连续变量秩和检验的精确功效
Exact Power of the Rank-Sum Test for a Continuous Variable
摘要：
精确的功效计算在包含昂贵实验单元或高风险暴露的小型研究中至关重要。在本文中，使用蒙特卡罗方法并定义P（X < Y）= p作为效应大小的度量来制定连续变量的Wilcoxon Mann-Whitney秩和检验的精确功效，其中X和Y表示来自假设在零值下相等的两个分布的随机观察值。效应大小p促进了有效的沟通，因为研究人员知道p = 0.5类似于公平的掷硬币，而p接近0或1代表了很大的效应。即使没有背景数据，这种方法也是可行的。进行了模拟，将精确幂方法与Rosner & Glynn（2009）、Shieh等人（2006）、Noether（1987）和O 'Brien-Casteldinger（2006）的现有方法进行比较。Noether和O 'Brien-Castellem的近似值对于小样本量是不准确的。Rosner & Glynn和Shieh等人的方法在许多小样本场景中表现良好，尽管这两种方法都局限于位置偏移替代方案，并且这两种方法在理论上都不适合小样本。推荐使用精确的方法，并在R包wmwpow中提供。关键词：Mann-Whitney检验，蒙特卡罗模拟，非参数，功效分析，Wilcoxon秩和检验
英文摘要：
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
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