1st Edition

The Theory of the Design of Experiments

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

    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.

    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


    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