= Lilliefors test
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{title2=$\sup_x|F_n(x)-\Phi((x-\overline X)/s)|$}
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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.<On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown by Hubert W. Lilliefors>[pp. 399-400: opening procedure and Table 1 of the original article; inspected mirrored text]{ref}
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