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Tests under simple order in one‐way ANCOVA

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  • Anjana Mondal
  • Somesh Kumar

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.

Suggested Citation

  • Anjana Mondal & Somesh Kumar, 2025. "Tests under simple order in one‐way ANCOVA," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 52(1), pages 104-144, March.
    • Handle: RePEc:bla:scjsta:v:52:y:2025:i:1:p:104-144
    DOI: 10.1111/sjos.12729
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