29. Upjohn, a pharmaceutical company, conducted a randomized clinical tnal comparing an active hypnotic drug with a placebo for patients suffering from insomnia. The outcome is patient response to the question, "How quickly did you fall asleep after going to bed?" Patients suffering froin insomnia were randomly assigned to receive the active drug or a placebo. The study measured patients' responses at the start and at the conclusion of a two-week treatment period. The study analyzed whether the active drug helps sub- jects with insomnia problems However, patients taking placebo may also tend to fall asleep more quickly at the conclusion of the study period, because of the placebo effect thinking they are taking a beneficial drug may psychologically have a positive effect. Is the improvement with the active drug better than with the placebo? Table 12.36 show's a SAS printout from an analysis of these data. "RESP1" refers to the response at the initial occasion, and "RESP2" the response at the follow-up occasion. The first part of the table shows results of one-way ANOVAS comparing the two groups separately at each time (For the raw data, see A. Agresti, Statistics in Medicine, Vol. 8. 1989. p 1209.) The sam- ple means are 50.0 initially and 27 8 at follow up for the 120 subjects taking active drug. and 50.3 initially and 37.4 at follow up for the 119 subjects taking placebo.

a) For the 239 observations at the imtial occasion. report and interpret the F test statistic for the one-way ANOVA comparing the two means.

b) For the 239 observations at the follow-up occasion, report and interpret the one-way ANOVA F test statistic. For this one-way ANOVA, show that the 95% confidence inter- val for the difference of means equals (4.2, 15.0). Interpret.

c) Now treat both occasions at once. with repeated-measures ANOVA. Report and inter- pret the F statistic for testing interaction.

d) Does it make sense to test main effects? If not, why not? If so, do so and interpret.

e) Using the sample means, interpret the interaction descriptively.

f) To make within-subjects comparisons of occasion means, for each treatment, show that a 95% confidence interval equals (18.0. 26.4) for the active drug and (8.7, 17 2) for placebo. Interpret.