On efficient exact experimental designs for ordered treatments

Satya Prakash Singh, Ori Davidov

Research output: Contribution to journalArticlepeer-review


In a recent paper Singh and Davidov (2019) derive approximate optimal designs for experiments with ordered treatments. Specifically, maxi–min and intersection–union designs were explored. These designs, which address different types of hypothesis testing problems, provide a substantial improvement over standard designs in terms of power, or equivalently, sample size requirements. In practice however, exact, not approximate designs are used. Therefore, in this paper, we develop methods for finding efficient exact designs for the testing problems considered in Singh and Davidov (2019). The proposed designs are compared numerically to some well known existing designs and it is shown that the new designs require fewer experimental units to attain prespecified power. A thorough sensitivity analysis shows that the proposed designs are robust against possible misspecification of the parameters under the alternative and the order relation among the treatment groups.

Original languageAmerican English
Article number107305
JournalComputational Statistics and Data Analysis
StatePublished - Dec 2021


  • Efficient exact designs
  • Intersection Union Tests
  • Likelihood ratio test
  • Order restricted inference
  • Rounding methods
  • Sensitivity analysis

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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