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Ranking of Normality Tests: An Appraisal through Skewed Alternative Space

Department of Economics, National University of Sciences & Technology, Islamabad 44000, Pakistan
Symmetry 2019, 11(7), 872; https://doi.org/10.3390/sym11070872
Received: 14 May 2019 / Revised: 9 June 2019 / Accepted: 18 June 2019 / Published: 3 July 2019
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Abstract

In social and health sciences, many statistical procedures and estimation techniques rely on the underlying distributional assumption of normality of the data. Non-normality may lead to incorrect statistical inferences. This study evaluates the performance of selected normality tests within the stringency framework for skewed alternative space. The stringency concept allows us to rank the tests uniquely. The Bonett and Seier test (Tw) turns out to represent the best statistics for slightly skewed alternatives and the Anderson–Darling (AD); Chen–Shapiro (CS); Shapiro–Wilk (W); and Bispo, Marques, and Pestana (BCMR) statistics are the best choices for moderately skewed alternative distributions. The maximum loss of Jarque–Bera (JB) and its robust form (RJB), in terms of deviations from the power envelope, is greater than 50%, even for large sample sizes, which makes them less attractive in testing the hypothesis of normality against the moderately skewed alternatives. On balance, all selected normality tests except Tw and Daniele Coin’s COIN-test performed exceptionally well against the highly skewed alternative space. View Full-Text
Keywords: power envelope; Neyman–Pearson tests; skewness; kurtosis power envelope; Neyman–Pearson tests; skewness; kurtosis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Islam, T.U. Ranking of Normality Tests: An Appraisal through Skewed Alternative Space. Symmetry 2019, 11, 872.

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