  Accurate power calculations are essential in small studies containing
expensive experimental units or high-stakes exposures. Herein, exact power of
the Wilcoxon Mann-Whitney rank-sum test of a continuous variable is formulated
using a Monte Carlo approach and defining P(X < Y) = p as a measure of effect
size, where X and Y denote random observations from two distributions
hypothesized to be equal under the null. Effect size p fosters productive
communications because researchers understand p = 0.5 is analogous to a fair
coin toss, and p near 0 or 1 represents a large effect. This approach is
feasible even without background data. Simulations were conducted comparing the
exact power approach to existing approaches by Rosner & Glynn (2009), Shieh et
al. (2006), Noether (1987), and O'Brien-Castelloe (2006). Approximations by
Noether and O'Brien-Castelloe are shown to be inaccurate for small sample
sizes. The Rosner & Glynn and Shieh et al. 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 exact method is recommended and available in the R package wmwpow.
  KEYWORDS: Mann-Whitney test, Monte Carlo simulation, non-parametric, power
analysis, Wilcoxon rank-sum test
