–

–

ni is the number of observations in the ith level of X

–

F is the pooled cumulative empirical distribution function

–

An asymptotic KolmogorovSmirnov statistic computed as , where n is the total number of observations.
The pvalue for the test. This is the probability that D exceeds the computed value under the null hypothesis of no difference between the levels.
The pvalue for the test of D+.
The pvalue for the test of D.
For the KolmogorovSmirnov exact test, the report gives the same statistics as does the asymptotic test, but the pvalues are computed to be exact.