Lilliefors test for normality compare two cumulative distribution functions (cdf's): the cdf from a normal distribution and the cdf corresponding to the given data (called the empirical cdf).

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The Lilliefors test is a goodness-of-fit test that compares the empirical cumulative distribution function of sample data with the cumulative distribution function of a normal distribution, to test the null hypothesis that the data are drawn from a normally distributed population.

Lilliefors Test for Normality Compare Two Cumulative Distribution Functions (Cdf's)