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Ranking of Normality Tests—An Appraisal through Skewed Alternative Space
Version 1
: Received: 14 May 2019 / Approved: 15 May 2019 / Online: 15 May 2019 (10:50:52 CEST)
A peer-reviewed article of this Preprint also exists.
Islam, T.U. Ranking of Normality Tests: An Appraisal through Skewed Alternative Space. Symmetry 2019, 11, 872. Islam, T.U. Ranking of Normality Tests: An Appraisal through Skewed Alternative Space. Symmetry 2019, 11, 872.
Abstract
In social & 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 on the stringency framework for the skewed alternative space. Stringency concept allows us to rank the tests uniquely. Bonett & Seier test (Tw) turns out to be the best statistics for slightly skewed alternatives and the Anderson-Darling (AD), Chen-Shapiro (CS), Shapiro-Wilk (W) and Bispo, Marques, & Pestana, (BCMR) statistics are the best choices for moderately skewed alternative distributions. 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 COIN performed exceptionally well against the highly skewed alternative space.
Keywords
power envelope; Neyman-Pearson tests; Skewness & Kurtosis
Subject
Business, Economics and Management, Econometrics and Statistics
Copyright: 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.
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