Çok değişkenli varyans analizinde kovaryans matrislerinin homojenliği ön şartı
The assumption of equality of population covariance matrices in manova
Yazar: EMİNE ARZU KANIK
Danışman: PROF.DR. FİKRET GÜRBÜZ
Ankara Üniversitesi / Fen Bilimleri Enstitüsü / Zootekni Ana Bilim Dalı
Derece: Doktora, 1999
Konu: Ziraat = Agriculture
Dizin: Benzetim = Simulation ; Kovaryans matrisleri = Covariance matrices ; Zootekni = Zootechnics ; Çok değişkenli varyans analizi = Multivariate variance analysis

Özet:
ABSTRACT Ph.D. Thesis THE ASSUMPTION OF EQUALITY OF POPULATION COVARUNCE MATRICES I N MANOVA Emine Arzu KANIK Ankara University Graduate School of Natural and Applied Sciences Department of Animal Sciences Supervisor: Prof.Dr. Fikret GÜRBÜZ In this study, equality of covariance matrices assumptions in MANOVA were investigated with simulation study. In simulation study, all samples generated from multivariate normal distribution and all observations in each group are independent In this study total number of combinations is 8175 and each combination simulated 10000 times. Most of researchers shown that inequality of covariance matrices effect type I error and Hotelling's T2, Wilks Lambda, Roys Largest Root and Pillai's V tests criteria» in MANOVA are not robust when this assumption are not met As a result not equal sample size and number of dependent variable bad effect on type I error when this assumption are not met Whenever number of dependent variables is 2 or 3 all test statistics except Roy' s (R) are generally robust For 10 dependent variables actual a is too big or small it depends on which group has large sample size. In this study calculated two new constans DP and K. There is a high relation between actual a and K. 1999,116 pages Key Words : Multivariate analysis of variance, equality of covariance matrices, assumptions, simulation study

Abstract:
ABSTRACT Ph.D. Thesis THE ASSUMPTION OF EQUALITY OF POPULATION COVARUNCE MATRICES I N MANOVA Emine Arzu KANIK Ankara University Graduate School of Natural and Applied Sciences Department of Animal Sciences Supervisor: Prof.Dr. Fikret GÜRBÜZ In this study, equality of covariance matrices assumptions in MANOVA were investigated with simulation study. In simulation study, all samples generated from multivariate normal distribution and all observations in each group are independent In this study total number of combinations is 8175 and each combination simulated 10000 times. Most of researchers shown that inequality of covariance matrices effect type I error and Hotelling's T2, Wilks Lambda, Roys Largest Root and Pillai's V tests criteria» in MANOVA are not robust when this assumption are not met As a result not equal sample size and number of dependent variable bad effect on type I error when this assumption are not met Whenever number of dependent variables is 2 or 3 all test statistics except Roy' s (R) are generally robust For 10 dependent variables actual a is too big or small it depends on which group has large sample size. In this study calculated two new constans DP and K. There is a high relation between actual a and K. 1999,116 pages Key Words : Multivariate analysis of variance, equality of covariance matrices, assumptions, simulation study