A CONFIDENCE-INTERVAL FOR PR(X-LESS-THAN- Y)-PR(X-GREATER-THAN-Y) ESTIMATED FROM SIMPLE CLUSTER SAMPLES

Distribution-free confidence intervals based on Somers' d (a simple fu nction 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 tw o independent populations. The approach accomodates a complex sampling design, and explicit formulas are given for simple cluster sampling. The method also accomodates simple progressive left- and right-censori ng. 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.