AN ALGORITHM FOR CONDUCTING EXACT SMIRNOV TESTS

We describe an algorithm for performing exact Smirnov tests in continuous or categorical data with balanced or unbalanced samples. We use the algorithm to evaluate the size of the asymptotic and exact tests based on the classical Smirnov statistic and the exact test based on a modified Smirnov statistic. The asymptotic test is very conservative even in large samples from continuous distributions, while the exact test based on the modified Smirnov statistic is uniformly least conservative for all distributions and all sample sizes studied. In categorical data the sizes of the two exact tests are similar, but in continuous data the modified test is significantly less conservative. Our estimator of size exploits properties of the algorithm, making it highly efficient relative to the Monte Carlo estimator usually used in simulation studies.