Abstract

For two independent random variables Yj (j = 1, 2), let p(x) = P(Y1 < Y2|X = x), where X is some covariate of interest. For m values of the covariate, x1 , . . . , xm, the paper deals with the goal of testing H0 : p(xj) = 0.5 (j = 1, . . . , m) in a manner that controls Family Wise Error Rate (FWE), the probability of one or more Type I errors. If m is relatively small, extant multiple comparison methods can be used to control FWE. But if m is relatively large, the actual level can be substantially smaller than the nominal level, raising concerns about relatively poor power. The paper describes a method for addressing this issue when p(x) is estimated via a running interval smoother.

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