SavedAdd your journal

Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2018 / Cilt: 22 - Sayı: 3

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

MANOVA Test İstatistiklerinin Monte-Carlo Simülasyonu ile Bernoulli Dağılımında Karşılaştırılması

MUSTAFA ŞAHİN
Şeyma KOÇ
Pages
1125–1131
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The researchers can decide according to the comparison results of the analysis's suggested decision stage.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:The researchers can decide according to the comparison results of the analysis's suggested decision stage.
🔬Design:Research Article
📍Scope:30,60 sample
⚙️Variables:Manova test istatistiği · Simülasyon çalışması · Monte Carlo

Abstract

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.

Özet

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.

🔖

Cite This Article

ŞAHİN, M., KOÇ, Ş. (2018). A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 22 - Sayı: 3, 1125–1131. https://ajindex.com/articles/310488

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  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.