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Optimum Experimental Designs, with SAS

A. C. Atkinson, A. N. Donev, and R. D. Tobias
Oxford University Press
Publication Date: 
Number of Pages: 
Oxford Statistical Science Series 34
[Reviewed by
Tom Schulte
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This self-contained text is an overview of optimal experiment design. As stated in the title, the SAS software package of statistical tools (for ANOVA, regression, multivariate analysis, and more) is a significant piece of the work. SAS code and exercise solutions are part of a fully-supported website for the book. From the introduction and on through the book, plenty of examples are pulled from real-world cases in biology, manufacturing, and other areas. These examples clarify key points, supported with plots, tables, and figures.

While most chapters conclude with SAS code and steps to follow using the ADX interface, SAS is really just a small portion of the content. Readers of this book using SAS will certainly benefit from this, but following through with SAS is not a requirement to get the full value of the examples and theory.

This work stands alone very well because it includes eight full chapters of background material. As a result, just the foundations of statistics are required for productive self-study. That is, a working knowledge of degrees of freedom, variance, residuals, etc. is all that is necessary to get started here. This first part of the book starts with the basics of models in the analysis of data including least squares fitting and simple experimental designs. These examples tend to include a forward reference to sections of the second part of the book where specific points will be delved into with more detail.

It is the second part that is a more detailed discussion of the general theory and offers a more full taxonomy on the variety of experiments. This includes response surface designs, blocking of experiments, designs for mixture experiments and both nonlinear and generalized linear models. Special attention is paid to the classifications of optimal design. Most attention is paid to the D- and G-optimality criteria, with many others touched on. Special approaches for clinical trials, neural networks and other topics are given brief treatment in a concluding section.

The consistent inclusion of clarifying examples and a full section of further reading for each chapter are key features to the structure of this text. The structure makes it an excellent introduction to the topic for use as a course textbook or a tool for personal reference or study.

Tom Schulte is a PhD candidate at Oakland University specializing in constraint programming for timetabling and scheduling.

I Background
1. Introduction
2. Some key ideas
3. Experimental strategies
4. The choice of a model
5. Models and least squares
6. Criteria for a good experiment
7. Standard designs
8. The analysis of experiments
II Theory and applications
9. Optimum design theory
10. Criteria of optimality
11. D-optimum designs
12. Algorithms for the construction of exact D-optimum designs
13. Optimum experimental design with SAS
14. Experiments with both qualitative and quantitative factors
15. Blocking response surface designs
16. Mixture experiments
17. Nonlinear models
18. Bayesian optimum designs
19. Design augmentation
20. Model checking and designs for discriminating between models
21. Compound design criteria
22. Generalized linear models
23. Response transformation and structured variances
24. Time-dependent models with correlated observations
25. Further topics
26. Exercises
Author index
Subject index