Question 1

What problem does the article address about Lilliefors’s normality test?

Accepted Answer

The article addresses inaccuracies in the critical values from Lilliefors (1967), including differences caused by too few simulation replications and cases where the original values are anti-conservative.

Question 2

How is the Dmax statistic defined in the paper?

Accepted Answer

Dmax is defined as the maximum absolute difference between the sample distribution function S(x) and the estimated cumulative normal distribution F*(x), with parameters estimated from the sample.

Question 3

What analytic approximation does the paper provide for the upper-tail probability of Dmax?

Accepted Answer

For p<0.100 and sample sizes n between 5 and 100, the paper gives an exponential-based approximation in terms of Dmax and n. For n>100, it uses the same form with Dmax and n modified by the provided scaling rules.