Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

EXERCISES FOR CHAPTER 17
1. How can a single experiment produce multiple false alarms? Multiple false alarms and multiple misses?
2. In the numerical example of Student–Newman range test, verify that the final outcome is the separation of the means into the following three subsets, each of which contains means that are not statsig different.

{A, B}, {B, C, D}, and {C, D, E}.

 a. Which two-mean comparisons are statsig? b. You notice that the means seem to fall into two clusters, {A, B} and {C, D, E}. Use the formula in Note 4.1.1b to get 14.83 ± 7.38 as a 95% confidence interval for the difference between the means of the two clusters. How much confidence do you have that this clustering is real?
3. You test four experimental conditions but the overall Anova falls somewhat short of statsig. However, your research assistant points out that your four experimental conditions form a clear a priori rank order and suggests that a linear trend test would be most effective. What do you do?
4. a. Show that the one-for-two rule of Section 17.3.2 yields α3 =.074 for a = 3 conditions. Compare with Student–Newman procedure.
5. In the familywise test of inverted-U shape (Section 17.4.2):
 a. What is the null hypothesis? Why is this null hypothesis appropriate? b. What is the familywise α if H0 is true? c. Suppose the expected maximum condition had not been specified beforehand, but selected by inspection of the data. Why exactly would this invalidate the analysis? What modification is needed in this case? d. Would you have any preference between Newman–Ryan and Tukey procedures for this question of inverted U shape?
6. With one-way design, a statsig range always demonstrates a two-mean difference, whereas a statsig F says only that not all true means are equal with little information about which means differ from which. Hence a range procedure such as Student–Newman might seem preferable to the overall F. Although the range procedures may have a little less power in most situations, they go beyond the overall F to say which means differ from which.

So: Why not make range procedures standard and forget about overall Anova? As a bonus, much material of previous chapters could be omitted; learning statistics would be much easier. What reason can you see for retaining the overall F for one-way designs?

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