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Kolmogorov-Smirnov


General Notes
 
When used to compare a set of data against a reference distribution, this is referred to as the one sample "K-S" test or the K-S Goodness of Fit test.

There is also a two-sample K-S test that is used to compare the empirical distribution functions of two samples.


From NIST - Kolmogorov-Smirnov:
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).

Per Fundamental Concepts in the Design of Experiments (Hicks), the one sample Kolmogorov-Smirnov test for goodness-of-fit might be preferred over the Shapiro-Wilk test when the sample size exceeds 50.
 


Assumptions
 
Per NIST: "The K-S test is only appropriate for testing data against a continuous distribution."



References
 


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