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MANOVA Test İstatistiklerinin Monte-Carlo Simülasyonu ile Bernoulli Dağılımında Karşılaştırılması

Year 2018, Volume: 22 Issue: 3, 1125 - 1131, 20.09.2018

Mustafa Şahin Şeyma Koç

https://doi.org/10.19113/sdufenbed.469282

Abstract

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.

Keywords

Manova test istatistiği Simülasyon çalışması Monte Carlo

References

  • [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.

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

Year 2018, Volume: 22 Issue: 3, 1125 - 1131, 20.09.2018

Mustafa Şahin Şeyma Koç

https://doi.org/10.19113/sdufenbed.469282

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.

Keywords

Manova test statistics Simulation study Monte Carlo

References

  • [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.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mustafa Şahin

Şeyma Koç

Publication Date September 20, 2018
Published in Issue Year 2018 Volume: 22 Issue: 3

Cite

APA Şahin, M., & Koç, Ş. (2018). A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(3), 1125-1131. https://doi.org/10.19113/sdufenbed.469282
AMA Şahin M, Koç Ş. A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. SDÜ Fen Bil Enst Der. September 2018;22(3):1125-1131. doi:10.19113/sdufenbed.469282
Chicago Şahin, Mustafa, and Şeyma Koç. “A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 3 (September 2018): 1125-31. https://doi.org/10.19113/sdufenbed.469282.
EndNote Şahin M, Koç Ş (September 1, 2018) A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 3 1125–1131.
IEEE M. Şahin and Ş. Koç, “A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution”, SDÜ Fen Bil Enst Der, vol. 22, no. 3, pp. 1125–1131, 2018, doi: 10.19113/sdufenbed.469282.
ISNAD Şahin, Mustafa - Koç, Şeyma. “A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/3 (September 2018), 1125-1131. https://doi.org/10.19113/sdufenbed.469282.
JAMA Şahin M, Koç Ş. A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. SDÜ Fen Bil Enst Der. 2018;22:1125–1131.
MLA Şahin, Mustafa and Şeyma Koç. “A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 3, 2018, pp. 1125-31, doi:10.19113/sdufenbed.469282.
Vancouver Şahin M, Koç Ş. A Monte Carlo Simulation Study Robustness of MANOVA Test Statistics in Bernoulli Distribution. SDÜ Fen Bil Enst Der. 2018;22(3):1125-31.
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