Optimum Experimental Designs, with SAS
The purpose of this book is to describe a sufficient amount of the theory to make apparent the overall pattern of optimum designs and to provide a thorough background for the use of packages of SAS software in the design of optimum experiments. The book is divided into two parts. The idea of the statistical design of experiments is introduced in the first shorter part. The theory of an optimum experimental design is developed in the second part together with many applications, procedures and examples. The first part (Background) consists of eight chapters. The authors discuss advantages of a statistical approach for the design of experiments and introduce many models and examples, which are applied mainly in the second part of the book. The first part describes stages in experimental research, the choice of model, the least squares method, a design matrix, standard design and analysis of experiments. The packages for data processing and statistical analysis (SAS software) are mentioned here and these packages are used in many examples in the second part (Theory and Applications).
The second part starts with a formulation of the general equivalence theorem. Then follows the criteria of A-, D- and E-optimality, algorithms for the construction of exact D–optimum design and optimum experimental design with SAS. Chapter 14 is concerned with the design of experiments, where the response depends on both qualitative and quantitative factors. Mixture experiments are described in chapter 15. The comprehensive chapter 17 describes an extension of previous techniques to nonlinear regression models, including those defined by systems of differential equations. The following chapters contain a discussion of Bayesian optimum designs, augmented design, model checking and design of discriminating between models, compound design criteria, generalized linear models, response transformation and structured variances, time–dependent models with correlated observations, design of clinical trials and exercises. The whole book is oriented to the practical mind with many examples and procedures. The examples are mainly drawn from scientific, engineering, pharmaceutical and agriculture practice. The book contains a large list of references. It can be recommended mainly to scientists and to students preparing a Masters or a doctoral thesis.