The Factorial Structure of the Raven Coloured Progressive Matrices Test
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Auteurs : Karl Heinz Wiedl ; Jerry S. CarlsonSource :
- Educational and Psychological Measurement [ 0013-1644 ] ; 1976-07.
Abstract
The Raven Coloured Progressive Matrices Test was administered to 180 first, second, and third grade children. Factor analysis revealed three orthogonal factors. They were interpreted as (1) concrete and abstract reasoning, (2) continuous and discrete pattern completion, and (3) pattern completion through closure. The results were discussed in context of the dimensions of the test which Raven and others have described. The issue of the relationship of item difficulty to the internal structure of the test was discussed as well as age-related differences of performance on the single factors.
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Factor analysis revealed three orthogonal factors. They were interpreted as (1) concrete and abstract reasoning, (2) continuous and discrete pattern completion, and (3) pattern completion through closure. The results were discussed in context of the dimensions of the test which Raven and others have described. The issue of the relationship of item difficulty to the internal structure of the test was discussed as well as age-related differences of performance on the single factors.</div></front></TEI><istex><corpusName>sage</corpusName><author><json:item><name>Karl Heinz Wiedl</name><affiliations><json:string>University of Trier, West Germany</json:string></affiliations></json:item><json:item><name>Jerry S. 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Müller</name></json:item></author><host><volume>172</volume><pages><last>116</last><first>82</first></pages><author></author><title>Zeitschrift für Psychologie</title></host><title>Möglichkeiten und Grenzen des Einsatzes einzelner diagnostischer Kurzverfahren bei der Schulerauslese: Dargestellt am Beispiel der Progressiven Matrizen von Raven</title></json:item><json:item><author><json:item><name>W. 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Factor analysis revealed three orthogonal factors. They were interpreted as (1) <italic>concrete and abstract reasoning,</italic> (2) <italic> continuous and discrete pattern completion,</italic> and (3) <italic>pattern completion through closure.</italic> The results were discussed in context of the dimensions of the test which Raven and others have described. The issue of the relationship of item difficulty to the internal structure of the test was discussed as well as age-related differences of performance on the single factors.</p></abstract><custom-meta-wrap><custom-meta xlink:type="simple"><meta-name>sagemeta-type</meta-name><meta-value>Journal Article</meta-value></custom-meta><custom-meta xlink:type="simple"><meta-name>search-text</meta-name><meta-value>409 The Factorial Structure of the Raven Coloured Progressive Matrices Test SAGE Publications, Inc.1976DOI: 10.1177/001316447603600220 Karl Heinz Wiedl University of Trier, West Germany Jerry S. Carlson University of California, Riverside The Raven Coloured Progressive Matrices Test was administered to 180 first, second, and third grade children. Factor analysis revealed three orthogonal factors. They were interpreted as (1) concrete and abstract reasoning, (2) continuous and discrete pattern completion, and (3) pattern completion through closure. The results were discussed in context of the dimensions of the test which Raven and others have described. The issue of the relationship of item difficulty to the internal structure of the test was discussed as well as age-related differences of performance on the single factors. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1976, 36, 409-413. THE internal structure of the Raven Coloured Progressive Matrices Test (CPM) has been described as heterogeneous by some authors. Raven (1965) has suggested that various sets of items require simple pattern completion, discrete pattern completion, pattern completion with closure, concrete reasoning by analogy, and abstract reasoning by analogy. Muller (1970) classified the test items as those that can be solved by perceptual processes and those which require conceptual solutions. The items which he placed under each category were similar but not identical to the Raven classification. By arranging items in groupings of similar levels of difficulty, Wenke and Muller (1966) have also suggested that the items may be conceptually differentiated. Sim- 1 Request for reprints should be sent to Jerry S. Carlson at the University of California, School of Education, Riverside, California 92592, or Karl Heinz Wiedl, Psychologische Abteilung der Universität Trier, D-5500 Trier, Federal Republic of Germany. 