Comparison of some multivariate normality tests: A simulation study

Alpu, Ozlem; Yuksek, Demet

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 3, Issue 12 (December 2016), Pages: 73-85

Title: Comparison of some multivariate normality tests: A simulation study

Author(s): Ozlem Alpu *, Demet Yuksek

Affiliation(s):

Department of Statistics, Eskisehir Osmangazi University, Eskisehir 26480, Turkey

https://doi.org/10.21833/ijaas.2016.12.011

Full Text - PDF XML

Abstract:

Many classical multivariate statistical methods are mostly based on the assumption of multivariate normality. Departures from normality, called non-normality, render those statistical methods inaccurate, so it is important to know if datasets are normal or non-normal. Especially in medical and life sciences, most statistical tests required the assumption of multivariate normality have been extensively used. In this study, after summarizing the properties of several most widely used multivariate normality tests, we aim to compare the power and type I error rates of these tests, which have been developed in recent years by many researchers. So, the reader will elucidate the differences and the similarities/superiorities and weaknesses of the tests in order to make the appropriate choice in their practical applications. For this purpose we carried a Monte Carlo simulation study with nominal α level, small, medium and large sample size, different dimension and multivariate distributions which includes different skewness and kurtosis. In conclusion, the results obtained from the comparative study are given.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Tests of multivariate normality, Power, Type I error, Multivariate normal distribution, generalized Shapiro-Wilk test

Article History: Received 5 September 2016, Received in revised form 10 November 2016, Accepted 7 December 2016

Digital Object Identifier: https://doi.org/10.21833/ijaas.2016.12.011

Citation:

Alpu O and Yuksek D (2016). Comparison of some multivariate normality tests: A simulation study. International Journal of Advanced and Applied Sciences, 3(12): 73-85

http://www.science-gate.com/IJAAS/V3I12/Alpu.html

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