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Optimal designs for testing pairwise differences: A graph‐based game theoretic approach

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  • Arpan Singh
  • Satya Prakash Singh
  • Ori Davidov

Abstract

In a variety of experimental settings there is an interest in comparing pairs–of–treatments. Such experiments usually address one of the following two scientific questions: (1) is there a difference within any of the selected pairs of treatments? or (2) is there a difference within all of the selected pairs of treatments? In this article, we propose max–min optimal designs for testing the above hypotheses using a graph‐based game theoretic approach. Some of the max–min designs obtained are well known, but not recognized as optimal, others are novel and provide an improvement over naive designs.

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  • Arpan Singh & Satya Prakash Singh & Ori Davidov, 2025. "Optimal designs for testing pairwise differences: A graph‐based game theoretic approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 52(2), pages 533-571, June.
    • Handle: RePEc:bla:scjsta:v:52:y:2025:i:2:p:533-571
    DOI: 10.1111/sjos.12757
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