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Experimental design: a chemometric approach. (English) Zbl 0671.62066

Data Handling in Science and Technology, Vol. 3. Amsterdam etc.: Elsevier. XIII, 285 p.; $ 100.00; Dfl. 225.00 (1987).
An interesting, refreshing in its presentation, and a very useful book on experimental designs. The authors, both analytic chemists, have taken great pains to present in an easy-to-understand fashion the basic concepts of experimental design without involving the rigor and intricacies of mathematics. As the authors mention in the preface, “Experimental design is a...highly developed area, but it is not easily or correctly applied. We believe that one of the reasons experimental design is not used more frequently (and correctly) by scientists is because the subject is usually taught from the point of view of the statistician rather than from the point of view of the researcher”. The intended audience for this book includes advanced undergraduate students, and researchers with minimal background in mathematics. The book is complete in itself, and the chapters from the beginning to the end are highly interdependent on each other. To have useful and gainful insights into the basic concepts of experimental designs, one must go through this book in its entirety.
The contents of this book are divided into 12 chapters. Most of the models discussed here are empirical in nature - dealing primarily with linear models and marix least squares. Chapter 1 is on system theory which has three basic elements: inputs, transforms, and outputs. The next two chapters are set aside for explaining the basic concepts of response surfaces, and elementary statistical ideas to be used in later chapters. Models such as deterministic, probabilistic, proportional, and multiparameter have been carefully explained by using one experiment (in which the experimenter uses only one specified level of the factor \(x_ 1\) and observes the associated response) in chapter 4. The next chapter considers the situations when two different levels of a single factor \(x_ 1\) are used by the experimenter, and includes replication as well as the estimation of purely experimental uncertainty (traditionally known as pure error). Chapter 6 is concerned with testing the adequacy of linear models, whereas the authors discuss at great length in chapter 7 the influence of the experimental design employed by the researcher on the variance-covariance matrix of the estimates.
Chapter 8 is still on a single-factor system, but the factor \(x_ 1\) is chosen at three levels (all same to all distinct). Analysis of variance (ANOVA) for linear models leading to the partitioning of the total sums of squares into various components is the subject matter of chapter 9. The authors bring into focus numerous salient features of experimental design with the help of an example from chemistry in which a single factor is at ten levels.
The last two chapters are set aside for multifactor response surfaces. This refers to the situations when there are two or more than two factors in the experiment. By using two factors in Chapter 11 the authors describe with great clarity the various kinds of response surfaces, rotatable designs, orthogonal designs, and canonical analysis (a valuable technique when used on full second-order polynomial models gives us the essential features of the response surface). The last chapter includes material on confounding, randomization, and some discussion on completely randomized designs, randomized paired comparison designs, and randomized complete block designs.
Each chapter is followed by a list of references and a set of exercises which tend to supplement as well as complement the material presented in the chapters. Numerically solved examples scattered through the book provide a valuable insight into the fundamentals of experimental design. No author index but a useful subject index. Results on matrices which are relevant to the material in the book in appendix A, and two statistical tables on t and F distributions are given at the end of the book. Additional features of the book are concerning the concepts of degrees of freedom and their calculations, sum of squares and degrees of freedom tree, and explaining the effects and usefulness of replication by the use of the J matrix.
There are some drawbacks in the book. It tends to be repetitive at times, and the authors miss including some of the important topics, but these do not affect the value of the book in a significant way. The authors set out to write this book with a definite purpose in mind, and they have succeeded to a great extent. It serves a useful need of applied researchers, and is a welcome addition to the statistical literature. Its reading should prove rewarding to both statisticians and experimenters. This reviewer would highly recommend it to all interested in learning the basic concepts and ideas of experimental design without the sophistication of mathematical tools.
Reviewer: D.V.Chopra

MSC:

62Kxx Design of statistical experiments
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics