A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions
This study compared the probability of Type I error and the power of three statistical tests (Bartlett, Levene and Cochran) by varying the sampling distribution, variances and sample sizes. Monte Carlo methods were used to generate responses based on sample sizes and distributions 1,000 times. The s...
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| Format: | Article |
| Language: | English |
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Prince of Songkla University
2004-05-01
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| Series: | Songklanakarin Journal of Science and Technology (SJST) |
| Subjects: | |
| Online Access: | http://www.sjst.psu.ac.th/journal/26-4pdf/11-error-of-assumption.pdf |
| _version_ | 1818929347473440768 |
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| author | Chukiat Viwatwongkasem Thavatchai Vorapongsathorn Sineenart Taejaroenkul |
| author_facet | Chukiat Viwatwongkasem Thavatchai Vorapongsathorn Sineenart Taejaroenkul |
| author_sort | Chukiat Viwatwongkasem |
| collection | DOAJ |
| description | This study compared the probability of Type I error and the power of three statistical tests (Bartlett, Levene and Cochran) by varying the sampling distribution, variances and sample sizes. Monte Carlo methods were used to generate responses based on sample sizes and distributions 1,000 times. The sample sizes were both equal and unequal: 15, 30 and 45. The data distributions were Normal, Gamma and Chi-square. It was found that Bartlett’s test was sensitive to the normality assumption whereas Cochran’s test and Levene’s test were robust when the normal assumption was violated. Moreover, Levene’s test was quite good for both equal and small sample sizes. In the case of power, Bartlett’s test had the highest power in all cases. When one variance was large, Cochran’s test was the best test. The recommendations from this study are that: Bartlett’s test is the best test for homogeneity of variances since it is not affected by sample size. When data are non-normally distributed, Levene’s test is a good choice for small equal sample sizes. Cochran’s test is best when sample size is large and unequal and one variance is larger. |
| first_indexed | 2024-12-20T03:43:22Z |
| format | Article |
| id | doaj.art-7b3d4cacbebf470badd9165fed04c55b |
| institution | Directory Open Access Journal |
| issn | 0125-3395 |
| language | English |
| last_indexed | 2024-12-20T03:43:22Z |
| publishDate | 2004-05-01 |
| publisher | Prince of Songkla University |
| record_format | Article |
| series | Songklanakarin Journal of Science and Technology (SJST) |
| spelling | doaj.art-7b3d4cacbebf470badd9165fed04c55b2022-12-21T19:54:40ZengPrince of Songkla UniversitySongklanakarin Journal of Science and Technology (SJST)0125-33952004-05-01264537547A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptionsChukiat ViwatwongkasemThavatchai VorapongsathornSineenart TaejaroenkulThis study compared the probability of Type I error and the power of three statistical tests (Bartlett, Levene and Cochran) by varying the sampling distribution, variances and sample sizes. Monte Carlo methods were used to generate responses based on sample sizes and distributions 1,000 times. The sample sizes were both equal and unequal: 15, 30 and 45. The data distributions were Normal, Gamma and Chi-square. It was found that Bartlett’s test was sensitive to the normality assumption whereas Cochran’s test and Levene’s test were robust when the normal assumption was violated. Moreover, Levene’s test was quite good for both equal and small sample sizes. In the case of power, Bartlett’s test had the highest power in all cases. When one variance was large, Cochran’s test was the best test. The recommendations from this study are that: Bartlett’s test is the best test for homogeneity of variances since it is not affected by sample size. When data are non-normally distributed, Levene’s test is a good choice for small equal sample sizes. Cochran’s test is best when sample size is large and unequal and one variance is larger.http://www.sjst.psu.ac.th/journal/26-4pdf/11-error-of-assumption.pdfhomogeneity of varianceBartlett’s testLevene’s testCochran’s testsimulation |
| spellingShingle | Chukiat Viwatwongkasem Thavatchai Vorapongsathorn Sineenart Taejaroenkul A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions Songklanakarin Journal of Science and Technology (SJST) homogeneity of variance Bartlett’s test Levene’s test Cochran’s test simulation |
| title | A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions |
| title_full | A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions |
| title_fullStr | A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions |
| title_full_unstemmed | A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions |
| title_short | A comparison of type I error and power of Bartlett’s test, Levene’s test and Cochran’s test under violation of assumptions |
| title_sort | comparison of type i error and power of bartlett s test levene s test and cochran s test under violation of assumptions |
| topic | homogeneity of variance Bartlett’s test Levene’s test Cochran’s test simulation |
| url | http://www.sjst.psu.ac.th/journal/26-4pdf/11-error-of-assumption.pdf |
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