168410 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT ilarly, Winkelmann (1972) has pointed out that the test consists of relatively easy perceptual items and more difficult conceptual items. In the studies just cited the classifications of items were done largely on the basis of inspection of the items themselves and calculations of item difficulties. To the knowledge of the writers, no investigation has been carried out which used factor analysis, an approach which can help clarify the different dimensions which constitute the test. The main purpose of the -present research was to analyze the internal structure of the test by this statistical approach. Method Sample The sample consisted of 180 first, second, and third grade children randomly selected from three schools broadly representative of the socio-economic class distribution in the city of Trier, West Germany. Sixty children from each grade level were chosen. Approximately equal numbers of males and females were in the sample. The average age of the entire sample was 7 years, 5 months. Test and Administration The Raven Coloured Progressive Matrices Test was administered individually to all children in a single session. The average time required was 17 minutes per child. Results The data were factor analyzed from phi-coefficients by the principal component method. Rotation was done according to the varimax criterion. The number of significant factors was determined by the Scree test (Cattell, 1966). In addition, item difficulties were computed inasmuch as these values may be related to the internal structure of the test. To check 'the marker items of the different factors for changes in item difficulty that may be related to age, item difficulties of first and third grade children were compared by one-tailed X2 test (items A 2 to B 7) and binomial tests (items B 8 to B 12). The first item, A 1, which was a practice item, was not included in the computations. Table I reports the results of these analyses. The three significant factors extracted accounted for 36% of the total variance. Factor I explained 37.33, Factor II for 29.55, and Factor III for 33.12% of the common variance. Factor loadings of .30 169411 WIEDL AND CARLSON TABLE I The Factorial Structure and Item Difficulties of the CPM *Difference in item difficulty between first and third grade pupils significant, p < ,05. **Difference in item difficulty between first and third grade pupils significant, p < .01. or greater were considered relevant for interpretation of the factors. Item description follows that of Raven. Factor I is marked by items Ab 8 and Ab 9 (discrete pattern completion of related figures as a whole), B 8 and B 9 (concrete reasoning by analogy), and B 10, B 11, and B 12 (abstract reasoning by analogy). Factor II is marked by items A 2, A 3, A 5, A 6, and A 7 (simple continuous pattern completion), Ab 2, B 1, and B 2 (discrete pattern completion), and B 3 (discrete pattern completion of related figures as a whole). Factor III is marked by A 4 (simple continuous pattern completion, A 9 and A 10 (pattern completion showing pro- 170412 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT gressive change), Ab 3 (discrete pattern completion), Ab 5, Ab 6, Ab 7, Ab 8, B 3, B 4, and B 5 (discrete pattern completion of related figures as a whole). According to the items which had the highest loadings on the factors which they marked, Factor I could clearly be interpreted as concrete and abstract reasoning, Factor II as continuous and discrete pattern completion, and Factor III as pattern completion through closure. To check the stability of these factors, further factor solutions with five to seven factors were computed. The three reported factors proved to be stable. Inspection of Table I reveals that the marker items for the three factors are different in item difficulty. Those which mark Factor II are least difficult (x = .80), those which define Factor I are most difficult (x = .14). Marker items of Factor III are of medium difficulty (x = .52). Comparison of levels of difficulty between first and third grade pupils for the marker items of the three factors showed statistically significant differences of Factors I and III only. The only exception was for item B 2 which loaded on Factor I. Discussion The results of the study have confirmed the heterogeneity of the Coloured Progressive Matrices Test. The three significant factors extracted (Factor I-concrete and abstract reasoning; Factor II-continuous and discrete pattern completion; and Factor III-pattern completion through closure) suggest a "middle