EXERCISES FOR CHAPTER 11
NOTE: For the following exercises, assume independent scores even in serial observation design unless otherwise indicated. Independence always needs careful consideration; it is assumed here in order to focus on other problems.1. You run four single subjects. Three show a substantial effect, comfortably statsig. The fourth shows nothing. You submit these results for publication, including four single subject Anovas. Among other editorial reactions, one reviewer requests a repeated measures Anova for all four subjects. The Editor indicates a revision should be acceptable, without remarking specifically on the repeated measures analysis.
|1. ||While you're fretting about how to handle the revision, your assistant rushes in, crying, “I've done the repeated measures analysis. Shall I show you the results right now?” How should you reply?|
|2. ||What do you conclude about the reviewer's request?|
|3. ||Suppose you conclude the repeated measures analysis requested by the reviewer is not appropriate. With your revision, you include a letter to the Editor that explains your reasoning. Nevertheless, the Editor makes this analysis prerequisite to publication. Now what do you do?|
2. Construct a very simple
conceptual example in which an A-B design suffers a total confounding that is revealed with an A-B-A design. Include a numerical, error-free example in graphic form.3. The preface to this chapter, considering whether the A-B difference is reliable in an A-B design, asserts “The answer obviously requires comparison of the mean difference between treatments to the variability within treatments.”
|1. ||Why exactly is this comparison required? (Of course, “mean” could be replaced by “median, ” for example, but this statisticality is ignored here.)|
|2. ||Do you think the word “obviously” is justified?|
4. To test relative efficacy of two therapy regimens (drug plus exercise) for a patient suffering chronic pain, a hypothetical patient–physician team used an A-B-A-B design. Each period was long enough to wash out effects of the previous period. Mild serial correlation seemed not unlikely so the response measure was taken as the mean over the last three observations in each period. At the end of the four successive periods, the response measures were 14, 19, 12, 17 (larger numbers mean greater pain).
|1. ||By visual inspection, guess how close F (1, 2) will be to the criterial 18.5.|
|2. ||Do the Anova and interpret the result.|
|3. ||Suppose this patient is a member of your family, not conversant with statistical analysis. In light of (b), what do you advise?|