A confidence interval for Pr(X < Y) - Pr(X > Y) estimated from simple cluster samples.

Distribution-free confidence intervals based on Somers' d (a simple function of the Mann-Whitney U statistic) are developed for Pr(X < Y) - Pr(X > Y), where X and Y are the ranks of any two observations from two independent populations. The approach accommodates a complex sampling design, and explicit formulas are given for simple cluster sampling. The method also accommodates simple progressive left- and right-censoring. The accuracy of the interval is shown to improve when the tanh-1 transform is used. A bootstrap solution was tried and did not perform as well as the proposed solution.