The Theory of the Design of Experiments

Intended for anyone concerned with the theoretical issues in the design of experiments, this well-organized book of 224 pages (8 chapters) of text and 74 pages of appendixes provides a clear account of the major topics in the area. The underlying theory of design of experiments is set out systematically, illustrations from a broad range of areas of application are taken to motivate the discussion, and examples are given to show some detailed methods. Bibliographic notes, further results, and exercises are presented to sketch historical and recent developments. Chapter 1 gives a concise description of some general concepts in the design of experiments. They include types of investigation, various forms of study such as prospective study and retrospective study, and requirements and key steps in design. A simplified model is given for the formulation of experimental design largely used in the book. Chapter 2 focuses on the issue of bias removal. Randomization and retrospective adjustment, two commonly used methods in reducing bias, are discussed in detail. Chapters 3 and 4 study the control of haphazard variation. Chapter 3 discusses five methods of reducing the effect of haphazard variability—to use more uniform material and more internal replication, to use more experimental units, to use the technique of blocking, to use retrospective adjustment, and to use special models. However, the emphasis has been placed on the method of blocking. Matched pair design and randomized block design are studied in detail in this chapter. Chapter 4 is a continuation of the study of blocking techniques, with Latin squares, incomplete block designs, and crossover designs being covered. Chapters 5 and 6 deal with factorial designs. In Chapter 5 the basic ideas involved in factorial experiments are discussed. They include main effects, interactions, contrasts, and extracting information from fractions of the full factorial designs. In Chapter 6, various more specialized topics related to factorial experiments are covered. They include confounding, factors at more than two levels, orthogonal arrays, split-plot designs, and response surface methods. Taguchi methods are also discussed. Chapter 7 concerns optimal designs. It begins with some simple but motivating examples. Then the general equivalence theorem of Kiefer and Wolfowitz is presented. Algorithms for finding optimal designs are discussed. The issue of optimality under the framework of nonlinear designs, space-filling designs, and Bayesian designs is also addressed. Chapter 8 talks about some additional topics. The issues of number of experimental units and sampling within units are studied first. Then, according to different situations, the following designs are studied: adaptive designs, sequential regression designs, designs for one-dimensional error structure, and spatial designs. Three appendixes cover the material supplementary to the main text. Appendix A presents some important results on the linear model and analysis of variance. Appendix B introduces some key algebraic ideas. Appendix C discusses the use of S-PLUS by providing code for the main examples in the text. In summary, this book is an excellent addition to the literature. It can serve as a cornerstone in a graduate student’s exploration in the theoretical aspects of experimental design and is a valuable reference for statisticians working in medicine, agriculture, the physical sciences, and other areas of biometry and industry.