Distribution-free confidence bounds for pr y< when fx and gy = fx-6 are continuous and symmetric

For and continuous and symmetric and differing at most by a shift parameter, distribution-free confidence intervals for are obtained by means of the Chebyshev inequality and an upper bound for the variance of the Mann-Whitney statistic. The (two-sided) intervals are reliable for small samples and about 20 to 30 per cent shorter than those obtained by Ury for and completely unknown for equal sample sizes, with larger savings otherwise. They are also shorter than the upper bounds obtained by Birnbaum and McCarty (1958) when the confidence coefficient does not exceed 0.95.