Chapter 8

A group of 30 postmenopausal women were given oral conjugated estrogen for one month. Plasma levels of plasminogen-activator inhibitor type 1 (PAI-1) went down for 22 of the women, but went up for 8 women. ${}^{15}$ The $P$ -value for a sign test, with a nondirectional alternative, is 0.016 . (a) State the null and alternative hypotheses in context. (b) If $\alpha =0.10,$ what is your conclusion regarding $H_0?$

Tobramycin is a powerful antibiotic. To minimize its toxic side effects, the dose can be individualized for each patient. Thirty patients participated in a study of the accuracy of this individualized dosing. For each patient, the predicted peak concentration of Tobramycin in the blood serum was calculated, based on the patient's age, sex, weight, and other characteristics. Then Tobramycin was administered and the actual peak concentration $(\mu \mathrm{g}/\mathrm{ml})$ was measured. The results were reported as in the table. $$\begin{array}{|lcc|}\hline & \text{ Predicted }& \text{ Actual }\\ \text{ Mean }& 4.52& 4.40\\ \text{ SD }& 0.90& 0.85\\ n& 30& 30\\ \hline\end{array}$$ Does the reported summary give enough information for you to judge whether the individualized dosing is, on the whole, accurate in its prediction of peak concentration? If so, describe how you would make this judgment. If not, describe what additional information you would need and why.

In a study, on the effect of caffeine on myocardial blood flow, 10 subjects had their blood flow measured before and after consuming caffeine. ${}^{21}$ For this setting the differences do not follow a normal distribution, so a $t$ test would not be valid. Use a Wilcoxon signed-rank test to test the null hypothesis of no difference against the alternative that caffeine has an effect on myocardial blood flow. Let $\alpha =0.01$.

Trichotillomania is a psychiatric illness that causes its victims to have an irresistible compulsion to pull their own hair. Two drugs were compared as treatments for trichotillomania in a study involving 13 women. Each woman took clomipramine during one time period and desipramine during another time period in a double-blind experiment. Scores on a trichotillomania-impairment scale, in which high scores indicate greater impairment, were measured on each woman during each time period. The average of the 13 measurements for clomipramine was $6.2;$ the average of the 13 measurements for desipramine was $4.2{.}^8$ A paired $t$ test gave a value of $t_s=2.47$ and a two-tailed $P$ -value of 0.03 . Interpret the result of the $t$ test. That is, what does the test indicate about clomipramine, desipramine, and hair pulling?

The study described in Example 8.1 .1 , involving the compound $\mathrm{mCPP}$, included a group of men. The men were asked to rate how hungry they were at the end of each 2-week period and differences were computed (hunger rating when taking mCPP minus hunger rating when taking the placebo). The distribution of the differences was not normal. Nonetheless, a sign can be conducted using the following information: Out of eight men who recorded hunger ratings, three reported greater hunger on $\mathrm{mCPP}$ than on the placebo and five reported lower hunger on $\mathrm{mCPP}$ than on the placebo. ${}^1$ Conduct a sign test at the $\alpha =0.10$ level; use a nondirectional alternative.