Comparison of test statistics of nonnormal and unbalanced samples for multivariate analysis of variance in terms of Type-I error rates

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dc.authorid0000-0003-2286-4398
dc.authorid0000-0003-1235-8117
dc.authorid0000-0002-4060-7048
dc.contributor.authorAteş, Can.
dc.contributor.authorKaymaz, Özlem.
dc.contributor.authorKale, H. Emre.
dc.contributor.authorTekindal, Mustafa Agah.
dc.date.accessioned2020-03-26T20:13:06Z
dc.date.available2020-03-26T20:13:06Z
dc.date.issued2019
dc.departmentSelçuk Üniversitesi, Tıp Fakültesi, Temel Tıp Bilimleri Bölümüen_US
dc.description.abstractIn this study, we investigate how Wilks' lambda, Pillai's trace, Hotelling's trace, and Roy's largest root test statistics can be affected when the normal and homogeneous variance assumptions of the MANOVA method are violated. In other words, in these cases, the robustness of the tests is examined. For this purpose, a simulation study is conducted in different scenarios. In different variable numbers and different sample sizes, considering the group variances are homogeneous (sigma(12) = sigma(22) == sigma(g2)) and heterogeneous (increasing) (sigma(12) < sigma(22) < ... < sigma(g2)), random numbers are generated from Gamma(4-4-4; 0.5), Gamma(4-9-36; 0.5), Student's t(2), and Normal(0; 1) distributions. Furthermore, the number of observations in the groups being balanced and unbalanced is also taken into account. After 10000 repetitions, type-I error values are calculated for each test for alpha=0.05. In the Gamma distribution, Pillai's trace test statistic gives more robust results in the case of homogeneous and heterogeneous variances for 2 variables, and in the case of 3 variables, Roy's largest root test statistic gives more robust results in balanced samples and Pillai's trace test statistic in unbalanced samples. In Student's t distribution, Pillai's trace test statistic gives more robust results in the case of homogeneous variance and Wilks' lambda test statistic in the case of heterogeneous variance. In the normal distribution, in the case of homogeneous variance for 2 variables, Roy's largest root test statistic gives relatively more robust results and Wilks' lambda test statistic for 3 variables. Also in the case of heterogeneous variance for 2 and 3 variables, Roy's largest root test statistic gives robust results in the normal distribution. The test statistics used with MANOVA are affected by the violation of homogeneity of covariance matrices and normality assumptions particularly from unbalanced number of observations.en_US
dc.identifier.citationAteş, C., Kaymaz, Ö., Kale, H. E., Tekindal, M. A. (2019). Comparison of Test Statistics of Nonnormal and Unbalanced Samples for Multivariate Analysis of Variance in terms of Type-I Error Rates. Computational and Mathematical Methods in Medicine, 2019.
dc.identifier.doi10.1155/2019/2173638en_US
dc.identifier.issn1748-670Xen_US
dc.identifier.issn1748-6718en_US
dc.identifier.pmid31396289en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://dx.doi.org/10.1155/2019/2173638
dc.identifier.urihttps://hdl.handle.net/20.500.12395/37619
dc.identifier.volume2019en_US
dc.identifier.wosWOS:000477824400001en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakPubMeden_US
dc.institutionauthorTekindal, Mustafa Agah.
dc.language.isoenen_US
dc.publisherHINDAWI LTDen_US
dc.relation.ispartofCOMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINEen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.subjectnonnormal
dc.subjectType-I error rates
dc.titleComparison of test statistics of nonnormal and unbalanced samples for multivariate analysis of variance in terms of Type-I error ratesen_US
dc.typeArticleen_US

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