Kolmogorov-Smirnov Test

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally distributed.

To apply the Kolmogorov-Smirnov test, calculate the cumulative frequency (normalized by the sample size) of the observations as a function of class. Then calculate the cumulative frequency for a true distribution (most commonly, the normal distribution). Find the greatest discrepancy between the observed and expected cumulative frequencies, which is called the "-statistic." Compare this against the critical -statistic for that sample size. If the calculated -statistic is greater than the critical one, then reject the null hypothesis that the distribution is of the expected form. The test is an R-estimate.