Summary: NEW TABLE AND NUMERICAL APPROXIMATIONS
PAUL MOLIN AND HERV´E ABDI
Abstract. We give new critical values for the Kolmogorov-Smir-
nov/Lilliefors/Van Soest test of Normality. These values are ob-
tained from Monte-Carlo simulations similar to the original pro-
cedure of Lilliefors and Van Soest. Because our simulations use
a very large number of random samples, the critical values ob-
tained are better estimations than the original values. In order
to allow hypothesis testing with arbitrary levels, we also derive
a polynomial approximation of the critical values. This facilitates
the implementation of Bonferonni or Sid´ak corrections for multiple
statistical tests as these procedures require unusual values.
The normality assumption is at the core of a majority of standard
statistical procedures, and it is important to be able to test this as-
sumption. In addition, showing that a sample does not come from
a normally distributed population is sometimes of importance per se.