A SAS Program to Assess the Sensitivity of Normality Tests On Non-Normal Data

In many statistical analyses, the data is usually assumed to be approximately normal or normally distributed. Unfortunately, not all data can be assumed normal in real life. To assess the normality of the data, there are four statistical tests, i.e. the Kolmogorov-Smirnov test, the Anderson-Darling test, the Cramer-von Mises test, and the Shapiro-Wilk test that are extensively used by practitioners. The general purpose of this article is to provide a demonstration of Base SAS programming codes of DATA STEP, PROC UNIVARIATE, PROC MEANS and SAS functions to evaluate the performance of the above mentioned tests, under various spectrums of non-normal distributions and different sample sizes. Another important goal is to help researchers adapt these codes to perform similar analyses for other non-normal distributions or other normality tests. This is to encourage the researchers to check the sensitivity of the normality tests before they implement any test that requires assumption of normality.