Chapter 9 described methods for comparing two independent groups, but often comparing more than two groups is of interest. For example, a researcher might have four methods for treating schizophrenia, in which case there is the issue of whether the choice of method makes a difference. As another example, several drugs might be used to control high blood pressure. Do the drugs differ in terms of side effects?
When comparing more than two groups, there is a collection of techniques aimed at two distinct goals. The first is to test some global hypothesis that the groups are, in some sense, identical. For instance, the hypothesis might be that all of the groups have the same mean or median. The other goal is to determine which groups differ. The first goal is the subject of this chapter. The second goal is addressed with methods in Chapter 12.
10.1 The Anova Test
Imagine that the goal is to compare independent groups having population means . A common strategy is to begin by testing
the hypothesis that all groups have equal means. ...