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Article

An Exhaustive Power Comparison of Normality Tests

1
Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
2
Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania
3
Department of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania
*
Author to whom correspondence should be addressed.
Academic Editor: Vasile Preda
Mathematics 2021, 9(7), 788; https://doi.org/10.3390/math9070788
Received: 12 February 2021 / Revised: 17 March 2021 / Accepted: 31 March 2021 / Published: 6 April 2021
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size n118. View Full-Text
Keywords: goodness of fit test; normal distribution; power comparison goodness of fit test; normal distribution; power comparison
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MDPI and ACS Style

Arnastauskaitė, J.; Ruzgas, T.; Bražėnas, M. An Exhaustive Power Comparison of Normality Tests. Mathematics 2021, 9, 788. https://doi.org/10.3390/math9070788

AMA Style

Arnastauskaitė J, Ruzgas T, Bražėnas M. An Exhaustive Power Comparison of Normality Tests. Mathematics. 2021; 9(7):788. https://doi.org/10.3390/math9070788

Chicago/Turabian Style

Arnastauskaitė, Jurgita, Tomas Ruzgas, and Mindaugas Bražėnas. 2021. "An Exhaustive Power Comparison of Normality Tests" Mathematics 9, no. 7: 788. https://doi.org/10.3390/math9070788

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