Modi ed tests for comparison of group means under heteroskedasticity and non-normality caused by outlier(s)

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.