Tests under simple order in one‐way ANCOVA
针对误差方差异质时单向协方差分析模型，研究了处理效应同质性对有序备择假设的检验问题，提出了似然比检验和两种近似检验，并扩展至多协变量情形。
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.