1. Simple ANOVA Comparing the Means of Three or More Groups Chapter 9

2. ANOVA Terminology The purpose of this experiment was to compare the effects of intensity of training (low, med, high) on aerobic fitness (VO 2 ). The purpose of this experiment was to compare the effects of intensity of training (low, med, high) on aerobic fitness (VO 2 ). The independent variable Intensity of Training is called a FACTOR. The independent variable Intensity of Training is called a FACTOR. The FACTOR has 3 LEVELS (low, med, high) The FACTOR has 3 LEVELS (low, med, high) The dependent variable in this experiment is VO 2 The dependent variable in this experiment is VO 2 ANOVA allows for multiple comparisons while still keeping alpha at 0.05. ANOVA allows for multiple comparisons while still keeping alpha at 0.05.

3. Familywise or Experimentwise Error Rate The purpose of this experiment was to compare the effects of NUMBER OF DAYS TRAINING PER WEEK (1, 2, 3, 4, 5, 6) on STRENGTH. The number of days training is a factor with 6 levels. We could use multiple t-tests to compare (1 v 2, 1 v 3, 1 v 4, 1 v 5, 1 v 6; 2 v 3, 2 v 4, 2 v 5, 2 v 6; 3 v 4, 3 v 5, 3 v 6; 4 v 5, 4 v 6; 5 v 6). That would require 15 t-tests. This would cause alpha to inflate from 0.05 to 0.26 greatly increasing the probability of making a Type I ERROR. ANOVA fixes this problem by doing only one test.

4. Assumptions of ANOVA

5. Sources of Variance Between Groups variance is the deviation of the group means from the Grand MEAN. Within Groups variance is the deviation of individual scores from their Group Means.

6. Mean Square and F Ratio

7. Strength Training Groups

8. Within Groups Deviations

9. Sum of Squared Within Deviations

10. Between Groups Deviations

11. Between Groups Sum of Squared Deviations

12. F Statistic is a Ration of Variances Each Sum of Squares is divided by its df to produce a Mean Square. F ratio is the ratio of variances F = MS b / MS e

13. Critical Values of F Statistic

14. Scheffe Post Hoc

15. Scheffe Results Scheffe is less powerful than Tukey

16. Tukey HSD

17. Tukey Results The Group 1 vs Group 2 was only significant at 0.05 with the more conservative Scheffe.

18. Critical Values of q Statistic

19. R 2 (also called eta 2 ) and ω 2 R 2 or eta 2 are rough estimates the size of the effect. ω 2 is a more exact test of the Effect.

20. Effects of Play on Stress

21. Scheffe Post Hoc

22. Tukey Post Hoc Again, Tukey is more powerful than Scheffe.

23. Single Factor (One-Way) ANOVA

24. Enter Value Labels for Independent Variable Group

25. One-Way or Single Factor ANOVA

26. Enter Independent and Dependent Variables

27. Options Button

28. Post hoc Tests Usually you would choose just one Post hoc test. Usually you would choose just one Post hoc test. Tukey is the most powerful, which is why it is used most often. Tukey is the most powerful, which is why it is used most often. Scheffe can handle unequal group sizes, but it is not very powerful Scheffe can handle unequal group sizes, but it is not very powerful

29. One-Way ANOVA Output: Descriptives

30. One-Way ANOVA Output: Homogeneity of Variance?

31. One-Way ANOVA Output: Summary Table

32. One-Way ANOVA Output: Means Plot

33. One-Way ANOVA Output: Tukey Post Hoc

34. One-Way ANOVA Output: Scheffe Post Hoc

35. One-Way ANOVA Output: