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Cauchy combination omnibus test for normality

Testing whether data are from a normal distribution is a traditional problem and is of great concern for data analyses. The normality is the premise of many statistical methods, such as t-test, Hotelling T(2) test and ANOVA. There are numerous tests in the literature and the commonly used ones are A...

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Autores principales: Meng, Zhen, Jiang, Zhenzhen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10399863/
https://www.ncbi.nlm.nih.gov/pubmed/37535617
http://dx.doi.org/10.1371/journal.pone.0289498
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author Meng, Zhen
Jiang, Zhenzhen
author_facet Meng, Zhen
Jiang, Zhenzhen
author_sort Meng, Zhen
collection PubMed
description Testing whether data are from a normal distribution is a traditional problem and is of great concern for data analyses. The normality is the premise of many statistical methods, such as t-test, Hotelling T(2) test and ANOVA. There are numerous tests in the literature and the commonly used ones are Anderson-Darling test, Shapiro-Wilk test and Jarque-Bera test. Each test has its own advantageous points since they are developed for specific patterns and there is no method that consistently performs optimally in all situations. Since the data distribution of practical problems can be complex and diverse, we propose a Cauchy Combination Omnibus Test (CCOT) that is robust and valid in most data cases. We also give some theoretical results to analyze the good properties of CCOT. Two obvious advantages of CCOT are that not only does CCOT have a display expression for calculating statistical significance, but extensive simulation results show its robustness regardless of the shape of distribution the data comes from. Applications to South African Heart Disease and Neonatal Hearing Impairment data further illustrate its practicability.
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spelling pubmed-103998632023-08-04 Cauchy combination omnibus test for normality Meng, Zhen Jiang, Zhenzhen PLoS One Research Article Testing whether data are from a normal distribution is a traditional problem and is of great concern for data analyses. The normality is the premise of many statistical methods, such as t-test, Hotelling T(2) test and ANOVA. There are numerous tests in the literature and the commonly used ones are Anderson-Darling test, Shapiro-Wilk test and Jarque-Bera test. Each test has its own advantageous points since they are developed for specific patterns and there is no method that consistently performs optimally in all situations. Since the data distribution of practical problems can be complex and diverse, we propose a Cauchy Combination Omnibus Test (CCOT) that is robust and valid in most data cases. We also give some theoretical results to analyze the good properties of CCOT. Two obvious advantages of CCOT are that not only does CCOT have a display expression for calculating statistical significance, but extensive simulation results show its robustness regardless of the shape of distribution the data comes from. Applications to South African Heart Disease and Neonatal Hearing Impairment data further illustrate its practicability. Public Library of Science 2023-08-03 /pmc/articles/PMC10399863/ /pubmed/37535617 http://dx.doi.org/10.1371/journal.pone.0289498 Text en © 2023 Meng, Jiang https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Meng, Zhen
Jiang, Zhenzhen
Cauchy combination omnibus test for normality
title Cauchy combination omnibus test for normality
title_full Cauchy combination omnibus test for normality
title_fullStr Cauchy combination omnibus test for normality
title_full_unstemmed Cauchy combination omnibus test for normality
title_short Cauchy combination omnibus test for normality
title_sort cauchy combination omnibus test for normality
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10399863/
https://www.ncbi.nlm.nih.gov/pubmed/37535617
http://dx.doi.org/10.1371/journal.pone.0289498
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