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Experimental Design for Formulation

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Wendell F. Smith
Publication Date: 
Number of Pages: 
ASA-SIAM Series on Satistics and Applied Probability 15
[Reviewed by
Gudmund Iversen
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The main thing wrong with this book is the title.  "Experimental Design" tells us the book is about planning of experiments, but "Formulation" is more troublesome.   Luckily, on page 3 we are told: "A formulation is nothing more than a mixture, being composed of two or more components."  With this terminology, the lowly chocolate chip cookie is a mixture (formulation) of several components; such as the chips, flour, sugar, yeast, etc. 

Analyzing formulations raises new statistical issues not present when the elements on which the dependent variable is measured on only one variable.  For example, if the percentage of one component is increased, the percentages of the other components are necessarily affected, since percentages always add up to 100.  Smith gives a very good presentation of the issues involved and how they can be dealt with. 

The book consists of four parts; preliminaries, design, analysis, and special topics.  It covers a great richness of topics within each of the parts.  The first part introduces the idea of a mixture space and discusses linear, quadratic and cubic models together with a discussion of model assumptions.  The design part similarly covers many different designs together with examples of their uses.  The analysis part takes up the building of models, model evaluation, model revision, effects and optimization.  Finally, the last part discusses the inclusion of process variables and a discussion of collinearity.

The book is well written, is a valuable and practical addition to the statistical literature and should fine wide usage by the audience for which it is intended, in spite of its title.

Gudmund Iversen received his PhD in statistics from Harvard University and taught statistics for many years at Swarthmore College until his retirement.

List of Figures; List of Tables; Preface; Part I: Preliminaries. Chapter 1: Introduction; Chapter 2: Mixture Space; Chapter 3: Models for a Mixture Setting; Part II: Design. Chapter 4: Designs for Simplex-Shaped Regions; Chapter 5: Designs for Non-Simplex-Shaped Regions; Chapter 6: Design Evaluation; Chapter 7: Blocking Mixture Experiments; Appendix 7A: Mates for Latin Squares of Order 4 and 5; Part III: Analysis. Chapter 8: Building Models in a Mixture Setting; Chapter 9: Model Evaluation; Chapter 10: Model Revision; Chapter 11: Effects; Chapter 12: Optimization; Part IV: Special Topics. Chapter 13: Including Process Variables; Chapter 14: Collinearity; Bibliography; Index