Chapter 15, Problem 20CP

Treating alcoholics The nonparametric statistics textbook by Hollander and Wolfe (1999) discussed a study on a social skills training program for alcoholics. A sample of male alcoholics was randomly split into two groups. The control group received traditional treatment. The treatment group received the traditional treatment plus a class in social skills training. Every two weeks for a year after the treatment, subjects indicated the quantity of alcohol they consumed during that period. The summary response was the total alcohol intake for the year (in centiliters).

1. a. Suppose the researchers planned to conduct a one-sided test and believed that the response variable could be highly skewed to the right. Why might they prefer to use the Wilcoxon test rather than a two-sample t test to compare the groups?
2. b. The data were

   Controls: 1042, 1617, 1180, 973, 1552, 1251, 1151, 1511, 728, 1079, 951, 1319

   Treated: 874, 389, 612, 798, 1152, 893, 541, 741, 1064, 862, 213

   Show how to find the ranks and the mean ranks for the two groups.

3. c. MINITAB reports the results shown in the output below. Report and interpret the P-value.
4. d. Report and interpret the confidence interval shown in the output.

MINITAB output

Point estimate for η1 − η2 is 435.5 95.5 Percent CI for η1 − η2 is (186.0, 713.0) Test of η1 = η2 vs η1 ≠ η2 is significant at 0.0009