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Experimental designs: construction and analysis. (Plans d’expériences: construction et analyse.) (French) Zbl 0855.62060
Paris: Tec & Doc Lavoisier. x, 700 p. (1995).
The authors have written a very lucid, useful, and interesting book on the construction and analysis of statistical designs of experiments. It covers many routine topics normally covered in standard textbooks on design of experiments. The material in the book is covered in five chapters, followed by eight useful appendixes.
The first two chapters deal with the basic definitions and concepts of experimental designs, and the primary steps needed to plan, execute, and data analysis. The topics covered in the next chapter are orthogonal designs, factorial and fractional factorial designs, and number of treatment-combinations. It also includes the construction of multifactorial designs, Latin squares, Graeco-Latin squares, $$2^{n - p}$$ designs due to Box and Hunter, tables of orthogonal differences, and some material on rotatable designs. Chapter 4 is set aside for optimality criteria and optimal designs together with an algorithm for constructing such designs. Balanced incomplete block designs (BIBDs), partially balanced incomplete block designs, and Youden squares, and simplex methods as used in response surfaces are also discussed in this chapter. The final Chapter 5 has material on fitting linear models by the Principle of Least Squares, coding the variables, and analysis of variance. Also this chapter deals with testing the adequacy of the fitted model and to search for a better model, analysis of orthogonal designs, finding an optimal response and an algorithm to search for it.
Of the seven hundred pages in this volume, nearly half are distributed amongst the eight very valuable and informative appendixes. The first four appendixes are on groups and finite groups, fields and Galois fields, multifactorial designs, simulation, and independence of the errors of estimation. Admissible regression models together with analysis of variance, and orthogonal difference tables are given in the next two appendixes. BIBDs form the subject matter of appendix 7, while orthogonal designs of resolutions III, IV, V for various symmetrical and asymmetrical factorial experiments are presented in the last appendix covering almost 140 pages. Also included is an index set. The bibliography and references are adequate.
The book is self contained, and the background knowledge needed to read it is a course on statistics and some mathematical maturity. The authors have done a commondable job in presenting with great clarity the basic and fundamental principles of experimental designs, pointing out the strengths and pitfalls of these techniques. An attractive feature of the book is to explain away complex and difficult concepts using illustrative examples and simple heuristic arguments. It is an appealing book for anyone starting with the first course in experimental designs. Being in French, its use in U.S. universities and colleges is going to be extremely limited. No statistical tables are included in this volume. The absence of any set of problems will restrict its use in the classroom. Bringing out its English edition with the inclusion of problem sets would make it a very attractive textbook for a first course in experimental designs. Recommended for all university libraries with generous budgets.

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