "cogni tive operations," Polya (33) stresses the importance of heuristic thinking to success in problem solving. Choice of Tentative Solutions. The set of alterna tive outcomes is compared with the search model, or the set of search models, and one tentative solution is selected from the possible pairs. It seems reasonable to presume that each alternative outcome ana each 3earch model has its own probability of success, at least subjectively, and that lb the more probable pairs are selected first. Reiteration occurs as the more apparent alternatives are rejected. Verification The rejection of a tentative solution occurs as a result of the fourth phase, verification. As several wri ters have pointeci out, if tne first attempt succeeds, no real problem any longer exists. The rejection of a tentative solution here refers to rejections made by the individual according to his own standards. Such subsequent attempts are thus a function of his understanding of the goal as well of his motivation. Reappl1cation Returning to previous stages with the intent to se lect another tentative solution constitutes the fifth phase in the system. However, these reapplications will occur only until an appropriate solution is reached, or until the individual's production of possible alternatives is ex hausted. Design of the Study Limitations Practical considerations limited the testing time available for this study to six hours, an amount much less 16 than would be needed to test adequately the hypotheses that could be derived from the complete schema described above. A relatively intensive exploration of one phase was consid ered feasible, and was preferred to a broad scanning of all five phases. The six hypotheses tested in this analysis pertain ;,o the production phase of the proolem-solving schema. Ap propriate productive efforts would seem to require a cer tain amount of previous analysis and prep-* rat ion. It 13 reasonable to assume that some verification and reapplica tion will also occur as the examinees seek the correct so lutions to the items in the problem-solving tests. For these reasons, the production phase was selected as the area of primary interest to this analysis. Procedure s Of the six hypotheses tested, four were concerned with working forward from the given information, and two were concerned with working backward from the goal. Twelve tests were developed especially for this study as measures of the six hypotheses concerning variables involved. Al ternative hypotheses in terms of known factors were sug gested for each of the six major hypotheses. Three problems tests were designed as criteria of problem-solving performance. In each of these, the Initial 17 Information and the goal were both described; the task was to indicate the intervening steps, i.e., the solution. Measures of additional reference factors were included. It was hoped that the rotated factor matrix would serve as a basis for inference regarding (1) the degree to which known factors could account for hypothesized abili ties in problem-solving, (2) the degree to which any new the hypothesised abilities are related to performance in the criterion tests, and (3) the degree to which known fac tors are related to criterion test performance. To this end, the decision was made to use simple structure and pos itive manifold as primary criteria for rotation, invoking psychological interpretability in the later stages for tne delineation of known factors, but not for the new tests or the criterion tests. In this way, the known factors would be used as statistical controls, and only common variance In otner than those factors would require appeals to new constructs for its explanation. The centroid method of extracting factors requires common variance to be present In at least two variables in order for a factor based on that common variance to emerge. Thus, If reference factors are to be included as statisti cal controls in an analysis, each must be marked by at least two tests. A minimum requirement would be the 18 presence of one highly saturated^ measure of the factor plus at lsa3t one other t©3t containing appreciable vari ance in the factor* This analysis of a complex phenomenon required the inclusion of many reference factors. Limit.atlons of test ing time did not permit the inclusion of two tests for ev ery reference factor. As a compromise, it was decided to use scores from alternate forms of highly saturated meas ures as separate variables in the analysis. The variance shared by alternate forms of highly saturated tests is pre dominantly factor variance that would be common with other tests of the factor, w^re they included in the analysis, however, a sizable portion of variance common to alternate forms may arise from sources specific to the test. In the compromise adopted was the risk that the use of alternate forms would lead to additional specific factors, or to the confounding of specific test variance with common factor variance, thu3 leading to difficulties of interpretation. The decision was made on the grounds that the greatest pos sible number of reference factors should be given an oppor tunity to emerge. a highly saturated measure of a factor Is one that has consistently high loadings on that factor, and no ap preciable loadings on other factors. In other words It has a high factorial validity. 19 Two groups of subjects were available for testing. These groups were composed of Naval Air Cadets ana Aviation Officer Candidates. Selection requirements used by the U. S. Navy were similar for the two groups. The Naval Air Ca dets were not college graduates; the Aviation Officer Can didates were college graduates. During the scoring, the suspicion crew that the two groups might not be homogeneous with respect to all the tests. Thu3 a Group Indicator var iable was Included in the analysis. It was decided to ro tate without reference to this variable, so that its final loadings might better represent its relationship to the different factors to be obtained. As an additional statistical control, a Random Var iable was included by assigning sequential entries from a table of random normal numbers as scores for tne examinees. The sequence of examinees was alphabetical by last name, so that the assignment was essentially at random. The load ings of this variable, which was not considered during ro tations, were expected to give some indication as to the standard error to be attributed to factor loadings. Summary Because of the limitations of available testing time, only six hypotheses derived from the production phase could be tested in this analysis. 20 Measures of reference factors were Included to act as statistical controls for variance in the new tests de veloped for the hypotheses and for the new tests developed as criteria of problem-solving performance. In some cases alternate forms of highly saturated tests were used as mar kers for the reference factors. Rotation of centroid factors was to proceed, under the joint criteria of simple structure and positive mani fold. Psychological Interpretability was to be used as a criterion for rotating reference factors In the later stages. This criterion was not to be used for the new tests or the criterion tests. A. Group Indicator and a Ran dom Variable were included as additional sources of infor mation. Hypotheses and Description of Teats Twelve new tests were developed as measures of the six hypothesized abilities. The new tests were extensively pretested using students at the University of Southern Cal ifornia1 and Los Angeles State College.^ Revisions were ^The writer is indebted to Dr. Constance Lovell and Dr. Everett Wyers, Department of Psychology, and to Mr. E. Spiegel, School of Law, for granting time for pretesting. ^The writer is indebted to Dr. Robert Morman, Los Angeles State College, for granting pretesting time at his institution. 21 made with attempts to Increase the reliability and univo- callty of the tests, and to allow the maximum amount of in formation to be collected in the shortest possible testing time. Where possible, alternate forms of each test were devised, to be of approximately equal means and variances. Within each of the alternate forms, items were arranged in order of Increasing difficulty. The hypotheses, with their alternatives, and the tests selected to measure them, are presented below. Each hypothesis from the theory is indicated by a roman numeral. Tests designed especially for the hypothesis are listed following the small letter "a." Alternative hypotheses and tests follow subsequent small letters. Tests are described in more detail in the listing following the discussion of hypotheses. Hypothesis I - the ability to think rapidly of several at tributes or characteristics of a given object. a. Tests of the hypothesis i j . . Attribute Listing I 11. Differences 30. Similarities These three teats require the examinee to think of attributes of given objects; in test I 4. he is to list them; in test 11 he must think of them prior to specifyin,, ways in which two objects differ; in test 30 be must think of them prior to finding similarities. Similarities has in a 22 previous study (2/|) defined the factor cognition of seman tic transformations. The test Is Included here because it logically fits the hypothesized ability. b. Alternative hypotheses and tests It is possible that tne nypoth©3ized ability can be accounted for in terms of divergent production of semantic units and divergent production of semantic relations. DMU lb. Ideational Fluency DMR 3* Associatlonal Fluency Hypothesis II - the ability to classify objects or Ideas. a. Tests of the hypothesis 27- Sentence Pairs ApO. Word Grouping In Sentence Pairs, sentences are to be matched In terms of similarity of content or expressed relationship. Word Grouping requires that twelve words be classified Into four groups, with no word in more than one group. b. Alternative hypotheses and tests An obvious alternative Is that, instead of defining a new factor, the variance in these tests would be ac counted for by the known factor cognition of semantic classes. CMC 35-3^. Verbal Classification, Parts I and II Hypothesis III - the ability to find different relation ships between attributes of an object or situation. a. Tests of the hypothesis 23 13• Figure Concepts (uncommonness) 21. Paired Similarities 20. Sequential Association Figure Concepts requires the selection of two from a set of 20 pictured objects and a statement of what they have in common. It was anticipated that the same object would be included in more than one pair. The weighting for uncommonness was employed as a means of accentuating the degree of difference between the stated relationships. In Paired Similarities, pairs of words are presented as test Items; the same word occurring In several different pair ings. Again the examinee is to state how the given pairs were similar. In Sequential Association, four given words could be associated pairwise in several different ways. The task requires the rearrangement of the words so that the first in the series Is associated with the second, the second with the third, and the third with the fourth. It was hypothesized that the examinee would need to consider a number of associated pairs before selecting the proper ones to make the required sequence. b. Alternative hypotheses and tests These tests should contain some variance in cogni tion of semantic relations and convergent production of se mantic relations. That these two factors account for most of the variance in the measures of Hypothesis III is the alternative to a new factor. 