Halperin, Max; Gilbert, Peter R.; Lachin, John M. Distribution-free confidence intervals for \(\Pr (X_ 1<X_ 2)\). (English) Zbl 0655.62052 Biometrics 43, 71-80 (1987). We review the problem of obtaining a distribution-free confidence interval for the probability (p) that one random variable is less than another independent random variable based on the two-sample uncensored Wilcoxon-Mann-Whitney statistic. The pivotal quantities used by P. K. Sen [Sankhyā, Ser. A 29, 95-102 (1967; Zbl 0173.209)] and Z. Govindarajulu [Ann. Inst. Stat. Math. 20, 229-238 (1968; Zbl 0176.486)] are modified to take into account that the variance of estimated p depends on p. A number of simulations were conducted to compare the various methods. The results suggest that the proposed modification is superior in the sense that over the entire range of p the modification generally yields values of coverage probability much closer to nominal coverage than the methods of Sen and Govindarajulu. Cited in 1 ReviewCited in 13 Documents MSC: 62G15 Nonparametric tolerance and confidence regions 62Q05 Statistical tables Keywords:two-sample uncensored Wilcoxon-Mann-Whitney statistic Citations:Zbl 0173.209; Zbl 0176.486 PDFBibTeX XMLCite \textit{M. Halperin} et al., Biometrics 43, 71--80 (1987; Zbl 0655.62052) Full Text: DOI