A Bayesian approach to the one way ANOVA under unequal variance

This study involves testing the equality of several normal means under unequal variances, which is the setup of one-way analysis of variances (one-way ANOVA). Several tests are available in the literature, however, most of them perform poorly in terms of type I error rate under unequal variances. In...

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Main Authors:	Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2016
Online Access:	http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/1/19%20Noppakun.pdf

id	ukm-10303
recordtype	eprints
spelling	ukm-103032017-04-06T09:32:00Z http://journalarticle.ukm.my/10303/ A Bayesian approach to the one way ANOVA under unequal variance Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued, This study involves testing the equality of several normal means under unequal variances, which is the setup of one-way analysis of variances (one-way ANOVA). Several tests are available in the literature, however, most of them perform poorly in terms of type I error rate under unequal variances. In fact, Type I errors can be highly inflated for some of the commonly used tests, a serious issue that seems to have been overlooked. Even though several tests have been proposed to overcome the problem, most of them show difficulty in calculation. Accordingly, the test for ANOVA with estimation of parameters using Bayesian approach is proposed as an alternative to such tests. The proposed test is compared with four existing tests such as the original test, James’s test, Welch’s test and the parametric bootstrap (PB) test. Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our results indicated that the performance of the proposed test is superior to the original test and is comparable to James’s test, Welch’s test and the PB test, controlling Type I error rate quite well and showing high power of the test. Our study suggested that the proposed test has high performance and should be used as an alternative to the four existing tests due to its simple formula. Penerbit Universiti Kebangsaan Malaysia 2016-10 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/10303/1/19%20Noppakun.pdf Noppakun Tongmol, and Wuttichai Srisodaphol, and Angkana Boonyued, (2016) A Bayesian approach to the one way ANOVA under unequal variance. Sains Malaysiana, 45 (10). pp. 1565-1572. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol45num10_2016/contentsVol45num10_2016.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	This study involves testing the equality of several normal means under unequal variances, which is the setup of one-way analysis of variances (one-way ANOVA). Several tests are available in the literature, however, most of them perform poorly in terms of type I error rate under unequal variances. In fact, Type I errors can be highly inflated for some of the commonly used tests, a serious issue that seems to have been overlooked. Even though several tests have been proposed to overcome the problem, most of them show difficulty in calculation. Accordingly, the test for ANOVA with estimation of parameters using Bayesian approach is proposed as an alternative to such tests. The proposed test is compared with four existing tests such as the original test, James’s test, Welch’s test and the parametric bootstrap (PB) test. Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our results indicated that the performance of the proposed test is superior to the original test and is comparable to James’s test, Welch’s test and the PB test, controlling Type I error rate quite well and showing high power of the test. Our study suggested that the proposed test has high performance and should be used as an alternative to the four existing tests due to its simple formula.
format	Article
author	Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued,
spellingShingle	Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued, A Bayesian approach to the one way ANOVA under unequal variance
author_facet	Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued,
author_sort	Noppakun Tongmol,
title	A Bayesian approach to the one way ANOVA under unequal variance
title_short	A Bayesian approach to the one way ANOVA under unequal variance
title_full	A Bayesian approach to the one way ANOVA under unequal variance
title_fullStr	A Bayesian approach to the one way ANOVA under unequal variance
title_full_unstemmed	A Bayesian approach to the one way ANOVA under unequal variance
title_sort	bayesian approach to the one way anova under unequal variance
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2016
url	http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/1/19%20Noppakun.pdf
first_indexed	2023-09-18T19:57:03Z
last_indexed	2023-09-18T19:57:03Z
_version_	1777406598839271424

A Bayesian approach to the one way ANOVA under unequal variance

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