A Note on the Possible Misuse of the Kolmogorov-Smirnov Test

Abstract

For univariate or one-dimensional distributions the standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely specified distribution. If one or more parameters must be estimated from the sample, then the standard tables are no longer valid. Other tables must be used. Lilliefors indicates the conservative extent of the tests when parameters are estimated for the sample and used with the standard tables. He provides valid tables for the univariate normal, exponential, gamma, and extreme value distributions when one or more parameters must be estimated from the sample. For the multivariate normal distributions the only tables known to the author are those of Malkovich and Afifi. This note brings the problem to the attention of scientists who rely on the tools developed by statisticians to help them to use the appropriate tools correctly.