1. PSY 1950 Factorial ANOVA October 8, 2008

3. Mean

4. Estimated Population Mean

5. Variance

6. Estimated Population Variance

7. Standardized Deviation (z-score)

8. One Sample z-test

9. Variance of Sampled Means

10. Standard Deviation of Sampled Means (Standard Error)

11. Probability of z-score

12. One Sample t-test

13. Estimated Variance of Sampled Means

14. Estimated Standard Deviation of Sample Means (Standard Error)

15. Probability of t-statistic

16. Independent Samples t-test

17. Estimated Variance of Difference Between Sampled Means

18. Estimated Standard Deviation of Difference Between Sampled Means (Standard Error)

19. Pooled Variance

20. Analysis of Variance (ANOVA) http://www.psych.utah.edu/stat/introstats/anovaflash.html

21. Total Sums of Squares

22. Between Groups Sums of Squares

23. Within Groups Sums of Squares

24. Additivity of Sums of Squares

25. Probability of an F-statistic

26. t-test is Special Case of ANOVA (k=2)

27. Why are SS additive? observation = overall mean + deviation of group from overall mean + deviation of observation from group mean deviation of observation from overall mean = deviation of group from overall mean + deviation of observation from group mean SS total = SS between +SS within G1G1 G2G2 G3G3 576524563 578521568 579521568 575522565

28. Logic of ANOVA Redux First, we assume equal variance among groups and estimate population variance Next, we assume equal variance and equal means (H 0 ) among groups and estimate population variance Finally, we compare these two estimates of variance to see how much they agree –If they agree, we retain the null hypothesis –If they disagree, we reject the null hypothesis

29. Logic of ANOVA First, we assume equal variance among groups and estimate population variance

30. Logic of ANOVA Next, we assume equal variance and equal means (H 0 ) among groups and estimate population variance

31. Logic of ANOVA Finally, we compare these two estimates of variance to see how much they agree –If they agree, we retain the null hypothesis –If they disagree, we reject the null hypothesis

32. G1G1 G2G2 G3G3 G4G4 5039 83511 6713 M83511 s2s2 9944 grand mean = 6.75

34. Factorial ANOVA Terminology –Factors –Levels –Cells –Main effect –Interaction effect –Simple effect Benefits –Generalizability –Interactions –Efficiency

35. Between Cells Sums of Squares

36. Interaction Sums of Squares

37. Between Cells Degrees of Freedom

38. Interaction Degrees of Freedom