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Design of experiments: a no-name approach. (English) Zbl 0853.62055

Statistics: Textbooks and Monographs. 139. New York, NY: Marcel Dekker. xii, 414 p. (1993).
This book on design of experiments is written at a level suitable for first year graduate students as well as for senior undergraduate students. The book is somewhat unique in the sense that the authors have de-emphasized the practice of describing design problems and solutions using “named designs”. Instead, they have chosen to present the basic concepts using which all of the standard designs and many other designs can be treated. The book has nine chapters.
Chapter 1 presents what is commonly regarded as the “scientific method” for designing an experiment. This covers the entire range – from problem formulation to final conclusions and implementation. Chapter 2 deals with one factor designs. Topics in this chapter include the underlying mathematical model and assumptions, the ANOVA table, mean comparisons, testing of assumptions, transformations of the response variable, and sample size calculations.
Factorial designs are the topic of chapter 3. The concept of fixed and random factors is introduced and explained. Rules for the calculation of various sums of squares and degrees of freedom appearing in the ANOVA table are explained under the assumption that the design is balanced. Rules for the calculation of expected mean squares are also given. Exact and approximate \(F\)-tests for various ANOVA hypotheses are described. Estimation of variance components is discussed for models involving both fixed and random factors. Chapter 4 introduces the concept of nesting. Mathematical models are presented for nested designs and the corresponding ANOVA is explained.
Chapters 2 through 4 consider only completely randomized experiments. Restricted randomization is introduced in chapter 5. It is shown in this chapter that a restriction on randomization is equivalent to adding a random term to the mathematical model and that this random term does not interact with any other term. Several examples, including one involving split plots, are given to illustrate this approach. In chapter 6 the authors use an example to provide a detailed illustration of all of the material discussed in the first five chapters.
Chapter 7 contains a discussion of two level fractional designs. Both fractionation and blocking are explained in a unified framework. Rules for calculation of expected mean squares in an ANOVA table are explained. This allows the consideration of both fixed and random factors when fractionating. Guidelines for selecting a fractional design are provided. Chapter 8 extends the discussions of chapter 7 to experiments involving three level or other prime level factors. Some discussion of mixed level factorials is also provided. Orthogonal main effects designs are introduced and discussed for mixed level factorials.
Chapter 9, which is the final chapter, treats response surface designs and response surface methodology. Standard topics are covered including first order designs, second order designs, central composite designs, rotatable designs, orthogonal blocking, and so on. A sequential or stagewise approach is introduced. A brief introduction to mixture designs is provided.
Each chapter includes several useful examples and an abundance of problems. Solutions are provided to selected problems. There is also a bibliography at the end of each chapter. There are seventeen appendices consisting of tables of percentage points for selected statistical distributions and tables of useful designs. A reasonably complete index is provided at the end of the book.
This book is somewhat different from most books on experimental designs in that, as advertised by the authors in the preface, the material on restriction errors and how to incorporate them into the underlying model, will help the reader in properly formulating and analyzing both standard and nonstandard design problems with relative ease. Apart from being an excellent candidate as a graduate level text book on applied experimental design, it should also be a valuable reference for practicing statisticians.

MSC:

62Kxx Design of statistical experiments
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62K10 Statistical block designs
62K15 Factorial statistical designs
62K99 Design of statistical experiments
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