Assessing Homoscedasticity Graphically

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...

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Main Author: Elsayed A. H. Elamir
Format: Article
Language:English
Published: Instituto Nacional de Estatística | Statistics Portugal 2023-07-01
Series:Revstat Statistical Journal
Subjects:
Online Access:https://revstat.ine.pt/index.php/REVSTAT/article/view/411
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author Elsayed A. H. Elamir
author_facet Elsayed A. H. Elamir
author_sort Elsayed A. H. Elamir
collection DOAJ
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.
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spelling doaj.art-790c472fef0b4e929b245dda4b7b4e0c2023-07-31T14:49:03ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712023-07-0121310.57805/revstat.v21i3.411Assessing Homoscedasticity GraphicallyElsayed A. H. Elamir 0University of Bahrain 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. https://revstat.ine.pt/index.php/REVSTAT/article/view/411Beta distributionBonferroni approximationhomogeneity of variancenonnormalitytest powertype I error
spellingShingle Elsayed A. H. Elamir
Assessing Homoscedasticity Graphically
Revstat Statistical Journal
Beta distribution
Bonferroni approximation
homogeneity of variance
nonnormality
test power
type I error
title Assessing Homoscedasticity Graphically
title_full Assessing Homoscedasticity Graphically
title_fullStr Assessing Homoscedasticity Graphically
title_full_unstemmed Assessing Homoscedasticity Graphically
title_short Assessing Homoscedasticity Graphically
title_sort assessing homoscedasticity graphically
topic Beta distribution
Bonferroni approximation
homogeneity of variance
nonnormality
test power
type I error
url https://revstat.ine.pt/index.php/REVSTAT/article/view/411
work_keys_str_mv AT elsayedahelamir assessinghomoscedasticitygraphically