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Decomposition tables for experiments. I. A chain of randomizations

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dc.contributor.authorBrien, C.J.
dc.contributor.authorBailey, R.
dc.date.issued2009
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.identifier.citationAnnals of Statistics, 2009; 37(6B):4184-4213
dc.identifier.doi10.1214/09-AOS717
dc.identifier.issn0090-5364
dc.identifier.orcidBrien, C.J. [0000-0003-0581-1817]
dc.identifier.urihttps://hdl.handle.net/1959.8/115089
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics
dc.rightsCopyright 2009 Institute of Mathematical Statistics
dc.source.urihttps://doi.org/10.1214/09-AOS717
dc.subjectanalysis of variance
dc.subjectbalance
dc.subjectdecomposition table
dc.subjectdesign of experiments
dc.subjectefficiency factor
dc.subjectintertier interaction
dc.subjectmultitiered experiments
dc.subjectorthogonal decomposition
dc.subjectpseudofactor
dc.subjectstructure
dc.subjecttier
dc.titleDecomposition tables for experiments. I. A chain of randomizations
dc.typeJournal article
pubs.publication-statusPublished
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