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ni is the number of observations in the ith level of X
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F is the pooled cumulative empirical distribution function
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An asymptotic Kolmogorov-Smirnov statistic computed as , where n is the total number of observations.
The p-value for the test. This is the probability that D exceeds the computed value under the null hypothesis of no difference between the levels.
The p-value for the test of D+.
The p-value for the test of D-.
For the Kolmogorov-Smirnov exact test, the report gives the same statistics as does the asymptotic test, but the p-values are computed to be exact.