Tables of Critical Values for a k-Sample Kolmogorov-Smirnov Test Statistic

Abstract

Let x _1j , x _2j , ···, x_nj ; j=1, 2, ···, k be k independent random samples drawn, respectively, from the distributions with cdf's F_j (x). Let F* _j (x) denote the empirical distribution function of the jth sample. Conover [3] and Wolf [6] derive the null distribution for the statistic sup _{x;i < k} [F* _i (x) – F* _i+1(x)]. This article presents tables of exact probabilities for this statistic for k = 3(1)10, and n = 5(1)20. An approximation based on Conover's limiting distribution for the statistic is evaluated, and its range of usefulness explored. Certain alternatives are described for which the test has reasonable power relative to parametric and distribution-free competitors.