Power analysis of several normality tests: A Monte Carlo simulation study

Abstract

In statistical inference, oftentimes the data are assumed to be normally distributed. Consequently, testing the validity of the normality assumption is an integral part of such statistical analyses. Here, we investigate twelve currently available tests for normality using Monte-Carlo simulation. Alternative distributions are used to calculate the empirical power of the tests studied here. The distributions considered arise from three different categories: symmetric short-tailed, symmetric long-tailed and asymmetric. In addition, power is calculated for several contaminated alternatives. As a direct consequence of this study, we recommend a two-tier approach: (i) observe the shape of the empirical data distribution using graphical methods, then (ii) select an appropriate test based on the likely distributional shape and the corresponding sample size. In general, with respect to power considerations, it is observed that for asymmetric distributions, the Shapiro-Wilk and Ryan-Joiner tests perform fairly well for all sample sizes studied here. Additionally, the Jarque-Bera, Modified Jarque-Bera, and Ryan-Joiner tests perform fairly well for contaminated normal distributions. The popular methods available in current software packages, such as the Shapiro-Wilk test, the Ryan-Joiner Normality test, and the Anderson-Darling goodness of test, work at least moderately well for most of the cases we considered.

Keywords:

• Normality test
• Skewed distributions
• Monte Carlo Simulation
• Assumptions of Normality
• Power comparison