Exemplary data set sample size calculation for Wilcoxon-Mann-Whitney tests.

Zhao, Rahardja and Qu consider sample size calculation for Wilcoxon-Mann-Whitney (WMW) tests for data with ties, and present a straightforward formula. We observe that the 'exemplary data set' approach, usually applied in more complex situations, has a close relationship to the Zhao-Rahardja-Qu method for WMW sample size estimation and they are asymptotically equivalent. Therefore, the exemplary data set approach can be used to easily obtain estimates similar to those that the closed formula gives. We illustrate application of both methods for a WMW sample size estimation example, and also extend the simulation study presented by Zhao et al. We find that the Zhao-Rahardja-Qu formula (and by extension the exemplary data set method) can give estimates just as accurate as those obtained using either the Kolassa approach (via nQuery Advisor) or the O'Brien-Castelloe approach (via SAS 9.2 PROC POWER), for 1:1 and 1:2 allocation ratios. However, the latter two methods can be more accurate for a ratio of 1:4 or 1:19. Finally, we note the general utility of the exemplary data set approach for sample size estimation, even in other situations where closed-form sample size formulae exist.