2k CMR 33-3U. Verbal Analogies I, Parts I arid II NMR 38-39. Vocabulary Completion, Parts I and II Hypothesis IV - the ability to think of alternative out comes or implications of a given situation, a. Tests of the hypothesis 18. Multiple Grouping 20. Object Synthesis III Botn of these tests require using the given infor mation in different ways to obtain different results. In Multiple Grouping the task is to group seven woras into several different categories baaed on size, color, uses, and similar characteristics. In Object Synthesis III, the task is to think of many different objects that could be made by combining two given objects. b* Alternative hypotheses and tests An Object Synthesis test requiring the production of just one new object for each pair of given objects has emerged in previous analyses as a measure of divergent pro duction of semantic transformations and divergent produc tion of semantic classes (17* 2I 4., 28). The variance common to Multiple Grouping and Object Synthesis III could well be accounted for in large part by these two factors. Since both tests may require thinking of many attrioute3 prior to stating the groups or the new objects, divergent production of semantic units may also be involved, as in lb. 2 5 DMC 6. Brick Uses (shifts) 19. Object Naming (shifts) DMT 7-8. Cartoons, Parts I and II DMU 13. Ideational Fluency Since Object Synthesis has also had 3ome variance in con vergent production of semantic transformations in one anal ysis (21), Object Synthesis III and Multiple Grouping may have some loading on that factor. NMT 1^. Gestalt Transformation Hypothesis V - the ability to list attributes of the speci fied goal or desired situation. a. Tests of the hypothesis 1. Apparatus Test (drastic) 2. Apparatus Test (minor) 5. Attribute Listing II The Apparatus Test requires the examinee to state two improvements for a common appliance. It is Included here on the presumption that an improvement corresponds to some attribute of a more desirable goal, in this case a better appliance. It was decided to use two scores to see whether both minor and drastic changes were on the same factorial dimensions. In Attribute Listing II, the exami nee must list separate characteristics of an object that would meet a described need, b. Alternative hypotheses and tests As an alternative, the tests hypothesized above could reasonably be accounted for by evaluation of semantic 26 Implications, a factor that Apparatus Test has helped de fine In previous studies (2i f . , 26, 28), There is also the possibility that the "drastic" score on Apparatus Test in volves enough of a change to introduce some variance in divergent production of semantic transformations. EMI 25-26. Seeing Problems, Parts I and II DMT 7-8. Cartoons, Parts I and II Hypothesis VI - the ability to educe logically sufficient antecedents to a specified situation. a. Tests of the hypothesis 9. Common Needs 10. Contingencies 12. Episodes 23. Possibilities Common Needs requires the examinee to pair objects that require the same antecedent before they can be used. Episodes requires two explanations for a described behavi or. Contingencies and Possibilities emphasize future events and require thinking of reasonable antecedents to those events. b. Alternative hypotheses and tests The leading alternative hypothesis is that all these tests are measures of cognition of semantic implica tions . as Contingencies proved to be in a previous analysis (13). That factor, formerly described as "conceptual fore sight," might be broad enough to include the awareness of antecedents as well as consequents. 27 CMI 22. Pertinent Questions The Criterion Tests In order to obtain measures of problem-solving ability, three tests were designed especially for tnis study. CP 17. Missing Links Predicaments 31. Transitions (coherence) 32. Transitions (logical aspects) In all three the initial information and the goal or desired situation are clearly stated. The task is to indicate the necessary steps In proceeding from the initial to the final events. In Missing Links, the examinee is re quired to think of three words to complete a chain of as sociations, first and fifth words being given. In Predica ments, a problem situation Is described and a solution is required, with the restriction that only 3ome combination of four given objects can be used in the solution. In Transitions, the beginning and ending of a very short story are presented; the examinee Is required to compose the mid dle part, making the total as complete and logical as he can. The "logical aspects" score was of primary interest in this study; the "coherence" score was included to see whether its factor composition differed from that of the "logical aspects" measure. 2 8 a. One hypothesis was that these three tests would generate a factor of their own which could be called "prob lem solving ability." b. One alternative was that they would all load primarily on a single known factor. c. A second alternative was that the tnree tests would load on different factors consistent with the nature of the different tasks. Additional Reference Tests In addition to the tests for the alternatives to the six hypotheses described above, measures of factors possibly related to the criterion problems were included in the test battery. These factors and their tests are listed below. EMR evaluation of semantic relationships 16. Logical Reasoning CMS cognition of semantic systems 29. Ship Destination CMTJ cognition of semantic units 37* Verbal Comprehension Description of Tests The listing below contains the name of each vari able used In this analysis, a summary of the task, a brief 29 statement of scoring procedures, a sample item {in most cases), the number of items and working time, and the hy pothesized factor content. The hypothesized factor content i3 coded to the preceding discussion of hypotheses. Homan numerals refer to the six hypothesized abilities, the let ters "CP" to the criterion tests, and the three-letter de signations to previously identified factors. Variables i j . 1 and I 4. 2, Group Indicator and Handom Variable, have no hypothesized factor content. 1. Apparatus Test - CS01B (drastic modifications) Task: suggest two improvements for each appliance. Score: number of improvements involving marked change from usual construction or use. Sample Item: Telephone a. A device that tells who is calling before you pick up the receiver. Parts: 1; items/part: 10; working time: 7 minutes hfc: Va, EMI 2. Apparatus Test - CS01B (minor modifications) Task: suggest two improvements for each appliance. Score: number of improvements involving slight changes or additions. Sample Item: Telephone 30 b. Luminous dials to see in the dark. Parts: 1; items/part: 10; working time: 7 minutes hfc: Va, EMI 3. Associational Fluency I, Form A, 1957 Task: write words similar In meaning to a given word. Score: number of acceptable similar words produced. Sample Item: Hard: difficult, solid, tough, severe Parts: 2; Items/part: 2; working time: l | . minutes hfc: lb, DMR 4. Attribute Listing I - HA01A Task: list attributes of a given object. Score: number of attributes of a morphological nature. (other kinds of attributes were not counted.) Sample Item: List all the attributes you can for CHEWING GUM wrapped in paper__________________ comes from chicle_________________ sticks to furniture_______________ Parts: 1; Items/part: 1; working time: 2 minutes hfc: la 5. Attribute Listing II - HS01A Task: list attributes of an object that would serve a given function. 31 Score: number of relevant attributes listed. Sample Item: You wish to drive a long nail Into a wooden post. You have none of the tools usually used for this purpose. List the attributes that a usable object or device would have. hold in hand___________ harder than the nail flat striking surface won't hurt hand________ Parts: 1; items/part: 1; working time: 2 minutes hfc: Va 6. Brick Uses (shifts) - CFOq_A Task: list different uses for a brick* Score: number of times the examinee shifts from one kind of use to another* Parts: 1; items/part: 1; working time: 10 minutes hfc: IVb, DMC 7-8. Cartoons - CN07A Task: supply clever "punch lines" for cartoons. Score: sum of ratings of responses for cleverness on a five-point scale* Parts: 2; items/part: 8; working time: li| minutes Note: variable 7 la Part I; variable 8 Is Part II* hfc: IVb, Vb, DMT 9. Common Needs - HN01A Task: select two objects that require the same preceding operation, or the presence of a third object, be fore they can be used* 32 Score: number correct, adjusted for chance success. Sample Item: Farts: 2; items/part: 6; working time: 3 minutes hfc: VTa 10. Contingencies - PX03A Task: state a condition that might require the use of a given object in a given situation. Score: number of plausible conditions listed. Samole Item: Sally and Jane are going out to a farm to pick berries. Their pay will be half the berries they pick. Included In the things they take are the objects listed below. For each object, state a condition or circumstance that may arise requiring the use of that object. Ointment if bitten by Insects or scratched________ Pins for rips that might occur in their clotnes Parts: 1; items/part: 20; working time: 6 minutes hfc : Via, CMI Task: list many ways in which two given objects differ. Score: number of acceptable differences listed. Sample Item: 1. banana 2. kite 3. stamp A. book of matches B. desk C. mailbox D. pull-toy Key: 1-A; 2-D; 3-C 11. Differences - HA02A banana differs from