Research Article
A Monte Carlo Simulation Study Robustness of Manova Test Statistics in Bernoulli and Uniform Distribution
Abstract
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.
Keywords
References
- 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.
A Monte Carlo Simulation Study Robustness of Manova Test Statistics in Bernoulli and Uniform Distribution
Abstract
References
- 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.
There are 18 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Submission Date | November 18, 2018 |
| Acceptance Date | February 13, 2019 |
| Publication Date | April 1, 2019 |
| Published in Issue | Year 2019 Volume: 2 Issue: 2 |