Abstract
The standardized mean difference is a well-known effect size measure for continuous, normally distributed data. In this paper we present a general basis for important other distribution families. As a general concept, usable for every distribution family, we introduce the relative effect, also called Mann-Whitney effect size measure of stochastic superiority. This measure is a truly robust measure, needing no assumptions about a distribution family. It is thus the preferred tool for assumption-free, confirmatory studies. For normal distribution shift, proportional odds, and proportional hazards, we show how to derive many global values such as risk difference average, risk difference extremum, and odds ratio extremum. We demonstrate that the well-known benchmark values of Cohen with respect to group differences-small, medium, large-can be translated easily into corresponding Mann-Whitney values. From these, we get benchmarks for parameters of other distribution families. Furthermore, it is shown that local measures based on binary data (2 × 2 tables) can be associated with the Mann-Whitney measure: The concept of stochastic superiority can always be used. It is a general statistical value in every distribution family. It therefore yields a procedure for standardizing the assessment of effect size measures. We look at the aspect of relevance of an effect size and-introducing confidence intervals-present some examples for use in statistical practice.