Results of simulationsclearly indicate that Generalized F-test modied with Huber'sM-estimators achieves the nominal type 1 error rate and provide higherpower 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:Thesetests are powerful and have nominal type 1 error rates but they are notperforming satisfactorily under non-normality caused by outlier(s).
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Conclusion & Impact:Results of simulationsclearly indicate that Generalized F-test modied with Huber'sM-estimators achieves the nominal type 1 error rate and provide higherpower than alternative methods.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
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. Thesetests are powerful and have nominal type 1 error rates but they are notperforming satisfactorily under non-normality caused by outlier(s). Tohandle this problem, we investigate tests that are powerful and providenominal type 1 error rates by using robust estimators both forlocation and scale parameters. The performance of the modied testsare examined with Monte-Carlo simulation studies. Results of simulationsclearly indicate that Generalized F-test modied with Huber'sM-estimators achieves the nominal type 1 error rate and provide higherpower than alternative methods.
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Cite This Article
YAZICI, B., ÇAVUŞOĞLU, M., SEZER, A. (2022). Modi ed 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/529933
Yazici, B., Sezer, A., Ozkip, E. Generalized p-value test to compare several population means for unequal variances, Joint Statistical Meetings Proceedings, San Diego, USA, 2012.
Yazici, B., Sezer, A., Ozkip, E. A simulation study to compare several population means under heteroskedasticity, Abstract Book of 5th International Conference of the ERCIM Working Group on Computing and Statistics, Oviedo, SPAIN, 2012. [43] Wu, L.L. Robust M-estimation of location and regression, Sociological Methodology 15, 316-388, 1985.
Wilcox, R.R. Introduction to Robust Estimation and Hypothesis Testing, Elsevier, 2012.
Wilcox, R.R. Simulation results on solutions to the multivariate Behrens-Fisher problem via trimmed means, The Statistician 44 2, 213-225, 1995.
Welch, B.L. On the comparison of several group means values, Biometrika 38, 330-336, 1951.
Weerahandi, S. Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models, Wiley, 2004.
Weerahandi, S. Exact Statistical Methods for Data Analysis, Springer, 1995.
Weerahandi, S. ANOVA under unequal error variances, Biometrics 51, 589-599, 1994.
Weerahandi, S. Testing variance components in mixed models with generalized p-values, Journal of the American Statistical Association 86, 151-153, 1991.
Tsui, K. and Weerahandi, S. Generalized p-values in signi cance testing of hypotheses in the presence of nuisance parameters, Journal of the American Statistical Association 84, 602-607, 1989.
Tiku, M. and Akkaya, A. Robust Estimation and Hypothesis Testing, New Age International, 2004.
Tan, W.Y. and Tabatabai, M.A. Some robust ANOVA procedures under heteroskedasticity and non-normality, Communications in Statistics 14 4, 1007-1026, 1985.
So, Y.C. and Sen, P.K. M-estimators based repeated signi cance tests for one-way ANOVA with adaptation to multiple comparisons, Communications in Statistics 1 2, 101-119, 1982.
Schrader, R.M. Robust analysis of variance, Communications in Statistics 6 9, 879-894, 1977.
Sadooghi-Alvandi, S.M., Jafari, A.A., Mardani-Ford, H.A. One-way ANOVA with unequal variances, Communications in Statistics 41, 4200-4221, 2012.
Rousseeuw, P. and Croux, C. Alternatives to the median absolute deviation, Journal of American Statistical Association 88 424, 1273-1283, 1993.
Reed, J.F. and Stark, D.B. Robust analysis of variance: a simulation study, Journal of Applied Statistics 22 1, 87-104, 1995.
Ozkip, E., Yazici, B., Sezer, A. Comparison of tests for the ANOVA with unequal variance, Joint Statis