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May 2009 A Multivariate Variance Components Model for Analysis of Covariance in Designed Experiments
James G. Booth, Walter T. Federer, Martin T. Wells, Russell D. Wolfinger
Statist. Sci. 24(2): 223-237 (May 2009). DOI: 10.1214/09-STS294


Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a multivariate variance components model for the joint distribution of the response and covariates. It is shown that, if the design is orthogonal with respect to (random) blocking factors, then appropriate adjustments to treatment means can be made using the univariate variance components model obtained by conditioning on the observed covariate values. However, it is revealed that some widely used models are incorrectly specified, leading to biased estimates and incorrect standard errors. The approach clarifies some issues that have been the source of ongoing confusion in the statistics literature.


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James G. Booth. Walter T. Federer. Martin T. Wells. Russell D. Wolfinger. "A Multivariate Variance Components Model for Analysis of Covariance in Designed Experiments." Statist. Sci. 24 (2) 223 - 237, May 2009.


Published: May 2009
First available in Project Euclid: 14 January 2010

zbMATH: 1328.62490
MathSciNet: MR2655851
Digital Object Identifier: 10.1214/09-STS294

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.24 • No. 2 • May 2009
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