Comparison of test statistics of nonnormal and unbalanced samples for multivariate analysis of variance in terms of Type-I error rates
Yükleniyor...
Dosyalar
Tarih
2019
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
HINDAWI LTD
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 (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.
Açıklama
Anahtar Kelimeler
nonnormal, Type-I error rates
Kaynak
COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
2019
Sayı
Künye
Ateş, 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.