apple A. long___________ round B. easy to peel hard to peel C. tropical cold climate Parts: 3; items/part: 1; working time: 3 minutes hfc: la 12. Episodes - HN02B Task: write two explanations for a specified action. Score: number of plausible explanations. Sample Item: A man is sitting in his chair reading a magazine. Suddenly he closes the magazine and strides out of the room. Write two possible explanations. A. he realizes he 13 late for an appointment______ B. his wife called him to dinner___________________ Parts: 2; items/part: 3J working time: i j . minutes hfc: Via 13. Figure Concepts Test (uncommonness) - CAYOijA Task: find qualities or features that are common to two or more pictured objects. Score: sum of response weights on three-point scale In verse to obtained frequency of response. Parts: 1; items/part: 1; working time: 3 minutes hfc: Ilia li|. Gestalt Transformation - CR03A Task: indicate object having a part that will serve a 3U specified purpose. Score: number correct, adjusted for chance success. Sample Item: To start a fire A. a fountain pen B. an onion C. a pocket watch Key: C. D. a light bulb E. a bowling ball Parts: 2; items/part: 10; working time: 10 minutes hf c: NMT 15* Ideational Fluency I, Form A, 1957 Task: list objects that belong to specified classes. Score: number of acceptable responses. Sample Item: Name fluids that will burn. ______ gasoline___________ _______kerosene___________ ______ hydrogen___________ _______alcohol____________ Parts: ii; items/part: 1; working time: 12 minutes hfc: lb, IVb, LMU 16. Logical Reasoning, Form A, 1955 Task: choose a statement logically consistent with the given statements. Score: number of correct choices, adjusted for chance success. Sample Item: No birds are insects. All swallows are birds, A. No swallows are insects. B. Some birds are not swallows. C. All birds are swallows. Key: A. D. No insects are birds. Parts: 2; iteins/part: 20; working time: 20 minutes hfc: EMR 17. Missing Links - HZ01A Task: produce three words to complete a chain of associa tions between two given words. Score: sum of weights for degree of completeness. Sample Item: red sunset weather cold beer Parts: 2; items/part: b; working time: b minutes hfc: CP 18. Multiple Grouping - HX01A Task: arrange given words into several different meaning ful groups. Score: number of correct placements of words in groups, adjusted for chance success. Sample Item: 1. arrow Group I: 1. 2, 5» 7 2. bee 3. crocodile Group II: 3» 6____ Zj. fish 5. kite Group III: 2, 3» U* 7 6. sailboat 7. sparrow Group IV:_______________ 36 Parta: 2; items/part: 1; working time: i j . minutes hfc; IVa 19. Object Naming (shifts) - CSXOUA Task: list names of objects in a given class. Score: number of times the examinee shifts from one sub class of objects to another. Farts: 1; items/part: 1; working time: 2 minutes hfc: IVb, m e 20. Object Synthesis III - HX02A Task; list as many as five things that could be made using both of two given objects. Score; number of acceptable responses. Sample Item: nail and cane spear____ hook________ Parts: 2; items/part: 2; working time: 4 minutes hfc: IVa 21. Paired Similarities - HR01A Task: state one way in which a given pair of words are similar. Same words used in several different pairs. Score: number of different similarities stated. Sample Item: quarter - fifth fractions nickel - quarter coins_____________________ quarter - inning time periods in sports 37 Parts: 2; Items/part: 8; working time: 6 minutes hfc: Ilia 22. Pertinent Questions - PR03A Task: write four questions, the answers to which would serve as a basis for making a decision in a given situation. Score: number of relevant questions. Parts: 2; items/part: I 4 .; working time: 12 minutes hfc: VIb, CMI 23. Possibilities - HN03B Task: name as many as four objects that could be used to perform a specified task. -Score: number of usable objects listed. Tarts: 2; Items/part: 3; working time: ^ minutes hfc: Via 24. Predicaments - HZ02B Task: describe two ways in which given objects could be used to solve a specified problem. Score: number of times given objects were incorporated as essential parts of adequate solution. Sample Item: You are on a picnic with some friends. Instead of bringing sandwiches already prepared, you have stopped at a store and bought the "makings." You discover that instead of sliced cheese you picked up a solid piece. How would you divide the cheese so that each person can make a sandwich, using only the objects given? 38 harmonica matches thermos bottle ukelele A. take string from ukelele, hold taut, press through cheese__________________________________ Parts: 2; item3/part: 3; working time: 10 minutes hfc: CP 25-26. Seeing Problems - CS06A Task: write as many as five problems arising from the presence of a given object. Score: number of appropriate problems listed. Parts: 2; items/part: 6; working time: 8 minutes Note: Variable 25 is Part I; Variable 26 i3 Part II. hfc: Vb, EMI 27. Sentence Pairs - riCOlA Task: choose two sentences that express the 3ame kind of idea. Score: number correct, adjusted for chance success. Sample Item: A. Cats are real companions. B. Deer are excellent game. C. Exercise promotes good health. D. The storm approached rapidly. E. The picture sold for twice its true value. 1. He walked home every night. 2. Some animals make good pets. 3. Artists are sometimes well paid. 1;. The train gathered speed as it left. Key: 1-C; 2-A; 3-E; U-D. Parts: 3i items/part: i j . ; working time: 6 minutes hfc: Ila 39 28. Sequential Association - HR02A Task: arrange four given words in sequence so that the first is associated with the second, the second with the third, and the third with the fourth. Score: number of correct sequences achieved. Sample Item: Indicate the best order for the following words: pen pig read write g i_ U 3 Parts: 2; items/part: 5; working time: 3 minutes hfc: Ilia 29. Ship Destination Test, Form A, 1955 Task: find the distance from snip to port, considering the influence of several variables. Score: number correct, adjusted for chance success. Parts: 1; Items/part: !;8; working time: 15 minutes hfc: CMS 30. Similarities - RCS01A Task: write six ways in which a pair of common objects are alike. Score: number of acceptable similarities given. Sample Item: Apple and orange are alike: A. sweet B. have seeds C. grow on trees Parts: hf c: Task: Score: Sample Parts: hf c: Task: Score: Sample Part s: ^ 0 1; Items/part: 6; working time: 5 minutes la 31. Transitions (coherence) - HZ03A write a coherent account logically connecting the given initial and final situations of a short story, rating of response on a five-point scale for coher ence of discourse. I tern: Jonas was not a hard man, at least in his own opin ion. He spent his money wisely, and did nothing more than require his daughter to do the same. Take the matter of the car. __________________________ Jonas heard her rapid steps across the porch, the slam of the door, and the crunch of gears. He watched from the window as the dust blew across the road, then turned slowly to ward the kitchen. It was almost dark enough to light the lamp. 2; items/part: 1; working time: 10 minutes CP 32, Transitions (logical aspects) - HZ03A same as variable 31* number of aspects inherent In given material which examinee accounted for in his response. Item: same as variable 31* 2; items/part: 1; working time: 10 minutes hfc: CP Task: Score: Sample Part s: Note: hfc: Task: Score: Sample Parts: Note: hfc: 41 33-34. Verbal Analogies I - RCR01C select the word to complete an analogy; finding the relation in the first pair is difficult. number correct, adjusted for chance success. Item: cloth : dye :: house : ? A - shade B - paint G - brush D - door E - wood Key: B. 2; itema/part: lb; working time: 12 minutes Variable 33 is Part I; Variable 34 I-3 Part II. Illb, CMR 35-36. Verbal Classification - EL16A assign given words to one or neither of two classes, each defined by four other words. number of correct assignments. Item: COW desk >/ TABLE HORSE V sheep CHAIR GOAT _____ rocker v' BOOKCASE DOG _____ tree _____LAMP ✓ cat_____________ _____ no 3 6 2; items/part: 40; working time: 8 minutes Variable 35 is Part I; Variable 36 is Part II. Ilb, CMC 37. Verbal Comprehension, Guilford-Zimmerman Apti tude Survey, Part I, 1947 Task: select the word that is similar in meaning to a gi en word. Score: number correct, adjusted for chance success. Parts: 1; items/part: ! | . 0 ; working time: 12 minutes hfc: CMU 38-39. Vocabulary Completion - REC06A Task: produce a word that fits a given definition and be gins with a given letter. Score: number correct. Sample Item: A contest of speed.......... (r) race Parts: 2; items/part: I 4.O; working time: 6 minutes Note: Variable 38 is Part I; Variable 39 is Part II. hfc: Illb, NMR / 4 .O. Word Grouping - HC02A Task: arrange given words into four mutually exclusive groups. Score: number of given words correctly grouped. Sample Item: 1• blue Group I: 2. cutter 3. driver Group II: 4. heavy 5. larger Group III: 6. light 7# little Group IV: 8. long 9. opener 10. orange 11. redder 12. short >, 7, 8, 12 4 - 1 6 2, 9 43 Parts: 2; Items/part: 2; working time: 3 minutes hfc: IIa 41. Group Indicator This variable was introduced to measure the effects of possible differences between Naval Air Cadets and Avia tion Officer Candidates. Score: Aviation Officer Candidates (college graduates); 1 Naval Air Cadets (not college graduates); 0 l \ . 2 . Random Variable This variable was Introduced to obtain an estimate of the standard error of factor loadings In this analysis. Values from a table of random normal deviates were assigned at random to the examinees and thereafter treated as scores. CHAPTEK IV TEDT ADM INI oT HAT 10 i N AND TREATMENT OP TiiE DATA The Administration and Sample The 33 tests were assembled into six booklets for convenience in administration. They were arranged so that similar tests appeared In different booklets. Each booklet required about 60 minutes total testing time. Time limits for the tests were observed as strictly as possible. Most of the tests contain two or more parallel parts that are separately timed. In the testing session, the administra tor read the instructions for each test aloud while the examinees read them silently. Questions were permitted; they were answered by reference to the pertinent part of the printed instructions. The battery was administered to 232 Naval Air Cad ets and Aviation Officer Candidates at Pensacola Naval Air 1+5 Station.