Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Abstract

Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.