Chapter 10 described how to test the hypothesis that two or more independent groups have a common mean. In symbols, the goal was to test
But typically, one wants to know more about how the groups compare: which groups differ, how do they differ, and by how much?
Note that rather than test the hypothesis given by Equation (12.1), another approach is to test the hypothesis of equal means for all pairs of groups. For example, if there are four groups (), methods in Chapter 9 could be used to test the hypothesis that the mean of the first group is equal to the mean of the second, the mean of first group is equal to the mean of third, and so on. In symbols, the goal is to test
There is, however, a technical issue that needs to be taken into account. Suppose there are no differences among the groups in which case none of the six null hypotheses just listed should be rejected. To keep things simple for the moment, assume that all four groups have normal distributions with equal variances, in which case Student's test in Chapter 9 provides exact control ...