## Statistical Science

- Statist. Sci.
- Volume 24, Number 2 (2009), 223-237.

### A Multivariate Variance Components Model for Analysis of Covariance in Designed Experiments

James G. Booth, Walter T. Federer, Martin T. Wells, and Russell D. Wolfinger

#### Abstract

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.

#### Article information

**Source**

Statist. Sci., Volume 24, Number 2 (2009), 223-237.

**Dates**

First available in Project Euclid: 14 January 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1263478383

**Digital Object Identifier**

doi:10.1214/09-STS294

**Mathematical Reviews number (MathSciNet)**

MR2655851

**Zentralblatt MATH identifier**

1328.62490

**Keywords**

Adjusted mean blocking factor conditional model orthogonal design randomized blocks design

#### Citation

Booth, James G.; Federer, Walter T.; Wells, Martin T.; Wolfinger, Russell D. A Multivariate Variance Components Model for Analysis of Covariance in Designed Experiments. Statist. Sci. 24 (2009), no. 2, 223--237. doi:10.1214/09-STS294. https://projecteuclid.org/euclid.ss/1263478383