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

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 (A computational
approach to statistical inferences, J. Appl. Probab. Stat. 2 (1), 13–35, 2007) developed a computational technique, called the Computational Approach Test (CAT), which looks similar to a parametric bootstrap for hypothesis testing. Chang and Pal (A revisit to the Behren-Fisher Problem: Comparison of five test methods, Communications in Statistics - Simulation and Computation 37 (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

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

Abstract

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