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Circular designs balanced for neighbours at distances one and two

Author

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  • R. E. L. Aldred
  • R. A. Bailey
  • Brendan D. Mckay
  • Ian M. Wanless

Abstract

We define three types of neighbour-balanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding self-neighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.

Suggested Citation

  • R. E. L. Aldred & R. A. Bailey & Brendan D. Mckay & Ian M. Wanless, 2014. "Circular designs balanced for neighbours at distances one and two," Biometrika, Biometrika Trust, vol. 101(4), pages 943-956.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:4:p:943-956.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu036
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    Cited by:

    1. Jitendra Kumar & Seema Jaggi & Eldho Varghese & Arpan Bhowmik & Cini Varghese, 2020. "First order rotatable designs incorporating differential neighbour effects from experimental units up to distance 2," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 923-935, November.

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