The Theory of the Design of Experiments: 1st Edition (Hardback) book cover

The Theory of the Design of Experiments

1st Edition

By D.R. Cox, Nancy Reid

Chapman and Hall/CRC

336 pages

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pub: 2000-06-06
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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.


"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

Table of Contents


Types of Investigation

Observational Studies

Some Key Terms

Requirements in Design

Interplay between Design and Analysis

Key Steps in Design

A Simplified Model

A Broader View


General Remarks


Retrospective Adjustment for Bias

Some More on Randomization

More on Causality


General Remarks

Precision Improvement by Blocking

Matched Pairs

Randomized Block Design

Partitioning Sums of Squares

Retrospective Adjustment for Improving Precision

Special Models of Error Variation


Latin Squares

Incomplete Block Designs

Cross-Over Designs


General Remarks


Main Effects and Interactions

Example: Continued

Two-Level Factorial Systems

Fractional Factorials



General Remarks

Confounding in 2k Designs

Other Factorial Systems

Split Plot Designs

Nonspecific Factors

Designs for Quantitative Factors

Taguchi Methods



General Remarks

Some Simple Examples

Some General Theory

Other Optimality Criteria

Algorithms for Design Construction

Nonlinear Design

Space-Filling Designs

Bayesian Design

Optimality of Traditional Designs


Scale of Effort

Adaptive Designs

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General