Bayesian and non-bayesian solutions to analysis of covariance models under heteroscedasticity

A single-factor fixed-effect analysis of covariance model with one or more covariates is considered without the assumption of equal error variance. Using the generalized definition of p-values, exact tests are derived for testing the equality of treatment effect and testing whether the effect of the covariate is significant. In a Bayesian setup, it is shown that these generalized p-values can be produced by the posterior predictive p-value approach by using an appropriate noninformative prior. Examples and simulation studies are given to illustrate the proposed procedures and their advantages over the classical F-tests.