^ Peraonnel at the Aviation Psychology Laboratory, Pensacola, administered the testa. Motivation was reported as high; there were no apparent anomalies in the adminis tration of the tests. Because complete data was not avail able for 13 examinees, they were omitted; the analyzed sam ple numbered 219* Treatment of Test Scores Scoring Twenty-six tests required the evaluation of comple tion-type responses. This evaluation was based upon scor ing guides developed during the pretesting, modified as necessary to assimilate the greater variety of responses obtained from the analyzed sample. Most of these te3ts were scored independently by two individuals and the scores averaged, in an attempt to minimize scorer bias. The rest of the tests of this type were scored by individuals who had scored the tests for previous analyses and were thus familiar with the scoring techniques. Seven tests in multiple-choice format were scored and checked by machine, using appropriate adjustment formu las to minimize chance success. iThe writer is indebted to Dr. Wilse B. Webb for making this testing possible at Pensacola, and to the staff of the Aviation Psychology Laboratory, U. S. Naval Air Sta tion, Pensacola, Florida, for their assistance. ^6 Rellabilities Coefficients of reliability were computed from al- ternate-form correlations, extended by the Spearman-Brown prophecy formula, wherever possible. For some tests, reli ability estimates were based on previous administrations; for others, the obtained communality was used as a lower- bound estimate. Table 1 shows the mean, standard deviation, and re liability of each variable used in the factor-analysis. Intercorrelations of scores Frequency distributions were made for all variables. None was markedly different from normal except for variable ij . 1 , Group Indicator, which by nature was dichotomous. Pear son product-moment coefficients were computed for all pairs of variables on the SVIAC (Standards Western Automatic Com puter). As this procedure yields point-biserial coeffi cients when one variable Is dichotomous, correlations In which Group Indicator was involved were adjusted to biserial coefficients for greater consistency with the other values. For the initial correlation matrix, one additional score from test I 4., Attribute Listing I, and part scores from tests 15, Ideational Fluency, 16, Logical Reasoning, 19, Ob ject Naming (shifts), and 22, Pertinent Questions were in- Table X Me ana, Standard Deviations, and HellabllltLes of Scores Te st n _ a rtt X. Apparatus Test (drastic! 5-76 3-01 -63 2. Apparatus Test (minor) 7-71 3.58 - 58 3. Assoclat ional Fluency 12 . 60 4 - 08 .63 4- Attribute Listing I 4-62 2 .64 . 256 5. Attribute Listing II 3.99 2.45 .418 6. Brick Uses — shifts 12. 70 5-65 .468 7 - Cartoons — Mart I 21 .62 5 - 66 -77+> 8 . Cartoons — Part II 21 .57 6 -Ol -488 9- Common Needs 7-58 2 . 06 . 32b io . Cont ingencies IO . 24 2 .69 .516 XX. Differences 16.73 4-40 - 53 X2. Ep isodes 7 .28 1 .88 .278 13. Figure Concepts Test 9-72 3-20 - 496 14- Gestalt Transformation IO .91 3.45 -53 X5. Ideational Fluency 51 - 86 13 . OO .77 16 . Logical Reasoning 25 . 5b 7-7t> .800 X7 . Missing Links 20 . 11 7.91 . 58 16. Multiple Grouping 23 . 28 5.53 -43 19 . Object Naming — shifts 4-43 1.71 . 398 20 . Object Synthesis III 6.71 2 .91 . 60 21. Paired Similarities 17 . IO 4-69 -47 22 . Pertinent Questions 27-13 3-73 -73 23. Possibilities 15-83 3-90 - 55 24- Predic aments 13-87 3-46 -55 25* Seeing Problems — Part 1 11 . 80 3 . 68 .5 28 26. Seeing Problems — Part II 13-37 4-85 . 528 27. Sentence Pairs 5 -83 2. 40 .18 8 28 . Sequential Association 4-11 2.61 .75 29. Ship Destination 34-02 8 .48 .87° 30. Similaritiea 20 .36 4-50 -578 31 - Transitions — coherence 5 . 78 2 .00 .46 32. Transitions — logical aspects 6.56 2. 27 .4.86 33- Verbal Analogies — Part I 8 . 09 2.84 .618 34- Verbal Analogies — Part II 6 .59 2.72 . 528 35- Verbal Classification — Part I 25 - 81 6.76 .428 36 . Verbal Classification — Part 11 31 - 71 4-34 -478 37. Verbal Comprehension 23.08 5.87 .82c 38. Vocabulary Completion — Part I 32.95 4-78 -758 39. Vocabulary Completion — Part II 32 .10 5- ci .72 1 +0. Word Grouping 26 .97 6 .92 .436 1+1 . Group Indicator - 83 -49 --- 1 +2. Random Variable 30 . 37 9.92 Reliabilities computed as alternate-fonn estimates us ing Spearman— Brown prophecy f omul a, except as noted. ^CommunaXities used as Xower-bonnd estimates of reliability. CKell at) iXity estimates from previoas studies. 1+8 eluded as separate variables. This step was introduced to increase the possibility of identifying the reference fac tors which, due to limitations on testing time, might be underdetermined in the correlation matrix. After the ma trix was inspected, it was decided to delete the additional score from te^t ip and one of the part scores from test 19, and to combine the coefficients of the other part scores into coefficients representing the correlation of total test scores. The final matrix of intercorrelations is pre sented in Table 2, The Factor Analysis Extraction of factors Fourteen factors were extracted from he correla tion matrix of ip2 variables, using Thurstone's complete centroid method and the computational facilities of the SWAG. The distribution of residual coefficients after the extraction of the fourteenth factor was leptokurtic about zero and contained no coefficient greater than .11 in abso lute value. A fifteenth factor was extracted but not used in the rotational solution, since its range of loadings ex ceeded that of the immediately preceding factor. Such a situation usually indicates the fortuitous concomitance of error variance, and the use of such a factor adds nothing to the systematic solution of the rotational problem. The Table 2 The Correlation Matrix* Te st 1 2 3 1+ c 6 7 8 9 IO 1. 2 . i: 5. Apparatus Test (drastic) Apparatus Test (minor) Aaaociational Fluency X Attribute Listing X Attribute Listing XX Oil -003 -072 — 0) 4 . 2 Oil 21)4 175 301 -003 21)+ 258 309 -072 175 258 115 — Oi.2 301 309 115 183 21+3 21+0 188 211 278 213 079 093 107 289 217 11+) 029 HO 01+6 -027 091 -OOI+ 106 150 298 260 230 206 6 . 7, 8. 9. IO. Brick Uses — shifts Cartoons — Part I Cartoons — Part II Common Needs Contingencies 183 278 289 0) 4 . 6 150 2X43 213 217 -027 298 21+0 079 11+2 091 260 186 093 029 -OO1 + 230 211 107 HO 106 206 199 191 ol+o 171+ 199 1+38 lo7 215 191 1+38 156 11+5 01+0 107 156 071 171+ 215 11+5 071 IX . 12. 13. 11+. 15 . Differences Ep i s ode s Figure Concepts Test Gestalt Transformation Ideational Fluency 120 159 159 -022 Ii4i4 310 125 085 038 2) _ ! 7 166 112 127 150 19b 158 131 156 160 196 21+8 136 156 071 160 236 133 277 190 334 203 01+3 15)+ 07 2 221 21+b 188 258 038 280 093 112 129 021 056 290 179 186 169 316 X6. 17 . 18. 19. 20. Logical Reasoning Missing Links Multiple Grouping Object Naming — shifts Object Synthesis III 080 073 080 157 106 022 221 233 160 301 317 362 233 223 292 181 213 156 156 208 155 192 217 138 153 183 251 358 21+2 386 01+8 171 118 077 285 130 252 210 170 257 292 175 131 -083 117 055 056 216 188 301 21 . 22 . 23- 21+. 25. Paired Similarities Pertinent Questions Possibilities Predicaments Seeing Problems — Part I 122 278 136 12)4 097 18) 4 . 287 206 300 138 21+0 313 315 213 179 113 222 208 130 11+e 228 361 270 125 2 35 177 276 235 138 219 230 306 11+5 175 265 197 302 223 11+9 167 178 208 050 106 026 220 353 251 311 257 26 . 27 . 28. 29. 30. Seeing Problems — Part II Sentence Pairs Sequential Association Ship Destination Similari tie s 073 051 -087 -0) 4 . 0 126 28 2 031 056 02 6 306 206 315 lOl 152 21+4+ 617 125 036 135 261+ O C * f 136 21)+ 261 15++ 251 -002 035 116 1+33 290 051 — Cl+9 018 117 183 096 -019 066 201+ 118 111 191 189 008 277 168 ll+o 023 303 31. 32. 33- 31+. 35. Transitions — coherence Transitions — logical aspects Verbal Analogies I — Part I Verbal Analogies I — Part II Verbal Classification - Part I 187 126 01+2 -Oli; OOl 152 182 036 -030 038 223 107 277 265 281 105 108 211 118 095 250 136 265 191 212 166 112 1X+5 1214 069 276 -022 080 — 01+6 232 221 015 -067 122 11+7 10)+ 133 111+ 175 185 266 178 01+1+ 161+ 36. 37. 36. 39. i+O. Verbal Classification — Part II Verbal Comprehension Vocabulary Completion — Part I Vocabulary Completion — Part II Word Grouping 031 -08S i)+7 oii+ 0) 4 . 0 -071 063 170 18 it 129 261+ 377 1+02 38L - 239 072 208 271 291 167 191 227 239 233 23& 030 062 11+6 118 196 -088 -129 -026 -Oil 009 020 -036 lOl 136 160 11+2 13U 238 139 121 109 130 276 256 090 1+1. 1+2. Group Indicator Random Variable 123 -010 152 OLS 092 -087 130 -003 192 032 119 — 066 177 01+1 01+1 065 11+0 -025 250 009 decimal points have been omitted. Table 2 (continued) Tli© Correlation Matrix Test 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 X . 2. 3- 4- 5. 120 310 166 158 248 159 123 112 131 138 159 085 127 156 158 -022 038 150 160 071 144 247 198 196 160 080 022 317 181 155 073 221 362 213 192 O&O 233 23 3 158 217 157 160 223 156 138 106 301 292 208 153 12^ 184 240 113 2 28 278 287 313 22 2 361 136 206 315 208 270 124 300 213 130 125 097 138 179 148 230 073 262 206 217 284 051 031 315 125 136 6. 7. 8. 9. IO. 236 203 248 093 290 133 043 088 112 179 277 m 129 186 190 072 038 021 169 334 221 280 056 316 183 048 130 292 045 251 171 252 175 056 358 118 210 131 216 242 077 170 -083 188 386 285 257 117 301 177 230 197 178 220 276 306 302 208 353 234 145 223 050 251 138 175 149 106 311 219 265 167 026 257 251 290 183 118 277 -002 051 096 111 166 XI. 12. 13- 14. 15- 186 276 142 446 186 146 028 240 276 li+6 151 280 142 028 151 163 446 240 280 163 009 051 182 199 056 262 231 253 122 337 291 268 287 106 307 169 111 170 -036 283 304 160 236 106 393 225 073 145 146 231 315 259 272 045 293 271 189 195 073 246 254 231 052 109 261 296 183 259 014 333 252 131 122 057 297 059 164 050 147 149 16. 17- 18. 19. 20. 009 291 169 304 031 2 31 268 111 160 182 253 287 170 236 199 122 106 -036 106 056 337 307 285 393 22 3 154 IOO 128 223 200 143 219 154 200 138 310 IOO 143 138 284 128 219 310 285 170 209 230 169 191 077 322 217 22 2 " 344 322 246 126 252 300 130 201 221 195 276 140 257 244 194 256 237 296 207 166 219 233 137 153 264 138 21 . 22. 23- 24- 25- 225 315 271 254 296 073 259 139 231 183 145 272 195 052 259 146 045 073 109 014 231 293 246 261 333 170 077 322 130 140 209 3 22 246 201 257 230 217 12 L 221 244 169 222 152 195 194 191 354 30 c 276 256 190 W3 223 255 190 298 389 385 173 296 736 221 223 385 2 36 267 2 55 384 221 267 192 408 259 347 48 5 184 183 197 272 129 26 . 27- 28 . 29- 30. 