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In statistics, the Lilliefors test, named after Hubert Lilliefors, professor of statistics at George Washington University, is an adaptation of the Kolmogorov–Smirnov test. It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e., it does not specify the expected value and variance of the distribution.
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In a Kolmogorov-Smirnov test for normality when the mean and standard deviation of the hypothesized normal distribution are not known (i.e., they are estimated from the sample data), the probability values tabulated by Massey (1951) are not valid. Instead, the so-called Lilliefors probabilities (Lilliefors, 1967) should be used in determining whether the KS difference statistic is significant.
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