A TEST BASED ON THE COMPUTATIONAL APPROACH FOR EQUALITY OF MEANS UNDER THE UNEQUAL VARIANCE ASSUMPTION

Authors : Esra Yiğit GÖKPINAR ,  fikri GÖKPINAR
Pages : 605-613
View : 123 | Download : 7
Publication Date : 2012-04-01
Article Type : Research Paper
Abstract :The classical F-test to compare several populations means depends on the assumption of homogeneity of variances of the population and on normality. When these assumptions - especially the equality of variance - is dropped, the classical F-test fails to reject the null hypothesis even if the data actually provide strong evidence for it. This can be considered a serious problem in some applications especially when the sample sizes are not large. To deal with this problem, a number of tests are available in the literature. Recently Pal, Lim and Ling insert ignore into journalissuearticles values(A computational approach to statistical inferences, J. Appl. Probab. Stat. 2 insert ignore into journalissuearticles values(1);, 13–35, 2007); developed a computational technique, called the Computational Approach Test insert ignore into journalissuearticles values(CAT);, which looks similar to a parametric bootstrap for hypothesis testing. Chang and Pal insert ignore into journalissuearticles values(A revisit to the Behren-Fisher Problem: Comparison of five test methods, Communications in Statistics - Simulation and Computation 37 insert ignore into journalissuearticles values(6);, 1064–1085, 2008); applied CAT to test the equality of two population means when the variances are unknown and arbitrary. In this study we apply a developed CAT to test the equality of k population means when the variances are unequal. Also the Brown-Forsythe, Weerahandi’s Generalized F, Parametric Bootstrap and Welch tests are recalled and a simulation study performed to compare these tests according to type one errors and powers in different combinations of parameters and various sample sizes.
Keywords : Brown Forsythe Test, Computational Approach Test, Generalized F test, Parametric Bootstrap Test, Classic F Test, Welch Test, 2000 AMS Classification 62 F 03

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