Comparison of selected tests for univariate normality based on measures of moments


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 21 , ISSUE 5 (December 2020) > List of articles

Comparison of selected tests for univariate normality based on measures of moments

Czesław Domański / Piotr Szczepocki

Keywords : normality tests, Monte Carlo simulation, power of test

Citation Information : Statistics in Transition New Series. Volume 21, Issue 5, Pages 151-178, DOI:

License : (CC BY-NC-ND 4.0)

Received Date : 17-September-2020 / Accepted: 07-November-2020 / Published Online: 20-December-2020



Univariate normality tests are typically classified into tests based on empirical distribution, moments, regression and correlation, and other. In this paper, power comparisons of nine normality tests based on measures of moments via the Monte Carlo simulations is extensively examined. The effects on power of the sample size, significance level, and on a number of alternative distributions are investigated. None of the considered tests proved uniformly most powerful for all types of alternative distributions. However, the most powerful tests for different shape departures from normality (symmetric short-tailed, symmetric long-tailed or asymmetric) are indicated.

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