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

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

3. Correlation Matrix 1 2 3 4 5 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 Factors III 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 n Identify clusters of questions n correlations n positive or negative n may load on more than one factor n score indicates strength of question

6. Types of factor analysis n Exploratory factor analysis n 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 1Factor 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 1Factor 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 1Factor 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 23456 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 AmbiguityClosed 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 45.xxx 46 47-.xxx

15. Hypothesis n 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

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