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October 2010 Decomposition tables for experiments. II. Two–one randomizations
C. J. Brien, R. A. Bailey
Ann. Statist. 38(5): 3164-3190 (October 2010). DOI: 10.1214/09-AOS785


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.


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C. J. Brien. R. A. Bailey. "Decomposition tables for experiments. II. Two–one randomizations." Ann. Statist. 38 (5) 3164 - 3190, October 2010.


Published: October 2010
First available in Project Euclid: 13 September 2010

zbMATH: 1200.62088
MathSciNet: MR2722467
Digital Object Identifier: 10.1214/09-AOS785

Primary: 62J10
Secondary: 62K99

Keywords: Analysis of variance , Balance , decomposition table , Design of experiments , efficiency factor , intertier interaction , multiphase experiments , multitiered experiments , Orthogonal decomposition , pseudofactor , structure , tier

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 5 • October 2010
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