1st Edition

# The Theory of the Design of Experiments

By D.R. Cox, Nancy Reid Copyright 2000
336 Pages
by Chapman & Hall

336 Pages
by Chapman & Hall

Also available as eBook on:

Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the special constraints of individual applications.

Written for a general audience of researchers across the range of experimental disciplines, The Theory of the Design of Experiments presents the major topics associated with experiment design, focusing on the key concepts and the statistical structure of those concepts. The authors keep the level of mathematics elementary, for the most part, and downplay methods of data analysis. Their emphasis is firmly on design, but appendices offer self-contained reviews of algebra and some standard methods of analysis.

From their development in association with agricultural field trials, through their adaptation to the physical sciences, industry, and medicine, the statistical aspects of the design of experiments have become well refined. In statistics courses of study, however, the design of experiments very often receives much less emphasis than methods of analysis. The Theory of the Design of Experiments fills this potential gap in the education of practicing statisticians, statistics students, and researchers in all fields.

SOME GENERAL CONCEPTS
Types of Investigation
Observational Studies
Some Key Terms
Requirements in Design
Interplay between Design and Analysis
Key Steps in Design
A Simplified Model
AVOIDANCE OF BIAS
General Remarks
Randomization
Some More on Randomization
More on Causality
CONTROL OF HAPHAZARD VARIATION
General Remarks
Precision Improvement by Blocking
Matched Pairs
Randomized Block Design
Partitioning Sums of Squares
Special Models of Error Variation
SPECIALIZED BLOCKING TECHNIQUES
Latin Squares
Incomplete Block Designs
Cross-Over Designs
FACTORIAL EXPERIMENTS: BASIC IDEAS
General Remarks
Example
Main Effects and Interactions
Example: Continued
Two-Level Factorial Systems
Fractional Factorials
Example
FACTORIAL EXPERIMENTS: FURTHER DEVELOPMENTS
General Remarks
Confounding in 2k Designs
Other Factorial Systems
Split Plot Designs
Nonspecific Factors
Designs for Quantitative Factors
Taguchi Methods
Conclusion
OPTIMAL DESIGN
General Remarks
Some Simple Examples
Some General Theory
Other Optimality Criteria
Algorithms for Design Construction
Nonlinear Design
Space-Filling Designs
Bayesian Design
Scale of Effort
Sequential Regression Design
Designs for One-Dimensional Error Structure
Spatial Designs
APPENDIX A: Statistical Analysis
APPENDIX B: Some Algebra
APPENDIX C: Computational Issues
Each chapter also contains Bibliographic Notes plus Further Results and Exercises

### Biography

D.R. Cox, Nancy Reid

"As the very antithesis of all those downmarket cookbooks of experimental design, this monograph is to be welcomed."
-D. A. Preece, Biometrics, March 2001

"This long awaited book is in the spirit of the classic introductory text by D. R. Cox … a compact and insightful presentation of an unusually wide range of design areas important for industrial and agricultural experiments, and clinical trials … The book will be particularly useful for statisticians who want to learn about design theory linked to practical problems, and for advanced undergraduate and post-graduate students … This approach enables a clear presentation of key ideas in the main areas of design, and gives an interesting and enjoyable read."
Short Book Reviews, Volume 20, No. 3, December 2000

"Intended for anyone concerned with the theoretical issues in the design of experiments, this well-organized book of 224 pages (8 chapters) of text and 74 pages of appendixes provides a clear account of the major topics in the area... In summary, this book is an excellent addition to the literature. It can serve as a cornerstone in a graduate student's exploration in the theoretical aspects of experimental design and is a valuable reference for statisticians working in medicine, agriculture, the physical sciences, and other areas of biometry and industry."
-Technometrics, Vol. 43, No. 4, November 2001

"…This approach is a refreshing change from the many contemporary expository books on statistical study design…this carefully written and concise book with its large, well-selected collection of references will be a useful addition to the library of any serious statistician."
-Statistics in Medicine, Vol. 21, 2002