Lilliefors test

The Lilliefors test checks whether data depart from a normal distribution. It is the Kolmogorov-Smirnov test with mean and standard deviation estimated from the data. p below .05 means: the distribution departs.

Example: D = .24, p = .003: the distribution departs from a normal distribution.

Caution: p above .05 does not mean the data are normally distributed, only that the test does not speak against it. With few people it misses large departures; the Q-Q plot shows more.