An empirical power comparison of univariate goodness-of-fit tests for normality

Abstract

A comprehensive power comparison study of existing tests for normality is proposed. Given the importance of this subject and the widespread development of normality tests, comprehensive descriptions and power comparisons of such tests are of considerable interest. Since recent comparison studies do not include several interesting and more recently developed tests, a further comparison of normality tests is considered to be of foremost interest. The study addresses the performance of 33 normality tests, for various sample sizes, considering several significance levels and for a number of symmetric, asymmetric and modified normal distributions. General recommendations for normality testing resulting from the study are defined according to the nature of the non-normality.

Keywords:

• normality test
• power comparison
• normal distribution
• goodness-of-fit test
• univariate

Acknowledgements

Financial support of the Portuguese Foundation for Science and Technology, through the PhD grant of the first author (SFRH/BD/32820/2007) is gratefully acknowledged.