Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://doi.org/10.57805/revstat.v21i3.411 |
Resumo: | The problem of homoscedasticity arises in several fields such as business, education, environments, and medicine, and common question in many statistical analyses. One of the most important tests in this direction is Levene test and its robust version Brown-Forsythe test. The goal of this paper is threefold. The first goal is to propose an expression that enable to develop a graphical way for Levene-Brown-Forsythe tests. The second goal is to derive the sampling distribution of the proposed expression as the generalized beta prime distribution. The third goal is to provide deep insight and understanding where the dispersion effects occur. Simulation study is carried out to study the level of significance and power of the proposed test in comparison with the original Levene-Brown-Forsythe tests. The results are of great values since the proposed method provides (a) powerful visual tool and deep insight for testing homoscedasticity, (b) keeps the size and power of the test similar to Levene-Brown-Forsythe tests, and (c) does not need to pairwise comparisons. Two applications are presented to show the utilities of the proposed method. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe ApproachesBeta distributionBonferroni approximationhomogeneity of variancenonnormalitytest powertype I errorThe problem of homoscedasticity arises in several fields such as business, education, environments, and medicine, and common question in many statistical analyses. One of the most important tests in this direction is Levene test and its robust version Brown-Forsythe test. The goal of this paper is threefold. The first goal is to propose an expression that enable to develop a graphical way for Levene-Brown-Forsythe tests. The second goal is to derive the sampling distribution of the proposed expression as the generalized beta prime distribution. The third goal is to provide deep insight and understanding where the dispersion effects occur. Simulation study is carried out to study the level of significance and power of the proposed test in comparison with the original Levene-Brown-Forsythe tests. The results are of great values since the proposed method provides (a) powerful visual tool and deep insight for testing homoscedasticity, (b) keeps the size and power of the test similar to Levene-Brown-Forsythe tests, and (c) does not need to pairwise comparisons. Two applications are presented to show the utilities of the proposed method.Statistics Portugal2023-07-31info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.57805/revstat.v21i3.411https://doi.org/10.57805/revstat.v21i3.411REVSTAT-Statistical Journal; Vol. 21 No. 3 (2023): REVSTAT-Statistical Journal; 389–404REVSTAT; Vol. 21 N.º 3 (2023): REVSTAT-Statistical Journal; 389–4042183-03711645-6726reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAPenghttps://revstat.ine.pt/index.php/REVSTAT/article/view/411https://revstat.ine.pt/index.php/REVSTAT/article/view/411/652Copyright (c) 2022 REVSTAT-Statistical Journalinfo:eu-repo/semantics/openAccessA. H. Elamir , Elsayed2023-08-12T06:30:24Zoai:revstat:article/411Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:26:50.342013Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
title |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
spellingShingle |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches A. H. Elamir , Elsayed Beta distribution Bonferroni approximation homogeneity of variance nonnormality test power type I error |
title_short |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
title_full |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
title_fullStr |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
title_full_unstemmed |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
title_sort |
Assessing Homoscedasticity Graphically: Levene-Brown-Forsythe Approaches |
author |
A. H. Elamir , Elsayed |
author_facet |
A. H. Elamir , Elsayed |
author_role |
author |
dc.contributor.author.fl_str_mv |
A. H. Elamir , Elsayed |
dc.subject.por.fl_str_mv |
Beta distribution Bonferroni approximation homogeneity of variance nonnormality test power type I error |
topic |
Beta distribution Bonferroni approximation homogeneity of variance nonnormality test power type I error |
description |
The problem of homoscedasticity arises in several fields such as business, education, environments, and medicine, and common question in many statistical analyses. One of the most important tests in this direction is Levene test and its robust version Brown-Forsythe test. The goal of this paper is threefold. The first goal is to propose an expression that enable to develop a graphical way for Levene-Brown-Forsythe tests. The second goal is to derive the sampling distribution of the proposed expression as the generalized beta prime distribution. The third goal is to provide deep insight and understanding where the dispersion effects occur. Simulation study is carried out to study the level of significance and power of the proposed test in comparison with the original Levene-Brown-Forsythe tests. The results are of great values since the proposed method provides (a) powerful visual tool and deep insight for testing homoscedasticity, (b) keeps the size and power of the test similar to Levene-Brown-Forsythe tests, and (c) does not need to pairwise comparisons. Two applications are presented to show the utilities of the proposed method. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-31 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.57805/revstat.v21i3.411 https://doi.org/10.57805/revstat.v21i3.411 |
url |
https://doi.org/10.57805/revstat.v21i3.411 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revstat.ine.pt/index.php/REVSTAT/article/view/411 https://revstat.ine.pt/index.php/REVSTAT/article/view/411/652 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2022 REVSTAT-Statistical Journal info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2022 REVSTAT-Statistical Journal |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Statistics Portugal |
publisher.none.fl_str_mv |
Statistics Portugal |
dc.source.none.fl_str_mv |
REVSTAT-Statistical Journal; Vol. 21 No. 3 (2023): REVSTAT-Statistical Journal; 389–404 REVSTAT; Vol. 21 N.º 3 (2023): REVSTAT-Statistical Journal; 389–404 2183-0371 1645-6726 reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133536421150720 |