Annals of Statistics

Decomposition tables for experiments. II. Two–one randomizations

C. J. Brien and R. A. Bailey

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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.

Article information

Ann. Statist., Volume 38, Number 5 (2010), 3164-3190.

First available in Project Euclid: 13 September 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J10: Analysis of variance and covariance
Secondary: 62K99: None of the above, but in this section

Analysis of variance balance decomposition table design of experiments efficiency factor intertier interaction multiphase experiments multitiered experiments orthogonal decomposition pseudofactor structure tier


Brien, C. J.; Bailey, R. A. Decomposition tables for experiments. II. Two–one randomizations. Ann. Statist. 38 (2010), no. 5, 3164--3190. doi:10.1214/09-AOS785.

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