While there appears to be a general consensus in the literature on the definition of the estimand and estimator associated with the Wilcoxon-Mann-Whitney test, it seems somewhat less clear as to how best to estimate the variance. In addition to the Wilcoxon-Mann-Whitney test, we review different proposals of variance estimators consistent under both the null hypothesis and the alternative. Moreover, in case of small sample sizes, an approximation of the distribution of the test statistic based on the t-distribution, a logit transformation and a permutation approach have been proposed. Focussing as well on different estimators of the degrees of freedom as regards the t-approximation, we carried out simulations for a range of scenarios, with results indicating that the performance of different variance estimators in terms of controlling the type I error rate largely depends on the heteroskedasticity pattern and the sample size allocation ratio, not on the specific type of distributions employed. By and large, a particular t-approximation together with Perme and Manevski's variance estimator best maintains the nominal significance level

翻译：虽然文献中似乎对与Wilcoxon-Mann-Whitney测试有关的估计和估计标准的定义有普遍共识,但对如何最好地估计差异似乎不太清楚。除了Wilcoxon-Mann-Whitney测试外,我们审查在无效假设和替代办法下一致的不同估计标准的不同建议。此外,在样本规模小的情况下,提议了基于T分布、对账转换和调整方法的测试统计分布近似。在t-接近方面,我们集中关注自由程度的不同估计标准,并对一系列情景进行了模拟,结果显示,不同差异估计者在控制I型错误率方面的表现主要取决于偏差性模式和抽样规模分配比率,而不是基于使用的具体分布类型。与 Perme 和 Manovisca 相比,最佳和最佳应用水平保持了最高和最高水平。