A comparison of various tests of normality

Yazici B., Yolacan S.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.77, no.2, pp.175-183, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1080/10629360600678310
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.175-183
  • 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, STATISTICS, GOODNESS, ENTROPY, FIT
  • Anadolu University Affiliated: Yes


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.