position" between the dimensions which Raven has put forth and those posited by Muller and Winkelmann. The fact that discrete and continuous pattern completion items loaded together on Factor II and that concrete and abstract reasoning items defined Factor I suggests that for children in the age range of the subjects in the sample studied the task structure is less differentiated than that which Raven has suggested. On the other hand, dual classification of the test items simply into perceptual and conceptual categories seems to be too broad. Also, the usefulness of differentiation of two perceptual factors is shown by comparison of item difficulties for the oldest and youngest subjects. Only one of the perceptual factors, pattern completion through closure, is markedly affected by age. Items of the simple and continuous pattern completion type are too easy to differentiate between the different age levels. On the other hand, items indicative of concrete and abstract reasoning show marked differentiation between first and third grade pupils in spite of their high overall as well as age-specific difficulties. For the present sample, age related differences in cognitive development thus may have played a role in performance for Factors I and III only. 171413 WIEDL AND CARLSON The rather small percentage of the total variance accounted for by the three main factors extracted may have been due to statistical reasons. The phi-coefficient used for the analysis of the relationship of data scored 1 or 0 is not independent from the level of difficulty of the items. Different levels of difficulty can markedly reduce the correlations of items that may measure the same intellectual capability. Although this circumstance need not change the conceptual structure of the solution obtained, it does affect the amount of variance in the item-pool which is explained by the factors extracted. The results of the factor analysis have shown that the three extracted factors represent conceptually different dimensions of the test. At the same time, the items that mark the factors tend to be of different levels of difficulty. The separation of factors not only according to conceptual characteristics but also according to item difficulty may be due, however, to the particular properties of the phi-coefficient. Methods of analysis are necessary which can separate parameters of item difficulty from those which tap different cognitive abilities. Such an approach is offered by the scaling model developed by; Rasch (1960), which has been extended by Fischer (1974). For the unequivocal application of these methods a much larger sample is required than the one that could be obtained for the present investigation. The replication of the current study in larger samples of differing age and experiential characteristics could serve to clarify the nature of the constructs portrayed by the CPM and thus could lead to an improved understanding of its factorial validity. REFERENCES Cattell, R. B. The Scree test for the number of factors. Multivariate Behavioral Research, 1966, 1, 245-276. Fischer, G. H. Einführung in die Theorie psychologischer Tests: Grundlagen und Anwendungen. Bern: Huber, 1974. Müller, R. Eine kritische empirische Untersuchung des "Draw-a-man test" und der "Coloured Progressive Matrices." Diagnostica, 1970, 16, 138-147. Rasch, G. Probabilistic Models of Some Intelligence and A ttainment Tests. Copenhagen: Nielson & Lydische, 1960. Raven, J. G. Guide to Using the Coloured Progressive Matrices Sets A, Ab, B. Dumfries: Grieve, 1965. Wenke, W. and Müller, U. Möglichkeiten und Grenzen des Einsatzes einzelner diagnostischer Kurzverfahren bei der Schulerauslese: Dargestellt am Beispiel der Progressiven Matrizen von Raven. Zeitschrift für Psychologie, 1966, 172, 82-116. Winkelmann, W. Normen für den Mann-Zeichen-Test von Ziler und die Coloured Progressive Matrices von Raven für 5-7 jahrige Kinder. Psychologische Beitrage, 1972, 14, 80-94.</meta-value></custom-meta></custom-meta-wrap></article-meta></front><back><notes><p><sup>1</sup> Request for reprints should be sent to Jerry S. Carlson at the University of California, School of Education, Riverside, California 92592, or Karl Heinz Wiedl, Psychologische Abteilung der Universität Trier, D-5500 Trier, Federal Republic of Germany.</p></notes><ref-list><ref><citation citation-type="journal" xlink:type="simple"><name name-style="western"><surname>Cattell, R. B.</surname></name><article-title>The Scree test for the number of factors</article-title>. <source>Multivariate Behavioral Research</source>, <year>1966</year>, <volume>1</volume>, <fpage>245</fpage>-<lpage>276</lpage>.