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Type: Journal article
Title: Randomization-based models for multitiered experiments: I. A chain of randomizations
Author: Bailey, R.
Brien, C.
Citation: Annals of Statistics, 2016; 44(3):1131-1164
Publisher: Institute of Mathematical Statistics
Issue Date: 2016
ISSN: 0090-5364
Statement of
R. A. Bailey and C. J. Brien
Abstract: We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
Keywords: Analysis of variance; expected mean square; mixed models; multiphase experiments; multitiered experiments; randomization-based model; REML; structure; Tier; QA Mathematics; 3rd-DAS
Rights: © 2016, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at /
DOI: 10.1214/15-AOS1400
Published version:
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Mathematical Sciences publications

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