Chapter 12

1. What is the null hypothesis tested by analysis of variance?

2. What are the assumptions of between-subjects analysis of variance?

3. What is a between-subjects variable?

4. Why not just compute t-tests among all pairs of means instead computing an analysis of variance

5. What is the difference between "N" and "n"?

6. How is it that estimates of variance can be used to test a hypothesis about means?

7. Explain why the variance of the sample means has to be multiplied by "n" in the computation of MSB.

8. What kind of skew does the F distribution have?

9. When do MSB and MSE estimate the same quantity?

10. If an experiment is conducted with 6 conditions and 5 subjects in each condition, what are dfn and dfe?

11. How is the shape of the F distribution affected by the degrees of freedom?

12. What are the two components of the total sum of squares?

13. How is the mean square computed from the sum of squares?

14. An experiment compared the ability of three groups of subjects to remember briefly-presented chess positions. The data are shown below. Compute an analysis of variance. Using the Tukey HSD procedure, which groups are significantly different from each other at the .05 level?

Group 1: Nonplayers
Group 2: Beginners
Group 3: Tournament players

1 22.1
1 22.3
1 26.2
1 29.6
1 31.7
1 33.5
1 38.9
1 39.7
1 43.2
1 43.2
2 32.5
2 37.1
2 39.1
2 40.5
2 45.5
2 51.3
2 52.6
2 55.7
2 55.9
2 57.7
3 40.1
3 45.6
3 51.2
3 56.4
3 58.1
3 71.1
3 74.9
3 75.9
3 80.3
3 85.3

15. If you plan to make 4 comparisons among means and keep the EER at .05, what should the PCER be?

16. What difference does it make whether or not comparisons are planned or not?

17. What is the difference between the Tukey HSD test and the Newman-Keuls test? Which is more conservative?

18. What procedure do you use to make unplanned comparisons? Computationally, how does it differ from the procedure for planned comparisons?

19. What are orthogonal comparisons? What is the maximum number of orthogonal comparisons that can be made among 6 means?

20. Test to see if there is a significant linear trend of chess skill in the dataset given in Problem 14. Test to see if there is a significant quadratic trend.

21. If there are three populations and m1= 6, m2 = 8, and m3 = 10, then what are: a1, a2, and a3? If Σ² = 25 and n = 10, what is the expected value of MSB?

22. What is the relationship between F and t?

23. When is the assumption of homogeneity of variance something to worry about?

24. Below are shown data from a hypothetical experiment on the effects of sleep deprivation on the time it takes to solve two anagram problems. Subjects went without sleep for either 16, 24, 32, or 40 hours. Are increased levels of sleep loss significantly (a = .05) associated with longer problem solving time? Do the test assuming this comparison was planned in advance and assuming it was not. Use two-tailed tests in both cases.

 Hours without Sleep 16 24 32 40 4 4 5 6 7 7 8 9 9 12 4 6 6 7 8 8 8 8 9 13 5 6 8 8 9 9 9 10 11 15 5 6 7 10 11 11 12 12 15 16

25. What coefficients could be used to test the null hypothesis: (a) m1 - (m2+m3)/2 = 0 (b) m1 - m2 = m3 - m4 (c) There is no difference between the mean of population means 1, 2, and 3 and the mean of population means 4 and 5.

26. What test should an experimenter use if he or she wishes to compare several means to a control mean? For the data in Problem 24, assume that 16 hours without sleep is the control condition and compare each of the other conditions to this control condition.

27. Give the coefficients for a set of four orthogonal comparisons among five means.