252 059 IOO 183 313 131 164 027 146 167 122 050 141 102 243 057 147 134 187 181 297 149 013 092 459 237 23 3 302 312 080 296 137 193 200 201 207 15 3 159 087 380 166 264 O Ol 176 234 219 138 03 6 048 336 192 285 178 094 230 408 183 016 244 259 259 197 121 117 261 347 272 076 211 312 485 129 042 160 322 157 225 151 265 157 -017 229 167 31- 32. 33- 34- 35. 334 224 061 075 139 238 133 140 07 2 181 160 163 257 098 235 080 090 315 115 118 291 259 087 025 159 233 020 39 8 327 321 173 202 221 251 216 188 163 087 167 153 102 133 017 235 153 148 152 175 174 196 217 127 120 255 27 2 404 175 113 15 7 279 008 192 206 167 163 311 156 038 225 258 376 051 195 207 265 326 211 195 229 225 lOl 170 085 232 36. 37 . 38. 39. 40. lOl 135 263 184 219 136 168 209 143 176 182 141 123 163 360 165 187 258 213 105 079 114 225. 270 22 9 341 448 363 340 190 233 243 267 241 22 3 091 217 273 273 231 210 120 114 140 221 093 037 153 044 097 185 155 246 177 192 119 116 286 267 230 169 111 238 276 034 075 165 257 233 116 185 136 132 063 180 108 2 32 224 152 153 260 235 210 190 154 41- 42. 105 098 103 031 098 054 072 071 153 -063 -008 -014 169 -043 008 039 -057 -055 139 049 -008 C83 329 -068 063 052 234 -0 35 151 -050 170 -118 040 -067 v n Table 2 (continued) Tine Correlation Matrix. Teat 28 29 30 31 32 33 3*4 35 36 37 38 39 *40 *4l *42 1 . -087 -0* 4 - 0 126 187 126 0*42 -01*4 001 031 -085 1*47 Oli+ 0*40 123 -OlO 2 . 056 026 306 152 182 03 6 -030 038 -071 063 170 18*4 129 152 0*45 3. lOl 152 21+14- 223 107 277 265 281 26*4 377 *402 38*4 239 092 -087 U r - 036 135 261+- 105 108 211 118 095 072 208 271 291 167 130 -003 5. 21*4- 261 15*4 250 136 265 191 212 191 227 239 233 238 19*4 032 6 . 035 116 *4-33 166 112 1*45 122 089 030 062 1*46 118 196 119 -066 7 - -0*4.9 018 117 21*4 278 -022 080 —0* 4 - 6 -088 -129 -026 -Oil 009 177 Oi+JL 8. -019 068 20* 4 . 232 221 015 -067 122 020 -036 lOl 136 160 0*41 065 9 . 191 189 008 l57 10* 4 . 133 11*4 175 1*4-2 13*4 238 139 121 1*40 -025 10 . 1*4-0 023 303 185 266 178 0*4*4 16*4 109 130 276 256 090 250 009 XI . IOO 185 313 33*4 22*4. 061 075 139 lOl 135 265 I8I 4 218 105 098 12 . 027 1*1-6 167 236 133 1*40 072 181 136 168 209 1*43 176 103 051 13- 1*4-1 102 21.3 160 16 3 257 098 235 182 144-1 123 163 360 098 05*4 1*4- 13*4- 187 181 080 090 315 115 118 165 18 7 258 213 105 072 071 15. 013 092 *4-59 291 259 087 025 159 079 11*4 22*4 270 229 153 -06 3 16. 310 312 080 233 020 *455 398 327 3*41 *+-*48 363 3440 190 -008 -01*4 17 - 193 200 201 321 173 202 221 251 233 2i+3 267 2*41 223 169 -0*43 18. 159 087 360 216 188 163 087 167 091 217 273 273 231 008 039 19. OOl 176 23*4- 153 102 133 017 2 35 210 120 11*4 1*40 221 -057 -055 20. 036 0*4 . 8 336 153 1*4-8 152 175 17*4 093 0 37 153 1*414 097 139 0*49 21 . 176 09*4- 230 196 217 127 120 255 185 155 2*46 177 192 -009 08 3 22. 016 2*4*4 259 272 * 4 . 0* 4 . 175 113 156 119 116 286 267 239 325 -068 23- 121 117 261 279 008 192 206 167 169 111 238 276 05*4 063 052 2*4-. 076 211 312 163 311 158 038 225 075 167 256 233 116 2 3*4 -035 25. OI4 . 2 160 322 258 376 051 195 207 185 138 132 063 180 151 -050 26. 225 151 265 265 326 211 195 229 108 232 2 PL 152 153 170 -118 27. -017 229 167 225 lOl 170 085 232 260 235 210 190 15*4 Oi+O -067 28 . 237 086 065 —0*4-2 330 286 176 229 28 2 195 19*4 HO -0*46 056 29. 237 08* 4 . 089 08l 265 220 209 298 2*48 250 186 21*4 017 -012 30. 086 08* 4 . 120 210 053 007 068 OlO 128 192 201 239 098 -1*40 31 - 065 089 120 295 152 127 216 168 25*4 3*40 327 188 136 -090 32. -0*4-2 081 210 295 022 026 IOO 023 013 11*4 055 228 2*42 -057 33- 330 265 053 152 022 *482 325 301 *40*4 397 336 162 163 11*4 3*4- 286 220 007 127 026 *482 293 350 3*46 2*49 213 019 0*45 037 35. 176 209 068 216 IOO 325 293 399 353 256 237 165 -053 -01*4 36. 229 298 OlO 168 023 301 350 399 385 28*4 313 13*4 -057 002 37. 282 2* 4 . 8 12b 25*4 013 *4-0*4 3*46 353 385 *472 1492 2*40 009 005 36. 195 250 192 3*40 11*4 397 2*49 256 28*4 *472 719 32*4 291 lOl 39. 19*4- 186 201 327 05 5 336 213 237 313 *492 719 286 081 095 U O . llO 21*4. 239 188 228 162 019 165 13*4 2*40 32*4 286 17*4 -023 *4-1. -0* 4 . 6 017 098 136 2*42 163 0*45 -053 057 009 291 081 17*4 -072 *4-2. 056 -012 -1*4-0 -090 -057 11*4 037 -01*4 002 005 lOl 095 -023 -072 V J T . 52 centroid matrix is presented in Table 3« Rotation of the axes Graphic orthogonal rotations were used in tnis an alysis (9, 39). Because of tne experimental design of this study, the four ”complete-problems” scores (Nos. 17, ?4, 3 1 , 3 2 ) , the Group Indicator (No. ipl), and the Random Vari able (No. i;2) were not considered in meeting the criteria of simple structure and positive manifold. frimary empha sis was placed on meeting these criteria with regard to the previously known factors. In the final rotations, psycho logical interpretability was imposed as a third criterion, especially with regard to the previously known factors. Within the limitations of these three criteria, 124 rota tions were made. The rotated factor matrix is presented in Table 4« T able 3 Centroid Matrix of Aptitude Measures'- A B c D E F G H I J K L M N 1. 21 30 -18 19 -23 -22 -13 14 17 14 16 13 -12 -04 45 2 . 37 26 18 -16 05 16 -16 ll -14 -13 -11 -09 08 09 40 3. 54 -20 12 -08 20 -11 -21 -04 -18 -03 -05 07 -12 -16 53 h • 37 -03 16 -12 05 03 -09 -18 -07 08 -02 05 04 12 25 5. 46 -06 04 -06 IO 18 -07 08 IO -11 -13 -22 -22 -08 42 6. 45 23 -io -24 -08 -08 -IO -22 -16 -05 12 -11 -07 -07 46 7. 31 30 -38 16 -16 30 -24 11 -15 24 -28 IO 22 -12 77 a. 38 30 -22 12 -19 -17 -IO 21 -15 04 -16 -06 09 06 48 9. 27 -15 -IO 29 -18 04 04 13 -05 -io 13 -17 -02 -15 32 io. 47 21 18 -17 -05 22 05 15 13 14 08 21 -11 -07 51 li. 49 06 -14 — 08 06 08 14 07 -ii -13 -09 05 IO 41 12. 36 08 06 07 06 -13 03 13 IO 09 io -17 16 -07 27 13. 43 06 -17 -13 — 25 -12 12 -13 12 21 -16 -24 -09 02 49 14- 28 -19 07 -11 —25 IO 04 -12 -12 16 08 09 07 06 28 15- 54 32 07 -15 -08 -12 12 -06 -03 -04 -05 04 11 05 48 16. 46 -44 -28 07 -04 -11 -08 -11 -06 -09 18 12 03 08 59 17. 52 -03 -08 08 08 -09 -08 -13 -04 -IO -16 -15 09 02 39 18. 47 09 07 -17 -14 -09 11 03 -06 -12 04 -14 IO -16 38 19. 36 11 —C8 -14 23 — 25 06 11 -09 20 -07 06 -15 12 39 20. 48 27 -11 -27 04 04 -11 04 -17 07 09 -02 05 -12 46 21. 42 -02 -07 -04 -09 05 13 16 -15 -IO -13 15 -11 -IO 33 22. 60 27 02 22 15 14 -13 07 07 13 -03 -13 -16 -03 62 23- 47 05 -12 -14 13 -07 -25 12 08 -07 08 08 -06 19 42 24. 48 17 13 12 15 14 12 15 -09 05 21 IO 13 09 46 25. 49 26 -12 07 18 08 20 -16 17 -io -15 14 -05 -05 52 26. 54 15 -07 13 19 22 05 -14 07 -21 -04 12 05 09 52 27 - 36 -12 09 11 22 -15 12 13 -18 17 11 19 -03 -05 38 28. 27 -33 -17 -13 -09 20 17 03 IO -24 10 -13 -02 14 42 29. 37 -28 -04 13 13 09 15 05 -11 06 07 -18 -06 18 37 30. 49 29 15 -24 -04 -09 16 -17 -20 -IO 16 08 -IO 08 57 31 - 49 05 06 18 —04 -16 -07 07 15 -16 -12 09 12 -13 42 32 . 38 29 11 29 -05 19 18 -08 -02 07 -20 12 06 -11 48 33- 46 -43 -IO -IO -06 15 -IO -12 16 22 20 -06 12 08 61 34. 35 -38 -29 —08 11 16 -14 -16 19 -05 .0 05 08 -15 52 35- 44 -27 -16 -05 18 -IO 21 08 08 06 -06 02 09 -09 42 36 . 38 -42 -16 -04 17 -13 16 IO 15 09 -02 06 -08 -07 48 37 • 46 -50 17 -03 07 -IO 07 -07 12 -IO -05 06 14 -03 56 38 . 60 -35 34 io -23 -04 -20 12 14 -05 07 09 -02 06 76 39- 54 -35 35 -07 -15 -16 — 22 15 07 -05 -08 13 06 13 71 40. 42 -06 16 07 -15 -15 15 -12 -04 08 -20 — 2 -18 08 43 41. 27 14 22 28 -07 25 -21 -17 09 15 11 -IO -12 -05 42 ■ 1 1 42. -Ol —08 -05 -15 -16 15 -08 24 07 07 -06 -IO 14 11 20 *Decimal points have been omitted. v n Table 1+ Rotated Factor Matrix of Aptitude Measures^ A CKU B CMI C DMU D EMI E CMR F DMR O CMC H NMR X DMT J NMI ? K CMS L NMC M Sp N R1 h2 1. -12 30 13 -Ol -Ol -06 06 0 1 4 - 1+7 -03 -07 Ol -08 -23 1+2 2 . 22 26 20 12 -11+ 26 -1 c Ol+ -09 07 IO -02 25 -07 37 3- 38 11 -Ol+ OO IO 1+3 23 17 09 -Ol 22 08 Ol+ Ol 50 1+. 19 11 15 06 15 19 Ol 27 -11 -06 11 05 06 02 21+ 5. 22 27 -03 09 IO 25 -Cl -07 -Ol 30 15 25 07 Ol+ 39 6 . 03 IO 36 Ol 20 1+6 -Ol+ 03 17 05 05 OO 07 -IO 1 + 1 + 7 - -IO 23 -05 26 13 -Ol -03 Ol 30 -09 06 -03 66 -22 71+ 8 . 05 12 25 Ol+ -12 02 -03 -Ol 1+0 -02 15 12 31 -27 1+6 9. IO -Ol -03 12 07 -OI4 . -03 -Oi+ 37 23 21 02 -Ol 11+ 29 IO . Ol 1+5 15 22 -02 19 18 27 OO 20 -09 OO 09 02 1+7 11 - 18 23 31+ 20 -09 12 -02 03 03 23 Ol 16 18 -11 39 12. 21 20 21+ 05 OO -Ol 06 -03 21 -OI+ Ol 12 Ol+ 17 21+ 13. -0 1 4 . 0I 4 - 31 -02 25 09 -Ol 11 20 16 -0 3 1+2 15 -07 1+5 1^4-. Ol+ -06 11+ 03 21 Ol+ 03 1+0 03 11+ 07 -06 IO 07 28 15- 11+ 13 1+7 23 -06 21+ 06 15 12 03 -02 13 12 -13 1+6 16. 29 -11 06 02 1+2 Ol 25 10 23 11+ 33 -08 -07 -11 55 17. 31+ 01+ 16 15 18 17 -Ol -01 11+ -02 21 22 12 -08 36 18. 20 02 33 13 -Ol 2? 03 05 21 20 -Oh 07 11 09 35 19. 03 18 25 -11 -05 17 35 05 03 -09 19 22 06 -11 37 20 . 05 25 32 05 IO 37 12 00 13 03 05 -07 28 -02 1 + 1 + 21 . 07 02 0I 4 19 -08 19 21 12 11+ 29 16 06 17 -11 32 22. 09 51+ 08 21+ 07 19 -02 Ol 21 -Ol 23 25 09 OO 57 23. 26 33 20 -OS 11+ 13 17 -02 OI+ 07 17 -03 02 — 26 39 2 1 4 . . 12 32 28 31 -07 03 lit 13 06 -Ol 25 -09 oi+ 21+ 1+7 25- 03 19 17 1+9 11 18 19 -08 03 OO 02 25 OO -16 1+8 26. 19 22 16 51 16 13 07 -Ol+ -02 02 21 07 Ol -15 1+9 27 . 12 IO 07 08 -08 09 39 19 13 -09 28 03 -03 25 28 . 15 -08 12 08 25 -07 03 -06 -IO 1+8 13 OO -02 03 36 29 . 13 05 IO 05 11+ -05 IO 06 OO 15 1+5 16 OO 19 35 30. OO IO 1+9 16 -03 U1+ 06 21 Ol 07 11 -Ol -07 -08 55 31- 38 13 07 27 -OI4 . 06 09 05 30 03 -03 13 Ol -13 38 32. -05 17 05 53 -09 08 -Oi+ 19 15 -07 05 20 11+ OO 1+6 33- 26 13 IO -ol+ 57 -08 13 21+ 03 17 12 Ol 07 16 58 3l+. 26 02 -IO 11 55 06 23 -08 03 15 05 -05 OI+ 02 1+9 35- 21+ -03 12 11 16 OO 1+2 -02 07 11 13 20 09 IO 38 36 . 22 -Ol -02 -02 21 -Oij. 1+7 02 07 19 15 23 -OI+ 08 1 + 1 + 37 ♦ 52 -IO 02 11 20 02 21+ 21+ -02 16 06 11+ -09 12 52 38 . 52 21 -Ol 02 09 Ol 02 1+8 20 29 IO Ol+ -12 Ol 70 39 . 59 13 06 -08 OO 03 09 1+6 07 21 08 06 -02 -09 66 1+0 . IO -02 16 03 03 15 -08 25 11+ 13 18 1+6 —oi+ 02 1+1 Ip . -Ol 37 -09 19 16 IO -30 22 11+ -06 06 07 -07 12 1+1 * r • 1 +2. 05 07 03 -11+ 02 -20 -07 Ol -07 20 -05 -OI+ 21+ 02 18 ^Decimal points have been omitted. CHAPTER V INTERPRETATION OF THE FACTORS This chapter is concerned wi tti the interpretation of the rotated factors. In general, the interpretations are based on loadings of .30 or higher. For each factor, the tests having loadings of *30 or higher will be listed in order of their loadings. Criterion tests are prefaced with an *. In parentheses following each test will be a notation indicatinr loadings of .30 or higher on other fac tors, if any. Some tests had no loadings of .30 or higher on any factor. Eacn of these tests is included, in parentheses, with the- factor on which it nad its highest loading. The nomenclature for the factors is that suggested by the "structure of intellect" model. The correspondence between this nomenclature and the previously used names for the factors was presented in Chapter II. The factors are discussed in sequence of their pro portion of total common variance in the battery, the lar gest first. 