Randomized rejection procedure for the two-sample Kolmogorov-Smimov statistic

The two-sample Kolmogorov-Smimov test is unable to achieve an arbitrary probability of Type 1 error because it can only take on a limited number of discrete values. We offer a randomized procedure that achieves any specified value of alpha. We derive formulas for approximating the achievable p-values immediately above and below the desired value of alpha. For the value of the statistic corresponding to the p-value greater than alpha, our procedure rejects the null hypothesis randomly with probability sufficient to achieve the specified alpha. Such a procedure is particularly appropriate for simulation studies. Our procedure leads to a different continuity correction than the one proposed by Kim (J. Amer. Statist. Assoc. 64 (1969) 1625), using the criterion that the continuity correction should cause the randomized procedure to reject the null hypothesis with probability alpha. (C) 2003 Elsevier B.V. All rights reserved.