Next Article in Journal
Race Walking Ground Reaction Forces at Increasing Speeds: A Comparison with Walking and Running
Previous Article in Journal
Motion Symmetry Evaluation Using Accelerometers and Energy Distribution
Open AccessArticle

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;
Received: 14 May 2019 / Revised: 9 June 2019 / Accepted: 18 June 2019 / Published: 3 July 2019
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
MDPI and ACS Style

Islam, T.U. Ranking of Normality Tests: An Appraisal through Skewed Alternative Space. Symmetry 2019, 11, 872.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map

Back to TopTop