</citation></ref><ref><citation citation-type="book" xlink:type="simple"><name name-style="western"><surname>Fischer, G. H.</surname></name><source>Einführung in die Theorie psychologischer Tests: Grundlagen und Anwendungen</source>. <publisher-loc>Bern</publisher-loc>: <publisher-name>Huber</publisher-name>, <year>1974</year>.</citation></ref><ref><citation citation-type="journal" xlink:type="simple"><name name-style="western"><surname>Müller, R.</surname></name><article-title>Eine kritische empirische Untersuchung des "Draw-a-man test" und der "Coloured Progressive Matrices."</article-title><source>Diagnostica</source>, <year>1970</year>, <volume>16</volume>, <fpage>138</fpage>-<lpage>147</lpage>.</citation></ref><ref><citation citation-type="book" xlink:type="simple"><name name-style="western"><surname>Rasch, G.</surname></name><source>Probabilistic Models of Some Intelligence and A ttainment Tests</source>. <publisher-loc>Copenhagen</publisher-loc>: <publisher-name>Nielson & Lydische</publisher-name>, <year>1960</year>.</citation></ref><ref><citation citation-type="book" xlink:type="simple"><name name-style="western"><surname>Raven, J. G.</surname></name><source>Guide to Using the Coloured Progressive Matrices Sets A, Ab, B</source>. <publisher-loc>Dumfries</publisher-loc>: <publisher-name>Grieve</publisher-name>, <year>1965</year>.</citation></ref><ref><citation citation-type="journal" xlink:type="simple"><name name-style="western"><surname>Wenke, W.</surname></name> and <name name-style="western"><surname>Müller, U.</surname></name><article-title>Möglichkeiten und Grenzen des Einsatzes einzelner diagnostischer Kurzverfahren bei der Schulerauslese: Dargestellt am Beispiel der Progressiven Matrizen von Raven</article-title>. <source>Zeitschrift für Psychologie</source>, <year>1966</year>, <volume>172</volume>, <fpage>82</fpage>-<lpage>116</lpage>.</citation></ref><ref><citation citation-type="journal" xlink:type="simple"><name name-style="western"><surname>Winkelmann, W.</surname></name><article-title>Normen für den Mann-Zeichen-Test von Ziler und die Coloured Progressive Matrices von Raven für 5-7 jahrige Kinder</article-title>. <source>Psychologische Beitrage</source>, <year>1972</year>, <volume>14</volume>, <fpage>80</fpage>-<lpage>94</lpage>.</citation></ref></ref-list></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>The Factorial Structure of the Raven Coloured Progressive Matrices Test</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>The Factorial Structure of the Raven Coloured Progressive Matrices Test</title></titleInfo><name type="personal"><namePart type="given">Karl</namePart><namePart type="family">Heinz Wiedl</namePart><affiliation>University of Trier, West Germany</affiliation></name><name type="personal"><namePart type="given">Jerry S.</namePart><namePart type="family">Carlson</namePart><affiliation>University of California, Riverside</affiliation></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><originInfo><publisher>Sage Publications</publisher><place><placeTerm type="text">Sage CA: Thousand Oaks, CA</placeTerm></place><dateIssued encoding="w3cdtf">1976-07</dateIssued><copyrightDate encoding="w3cdtf">1976</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">The Raven Coloured Progressive Matrices Test was administered to 180 first, second, and third grade children. Factor analysis revealed three orthogonal factors. They were interpreted as (1) concrete and abstract reasoning, (2) continuous and discrete pattern completion, and (3) pattern completion through closure. The results were discussed in context of the dimensions of the test which Raven and others have described. The issue of the relationship of item difficulty to the internal structure of the test was discussed as well as age-related differences of performance on the single factors.</abstract><relatedItem type="host"><titleInfo><title>Educational and Psychological Measurement</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0013-1644</identifier><identifier type="eISSN">1552-3888</identifier><identifier type="PublisherID">EPM</identifier><identifier type="PublisherID-hwp">spepm</identifier><part><date>1976</date><detail type="volume"><caption>vol.</caption><number>36</number></detail><detail type="issue"><caption>no.</caption><number>2</number></detail><extent unit="pages"><start>409</start><end>413</end></extent></part></relatedItem><identifier type="istex">EA518D5AAD2FE51E752C60C82F97350D0D4C6EAB</identifier><identifier type="DOI">10.1177/001316447603600220</identifier><identifier type="ArticleID">10.1177_001316447603600220</identifier><recordInfo><recordContentSource>SAGE</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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