What can lattices do for experimental designs?

• Published in: Mathematical social sciences Vol. 11; no. 3; pp. 243 - 281
• Main Author: Duquenne, V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.1986; Elsevier
• Series: Mathematical Social Sciences
• Subjects: analysis of variance; canonical decomposition; direct meet representation; Experimental design; formulae for canonical decompositions; modular lattices; Möbius function; permutable partitions; projective interval; canonical decomposition; permutable partitions; modular lattices; analysis of variance; projective interval; Experimental design; Möbius function

Let x 1:=((x 1)iϵI)ϵ R′ be a finite data set weighted by n 1:=((n 1)iϵI)ϵ R′ (reflecting a previous derivation or is constant), F: = {A,B,…} be a set of factors which index partitions of 1 (denoted by A, B…) together with ‘experimental dimensions’ (subjects' ages…), the experimental design be D...