Precise and accurate power of the rank-sum test for a continuous outcome

J Biopharm Stat. 2020 Jul 3;30(4):639-648. doi: 10.1080/10543406.2020.1730866. Epub 2020 Mar 4.


Accurate power calculations are essential in small studies containing expensive experimental units or high-stakes exposures. Herein, power of the Wilcoxon Mann-Whitney rank-sum test of a continuous outcome is formulated using a Monte Carlo approach and defining [Formula: see text] as a measure of effect size, where [Formula: see text] and [Formula: see text] denote random observations from two distributions hypothesized to be equal under the null. Effect size [Formula: see text] fosters productive communications because researchers understand [Formula: see text] is analogous to a fair coin toss, and [Formula: see text] near 0 or 1 represents a large effect. This approach is feasible even without background data. Simulations were conducted comparing the empirical power approach to existing approaches by Rosner & Glynn, Shieh and colleagues, Noether, and O'Brien-Castelloe. Approximations by Noether and O'Brien-Castelloe are shown to be inaccurate for small sample sizes. The Rosner & Glynn and Shieh, Jan & Randles approaches performed well in many small sample scenarios, though both are restricted to location-shift alternatives and neither approach is theoretically justified for small samples. The empirical method is recommended and available in the R package wmwpow.

Keywords: Mann–Whitney test; Monte Carlo simulation; Wilcoxon rank-sum test; non-parametric; power analysis.

Publication types

  • Research Support, N.I.H., Extramural