An exact Kolmogorov–Smirnov test for whether two finite populations are the same

We develop an algorithm for finding exact critical values for the two-sample Kolmogorov–Smirnov test in the finite-population case. We then compare these exact critical values to the asymptotic values that are available in the literature. The asymptotic critical values work well for equal sample sizes, but can be excessively conservative when the sample sizes differ.