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dc.contributor.authorBrien, C. J.
dc.contributor.authorBailey, Rosemary Anne
dc.identifier.citationBrien , C J & Bailey , R A 2009 , ' Decomposition tables for experiments I. A chain of randomizations ' , Annals of Statistics , vol. 37 , no. 6B , pp. 4184-4213 .
dc.identifier.otherPURE: 49887279
dc.identifier.otherPURE UUID: 24f241c2-23d9-422a-b293-b7166db38542
dc.identifier.otherWOS: 000271673700017
dc.identifier.otherScopus: 73949092785
dc.identifier.otherORCID: /0000-0002-8990-2099/work/39600083
dc.description.abstractOne aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a single-randomization experiment that is "structure balanced." The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for Such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.
dc.relation.ispartofAnnals of Statisticsen
dc.rights© Institute of Mathematical Statistics, 2009. This is an open access article.en
dc.subjectAnalysis of varianceen
dc.subjectDecomposition tableen
dc.subjectDesign of experimentsen
dc.subjectEfficiency factoren
dc.subjectMultiphase experimentsen
dc.subjectMultitiered experimentsen
dc.subjectOrthogonal decompositionen
dc.subjectQA Mathematicsen
dc.titleDecomposition tables for experiments I. A chain of randomizationsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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