Optimal design of the Wilcoxon-Mann-Whitney-test

Abstract

In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes m and n for fixed N=m+n) that maximizes the power of the applied statistical test. It is known that the two-sample t-tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the nonparametric Wilcoxon-Mann-Whitney-test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design m=n in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions.

Keywords: Optimal design; Statistical power; Wilcoxon-Mann-Whitney-test.