5 5 56 Factor A. Cognition of semantic units (CMU) 39. Vocabulary Completion, Part I .59 (NMR .1+6) 38. Vocabulary Completion, Part II .52 (NMR -J 4. 8) 37. Verbal Comprehension .52 *31. Transitions (coherence) .38 (DMT .30) 3. Associat Ional Fluency I .38 (DMR .1+3) *17. Missing Links . 31+ Verbal Comprehension was Included as the marker test for this factor. Vocabulary Completion had high load ings on this factor in two previous studies (li+j 21+) . The higher degree of saturation obtaining In this analysis may be due to the fact that test 38 and 39 are alternate forms. It Is reasonable that Transitions (coherence) ap pears on this factor, since the coherence rating of pro duced discourse would emphasize greater awareness of the meanings of word3. AssociatIonal Fluency is a measure of the factor divergent production of semantic relations that has not been used In Its present form in previous analyses; similar tests have had loadings on the factor being dis cussed here. The appearance of Missing Links is to be ex pected, since the meanings of words must be known before they can be produced in the situation required. The cri terion variables are discussed in detail in Chapter VI. Factor B. Cognition of semantic Implications (CMI) 22. Pertinent Questions .51+ 10. Contingencies .1+5 1+1. Group Indicator .37 (CMC -.30) 23. Possibilities .33 *21+. Predicaments .32 (EMI .31) 1. Apparatus Test (drastic) .30 (DMT .1+7) Si [2. Apparatus Test (minor) .26 (DMR .26J J Pertinent Questions is a reliable marker for this factor (13). Contingencies and Possibilities fit tne fac tor well, both requiring the examinee to speculate on as pects of an hypothesized situation. The two scores from the Apparatus Te3t are not entirely out of place, since the ta3k of suggesting improvements requires a modicum of fore- s ight. The loading of Predicaments, one of the criterion tests, is of interest; the criterion tests are discussed in detail in Chapter VI. The Group Indicator loading may in dicate that graduating from colLege increases one's tenden cy to look ahead. Factor C. Divergent Production of Semantic Units (DMU) 30. Similarities • 49 (DMR • 44) IS. Ideational Fluency • 47 • 4&) 6. Brick Uses (shifts) .36 ( DMR 11. Differences .34 18. Multiple Grouping .33 20. Object Synthesis III .32 (DMR .37) 13. Figure Concepts (uncoramonness) .31 (NMC .42) (12. Episodes *2lj.) The second test on this factor was included as a marker for divergent production of semantic unit3. That ability is clearly involved in all the tests In the above list. In a previous study (24)* Similarities helped define cognition of semantic transformations. Its behavior in this analysis appears to result from the lack of sufficient 58 common variance in that factor* In a previous study ( ) « Similarities was loaded *26 on the factor under discussion here; in this analysis its vector may have a greater pro jection because of the absence of a more appropriate dimen sion. Brick Uses (shifts) was intended to be a marker for divergent production of semantic classes* the factor ad joining this one in the structure of intellect. It appears that too many categories of use were differentiated, per mitting the number of "shifts" to approach the total number of responses, the latter being a measure of the present factor. Differences was designed as a companion test to Similarities* Evidently their common variance was shared by Ideational Fluency. Multiple Grouping required the examinee to assign given objects to as many groups as possible, each baaed on a different characteristic. Its loading here may indicate that thinking of many attributes is a more important part of the test than is classifying In terms of them. Another possibility Is that DMU and DMC are confounded In this bat tery. In Object Synthesis III, the examinee must list ob jects that can be made from two given objects. The simil arity to the task in Ideational Fluency Is clear. Figure Concepts, like other tests in this list, requires the exam inee to think of characteristics of objects before combin ing them in terms of those characteristics. Factor D. Evaluation of semantic implicatLons {EKI) *>32. Transitions (logical aspects) .53 26. Seeing Problems, Part II .51 25. Seeing Problems, Part I .1+9 #2i+. Predicaments .31 (CMI .32) The two alternate forms of Seeing Problems define this factor as intended. The Transitions (logical aspects) score evidently emphasizes the selection of critical vari ables in a situation. Similarly, the presence of Predica ments serves to support the claim of this factor as being important to problem-solving. Factor E. Cognition of semantic relationships (CMH) 33. Verbal Analogies I, Part I .57 31+. Verbal Analogies I, Part II .55 16. Logical Reasoning ./+2 (CMS .33) The alternate forms of Verbal Analogies I were In cluded as markers for this factor. As for Logical Reason ing, It is reasonable that the examinee must be aware of semantic relationships before he can evaluate them. The absence In this battery of any other strong test of evalu ation of semantic relations left Logical Reasoning to find what common variance It could. Its communallty was only .1+8, in contrast to Its reliability of .80. Factor F. Divergent production of semantic relationships (DMR) 60 6. Brick Uses (shifts) .i|6 (DMU .36) 30. Similarities . ) + ] + (DMU .1*9) 3. As3ociational Fluency I .I4 . 3 (CMTJ *38) 20. Object Synthesis III .37 (DMU .32) [2. Apparatus (minor) .26 (CMI *26jJ Associational Fluency I was included as a marker for this factor. The presence of the other tests may be explained by noting that a variety of relationships are in volved in Similarities and Object Synthesis III, and that the "shifts" score for Brick Uses may have capitalized on a variety of relationships of a brick to other elements in the environment. Factor G. Cognition of semantic classes (CMC) 36. Verbal Classification, Part II .(4 . 7 35. Verbal Classification, Part I . i j . 2 27. Sentence Pairs .39 19. Object Naming (shifts) .35 i|l. Group Indicator -.30 (CMI .37) The two leading variables were included as markers for this factor. The presence of Sentence Pairs and Object Naming (shifts) serves to extend the interpretation of the factor from Just words to broader ideas as classifiable ob jects . What inference should be drawn from the negative loading of the Group Indicator is not clear. Perhaps a college education in some way inhibits the ability to clas sify more or less ambiguous material, or increases the ten dency to perseverate within an established class. 61 Factor H. Convergent production of semantic relationships (NMR) 38. Vocabulary Completion, Part I .I 4 .B (CMU .52) 39. Vocabulary Completion, Part II .Jp6 (Ci^U .59) l L } . . Gestalt Transformation . i f . 0 ( l j . . Attribute Listing I .27) The alternate forms of Vocabulary Completion were included as markers for this factor. The name convergent production of semantic relationships is given this factor although the loadings on Factor A are higher, due to the univocallty of Verbal Comprehension on Factor A and the presence here of Gestalt Transformation. Evidently the ab sence of the factor convergent production of semantic transformations, the factor usually identified by Gestalt Transformation in previous studies (21, 26), allowed the test to capitalize on its requirement of seeing necessary relationships rather than the usually dominant aspect of redefining the use of a given object. The alternate forms of Cartoons were intended as markers for this factor. It appears that their aspect of ’ ’cleverness” is not shared by tae other tests, but may be Factor I. Divergent production of semantic transformations (EMT) 1. Apparatus (drastic) 8. Cartoons, Part II 9. Common Needs 7. Cartoons, Part I .47 (CMI .30) J».o (sP .31) .37 *31• Transitions (coherence) .30 (Sp .66) .30 (CMU .38) 62 the source of the Specific factor. What Cartoons does have in common with the other three tests is the uncomraonnes3 aspect of the responses. A high score on Apparatus Test (drastic) implies that the examinee has thought of a rather uncommon change prior to suggesting the improvement. In Common Needs, the examinee must think of a variety of ante cedents, some of which are uncommonly thought of, before he can pair the objects requiring the s.une antecedent. The loading of Transitions (coherence) may arise from a facil ity In producing a series of meaningful changes. Factor J. Convergent production of semantic implications 28. Sequential Association .I1 . 8 5. Attribute Listing II .30 (21. Pairnd Similarities *29) Although this factor might be left as an unidenti fied doublet, it appears to fit fairly well the traditional definition of "deduction" as discussed by French (4)« He places tests of disarranged words and disarranged mor phemes on the factor, as well as number-series tests. In the structure of intellect, "deduction" has been assigned to the cell convergent production of semantic implications. Sequential Association Is certainly convergent, and the task Is to produce a sequence inherent in the given words. Attribute Listing II requires the production of antece dents, each focused on the specified goal; further, the 63 instructions for the test emphasized providing specific at tributes of the general situation. Paired Similarities was hypothesized to deal with the same ability as was Sequential Association, (Hypothesis III). Factor K. Cognition of semantic systems (CMC) 29. Ship Destination .i|5 16. Logical Reasoning .33 (CMR ,/p2} Ship Destination is a well-known marker for this factor, previously called "general reasoning." The presence of Logical Reasoning may result in part from the lack of a second test of its usual factor, as discussed in connection with Factor E. Factor L. Convergent production of semantic classes (NMC) I 4.O. Word Grouping .J( . 