Kolmogorov–Smirnov Test

The Kolmogorov–Smirnov (KS) test is a statistical procedure for comparing the distribution of random samples. The one-sample KS test can be used to determine whether a data set follows any hypothesized (but fully specified) continuous density. Perhaps its most common use is to verify whether a data sample follows the normal (or Gaussian) density, such as checking the assertion that residuals from a fitted regression model follow the normal density. In the two-sample case, the KS procedure tests whether two data samples have equal underlying distributions. An example is comparing assessment scores for two different schools, when it is known that the scores do not follow the normal distribution.

This entry describes the basic principles of the KS test, including the cumulative distribution function (CDF) and ...