Varyansların Homojenliği için Kullanılan Yeniden Örneklemeye Dayalı Testler ve Simülasyon Çalışması

Yıl 2018, Cilt: 22 Sayı: 2, 644 - 653, 15.08.2018

Esra Gökpınar

Öz

Bu çalışmada normal dağılıma sahip k sayıda yığının varyans homojenliği testi üzerinde durulmuş ve son yıllarda yaygın olarak kullanılan yeniden örnekleme yöntemlerine dayalı testler incelenmiştir. Simülasyon çalışmasında testlerin performansını belirlemek amacıyla tüm testler deneysel I. tip hata oranı ve güç bakımından karşılaştırılmıştır. Bu amaçla farklı grup sayısı, farklı örnek çapı ve farklı yığın varyansları alınarak bir simülasyon çalışması yapılmış ve sonuçları yorumlanmıştır.

Anahtar Kelimeler

Varyans homojenliği, Yeniden örnekleme; Simülasyon çalışması

Kaynakça

• [1] Yiğit, E., Gökpınar, F., 2010. A Simulation Study on Tests for One-Way Anova under Unequal Variance Assumption, Communication Faculty of Science University of Ankara, 2:15-34.
• [2] Weerahandi, S., 1995. ANOVA under Unequal Error Variances, Biometrica, 38:330–336.
• [3] Welch, B.L., 1951. On the comparison of several mean values: An alternative approach. Biometrica. 38:330–336.
• [4] Krishnamoorthy, K., Lu, F., Thomas M., 2007. A Parametric Bootstrap Approach for ANOVA with Unequal Variances: Fixed and Random Models, Computational Statistics and Data Analysis, 51:5731–5742.
• [5] Xu, L., Wang, S., 2007. A new generalized p-value for ANOVA under heteroscedasticity, Statistics and Probability Letters, 78:963–969.
• [6] Gökpınar, E. Y., Gökpınar, F., 2012. A Test Based on Computational Approach for Equality of Means under Unequal Variance Assumption, Hacettepe Journal of Mathematics and Statistics, 41(4):605-613.
• [7] Mutlu, H. T., Gökpınar, F., Gökpınar, E., Gül, H. H., Güven, G., Testing Homogeneity of İnverse Gaussian Scale Parameters on CAT Method, Communications in Statistics-Simulation and Computation, Doi: 10.1080/03610926.2016.1177082.
• [8] Bartlett, M. S., 1937. Properties of Sufficiency and Statistical Test, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 160(901): 268-282.
• [9] Cochran, W. G., 1951. Testing a Linear Relation among Variances, Biometrics, 7(1):17-32.
• [10] Hartley, H. O., 1950. The Maximum F-Ratio as a Short-Cut Test for Heterogeneity of Variance, Biometrika, 37(3/4):308-312.
• [11] Box, G. E. P., 1953. Non-Normality and Tests on Variances, Biometrika, 40:318-335.
• [12] Levene, H., 1960. Robust Tests for Equality of Variances. In Contributions to Probability and Statistics: Essays in honor of Harold Hotelling, 2:278-292.
• [13] Brown, M. B., Forsythe, A. B., 1974. Robust Tests for the Equality of Variances, Journal of the American Statistical Association, 69(346):364-367.
• [14] Canover, W. J., Johnson, M. E. , Johnson, M. M., 1981. A comparative study of tests for homogneity of variances, with applications to outer continental shelf bidding data, Technometrics, 23:351-361.
• [15] Loh, W. Y., 1987. Some Modifications of Levene’s Test of Variance Homogeneity, Journal of Statistical Computation and Simulation, 28:213-226.
• [16] Keyes, T. K., Levy, M. S., 1997. Analysis of Levene’s Test under Design Inbalance, Journal of Educational and Behavioral Statistics, 22(2):227-236.
• [17] Bhandary, M., Dai, H., 2009. An Alternative Test for the Equality of Variances for Several Populations When the Underlying Distributions are Normal. Communications in Statistics-Simulation and Computation, 38(1) 109-117.
• [18] Mirtagioğlu, H., Yiğit, S., Mendeş, E., Mendeş, M., 2017. A Monte Carlo Simulation Study for Comparing Performances of Some Homogeneity of Variances Tests. Journal of Applied Quantitative Methods, 12(1).
• [19] Mendeş M., Turhan N., Gürbüz F., 2006. A New alternative in testing for homogeneity of variances, Journal of Statistical Research, 2:65-83.
• [20] Mendeş M., Çamdeviren H., 2005. A Simulation Study for Type III Error Rates of Some Variance Homogeneity Tests, Pakistan Journal of Statistics, 2:223-234.
• [21] Mendeş M., 2003. Levene, Bartlett, Neyman-Pearson ve Bartlett 2 Testlerinin 1.Tip Hata Olasılıkları Bakımından Karşılaştırılması, Ankara Üniverstesi Ziraat Fakültesi Tarım Bilimler Dergisi, 2:143-146.
• [22] Keskin, S., 2002. Varyansların Homojenliğini Test Etmede Kullanılan Bazı Yöntemlerin I. Tip Hata ve Testin Gücü Bakımından İrdelenmesi, Ankara Üniversitesi Fen Bilimleri Enstitüsü Zootekni Anabilim Dalı, Aralık.
• [23] Tsui, K., Weerahandi, S., 1989. Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parametres, Journal of the American Statistical Assocation, 84:602– 607.
• [24] Weerahandi, S., 2004. Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models, Wiley, New York.
• [25] Pal, N., Lim, W. K., Ling, C. H., 2007. A Computational Approach to Statistical Inferences, Journal of Applied Probability and Statistics, 2(1):13-35.
• [26] Gökpınar, E.Y., Polat, E., Gökpınar, F., Günay, S., 2013. A new computational approach for testing equality of inverse Gaussian means under heterogeneity, Hacettepe Journal of Mathematics and Statistics, 42(5): 581-590.
• [27] Gökpınar, F., Gökpınar, E., 2015. A computational approach for testing equality of coefficients of variation in k normal populations, Hacettepe Journal of Mathematics and Statistics, 44(5): 1197-1213.
• [28] Gökpınar, F., Gökpınar, E., 2017. Testing the equality of several log-normal means based on a computational approach, Communications in Statistics-Simulation and Computation, 46(3):1998-2010.
• [29] Liu, X., Xu, X., 2010. A New Generalized p-value Approach for Testing the Homogeneity of Variances, Statistics & probability letters, 80(19):1486-1491.
• [30] Gökpınar, E., Gökpınar, F., 2015. Testing Equality of Variances for Several Normal Populations, Communications in Statistics-Simulation and Computation, 46(1):38-52.
• [31] Chang, C-H., Pal, N., Lin, J-J., 2016. A Revisit to Test the Equality of Variances of Several Populations, Communications in Statistics-Simulation and Computation, Doi: 10.1080/03610918.2016.1202277.