E. Dallal, Gerard et Wilkinson, Leland, An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality, American statistician , 40(4), 1986, pp. 294-296
Table 1 corrects the critical values for testing normality reported by Lilliefors (1967).The corrected table allows us to derive a simple analytic approximation to the upper tail probabilities of his test statistic for probabilities less than .10.With few exceptions, the approximation is more accurate than Lilliefors's original table.