  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
