A method for clustering group means with analysis of variance

Abstract

In comparing treatment means, one is interested in partitioning the treatments into groups, with hopefully the same mean for all treatments in the same group. This makes particular sense if on general grounds, it is likely that the treatments fall into a fairly small number of such groups.A statistic, which appears in a decomposition of the sample variance, is used to define a test statistic for breaking up treatment means in distinct groups of means that are alike, or simply assert they all form one group. The observed value is compared for significance with empirical quantiles, obtained via Monte Carlo simulation. The test is successfully applied in examples; it is also compared with other methods.