Atkinson A., Donev A., Tobias R. Optimum Experimental Designs, with SAS

Oxford University Press, 2007. — 527 p. — ISBN: 019929660X, 9780199296590, 9780199296606.Experiments on patients, processes or plants all have random error, making statistical methods essential for their efficient design and analysis. This book presents the theory and methods of optimum experimental design, making them available through the use of SAS programs. Little previous statistical knowledge is assumed. The first part of the book stresses the importance of models in the analysis of data and introduces least squares fitting and simple optimum experimental designs. The second part presents a more detailed discussion of the general theory and of a wide variety of experiments. The book stresses the use of SAS to provide hands-on solutions for the construction of designs in both standard and non-standard situations. The mathematical theory of the designs is developed in parallel with their construction in SAS, so providing motivation for the development of the subject. Many chapters cover self-contained topics drawn from science, engineering and pharmaceutical investigations, such as response surface designs, blocking of experiments, designs for mixture experiments and for nonlinear and generalized linear models. Understanding is aided by the provision of "SAS tasks" after most chapters as well as by more traditional exercises and a fully supported website. The authors are leading experts in key fields and this book is ideal for statisticians and scientists in academia, research and the process and pharmaceutical industries.From authors about SAS software:
SAS software is one of the world's best established packages for data processing and statistical analysis. We will demonstrate the ideas and techniques that we discuss in this book with SAS tools. Most often, these tools take the form of SAS programs, but we will also touch on SAS point-and-click interfaces.
While most of the SAS facilities that we employ are available in any recent version of the software, the code that we will present was developed using SAS 9.1, released in 2004. SAS software tools comprise a number of different products. Base SAS is the foundation product, and SAS/STAT provides tools for statistical analysis. SAS facilities for construction of experimental designs, including optimal designs, are located in SAS/QC software. SAS/IML provides a language for matrix programming and facilities for optimization.
You will need all of these products to run all the SAS code presented in this book. Note that most universities and business organizations license a bundle of SAS products that includes these tools.Some Key Ideas
Experimental Strategies
The Choice of a Model
Models and Least Squares
Criteria for a Good Experiment
Standard Designs
The Analysis of Experiments
Optimum Design Theory
Criteria of Optimality
D-optimum Designs
Algorithms for the Construction of Exact D-optimum Designs
Optimum Experimental Design with SAS
Experiments with Both Qualitative and Quantitative Factors
Blocking Response Surface Designs
Mixture Experiments
Non-linear Models
Bayesian Optimum Designs
Design Augmentation
Model Checking and Designs for Discriminating Between Models
Compound Design Criteria
Generalized Linear Models
Response Transformation and Structured Variances
Time-dependent Models with Correlated Observations
Further Topics
Exercises