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On the design of experiments with ordered treatments

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  • Satya Prakash Singh
  • Ori Davidov

Abstract

There are many situations where one expects an ordering among K⩾2 experimental groups or treatments. Although there is a large body of literature dealing with the analysis under order restrictions, surprisingly, very little work has been done in the context of the design of experiments. Here, a principled approach to the design of experiments with ordered treatments is provided. In particular we propose two classes of designs which are optimal for testing different types of hypotheses. The theoretical findings are supplemented with thorough numerical experimentation and a concrete data example. It is shown that there is a substantial gain in power, or alternatively a reduction in the required sample size, when an experiment is both designed and analysed by using methods which account for order restrictions.

Suggested Citation

  • Satya Prakash Singh & Ori Davidov, 2019. "On the design of experiments with ordered treatments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(5), pages 881-900, November.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:5:p:881-900
    DOI: 10.1111/rssb.12335
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    Cited by:

    1. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    2. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.
    3. Singh, Satya Prakash & Davidov, Ori, 2021. "On efficient exact experimental designs for ordered treatments," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).

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