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Analysis of covariance models are used when apart from treatments, some covariates also have effects on the response variables. An one-way ANCOVA model is considered here when there are one or more covariates and error variances are heteroscedastic. The problem of testing the homogeneity of treatment effects against order restrictions is investigated in detail. We propose two parametric bootstrap tests for single covariate model based on pair-wise comparisons of treatment effects. The asymptotic accuracy of the bootstrap tests is established. The test procedures are extended to the case of several covariates. Robustness of the tests under departure from normality is also studied. Two user-friendly ‘R’ packages ‘OneWayANCOVA1’ and ‘OneWayANCOVA’ have been developed for using the test procedures on real data sets. Finally, the test procedures are illustrated with one practical example.

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Testing Against Ordered Alternatives in One-Way ANCOVA

  • 章节

  • 发表日期：

    2025年

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  • Anjana Mondal,
  • Somesh Kumar

摘要

Analysis of covariance models are used when apart from treatments, some covariates also have effects on the response variables. An one-way ANCOVA model is considered here when there are one or more covariates and error variances are heteroscedastic. The problem of testing the homogeneity of treatment effects against order restrictions is investigated in detail. We propose two parametric bootstrap tests for single covariate model based on pair-wise comparisons of treatment effects. The asymptotic accuracy of the bootstrap tests is established. The test procedures are extended to the case of several covariates. Robustness of the tests under departure from normality is also studied. Two user-friendly ‘R’ packages ‘OneWayANCOVA1’ and ‘OneWayANCOVA’ have been developed for using the test procedures on real data sets. Finally, the test procedures are illustrated with one practical example.