Heteroscedastic Analysis of Means (Hanom)

Abstract

SYNOPTIC ABSTRACTThe analysis of means (ANOM) is a method that can compare a group of treatment means to see if any of those means are significantly different from the overall mean. It can be thought of as an alternative to the analysis of variance for analyzing fixed main effects in a designed experiment. The ANOM has advantages: it identifies any treatments that are different from the overall mean and has a graphical display that helps one to assess practical significance. Sample size tables and power curves have previously been developed for using ANOM to detect differences among I treatments when two of them differ by at least a specified amount δσ, where σ is the common standard deviation of the treatments (or processes).More recently results for the heteroscedastic situation where the different processes do not necessarily have equal standard deviations were presented. These new results allow an experimenter to set a goal of detecting differences among I treatment means when two of them differ by at least a specified amount δ, which does not depend on the (possibly different) standard deviations of the processes. In this paper we present power curves for α = 0.1, 0.05, 0.01 and I = 2(1)10, 12, 15, 20; compare the power with that of heteroscedastic analysis of variance; and give two examples.