An Extensive Comparisons of 50 Univariate Goodness-of-fit Tests for Normality

Abstract

The assumption of normality needs to be checked for many statistical procedures, namely parametric tests, because their validity depends on it. 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. This study addresses the performance of 50 normality tests available in literature, from 1900 until 2018. Because a theoretical comparison is not possible, Monte Carlo simulation were used from various symmetric and asymmetric distributions for different sample sizes ranging from 10 to 100. The simulations results show that for symmetric distributions with support on (−∞, ∞) the tests Robust Jarque–Bera and Gel–Miao–Gastwirth have generally the most power. For asymmetric distributions with support on (−∞, ∞) the tests 1st Cabana-Cabana
and 2nd Zhang-Wu have the most power. For distributions with support on (0, ∞), and distributions with support on (0, 1) the test 2nd Zhang-Wu has generally the most power.