A power comparison of various normality tests

Abstract

The assumption of normality is very important because it is used in many statistical procedures such as Analysis of variance, linear regression analysis, discriminant analysis and t-tests. The three common procedures are used for assessing the assumption of normality that is graphical methods, numerical methods and formal normality tests. In the literature, significant amount of normality tests are available. In this paper, only eight different tests of normality are discussed. The tests consider in the present study are Shapiro Wilk, Shapiro Francia, Kolmogrov Smirnov, Anderson Darling, Cramer von Mises, Jarque Bera, Geary and Lilliefors test. Power comparisons of each test are obtained by using Monte Carlo computation of sample data generated from different alternate distributions by using 5% level of significance. The results show that power of each test is affected by sample size and alternate distribution. Shapiro Francia and Kolmogrov Smirnov test perform well for Cauchy exponential distribution respectively. For t-distribution Geary, Shapiro Francia and Jarque Bera test perform well for degrees of freedom 5, 10 and 15 respectively.