In this exercise, we see that it is possible to use counts instead of
proportions in testing a categorical variable. Data 4.7 describes an
experiment to investigate the effectiveness of the two drugs desipramine and
lithium in the treatment of cocaine addiction. The results of the study are
summarized in Table 4.14 on page \(323 .\) The comparison of lithium to the
placebo is the subject of Example 4.34 . In this exercise, we test the success
of desipramine against a placebo using a different statistic than that used in
Example 4.34. Let \(p_{d}\) and \(p_{c}\) be the proportion of patients who
relapse in the desipramine group and the control group, respectively. We are
testing whether desipramine has a lower relapse rate then a placebo.
(a) What are the null and alternative hypotheses?
(b) From Table 4.14 we see that 20 of the 24 placebo patients relapsed, while
10 of the 24 desipramine patients relapsed. The observed difference in
relapses for our sample is
$$\begin{aligned}D &=\text { desipramine relapses }-\text { placebo relapses }
\\\&=10-20=-10\end{aligned}$$
If we use this difference in number of relapses as our sample statistic, where
will the randomization distribution be centered? Why?
(c) If the null hypothesis is true (and desipramine has no effect beyond a
placebo), we imagine that the 48 patients have the same relapse behavior
regardless of which group they are in. We create the randomization
distribution by simulating lots of random assignments of patients to the two
groups and computing the difference in number of desipramine minus placebo
relapses for each assignment. Describe how you could use index cards to create
one simulated sample. How many cards do you need? What will you put on them?
What will you do with them?