6 13. Figure Concepts (uncommonness) ,l\2 (DMU .31) The factor indicated by this doublet appears to be the first evidence for the existence of convergent produc tion of semantic classes, a factor predicted by the struc ture of intellect but not heretofore isolated. Both tests involve the production of classes. In Word Grouping, the classes must be mutually exclusive. In Figure Concepts (uncommonness) the more unique classes con tributed more to the total score. In a previous study (28), Figure Concepts (uncommonness) had Its highest, barely sig nificant, loading on "originality." In this study, the time was shortened from 5 minutes to 3 minutes, with the 6it result that very few examinees used the same pictured ob ject in more than one group. The most important aspect of the test as used here seems to be the production of classes without much variance attributable to seeing different as pects of the same object, hence less divergent thinking. Factor h. Cartoons Specific (Sp) 7. Cartoons, Part I .66 (DMT .30) 8. Cartoons, Part II .31 (DMT ./|0' This factor results from using alternate forms of the Cartoons test, scored for "cleverness," without addi tional measures emphasizing "cleverness1 1 in the battery. Factor N. Residual There were no loadings greater than .2? in absolute value on this factor. CHAPTEH VI DISCUSSION The discussion of the outcome of this analysis Is concerned with an evaluation of the six hypotheses and their alternatives, the factor content of the three cri terion problems, and the general conclusions that can be inferred. Table 5 contains a comparison of the hypotheses, alternatives, and outcomes of the analysis. Hypothesis I — the ability to think rapidly of several attributes or char acteristics of a given object— seems well accounted for by its alternatives, divergent production of semantic units and divergent production of semantic relations. Hypothesis II — the ability to classify objects or ideas— was accounted for in part by its alternative, cognition of semantic classes, and in part by the factor newly isolated in this analysis, convergent production of semantic classes. How ever, the tests defining the new factor were not both de signed for Hypothesis II. Hypothesis III tests also 65 66 Table 5 Fate of the Hypotheses Hypothesis Alternatives^ ■ ■ b Obtained^ I DMU, DMR DMU-*, DMR* II CMC CMC*, NMC III CMR, NMR DMU, NMC, NMI? IV DMU, DMC, DMT, NMT DMU*, DMR V DMT, EMI CMI, DMT*, NMI? VI CMI CMI*, DMT ^Coded as discussed in Chapter III. ^Obtained means that one or more of the tests under the hypothesis had a significant loading on the indicated factor• Obtained as hypothesized alternative. 67 separated, one pairing up with a test from Hypothesis II to form the new factor NMC, the other two holding together on the factor tentatively Identified as convergent production of semantic implications. Hypothesis IV— the ability to think of alternative outcomes—-seems well accounted for by divergent production of semantic units, one of its alterna tives, and by divergent production of semantic relation ships , perhaps because the outcomes required by the tests were, in general, relationships. The tests for Hypothesis V— the ability to think of attributes of a desired goal— separated, with only one test loading on an alternative, and no evidence of a separate factor. For Hypothesis Vir tue ability to educe logically suificient antecedents — three of the tests held together and were loaded on the al ternative cognition of semantic implications. The fourth helped define divergent production of semantic transforma tions . In review, It would appear that the production processes discussed by problem-solving theorists and tested in this study can be explained in terms of factor dimen sions that have logical positions in the structure of in tellect. Of the two new factors in this analysis, one was predictable from that structure but had not been previously isolated, and the other had been found by previous investi gators, and had recently been assigned a position in the 68 structure. Of greater Interest is the result that only the tests designed for Hypotheses V and VI, both Involving working backward from the goal, had common variances with the criterion-problem tests used here. The criterion tests themselves had significant loadings on but four factors, all previously known. As may be seen in Table 6, two of the criterion measures were loaded on cognition of semantic units, and the otner two were loaded on evaluation of semantic implications. Only Predicaments was loaded on cognition of semantic implica tions ; only Transitions (coherence) was loaded on divergent production of semantic transformations. The ambiguity re garding the interpretation of Factor A shoul d be recalled. It seems more likely that the loadings of Missing Links and Transitions (coherence) derive as much from the measures of convergent production of semantic relationships (Vocabulary Completion) as from the measure of cognition of semantic units (Verbal Comprehension). In any case, there is no evidence whatever that problem solving as measured by these criterion tests is a unitary ability. EMI and CMI are possible candidates for Interpretation as such a factor, but clearly they are not broad enough to include even the limited types of problems used in this analysis. From the absence of significant 69 Table 6 Factor Content of Criterion Tests Tea t CMU CMI DMT EMI h2 rtt 17. Miasing Links .39 .01+ .14 .16 .39 .58 2l±. Predicaments .12 .32 .06 .31 •U7 .55 31. Transitions (coherence) .38 .13 .30 .27 . Uj CD • I 4 . 6 32. Transitions {logical aspects) -.05 .17 .15 .53 .{4 . 6 .I48 70 loadings of these criterion tests on the factor cognition of semantic systems, It would appear that "good reasoners" would not necessarily do well on the types of problems used here. The lacic of significant loadings of the criterion tests on divergent production of semantic units would seem to Indicate that "brainstorming" and similar techniques that emphasize merely fluency of ideation are not suffi cient for the solution of the kinds of problems investi gated in this study . In summary, these results tend to confirm the im portance of the analysis of goals and the development of a search model or anticipatory schema in the production of solutions to problems. Having come full circle, the wheel rests again at Wurzburg. CHAPTER VII COMMENTS OK CERTAIN METHODOLOGICAL ASPECTS Several techniques used In this study do not have universal acceptance. It is appropriate to discuss their outcomes. Scores from Alternate Forms Five previously known factors were represented in this analysis by alternate forms of the same test. DMT 7- 8. Cartoons EMI 25-26. Seeing Problems CMR 33-3J+* Verbal Analogies I CMC 35-36. Verbal Classification NMR 38-39. Vocabulary Completion The alternate-form scores from Cartoons defined a specific factor, as well as contributing to factor DMT. Scores from Vocabulary Completion appeared to result in the confounding of NMR and cognition of semantic units, a fac tor the test had been loaded on in previous analyses ( l / j . » 24). In terms of the obtained factors, it might have been well to have used alternate form scores from test 16, 71 72 Logical Reasoning, to help define evaluation of semantic relationships, which was not obtained as a separate factor. The use of alternate-form scores from te3t ll|, Gestalt Transformation, might have permitted the identification of convergent production of semantic transformations; however, the reliability of this test wa3 not considered high enough for this separation. The other alternate form scores ware useful In defining tne intended factors. It would appear that alternate-form scores may be used, with some risk from confounding or from the formation of specific factors. Group Indicator Variable Z j . 1 was Included to measure, by its rotated loadings, the degree of its relationships to the obtained factors. The loadings were interpretable after a fashion. In terms of the additional information to be gained, it seems advisable to Include such a variable in the factor analysis and obtain a measure of its effects, rather than to make a presupposition about its lack of contribution. Random Variable To obtain Variable l j . 2 , values of a random normal deviate were assigned as scores to the examinees as an ap proach to estimating the standard error of a factor load- 73 Ing. In this analysis, the coramunality of the random vari able was 0.16; the loadings ranged froxa -0.20 to 0.2ij.; the mean of the loadings was 0.01; the standard deviation of the loadings was 0.11. Let the theoretical population of factor loadings on a single variable have a mean value of (h/k) where h is the length of the test vector and k the number of factors. Let the standard deviation of this population be 0.11, the value obtained for the random variable. The critical region for rejection of the hypothesis that a factor loading X comes from the described population Is x > xc = »k-i + <hA)• For o<= 0.05* k = lUt Student's t = 2.16, and the critioal value for the factor loading is Xc = .21* + (h/k). Now if h takes Its maximum value of 1.00, (h/k) has a value of 0.07, and Xc = .31 For h <1.00, Xc would be less. From these considerations, although they do not constitute a completely formal proof, It would seem that the use of 0.30 as a lower bound for a significant factor loading In this study is justified. CHAPTER VIII SUMMARY The intent of this study was to explore the possi bility of explaining certain processes of adult problem solving in terms of factor dimensions. A modified theory of problem-solving was developed, hypothesizing five phases: preparatio 1, analysis, produc tion, verification, and reapplication. Because of the lim itations of testing time and the necessity of spanning a large number of previously known factors, it was decided to test only six major hypotheses as to basic abilities in volved, all pertaining to aspects of the production phase* The six are: I - listing attributes of given material II - classifying attributes III - finding different relationships between attributes IV - producing alternative outcomes V - listing attributes of the goal VI - educing logically sufficient antecedents 75 For eacn of the above hypotheses, alternatives were suggested in terms of previously known factors. Twelve new tests were developed as measures of the hypothesized abilities. Three new tests were developed for use as criteria of problem-solving performance. One of these tests requires the production of three words to com plete an associative chain, first and fifth words of the chain being given. The second criterion test describes a problem situation and requires a solution, with the re striction that only some combination of four given objects can be used. The third criterion test presents the begin ning and ending of a very short story, and requires the production of a middle, connecting portion that is to be as coherent and logical as possible. Two scores, one based on coherence, the other bamd on logical aspects, were ob tained from this test. Eighteen tests of previously