caa a22 4500 477040187 CHVBK 20180405111316.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF00173304 doi (NATIONALLICENCE)springer-10.1007/BF00173304 Bailey R. School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, E1 4NS, London, UK aut Orthogonal partitions in designed experiments [Elektronische Daten] [R. Bailey] A survey is given of the statistical theory of orthogonal partitions on a finite set. Orthogonality, closure under suprema, and one trivial partition give an orthogonal decomposition of the corresponding vector space into subspaces indexed by the partitions. These conditions plus uniformity, closure under infima and the other trivial partition give association schemes. Examples covered by the theory include Latin squares, orthogonal arrays, semilattices of subgroups, and partitions defined by the ancestral subsets of a partially ordered set (the poset block structures). Isomorphism, equivalence and duality are discussed, and the automorphism groups given in some cases. Finally, the ideas are illustrated by some examples of real experiments. Kluwer Academic Publishers, 1996 association scheme nationallicence block structure nationallicence crossing nationallicence infimum nationallicence nesting nationallicence orthogonality nationallicence partition nationallicence poset nationallicence supremum nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 8/3(1996-06-01), 45-77 0925-1022 8:3<45 1996 8 10623 https://doi.org/10.1007/BF00173304 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00173304 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bailey R. School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, E1 4NS, London, UK aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 8/3(1996-06-01), 45-77 0925-1022 8:3<45 1996 8 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 477040187 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer