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Decomposition tables for experiments I. A chain of randomizations

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euclid.aos.1256303541.pdf (760.8Kb)
Date
12/2009
Author
Brien, C. J.
Bailey, Rosemary Anne
Keywords
Analysis of variance
Balance
Decomposition table
Design of experiments
Efficiency factor
Multiphase experiments
Multitiered experiments
Orthogonal decomposition
Pseudofactor
Structure
Tier
QA Mathematics
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Abstract
One 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.
Citation
Brien , 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 . https://doi.org/10.1214/09-AOS717
Publication
Annals of Statistics
Status
Peer reviewed
DOI
https://doi.org/10.1214/09-AOS717
ISSN
0090-5364
Type
Journal article
Rights
© Institute of Mathematical Statistics, 2009. This is an open access article.
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/3478

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

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