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Decomposition tables for experiments. II. Two–one randomizations

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euclid.aos.1284391761.pdf (646.3Kb)
Date
10/2010
Author
Brien, C. J.
Bailey, Rosemary Anne
Keywords
Analysis of variance
Balance
Decomposition table
Design of experiments
Efficiency factor
Intertier interaction
Multiphase experiments
Multitiered experiments
Orthogonal decomposition
Pseudofactor
Structure
Tier
QA Mathematics
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Abstract
We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.
Citation
Brien , C J & Bailey , R A 2010 , ' Decomposition tables for experiments. II. Two–one randomizations ' , Annals of Statistics , vol. 38 , no. 5 , pp. 3164-3190 . https://doi.org/10.1214/09-AOS785
Publication
Annals of Statistics
Status
Peer reviewed
DOI
https://doi.org/10.1214/09-AOS785
ISSN
0090-5364
Type
Journal article
Rights
© Institute of Mathematical Statistics, 2010. This is an open access article
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/3479

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