Chapter 15 Introduction to the Analysis of Variance

Chapter 15 – Introduction to the Analysis of Variance Know and Be Able To Do

1. You should be able to define the terms in the “Important Terms” section of this chapter.

2. You should know that Fobt is the ratio of two independent estimates of the population variance.

3. You should be able to define the sampling distribution of F and state its characteristics.

4. You should be able to state the null and alternative hypotheses for one-way, independent groups ANOVA in terms of μ1, μ2,… μk.

5. You should understand and be able to state the partitioning of the total variability of the data (SST) into its two components, the formation of variance estimates from each component and finally the formation of the F ratio from these variance estimates.

2 2 2 6. You should know that Fobt is the ratio of sB to sW with sB always in the numerator.

2 7. You should understand the Within-Groups Variance Estimate, sW and be able to compute it.

2 8. You should understand the Between-Groups Variance Estimate, sB and be able to compute it.

2 2 9. You know how to compute Fobt once you have computed sB and sW ; and you should 2 be able to explain why sB is always put in the numerator.

2 10. You should understand why sB is sensitive to the real effects of the independent 2 variable and sW is not.

11. You should understand the logic underlying the one-way ANOVA.

12. You should understand why the alternative hypothesis in one-way ANOVA is always nondirectional.

13. You should understand why even though H1 is nondirectional, we evaluate it with a one-tailed evaluation.

14. You should be understand and be able to solve the illustrative example and practice problems on one-way ANOVA presented in this chapter.

15. You should understand and be able to state the assumptions underlying the one-way, independent groups ANOVA. 17. You should understand the relationship between F and t.

18. You should understand and know how to calculate the size of effect for a one-way ANOVA using two different estimates; you should be able to compare ω2 and η2.

19. You should understand and be able to state how power in experiments using one-way ANOVA varies with changes in N, size of the real effect of the independent variable, and sample variability.

20. You should understand the difference between a priori (planned) and a posteriori (post hoc) comparisons, and why planned are more powerful than post hoc comparisons.

21. You should be able to do planned comparisons for any pair of groups in the ANOVA.

2 22. You should understand why sW from the ANOVA is used in planned comparisons.

23. You should understand and be able to explain the difference between experiment- wise error rate and comparison-wise error rate.

24. You should understand that both the Tukey HSD test and the Newman-Keuls test use Q distributions.

25. You should understand why Qobt is always positive.

26. You should be able to do post hoc comparisons using the Tukey HSD test and the Newman-Keuls test.

27. You should be able to explain why the Newman-Keuls test is more powerful than the Tukey HSD test, even though they both maintain the error rate at α.

28. You should be able to explain why two different researchers might differ between choosing the Newman-Keuls test or the Tukey HSD test to do post hoc comparisons on their data.

29. You should understand and be able to do the illustrative example and practice problems pertaining to multiple comparisons.