Lilliefors test (${\sup }_x|F_n(x)-\Phi ((x-\overline{X})/s)|$)

The Lilliefors test calibrates the Kolmogorov-Smirnov statistic against a normal distribution whose mean and variance are estimated from the tested observations. In the original procedure, $s^2$ is the sample variance with denominator $n-1$, and $\Phi$ is the standard normal distribution function. Its reference law includes this fitting step. The original paper's opening procedure and Table 1 explain the changed calibration.^[ref]