# Exact Power of the Rank-Sum Test for a Continuous Variable

arXiv: https://arxiv.org/abs/1901.04597 · HTML: https://mlsanity.com/paper/1901.04597/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Uncertainty quantification and exploration-exploitation trade-off in humans](https://mlsanity.com/paper/2102.07647/) (2021)

## Abstract (arXiv)

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