Lilliefors/Van Soest’s test of normality

The normality assumption is at the core of a majority of standard statistical procedures, and it is important to be able to test this assumption. In addition, showing that a sample does not come from a normally distributed population is sometimes of importance per se. Among the many procedures used to test this assumption, one of the most well-known is a modification of the Kolomogorov-Smirnov test of goodness of fit, generally referred to as the Lilliefors test for normality (or Lilliefors test, for short). This test was developed independently by Lilliefors (1967) and by Van Soest (1967). The null hypothesis for this test is that the error is normally distributed (i.e., there is no difference between the observed distribution of the error and a normal distribution). The alternative hypothesis is that the error is not normally distributed. Like most statistical tests, this test of normality defines a criterion and gives its sampling distribution. When the probability associated with the criterion is smaller than a given α-level, the