Precise and accurate power of the rank-sum test for a continuous outcome
Katie R. Mollan, Ilana M. Trumble, Sarah A. Reifeis, Orlando Ferrer, Camden Bay, Pedro L. Baldoni, Michael G. Hudgens
Abstract
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.