Power Comparison of Various Normality Tests

Rehan Ahmad Khan, Fiaz Ahmad

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 not satisfy. Therefore, assumption 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 choice of appropriate test always remains a key importance in assessment of normality assumption. In present study, power comparison of twelve standard normality tests were 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 5% level of significance and Jarque Bera test at 1% level of significance. Under alternate Cauchy distribution, Shapiro Francia test perform well at 5% level of significance while at 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. 


Keywords


Normality Tests, Power of a Test



DOI: http://dx.doi.org/10.18187/pjsor.v11i3.1082

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Title

Power Comparison of Various Normality Tests

Keywords

Normality Tests, Power of a Test

Description

Standard statistical procedures often require data to be normally distributed and the results of these methods will be inappropriate when the assumption of normality not satisfy. Therefore, assumption 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 choice of appropriate test always remains a key importance in assessment of normality assumption. In present study, power comparison of twelve standard normality tests were 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 5% level of significance and Jarque Bera test at 1% level of significance. Under alternate Cauchy distribution, Shapiro Francia test perform well at 5% level of significance while at 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. 


Date

2017-10-23

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 11 No. 3, 2015



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810