Abstract

A well-known approach to comparing two independent groups is to focus on the probability that a randomly sampled observation from the first group is less than a randomly sampled observation from the second group. The paper suggests a generalization that can be used with any linear contrast based on J>2 independent groups. Roughly, the proposed measure of effect size  reflects the probability that among 2K random variables, the typical average associated with first K variables is less than the typical average among the other K variables. In effect, it represents a relatively simple measure of effect size that might be used to supplement other measures of effect size when dealing with two-way and higher designs.

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