Exact Analysis of Means With Unequal Variances

The analysis of means (ANOM) is a technique for comparing a group of treatment means to see if any one of them differs significantly from the overall mean. It can be viewed as an alternative to the analysis of variance (ANOVA) for analyzing fixed main effects in a designed experiment. The ANOM has the advantages that it identifies any treatment means that differ from the overall mean (something the ANOVA does not do), and enables a graphical display that aids in assessing practical significance. Sample size tables and power curves have previously been developed for detecting differences among I treatments when two of them differ by at least a specified multiple of the common population standard deviation. Here, we consider the heteroscedastic situation where the different processes or populations from which the samples are drawn do not necessarily have equal standard deviations. In addition, we provide power curves that enable an experimenter to design a study for detecting differences among I treatment means when any two of them differ by at least a specified amount δ, independent of these standard deviations.