Kolmogorov–Smirnov Test: Overview

Abstract While often confused, the Kolmogorov–Smirnov test and the Smirnov test are actually distinct. Specifically, the Kolmogorov–Smirnov test is used to test the goodness of fit of a given set of data to a theoretical distribution, making this a one‐sample test. In contrast, the Smirnov test is a two‐sample test, used to determine if two samples appear to follow the same distribution. The intuition behind the two tests is the same, however, in that both compare cumulative distribution functions, either two empirical cumulative distribution functions for the two‐sample Smirnov test, or one empirical cumulative distribution function and one known cumulative distribution function for the one‐sample Kolmogorov–Smirnov test.

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