known factors were included in the test battery. The test battery was administered in late 1957 and early 1959 to 232 Naval Air Cadets and Aviation Officer Candidates at Pensacola Naval Air Station. Data from 13 examinees were Incomplete so they were not included in the analysis. Since so many reference factors were included, there was a possibility that some of them would be under- determined for lack of sufficient common variance. To 76 guard against this eventuality, scores from alternate forms of the same highly saturated tests of selected factors were included as separate variables in the analysis. There was a possibility that the Naval Air Cadets and Aviation Offi cer Candidates were not entirely homogeneous with respect to the scores obtained* Accordingly, a Group Indicator variable wa3 included In the analysis to measure the rela tionship of possible group differences to the factors. A Random Variable was included in an attempt to determine an appropriate value for the standard error of a factor load ing in this analysis. Scores from l\2 variables were inter correlated and 14 centroid factors were extracted. A total of 12i| graphic orthogonal rotations were performed, using the criteria of simple structure and positive manifold. A third criterion, psychological lnterpretabllity, was imposed on the later rotations with regard to the reference factors, but not with regard to the new tests of the hypotheses or the cri terion tests. Ten rotated factors were Identified as previously known dimensions: cognition of semantic units, cognition of semantic implications, divergent production of semantic units, evaluation of semantic implications, cognition of semantic relationships, divergent production of semantic relationships, cognition of semantic classes, convergent 77 production of semantic relationships, divergent production of semantic transformatlons, and cognition of semantic sys tems. One factor, tentatively Identified as convergent production of semantic Implications, had been suggested by other investigators, but no clear measures of it were avail able for this study. One factor, not previously identified, appeared as the first evidence for a factor predicted by the structure of intellect: convergent production of se mantic classes. One factor was a specific generated from alternate forms of the same test. The remaining factor was a residual, having no significant loadings. The six hypothesized abilities were, for the most part, accounted for by previously known factors. The new factor, NMC, was identified by one test from Hypothesis II and one from Hypothesis 111. The factor NMI was most close ly related to Hypothesis III. The criterion tests had significant loadings on four factors, all previously known: cognition of semantic units, cognition of semantic implications, divergent production of semantic transformations, and evaluation of semantic impli cations . The two hypothesized abilities most related to the criterion tests were Hypotheses V and VI, both con cerned with working backward from the goal. It was Inferred that the development of a search model or anticipatory schema played an Important role in solving problems of the 78 kind included in this study. There was no evidence of a unitary problem-solving ability. An evaluation of the use of scores from alternate forms indicated that the procedure is usable, though not without risk of generating specific factors. The use of variables like the Group Indicator appeared to be worth while for situations in which such questions arise. The loadings of the Kandom Variable indicated that the value of 0.30 as a lower bound for significant factor loadings was justifiable in this analysis. REFERENCES 1. Berger, R.M., Guilford, J.P., 8c Christensen, P.R. A factor-analytic study of planning. Psychol. Monogr., 1957, No. k 3 $ . 2. Burack, B. The nature and efficacy of methods of at tack on reasoning problems. Psychol. Monogr., 1950* 6^, No. 313. 3. Duncker, K. On Problem Solving (trans. L. S. Lees). Psychol. Monogr., 191*5* £8* No* 270. t+. French, J.W. The description of aptitude and achieve ment tests in terms of rotated factors. Psychometric Monogr., Chicago: TJniver. of Chicago Press, 1^51* fto. 5 • 5. Gagne, R.M. Problem Solving and Thinking. Ann. Rev. Psychol., 1959* 10* PP» 11*7-72. 6. Green, R.F., Guilford, J.P., Christensen, P.R., & Comrey, A.L. A factor-analytic study of reasoning abilities. Psychometrlka, 1953* 18* 135-160. 7. Guilford, J.P. Factors in problem solving. AHTC Instr. J., 1951*. k* 197-201*. 8. Guilford, J.P. Personality. New York; McGraw-Hill Book Co., 1958. 9* Guilford, J.P. Psychometric Methods, 2nd ed., New York: McGraw-Hill Book do., 195l*» 10. Guilford, J.P. A revised struoture of intellect. Rep, psychol. Lab., No. 19* Los Angeles: Univer. of Southern Calif., April, 1957* 79 80 11. Guilford, J.P. ^Bie structure of intellect. Psychol. Bull., 1956, Vol. 53, NO. I*. 12. Guilford, J.P., Berger, R.M., & Christensen, P.R. A factor-analytic study of planning, I. Hypotheses and description of tests. Rep. d aycho1. Lab., No. 10. Los Angeles; Univer. of Soutnern Call!4., July, 1954* 13* Guilford, J.P., Berger, R.M., & Christensen, P.R. A factor-analytic study of planning, II. Administration of tests and analysis of results. Rep, psychol. Lab., No. 12. Los Angeles; Univer. of Southern Calif., May, 1955. IJ4. Guilford, J.P. Sc Christensen, P.R. A factor-analytic study of verbal fluency. Rep, psychol. Lab., No. 17. Los Angeles; Univer. of Southern Calif., September, 1956. 15* Guilford, J.P., Christensen, P.R., Kettner, N.W., Green, R.F., Sc Hertzka, A.P. A factor-analytic study of Navy reasoning tests vlth the Air Force Aircrew Classification Battery. Bduc. psychol. Measmt., 195U, ik, 301-325. l6. Guilford, J.P., Comrey, A.L., Green, R.F., & Christen sen, P.R. A factor-analytic study of reasoning abil ities, I. Hypotheses and description of tests. Rep. psychol. Lab., No. 1. Los Angeles: Univer. of southern Calif., June, 1950* 17* Guilford, J.P., Frick, J.W., Christensen, P.R., & Mer- rifleld, P.R. A factor-analytic study of flexibility in thinking. Rep, psychol. Lab., No. 18. Los Ange les: Univer. of Southern Calif., April, 1957* 18. Guilford, J.P., Green, R.F., & Christensen, P.R. A factor-analytic study of reasoning abilities, II. Ad ministration of tests and analysis of results. Rep. psychol. Lab., No. 3* Los Angeles: Univer. of Southern dalif., April, 1951* 19* Guilford, J.P., Green, R.F., Christensen, P.R., Hertz ka, A.F., & Kettner, N.W. A factor-analytic study of Navy reasoning tests with the Air Force Aircrew Class ification Battery. Rep, psychol. Lab.. No. 6. Los Angeles: Univer. of Southern dallf., June, 1952. 81 20. Guilford, J.P., Hertzka, A.P., Berger, R.M., & Chris tensen, P.R. A factor-analytic study of evaluative abilities, I. Hypotheses and description of testa. Rep, psychol. Lab., No. 7. Los Angeles: Univer. of Southern dailf., July, 1952. 21. Guilford, J.P., Hertzka, A.P., A Christensen, P.R. A factor-analytic study of evaluative abilities, II. Ad ministration of tests and analysis of results* Rep. S sychol. Lab., No. 9* Los Angeles: Univer. of outhern dalif *, July, 1953* 22. Guilford, J.P., Kettner, N.W., 8c Christensen, P.R. A factor-analytic investigation of the factor called general reasoning. Rep. psychol. Lab., No. l l | . . Los Angeles: Univer. of Southern Calif., August, 1955* 23. Guilford, J.P., Kettner, N.W., 8c Christensen, P.R. A factor-analytic study across the domains of reasoning, creativity, and evaluation, I. Hypotheses and descrip tion of tests. Rep, psychol. Lab., No. 11. Los An geles: Univer. of Southern Calif., July, 195U* Guilford, J.P., Kettner, N.W., & Christensen, P.R. A factor-analytio study across the domains of reasoning, creativity, and evaluation, II. Administration of tests and analysis of results. Rep, psychol. Lab.. No. 16. Los Angeles: Univer. of Southern Caiif., March, 1956* 2^. Guilford, J.P., Kettner, N.W., 8c Christensen, P.R. The nature of the general reasoning factor. Psych. Rev., 1956, Vol. 63, No. 3. -- 26. Guilford, J.P. , Kettner, N.W., 8c Christensen, P.R. The relation of certain thinking factors to training criteria in the U.S. Coast Guard Academy. Rep. f syohol. Lab., No. 13. Los Angeles: Univer. of outhern Calif., May, 1955* 27. Guilford, J.P., Wilson, R.C., Christensen, P.R., 3c Lewis, D.J. A factor-analytic study of creative thinking, I. Hypotheses and description of tests. Rep, psychol. Lab.. No. l± , Los Angeles: Univer. of Southern dallf., April, 1951* 28. Guilford, J.P., Wilson, R.C., 8c Christensen, P.R. A factor-analytic study of creative thinking, II. Admin istration of tests and analysis of results. Rep. S sychol. Lab., No. 8. Los Angeles: Univer. of outhern dalif., July, 1952. 82 29- Hartska, A.F., Guilford, J.P*, Christansan, P.R., & Bargar, R.M. A factor-analytic study of evaluative abilities. Educ. psychol. Meaamt., 1951+, lit, 581-97* 30. Johnson, Donald M. The psychology of thought and Judgment. New York: riarper & Brothers, 1355* 31. Kettner, N.W., Guilford, J.P., Sc Christensen, P.R. A factor-analytic investigation of the factor called general reasoning. Educ. psychol. Meaamt., 1956, 16, 438-I+53. 32. Murphy, Gardner. Historical Introduction to Modern Psychology. Naw York: Sarcourt, Brace, & do., 191+9* 33* Polya, G* How to solve It. Princeton: Princeton Univer. Press, 191 +6. 3l+. Ray, W.3. Complex Tasks for Use in Human Problem- Solving Research. Psychol. Bull., 1955* 52, I3I 4 .-I+9. 35* _____ ^ Framework for Problem-Solving. Labora tory Note SCRL 55-8, AFPRTC. Lackland APB, Texas. August, 1955 (unpublished draft). 36. Taylor, D.W. & McNemar, O.W. Problem Solving and Thinking. Ann. Rev. Psychol., 1955, 6, pp. 1+55-82. 37* Thurstone, L.L. Multiple faotor-analyala. Chicago: Chicago Univer. Press, l^l+t* 38. Wilson, R.C., Guilford, J.P., Christensen, P.R., & Lewis, D.J. A factor-analytic study of creative- thinking abilities. Paychometrlka, 1951+, 19, 297-311. 39* Zimmerman, W.S. A simple graphical method for orthog onal rotation of axes. Psychometrlka. 191+6, JUL, 51-

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Creator Merrifield, Philip Ralph (author)

Core Title A Factor-Analytic Study Of Problem-Solving Abilities

Degree Doctor of Philosophy

Degree Program Psychology

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

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Advisor Guilford, Joy P. (committee chair), [illegible] (committee member), Meyers, Charles Edward (committee member)

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