The Theory of the Design of Experiments

ISBN-13: 9781584881957 / Angielski / Twarda / 2000 / 336 str.

D. R. Cox; N. Reid

Opis

This monograph is designed to help researchers understand the theory of the design of experiments, so they can easily adapt general principles to their specialty. It seeks to bring the theory to non-statisticians at a reasonable mathematical level so that they can apply and adapt the designs. The authors use self-contained chapters, illustrated applications, and examples to teach the ideas and concepts needed for sound experiment design, and consequently, analysis. The volume includes extensive bibliographic notes and a detailed account of S-Plus.

Recenzje

"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

Spis treści

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
A Broader View
AVOIDANCE OF BIAS
General Remarks
Randomization
Retrospective Adjustment for Bias
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
Retrospective Adjustment for Improving Precision
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
Optimality of Traditional Designs
SOME ADDITIONAL TOPICS
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

O autorze

D.R. Cox, Nancy Reid