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 $P(X<Y)\equiv p$ 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 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.

在包含昂贵的实验单元或高风险暴露的小型研究中，准确的功率计算是必不可少的。在此，连续结果的 Wilcoxon Mann-Whitney 秩和检验的功效是使用蒙特卡罗方法制定的，并定义$磷(X<是)\equiv 磷$ 作为效应大小的度量，其中 $X$ 和 $是$表示假设在零下相等的两个分布的随机观察。规模效应$磷$ 促进富有成效的交流，因为研究人员了解 $磷=0.5$ 类似于一次公平的抛硬币，并且 $磷$接近 0 或 1 表示效果很大。即使没有背景数据，这种方法也是可行的。Rosner & Glynn、Shieh 及其同事、Noether 和 O'Brien-Castelloe 进行了模拟，将经验功效方法与现有方法进行了比较。Noether 和 O'Brien-Castelloe 的近似值被证明对于小样本量是不准确的。Rosner & Glynn 和 Shieh、Jan & Randles 方法在许多小样本场景中表现良好，尽管两者都仅限于位置偏移替代方案，而且这两种方法在理论上都不适用于小样本。R 包 wmwpow 中推荐并提供了经验方法。