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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.
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