Symmetry Models and Hypotheses for Structured Data Layouts

A. P. Dawid

40 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Optimal Experimental Design Methods Statistical Methods and Applications Statistical Methods and Bayesian Inference

Abstract

SUMMARY The structure of a data layout may be usefully described in terms of its symmetries, i.e. transformations which do not affect attitudes to the data. Interesting null hypotheses may be considered as imposing still further symmetries. These symmetry properties may be used to derive valid tests of such null hypotheses, and to construct appropriate statistical models for the data. The general ideas are developed and illustrated in the context of a replicated two-way classification.

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1935Statistical Problems in Agricultural Experimentation 1965The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance 1956Average Values of Mean Squares in Factorials 1984Analysis of Variance Models in Orthogonal Designs 1955Fixed, Mixed, and Random Models 1950Restricted Randomization and Quasi-Latin Squares 1957The Relationship Algebra of an Experimental Design 1958THE INTERPRETATION OF THE EFFECTS OF NON-ADDITIVITY IN THE LATIN SQUARE

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