Evaluation of Noether's Method of Sample Size Determination for the Wilcoxon‐Mann‐Whitney Test

NOETHER (1987) proposed a method of sample size determination for the Wilcoxon‐Mann‐Whitney test. To obtain a sample size formula, he restricted himself to alternatives that differ only slightly from the null hypothesis, so that the unknown variance o 2 of the Mann‐Whitney statistic can be approximated by the known variance under the null hypothesis which depends only on n. This fact is frequently forgotten in statistical practice. In this paper, we compare Noether's large sample solution against an alternative approach based on upper bounds of σ 2 which is valid for any alternatives. This comparison shows that Noether's approximation is sufficiently reliable with small and large deviations from the null hypothesis.