Modified tests for generalized behrens-fisher problem in the presence of outlier

Classical F-test is fairly strong for testing the equality of several population means when the assumptions are hold. Nevertheless, Classical F-test lose power in case of non-homogeneous variances. The problem of testing the equality of several population means with non-homogeneous variances, is called Generalized Behrens-Fisher problem. The approximate tests are Welch F-test, Parametric Bootstrap test, Generalized F-test are developed for solving this problem. These tests based on normality assumption, are powerful in case of non-homogeneous variances. Normality assumption can be violated because of some reasons. In this thesis, the violation of normality assumption causing by outlier is considered. For obtaining powerful tests over violation of normality causing by outlier, some modifications are proposed to the approximate tests with maximum likelihood estimators for location and scale parameters replaced with some robust estimators. The performance of the modified tests with trimmed mean and variance, median and median absolute deviation and Huber' s M-estimators are evaluated with Monte-Carlo simulation studies in terms of power of the tests and type 1 error rates.