A simple method for testing the probability that a set of numbers is a sample from a known distribution consists of comparing the empirical cumulative distribution function of the sample, S n (x), with the known cumulative distribution function F(x). Both D n = maximum {S n (x) – F{x)} and D n * = maximum | S n (x) – F(x) | are random variables, independent of the special form of F(x), if F(x) is continuous. This paper contains more extensive tables of the percentage points in the distributions of D n and D n * than have been published previously. These values are obtained by empirical modification of a known asymptotic formula.