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,Sn(x), with the known cumulative distribution functionF(x). BothDn= maximum {Sn(x) –F{x)} andDn* = maximum |Sn(x) –F(x) | are random variables, independent of the special form ofF(x), ifF(x) is continuous. This paper contains more extensive tables of the percentage points in the distributions ofDnandDn* than have been published previously. These values are obtained by empirical modification of a known asymptotic formula.