The Lilliefors test determines whether a dataset matches a particular distribution, and is identical to the Kolmogorov-Smirnov test except that conversion to Z-scores is made. The Lilliefors test is therefore a modification of the Kolmogorov-Smirnov test. The Lilliefors test computes the Lilliefors statistic and checks its significance. Exact tables of the quantiles of the test statistic were computed from random numbers in computer simulations. The computed value of the test statistic is compared with the quantiles of the statistic.
When the test is for the normal distribution, the null hypothesis is that the distribution function is normal with unspecified mean and variance. The alternative hypothesis is that the distribution function is nonnormal. The empirical distribution of X is compared with a normal distribution with the same mean and variance as X. It is similar to the Kolmogorov-Smirnov test, but it adjusts for the fact that the parameters of the normal distribution are estimated from X rather than specified in advance.
In this test, the user can specify group-by variables (GBVs) so a separate test will be done for every unique set of values of the GBVs.