Analysis of covariance is a very useful but often misunderstood methodology for analyzing data where important characteristics of the experimental units are measured but not included as factors in the design. Analysis of Messy Data, Volume 3: Analysis of Covariance takes the unique approach of treating the analysis of covariance problem by looking at a set of regression models, one for each of the treatments or treatment combinations. Using this strategy, analysts can use their knowledge of regression analysis and analysis of variance to help attack the problem.
The authors describe the strategy for one- and two-way treatment structures with one and multiple covariates in a completely randomized design structure. They present new methods for comparing models and sets of parameters, including beta-hat models. They carefully investigate the effect of blocking, explore mixed models, and present a new methodology for using covariates to analyze data from nonreplicated experiments.
Analysis of covariance provides an invaluable set of strategies for analyzing data. With its careful balance of theory and examples, Analysis of Messy Data: Volume 3 provides a unique and outstanding guide to the strategy's techniques, theory, and application.
Table of Contents
Introduction to the Analysis of Covariance
One-Way Analysis of Covariance-One Covariate in a Completely Randomized Design Structure
Examples: One-Way Analysis of Covariance-One Covariate in a Completely Randomized Design Structure
Multiple Covariates in a One-Way Treatment Structure in a Completely Randomized Design Structure
Two-Way Treatment Structure and Analysis of Covariance in a Completely Randomized Design Structure
Variable Selection in the Analysis of Covariance Models
Comparing Models for Several Treatments
Two Treatments in a Randomized Complete Block Design Structure
More than Two Treatments in a Blocked Design Structure
Covariates Measured on the Block in RCB and Incomplete Block Design Structures
Random Effects Models with Covariates
Analysis of Covariance Models with Heterogeneous Errors
Analysis of Covariance for Split-Plot and Strip-Plot Design Structures
Analysis of Covariance for Repeated Measures Designs
Analysis of Covariance for Nonreplicated Experiments
Special Applications of Analysis of Covariance
"We owe [the authors] a huge debt for their 25 years (since they began writing) of persistence. As with the previous volumes, the authors go systematically and solidly through their material…In the years to come, many consulting statisticians will say to their clients, 'Why don't we see what Milliken and Johnson have to say on that?' as they pull this book from their shelves."
Short Book Reviews of the ISI
"this book covers, in depth, analysis of covariance and offers a unique approach to this somewhat complex topic, through the analysis of a set of regression models, one for each treatment or combination of treatments … A very detailed and complete coverage of analysis of variance is presented…Highly recommended. Upper-division undergraduates through professionals."
- CHOICE Magazine, May 2002
"The ANALYSIS OF MESSY DATA VOLUME I is one of my most tattered and torn books from the many years of using it to help analyze data. I was most excited when given the opportunity to review Volume III and to add another valuable book to my collection. Simply put, I was not disappointed. The authors' stated goal is to present the structure and philosophy for using the analysis of covariance. They do this very effectively by providing detailed explanations of the methods and by analyzing numerous datasets using PROC GLM and MIXED of SAS and JMP. …anyone confronted with an analysis of covariance should consult this book, which is definitely targeted for researchers who want to apply the methods. Each chapter has detailed examples and includes computer programs that provide the desired computations. The text is well written, exhaustive in scope, and a solid contribution to the literature."
- Richard K. Burdick, Arizona State University in Technometrics, August 2002