Alternative tests for one-way ANCOVA under heteroscedasticity

Testing for treatment effects without adjusting for the covariates may lead to erroneous conclusions. In many situations, ignoring variance heteroscedasticity can have serious consequences. In this article, new test procedures are proposed to test the homogeneity of treatment effects in a one-way ANCOVA model with heteroscedastic error variances. Most of the existing studies on this problem deal with non-parametric or semi-parametric situations. In a fully parametric setting, earlier one plug-in test statistic has been proposed using bootstrap approach. In this study, we develop the likelihood ratio test (LRT) and a test utilizing pair-wise differences between treatment effects. The parametric bootstrap is employed for determining the critical points. Extensive simulation studies demonstrate that the proposed tests perform better than the existing tests in some situations. The applicability of these approaches is illustrated using three datasets. Some 'R' functions are made available in 'GitHub' for easy computation.