Comparing Individual Means in the Analysis of Variance

The practitioner of the analysis of variance often wants to draw as many conclusions as are reasonable about the relation of the true means for individual treatments, and a statement by the F-test (or the z-test) that they are not all alike leaves him thoroughly unsatisfied. The problem of breaking up the treatment means into distinguishable groups has not been discussed at much length, the solutions given in the various textbooks differ and, what is more important, seem solely based on intuition. After discussing the problem on a basis combining intuition with some hard, cold facts about the distributions of certain test quantities (or statistics) a simple and definite procedure is proposed for dividing treatments into distinguishable groups, and for determining that the treatments within some of these groups are different, although there is not enough evidence to say which is which. The procedure is illustrated on examples.