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

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

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.

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  • 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.