Optimal sample size planning for the Wilcoxon ‐Mann‐Whitney test

We present a unified approach that covers metric data with and without ties, count data, ordered categorical data, and even dichotomous data. For that, we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following “synthetic data” approach. We evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities. Then, well‐known relations for the ranks of the data are used for the calculations.In addition to computing the necessary sample sizeN for a fixed allocation proportiont = n1/N, wheren1 is the sample size in the first group andN = n1 + n2 is the total sample size, we provide an interval for the optimal allocation ratet, which minimizes the total sample sizeN. It turns out that, for certain distributions, a balanced design is optimal. We give a characterization of such distributions. Furthermore, we show that the optimal choice oft depends on the ratio of the two variances, which determine the variance of the Wilcoxon ‐Mann‐Whitney statistic under the alternative. This is different from an optimal sample size allocation in case of the normal distribution model.

Source: Statistics in Medicine - October 8, 2018 Category: Statistics Authors: Martin Happ, Arne C. Bathke, Edgar Brunner Tags: RESEARCH ARTICLE Source Type: research