Two-sample Kolmogorov–Smirnov Test
The Kolmogorov–Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. In this case, the Kolmogorov–Smirnov statistic is
where and are the empirical distribution functions of the first and the second sample respectively.
The null hypothesis is rejected at level if
Note that the two-sample test checks whether the two data samples come from the same distribution. This does not specify what that common distribution is (e.g. normal or not normal). Again, tables of critical values have been published.
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