On the design of experiments with ordered treatments

Satya Prakash Singh, Ori Davidov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)881-900
Number of pages20
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number5
StatePublished - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019 Royal Statistical Society


  • Intersection–union tests
  • Least favourable configuration
  • Likelihood ratio test
  • Maxi-min designs
  • Non-centrality parameter
  • Order restricted inference
  • Power

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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