An Exhaustive Power Comparison of Normality Tests
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 ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/7/788 |
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| author | Jurgita Arnastauskaitė Tomas Ruzgas Mindaugas Bražėnas |
| author_facet | Jurgita Arnastauskaitė Tomas Ruzgas Mindaugas Bražėnas |
| author_sort | Jurgita Arnastauskaitė |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>118</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T12:35:10Z |
| format | Article |
| id | doaj.art-c223ca2c7c3b46b68134a658be8ec6fe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:35:10Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c223ca2c7c3b46b68134a658be8ec6fe2023-11-21T14:22:11ZengMDPI AGMathematics2227-73902021-04-019778810.3390/math9070788An Exhaustive Power Comparison of Normality TestsJurgita Arnastauskaitė0Tomas Ruzgas1Mindaugas Bražėnas2Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, LithuaniaDepartment of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, LithuaniaDepartment of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, LithuaniaA 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>118</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/9/7/788goodness of fit testnormal distributionpower comparison |
| spellingShingle | Jurgita Arnastauskaitė Tomas Ruzgas Mindaugas Bražėnas An Exhaustive Power Comparison of Normality Tests Mathematics goodness of fit test normal distribution power comparison |
| title | An Exhaustive Power Comparison of Normality Tests |
| title_full | An Exhaustive Power Comparison of Normality Tests |
| title_fullStr | An Exhaustive Power Comparison of Normality Tests |
| title_full_unstemmed | An Exhaustive Power Comparison of Normality Tests |
| title_short | An Exhaustive Power Comparison of Normality Tests |
| title_sort | exhaustive power comparison of normality tests |
| topic | goodness of fit test normal distribution power comparison |
| url | https://www.mdpi.com/2227-7390/9/7/788 |
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