Comparisonwise error rate

Often in the context of planning an experiment or analyzing data after an experiment has been completed, we find that comparison of specific pairs or larger groups of treatment means are of greater interest than the simple question posed by an analysis of variance - do at least two treatment means differ? It may be that embedded in a group of treatments there is only one "control" treatment to which every other treatment should be compared, and comparisons among the non-control treatments may be uninteresting.

One may also, after performing an analysis of variance and rejecting the null hypothesis of equality of treatment means want to know exactly which treatments or groups of treatments differ. To answer these kinds of questions requires careful consideration of the hypotheses of interest both before and after an experiment is conducted, the Type I error rate selected for each hypothesis, the power of each hypothesis test, and the Type I error rate acceptable for the group of hypotheses as a whole.