MANOVA Test İstatistiklerinin Monte-Carlo Simülasyonu ile Bernoulli Dağılımında Karşılaştırılması

Bu çalışmanın amacı, Manova test istatistiklerinin sağlamlığını Monte Carlo simülasyonunu kullanılarak I.tip hata bakımından kıyaslamaktır. Yöntemde, sayılar g = 3,4,5 grup için p = 3,5,7 bağımlı değişkene ait n = 10,30,60 örneklem büyüklüğü kullanılarak sabit ve artan varyansta R programlama dili kullanılarak üretilmiştir. 54 kombinasyonda hesaplanan I.Tip hatalardan, nominal α =0.05 değerinden en az uzaklaşan test istatistiği Pillai İz test istatistiği olmuştur. Wilk Lambda ve Hotelling-Lawley İz test istatistikleri ise birbirlerine yakın sonuç vermişlerdir. Araştırıcılar analizlerinin karar aşamasında önerilen kıyaslama sonuçlarına göre karar verebilirler.

Anahtar Kelimeler:

Manova test istatistiği, Simülasyon çalışması, Monte Carlo

A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution

The aim of this study is to compare the robustness of Manova test statistics against Type I error rate using the Monte Carlo simulation technique. In the method, numbers are 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 R. Numbers have been produced using these 54 combinations. Pillai Trace test statistic has been the least deviating from the nominal α =0.05 value. Wilk Lambda and Hotelling-Lawley Trace test results were close to each other. The researchers can decide according to the comparison results of the analysis's suggested decision stage.

Keywords:

Manova test statistics, Simulation study, Monte Carlo,

PDF

___

[1] Wilks, S.S., 1932. Certain generalizations made in the analysis of variance, Biometrica 24:471-494.
[2] Johnson, R. A.. Wichern D. W., 1982. Applied Multivariate Statistical Analysis. Prentice-Hall, Inc. USA,594s.
[3] Bartlett, M.S., 1954. A Note on the Multiplying Factors for Various chi-square pproximations. Journal of the Royal Statistical Society Series B (Methodological):pp 296-298.
[4] Seber, G. A. F., 1984. Multivariate Observations. John Wiley & sons, Inc., USA,686.
[5] Lawley, D. N., 1939. A generalization of Fisher's z test. Biometrika 30: 467-469.
[6] Hotelling, H., 1931. The generalization of student's ratio. Annals of Mathematical Statistics 2: 360-378.
[7] Pillai, K.C.S., 1955. Some New Test Criteria in Multivariate Analysis. The Annals of Mathematical Statistics 26:117-121.
[8] Davis, A.W.,1980. On The Effects Of Nonnormality On The Likelihood Ratio Criterion Wilks's Moderate Multyvariate. The Journal Of the American Statistical Association 67:419-427.
[9] Davis, A. W., 1982. On The Effects Of The Moderate Multivariate Nonnormality On Roy's Largest Root Tests. The Journal Of the American Statistical Association 77:986-990.
[10] Holloway, L.N., Dunn O.J., 1967. The robestness of Hotelling's T2. The Journal Of the American Statistical Association 62:124-136.
[11] Olson, C.L., 1974. Copperative Robustness Of Multivariate Analysis Of Six Tests In Variance. The Journal Of the American Association 69 (348): 894-907.
[12] Ito, K., 1969. On The Effect Of Homoscedasticity And Nonnormality Upon Some Multivariate Procedures. In Multivariate Analysis 2:87-120.
[13] Korin, B.P.,1972. Some comment on the Homoscedasticity Criterion M and the multivariate analysis of varia as test T2 , W. and R. Biometrica 59:215-216.
[14] Hopkins, J.W., Clay P.P.F., 1963. Some Bivariate Distribution Of Emprical T2 And Homoscedasticity Criterion M Under Unecual Variance And Leptokurtosis. The Journal Of the American Statistical Association 58:1048-1053.