## Abstract

The Wilcoxon-Mann-Whitney test, as well as modern improvements, are based in part on an estimate of p = P(D < 0), where D = X−Y and X and Y are independent random variables; a common goal is to test H_{0}: p = 0.5. This corresponds to testing H_{0}: ξ_{0.5}, where ξ_{0.5} is the 0.5 quantile of the distribution of D. If the distributions associated with X and Y do not differ, then D has a symmetric distribution about zero. In particular, ξ_{q} + ξ_{1-q} = 0 for any q ≤ 0.5, where ξ_{q} is the q^{th} quantile. Methods aimed at testing H_{0}: p = 0.5 are generalized by suggesting a method for testing H_{0}: ξ_{q} + ξ_{1-q} = 0, q < 0.5

## DOI

10.22237/jmasm/1351742460

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Applied Statistics Commons, Social and Behavioral Sciences Commons, Statistical Theory Commons