Summary: The classical F-test to compare several population means depends on the assumption of homogeneity of variance of the population and the normality. When these assumptions, especially the equality of variance, are 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 size is not large. To deal with this problem, a number of tests are available in the literature.
In this study, the Brown-Forsythe, Weerahandi’s Generalized F, Parametric Bootstrap, Scott-Smith, One-Stage, One-Stage Range, Welch and Xu-Wang’s Generalized F-tests are introduced and a simulation study is performed to compare these tests according to type-1 errors and powers in different combinations of parameters and various sample sizes.