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Orthogonal Partitions in Designed Experiments

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Abstract

A survey is given of the statistical theory of orthogonalpartitions on a finite set. Orthogonality, closure under suprema,and one trivial partition give an orthogonal decomposition ofthe corresponding vector space into subspaces indexed by thepartitions. These conditions plus uniformity, closure under infimaand the other trivial partition give association schemes. Examplescovered by the theory include Latin squares, orthogonal arrays,semilattices of subgroups, and partitions defined by the ancestralsubsets of a partially ordered set (the poset block structures). Isomorphism, equivalence and duality are discussed, and theautomorphism groups given in some cases. Finally, the ideas areillustrated by some examples of real experiments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Maryand Westfield College, Mile End Road, London, E1 4NS, U.K

    R.A. Bailey

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Bailey, R. Orthogonal Partitions in Designed Experiments. Designs, Codes and Cryptography 8, 45–77 (1996). https://doi.org/10.1023/A:1018072606346

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