Sample size calculation for the Wilcoxon–Mann–Whitney test adjusting for ties

In this paper we study sample size calculation methods for the asymptotic Wilcoxon-Mann-Whitney test for data with or without ties. The existing methods are applicable either to data with ties or to data without ties but not to both cases. While the existing methods developed for data without ties perform well, the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties. We propose a new method which has a closed-form formula and therefore is very easy to calculate. In addition, the new method can be applied to both data with or without ties. Simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers.