Results of simulations clearly indicate that Generalized F-test modied with Huber's M-estimators achieves the nominal type 1 error rate and provide higher power than alternative methods.
📌 3 Key Takeaways
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Objective & Hypothesis:There are several approximate tests proposed such as Welch's F-test (W), the Parametric Bootstrap Test (PB) and Generalized F-test (GF) for comparing several group means under heteroskedasticity.
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Key Findings & Data:These tests are powerful and have nominal type 1 error rates but they are not performing satisfactorily under non-normality caused by outlier(s).
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Conclusion & Impact:Results of simulations clearly indicate that Generalized F-test modied with Huber's M-estimators achieves the nominal type 1 error rate and provide higher power than alternative methods.
There are several approximate tests proposed such as Welch's F-test (W), the Parametric Bootstrap Test (PB) and Generalized F-test (GF) for comparing several group means under heteroskedasticity. These tests are powerful and have nominal type 1 error rates but they are not performing satisfactorily under non-normality caused by outlier(s). To handle this problem, we investigate tests that are powerful and provide nominal type 1 error rates by using robust estimators both for location and scale parameters. The performance of the modified tests are examined with Monte-Carlo simulation studies. Results of simulations clearly indicate that Generalized F-test modied with Huber's M-estimators achieves the nominal type 1 error rate and provide higher power than alternative methods.
CAVUS, M., YAZİCİ, B., SEZER, A. (2017). Modified tests for comparison of group means under heteroskedasticity and non-normality caused by outlier(s). Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 3, 493–510. https://ajindex.com/articles/669477
Barnett, V. and Lewis, T. Outlier in Statistical Data, Wiley and Sons, 1994.
Ben, M.G. and Yohai, V.J. Robust analysis of variance for randomized block design, Com- munications in Statistics 216, 1779-1798, 1992.
Braun, H.I. and McNeil, D.R. Testing in robust ANOVA, Communications in Statistics 102, 149-165, 1981.
Chang, C.H., Pal, N., Lim, W.K., Lin, J.J. Comparing several population means: a para- metric bootstrap method and its comparison with usual ANOVA F-test as well as ANOM, Computational Statistics 25, 71-95, 2010.
Chang, C.H., Lin, J.J., Pal, N. Testing the equality of several gamma means: a parametric bootstrap method with applications, Computational Statistics 76, 26-55, 2011.
Cavus, M., Yazici, B., Sezer, A. Comparison of means under non-normality with outliers for unbalanced data, 8th International Conference of the ERCIM Working Group on Computing and Statistics Proceedings, London, ENGLAND, 2015.
Cavus, M., Yazici, B., Sezer, A. Robust methods to compare means under violation of nor- mality with outliers, 12th German Probability and Statistics Days Proceedings, Bochum, GERMANY, 2016.
Cavus, M., Yazici, B., Sezer, A. Modi fied tests for comparison of group means in the presence of outlier(s), 2th International Researchers-Statisticians and Young Statisticians Congress Proceedings, Ankara, TURKEY, 2016.
Fan, W. and Hancock, G. Robust mean modelling: an alternative for hypothesis testing of independent means under variance heterogeneity and nonnormality, Journal of Educational and Behavioral Statistics 37, 137-156, 2012.
Fisher, R.A. Statistical methods and scientifi c inference, Oliver and Boyd, 1925.
Gamage, J. and Weerahandi, S. Size performance of some tests in one-way ANOVA, Com- munications in Statistics 273, 625-640, 1998.
Gokpinar Yigit, E., Polat, E., Gokpinar, F., Gunay, S. A new computational approach for testing equality of inverse Gaussian means under heterogeneity, Hacettepe Journal of Mathematics and Statistics 42 5, 581-590, 2013.
Huber, P.J. Robust estimation of a location parameter, The Annals of Mathematical Statis- tics 69, 73-101, 1964.
Huber, P.J. and Ronchetti, E.M. Robust Statistics, John Wiley and Sons, New Jersey, 2009.
Jian-Hong, S. and Jiang-Long, L. A new generalized p-value for testing equality of inverse Gaussian means under heterogeneity, Statistics and Probability Letters 82, 96-102, 2012.
Karagoz, D. Modi ed Welch test statistic for ANOVA under Weibull distribution, Hacettepe Journal of Mathematics and Statisti