A Monte Carlo Simulation Study Robustness of Manova Test Statistics in Bernoulli and Uniform Distribution

Yıl 2019, Cilt: 2 Sayı: 2, 42 - 51, 01.04.2019

Şeyma Koç Demet Çanga Ayşe Betül Önem Esra Yavuz Mustafa Şahin

Öz

The
aim of this study is to compare the robustness of Manova test statistics
against the Type I error rate using the Monte Carlo simulation in Bernoulli and
Uniform distribution. In the method, numbers have been generated according to
constant and increasing variance for g= 3, 4, 5 group p= 3, 5, 7 dependent
variables n= 10, 30, 60 sample size using the RStudio. The specified
combinations have been repeated 10,000 times. As the result Pillai Trace test
statistic has been the least deviating from the nominal α =0.05 value. Wilk
Lambda and Hotelling-Lawley Trace test statistics results have been close to
each other. Researchers can get help from these suggested results during their
own study.

Anahtar Kelimeler

Monte-Carlo, Simulation, Bernoulli, Uniform

A Monte Carlo Simulation Study Robustness of Manova Test Statistics in Bernoulli and Uniform Distribution

Öz

Kaynakça

• Alpar R. 2013. Uygulamalı çok değişkenli istatistiksel yöntemler. ISBN: 978-605-5437-42-8, Ankara, 886p.
• Bartlett MS. 1954. A note on multiplying factors for various chi-squared approximations. J Royal Stat Soc Series, B 16: 296–298.
• Davis A W. 1980. On the effects of the moderate multivariate nonnormality on Wilks’s Likelihood Ratio Criterion. J American Stat Assoc, 67: 419-427.
• Davis AW. 1982. On the effects of the moderate multivariate nonnormality on Roy’s Largest Root Test. J American Stat Assoc, 77: 986-990.
• Holloway LN, Dunn OJ. 1967. The robustness of Hotelling’s T2. J American Stat Assoc, 62: 124-136.
• Hopkins JW, Clay PPF. 1963. Some emprical distribution of bivariate T2 and homoscedasticity criterion M under unecual variance and leptokurtosis. J American Stat Assoc, 58: 1048-1053.
• Hotelling H. 1931. The generalization of student's ratio. Annals Math Stat, 2: 360-378.
• Ito K. 1969. On the effect of homoscedasticity and nonnormality upon some multivariate procedures. Multivariate Analysis, 2: 87-120.
• Johnson RA. Wichern DW. 1982. Applied multivariate statistical analysis. Prentice-Hall, Inc., 594p, USA.
• Kanık A. 1999. Çok değişkenli varyans analizinde kovaryans matrislerinin homejenliği ön şartı. Doktora tezi, Ankara Üniversitesi, Fen Bilimleri Enstitüsü.
• Lawley DN. 1939. A generalization of Fisher's z test. Biometrica 30: 467-469.
• Korin BP. 1972. Some comment on the homoscedasticity criterion M and the multivariate analysis of variance test T2, W and R. Biometrica, 59: 215-216.
• Morrison FD. 1976. Multivariate statistical methods. MC Graw Hill Book Company, 2nd edition, 410p, USA.
• Olson CL. 1974. Copperative robustness of six tests in multivariate analysis of variance. J American Stat Assoc, 69(348): 894-907.
• Pillai, K.C.S., 1955. Some New Test Criteria in Multivariate Analysis. Annals Math Stat, 26:117-121.
• Seber GAF. 1984. Multivariate observations. John Wiley & Sons, Inc., 686p, USA.
• Stevens J. 1986. Applied multivariate statistic for the social sciences. Lowrance Erlbaum associates, Inc., London, England.
• Wilks SS. 1932. Certain generalizations in the analysis of variance. Biometrica, 24: 471-494.