Confidence intervals for the Mann–Whitney test

. This measure is often referred to as the degree of overlap or the probabilistic index; it is in one-to-one relationship with the Mann-Whitney test statistic. The measure equals the area under the ROC curve. Several methods have been proposed for the construction of the confidence interval for this measure, and we review the most promising ones and explain their ideas. We study the properties of different variance estimators and small sample problems of confidence intervals construction. We identify scenarios in which the existing approaches yield inadequate coverage probabilities. We conclude that the DeLong variance estimator is a reliable option regardless of the scenario, but confidence intervals should be constructed using the logit scale to avoid values above 1 or below 0 and the poor coverage probability that follows. A correction is needed for the case when all values from one sample are smaller than the values of the other. We propose a method that improves the coverage probability also in these cases.