An Exhaustive Power Comparison of Normality Tests

Jurgita Arnastauskaitė, Tomas Ruzgas and Mindaugas Bražėnas
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Jurgita Arnastauskaitė: Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
Tomas Ruzgas: Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania
Mindaugas Bražėnas: Department of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania

Mathematics, 2021, vol. 9, issue 7, 1-20

Abstract: 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 n ? 118 .

Keywords: goodness of fit test; normal distribution; power comparison (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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