7. Product and Process Comparisons
7.2. Comparisons based on data from one process
7.2.1. Do the observations come from a particular distribution?

## Kolmogorov- Smirnov test

The K-S test is a good alternative to the chi-square test. The Kolmogorov-Smirnov (K-S) test was originally proposed in the 1930's in papers by Kolmogorov (1933) and Smirnov (1936). Unlike the Chi-Square test, which can be used for testing against both continuous and discrete distributions, the K-S test is only appropriate for testing data against a continuous distribution, such as the normal or Weibull distribution. It is one of a number of tests that are based on the empirical cumulative distribution function (ECDF).
K-S procedure Details on the construction and interpretation of the K-S test statistic, $$D$$, and examples for several distributions are outlined in Chapter 1.
The probability associated with the test statistic is difficult to compute. Critical values associated with the test statistic, $$D$$, are difficult to compute for finite sample sizes, often requiring Monte Carlo simulation. However, some general purpose statistical software programs support the Kolmogorov-Smirnov test at least for some of the more common distributions. Tabled values can be found in Birnbaum (1952). A correction factor can be applied if the parameters of the distribution are estimated with the same data that are being tested. See D'Agostino and Stephens (1986) for details.