Optimum Experimental Designs, With SAS
OUP Oxford, May 24, 2007 - Business & Economics - 511 pages
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.
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Some Key Ideas
The Choice of a Model
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algorithm allocation analysis approximation Atkinson augmentation design Bayesian blocking variables candidate points central composite design centre point Chapter compound design constraints construction continuous design correlated covariance covariance matrix criteria D-efficiency D-optimality data set defined depend design criterion design matrix design of experiments design of Table design points design region design weights discussed Donev efficiency equivalence theorem error exact designs Example experimental design exponential decay Figure first-order model first-order reactions grid information matrix interactions least squares levels linear models locally D-optimum design locally optimum measure minimize mixture experiments model checking non-linear models number of trials optimality optimum design orthogonal output parameter estimates parameter values plot points of support polynomial prior distribution prior information proc optex procedure quadratic model qualitative factor random reaction replicated SAS Task second-order model second-order response surface secondary terms standard support points theophylline transformation treatment variance vector zero