Some practical reasons for reconsidering the Kolmogorov‐Smirnov test

Source abstract

The Kolmogorov‐Smirnov test is a method for comparing the distributions of two independent groups that has virtually disappeared from applied research and introductory statistics books for the social sciences. The apparent reason is the perception that it has low power compared to methods for comparing means in particular and measures of location in general. However, extant studies comparing the power of the Kolmogorov‐Smirnov test to other methods for comparing means are limited to normal distributions having a common variance. This note points out that, even under a shift model, the Kolmogorov‐Smirnov test not only can have high power relative to methods for comparing robust measures of location, there are situations where it has higher power than methods for comparing robust measurement of location. Some additional features of the Kolmogorov‐Smirnov test are noted, and a simple S‐PLUS program for computing the exact significance level is provided. Data from a study on the effects of drinking alcohol are used to illustrate the potential advantage of the Kolmogorov‐Smirnov test.