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 4.9 on page 267. The comparison of lithium to the placebo is the subject of Example 4.29. In this exercise, we test the success of desipramine against a placebo using a different statistic than that used in Example 4.29. Let p_dand p_cbe 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 than a placebo.

(a) What are the null and alternative hypotheses?

(b) From Table 4.9 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

D = desipramine relapses ˆ’ placebo relapses

 = 10 ˆ’ 20 = ˆ’10

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?  

Data 4.7

Cocaine addiction is very hard to break. Even among addicts trying hard to break the addiction, relapse is common. (A relapse is when a person trying to break out of the addiction fails and uses cocaine again.) One experiment investigates the effectiveness of the two drugs desipramine and lithium in the treatment of cocaine addiction. The subjects in the study were cocaine addicts seeking treatment, and the study lasted six weeks. The 72 subjects were randomly assigned to one of three groups (desipramine, lithium, or a placebo, with 24 subjects in each group) and the study was double blind. The results of the study are summarized in Table 4.9.

Transcribed Image Text:

No Relapse Relapse Desipramine 10 14 Lithium 18 20 4 Placebo