Skip to main content
Article thumbnail
Location of Repository

Normality Testing- A New Direction

By Tanweer ul Islam


Abstract This paper is concerned with the evaluation of the performance of the normality tests to ensure the validity of the t-statistics used for assessing significance of regressors in a regression model. For this purpose, we have explored 40 distributions to find the most damaging distribution on the t-statistic. Power comparisons are conducted to find the best performing test against these distributions. It is found that Anderson-Darling statistic is the best option among the five normality tests, Jarque-Bera, Shapiro-Francia, D’Agostino & Pearson, Anderson-Darling & Lilliefors.Normality test, power of the test, t-statistic

OAI identifier:

Suggested articles


  1. (1968). A Comparative Study of Various Tests of Normality.
  2. (2007). A comparison of various tests of normality.
  3. (2004). A Robustification of the Jarque-Bera test of Normality. Physica-Verlag
  4. (2003). A test for normality based on robust regression residuals. In: Dutter et. al (Eds.), Development in Robust Statistics. Physica-Verlag,
  5. (1987). A Test for Normality of Observations and Regression Residuals.
  6. (2002). A Test of Normality Using Geary’s Skewness and Kurtosis Statistics. Working Papers,
  7. (2002). A test of normality with high uniform power.
  8. (2003). Asymptotic expansion of the null distribution of test statistic for linear hypothesis in non-normal linear models.
  9. (2001). Econometric applications of high-breakdown robust regression techniques.
  10. (2007). Jarque-Bera Test and its Competitors for Testing Normality – A Power Comparison.
  11. (1972). More lights on the kurtosis and related statistics.
  12. (1996). On the correct use of onimbus tests for normality.
  13. (2007). Robust direct tests of normality against heavytailed alternatives.
  14. (2005). Robust tests for normality of errors in regression models.
  15. (1998). Simulation-based finite sample normality tests in linear regressions.
  16. (1947). Testing for normality.
  17. (1977). Tests for Departure from Normality: Comparison of Powers.
  18. (1973). Tests for departure from normality. Empirical results for the distributions of b2 and √b1.
  19. (2005). The use of mixtures for dealing with non-normal regression errors.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.