Tests under simple order in one‐way ANCOVA

Abstract Analysis of covariance (ANCOVA) models are used when apart from the main treatments, some covariates also affect the response variable. In this article, the problem of testing the homogeneity of treatment effects against ordered alternatives is addressed in a fixed effects one‐way ANCOVA model when error variances are heterogeneous. The likelihood ratio test (LRT) and two approximate tests based on the asymptotic distributions of some union‐intersection type test statistics are proposed. A parametric bootstrap technique has been used to implement the LRT and its asymptotic validity is proved. A method to construct simultaneous confidence intervals is proposed. All the test procedures are further extended to the case of more than one covariate. The robustness of tests is also studied under departure from normality. Extensive simulation studies show that the proposed test procedures perform well in terms of achieving the nominal size value and good power values.