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Comparison of Test Statistics of Nonnormal and Unbalanced Samples for Multivariate Analysis of Variance in terms of Type-I Error Rates
المؤلفون المشاركون
Ateş, Can
Kaymaz, Özlem
Kale, H. Emre
Tekindal, Mustafa Agah
المصدر
Computational and Mathematical Methods in Medicine
العدد
المجلد 2019، العدد 2019 (31 ديسمبر/كانون الأول 2019)، ص ص. 1-8، 8ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2019-07-18
دولة النشر
مصر
عدد الصفحات
8
التخصصات الرئيسية
الملخص EN
In 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 σ12=σ22=⋯=σg2 and heterogeneous (increasing) σ12<σ22<⋯<σg2, 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 α = 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.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Ateş, Can& Kaymaz, Özlem& Kale, H. Emre& Tekindal, Mustafa Agah. 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،Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1130495
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Ateş, Can…[et al.]. 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 No. 2019 (2019), pp.1-8.
https://search.emarefa.net/detail/BIM-1130495
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Ateş, Can& Kaymaz, Özlem& Kale, H. Emre& Tekindal, Mustafa Agah. 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. Vol. 2019, no. 2019, pp.1-8.
https://search.emarefa.net/detail/BIM-1130495
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1130495
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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