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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/1/19%20Noppakun.pdf |
| _version_ | 1848812345912983552 |
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| author | Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued, |
| author_facet | Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued, |
| author_sort | Noppakun Tongmol, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T00:00:50Z |
| format | Article |
| id | oai:generic.eprints.org:10303 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:00:50Z |
| publishDate | 2016 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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 |
| spellingShingle | Noppakun Tongmol, Wuttichai Srisodaphol, Angkana Boonyued, A Bayesian approach to the one way ANOVA under unequal variance |
| title | 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_short | A Bayesian approach to the one way ANOVA under unequal variance |
| title_sort | bayesian approach to the one way anova under unequal variance |
| url | http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/ http://journalarticle.ukm.my/10303/1/19%20Noppakun.pdf |