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Measuring asymmetry and testing symmetry

Partlett, Christopher; Patil, Prakash

Authors

CHRIS PARTLETT Chris.Partlett@nottingham.ac.uk
Assistant Professor of Medical Statistics and Clinical Trials

Prakash Patil



Abstract

In this paper, we show that some of the most commonly used tests of symmetry do not have power which is reflective of the size of asymmetry. This is because the primary rationale for the test statistics that are proposed in the literature to test for symmetry is to detect the departure from symmetry, rather than the quantification of the asymmetry. As a result, tests of symmetry based upon these statistics do not necessarily generate power that is representative of the departure from the null hypothesis of symmetry. Recent research has produced new measures of asymmetry, which have been shown to do an admirable job of quantifying the amount of asymmetry. We propose several new tests based upon one such measure. We derive the asymptotic distribution of the test statistics and analyse the performance of these proposed tests through the use of a simulation study.

Journal Article Type Article
Publication Date 2017-04
Journal Annals of the Institute of Statistical Mathematics
Print ISSN 0020-3157
Electronic ISSN 1572-9052
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 69
Issue 2
Pages 429-460
APA6 Citation Partlett, C., & Patil, P. (2017). Measuring asymmetry and testing symmetry. Annals of the Institute of Statistical Mathematics, 69(2), 429-460. doi:10.1007/s10463-015-0547-4
DOI https://doi.org/10.1007/s10463-015-0547-4
Publisher URL https://link.springer.com/article/10.1007%2Fs10463-015-0547-4
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