Bivariate Continuous Distributions with Specified Conditional Hazard Functions

Analysis of covariance (ANCOVA) is the standard procedure for comparing several treatments when the response variable depends on one or more covariates. We consider the problem of testing the equality of treatment effects when the variances are not assumed to be equal. It is well known that classical F test is not robust with respect to the assumption of equal variances and may lead to misleading conclusions if the variances are not equal. Ananda (1998 Ananda , M. M. A. ( 1998 ). Bayesian and non-Bayesian solutions to analysis of covariance models under heteroscedasticity . J. Econometrics 86 : 177 – 192 .Crossref], Web of Science ®] , Google Scholar]) developed a generalized F test for testing the equality of treatment effects. However, simulation studies show that the actual size of this test can be much higher than the nominal level when the sample sizes are small, particularly when the number of treatments is large. In this article, we develop a test using the parametric bootstrap approach of Krishnamoorthy et al. (2007 Krishnamoorthy , K. , Lu , F. , Mathew , T. ( 2007 ). A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models . Computat. Statist. Data Anal. 51 : 5731 – 5742 .Crossref], Web of Science ®] , Google Scholar]). Our simulations show that the actual size of our proposed test is close to the nominal level, irrespective of the number of treatments and sample sizes. Our simulations also indicate that our proposed PB test is more robust, with respect to the assumption of normality, than the generalized F test. Therefore, our proposed PB test provides a satisfactory alternative to the generalized F test.