A comparison of various tests of normality

Abstract

This article studies twelve different normality tests that are used for assessing the assumption that a sample was drawn from a normally distributed population and compares their powers. The tests in question are chi-square, Kolmogorov–Smirnov, Anderson–Darling, Kuiper, Shapiro–Wilk, Ajne, modified Ajne, modified Kuiper, D’Agostino, modified Kolmogorov–Smirnov, Vasicek, and Jarque–Bera. Each test is described and power comparisons are also obtained by using Monte Carlo computations. To do this, first, normally distributed populations with different standard deviations are taken and then simulation is conducted for nonnormal populations. The results are discussed and interpreted separately.

Keywords:

• Test of normality
• Monte Carlo simulation
• Power of the test
• Chi-square
• Kolmogorov–Smirnov
• Anderson–Darling
• Kuiper
• Shapiro–Wilk
• Ajne
• D’Agostino
• Vasicek
• Jarque–Bera

Acknowledgements

We thank Professor Dr Yaning Yang for his suggestions on simulation study.