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Factor Analysis

Factor Analysis. The purpose of factor analysis is to discover patterns in the relationships among the variables. Factor Analysis. Form of multiple correlations Checking for construct validity Do questions measure the same dimension? For use between or within a test

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Factor Analysis

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  1. Factor Analysis The purpose of factor analysis is to discover patterns in the relationships among the variables

  2. Factor Analysis • Form of multiple correlations • Checking for construct validity • Do questions measure the same dimension? • For use between or within a test • Identify items which cluster together

  3. Correlation Matrix 1 2 3 4 5 1. Vocab 1.00 .22 .77 .20 .50 2. Algebra .22 1.00 .21 .65 .48 3. Analogy .77 .21 1.00 .19 .52 4. Geom .20 .65 .19 1.00 .47 5. Alg-wrd .50 .48 .52 .47 1.00

  4. Factor analysis of 5 items Factors I II Vocabulary .917 .101 Algebra .113 .885 Analogy .925 .094 Geometry .086 .891 Algebra-Word .594.573 % of variance 54.00 26.00

  5. Factor loadings • Identify clusters of questions • correlations • positive or negative • may load on more than one factor • score indicates strength of question

  6. Types of factor analysis • Exploratory factor analysis • Confirmatory factor analysis

  7. Confirmatory factor analysis Strong hypothesis -- There are two factors in this test -- questions 1-5 load onto one factor -- questions 6-10 load onto the other factor

  8. Factor loadings - 1 Qs# Factor 1 Factor 2 1 .63 2 .52 3 .43 4 .89 5 .74 6 .36 7 .74 8 .86 9 .64 10 .52

  9. Factor loadings - 2 Qs# Factor 1 Factor 2 1 .63 2 .52 3 .43 4 .89 5 .74 6 .36 7 .74 8 .86 9 .64 10 .52

  10. Factor loadings - 3 Qs# Factor 1 Factor 2 1 .63 2 -.52 3 .43 4 .89 5 -.74 6 .36 7 .74 8 -.86 9 .64 10 -.52

  11. Locus of Control – 1 factor Qs# Factor 1 1 .63 2 .52 3 -.43 4 -.89 5 -.74 6 .32 7 .26 8 .75 9 .19 10 -.80

  12. Locus of Control multiple factors Qs# 1 2 3 4 5 6 1 .56 2 .45 3 .34 4 .78 5 .39 6 .40 8 .67 9 .50 14 .34 18 .75

  13. Need for Closure – factors example Qs# Order Predict Decisive Ambiguity Closed minded 1.xxx 2 -.xxx 3 .xxx 4 .xxx x-.xxx x.xxx x -.xxx x .xxx .xx x x .xxx x .xxx -.x x .xxx x .xxx x -.xxx 45 .xxx 46 47 -.xxx

  14. Hypothesis • This test measures 4 different factors questions 1-5 are one factor questions 6-10 are a second factor questions 11-15 are a third factor questions 16-20 are a fourth factor

  15. Project question • What do you think the factor structure of your test would look like?

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