Power comparison of various normality tests

Abstract

Standard statistical procedures often require data to be normally distributed and the results of these methods will be inappropriate when the assumption of normality is not satisfied. Therefore, the postulation of normality is strictly required before proceeding statistical analysis. Although a number of criteria's have been available to assess the assumption of normality, but these tests do not have the same nature and power to diagnose the departures of a data set from normality, thus the choice of appropriate test always remains a key importance in the assessment of normality assumption. In the present study, power comparison of twelve standard normality tests was examined using simulated data generated from four distributions; Cauchy, Exponential, Weibull and Logistic under different sample sizes by using R codes. Results showed that under logistic distribution data, Geary test was observed most powerful test at the 5 % level of significance and Jarque Bera test at the 1 % level of significance. Under alternate Cauchy distribution, Shapiro Francia test performs well at the 5 % level of significance while at the 1 % level of significance, Shapiro Francia, Anderson Darling, Cramer von mises and Watson tests equally observed the power of a test. Shapiro Wilk test was highlighted as a more powerful test for data generated under Weibull distribution.