Designs for half-diallel experiments with commutative orthogonal block structure

R. A. Bailey*, Peter J. Cameron, Dario Ferreira, Sandra S. Ferreira, Celia Nunes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In some experiments, the experimental units are all pairs of individuals who have to undertake a given task together. The set of such pairs forms a triangular association scheme. Appropriate randomization then gives two non-trivial strata. The design is said to have commutative orthogonal block structure (COBS) if the best linear unbiased estimators of treatment contrasts do not depend on the stratum variances. There are precisely three ways in which such a design can have COBS. We give a complete description of designs for which all treatment contrasts are in the same stratum. Then we give a very general construction for designs with COBS which have some treatment contrasts in each stratum.
Original languageEnglish
Article number106139
Number of pages14
JournalJournal of Statistical Planning and Inference
Early online date26 Dec 2023
Publication statusE-pub ahead of print - 26 Dec 2023


  • Half-diallel experiments
  • Commutative orthogonal block structure
  • Linear model
  • Triangular association scheme


Dive into the research topics of 'Designs for half-diallel experiments with commutative orthogonal block structure'. Together they form a unique fingerprint.

Cite this