Block designs. Analysis, combinatorics and applications.

*(English)*Zbl 1102.62080
Series on Applied Mathematics (Singapore) 17. Hackensack, NJ: World Scientific (ISBN 981-256-360-1/hbk; 978-981-270-109-1/ebook). xi, 211 p. (2005).

The first author wrote a classic book [Constructions and combinatorial problems in design of experiments. (1971; Zbl 0222.62036)] whose purpose was to discuss the design combinatorics most useful to statisticians, which has proved to be of lasting interest and use also for mathematical researchers in design theory. The present book is intended for researchers working in experimental designs and related areas, and its main objective is “to update the constructions and combinatorial aspects of block designs from the 1971 book, bring together the diversified applications, and elegantly provide the mathematics of statistical analysis of block designs”.

The authors have succeeded in their objective and the new book should be on the desk of any researcher or teacher in statistical analysis or user of block designs. If the first book can be said to have emphasized the mathematical aspects of the constructions, this book can be characterized as emphasizing statistical applications of the constructions. Indeed, an important purpose of the book is to lead the statistical student into more sophisticated areas of the usage of block designs for a very wide range of applications. The book would be very suitable for a seminar or special topics course in the subject.

The chapters are titled: (1) Linear estimation and tests for linear hypotheses; (2) General analysis of block designs; (3) Randomized block designs; (4) Balanced incomplete block designs-analysis and combinatorics; (5) Balanced incomplete block designs – applications; (6) \(t\)-designs; (7) Linked block designs; (8) Partially balanced incomplete block designs; (9) lattice designs; (10) Miscellaneous designs. There are 23 pages of references, an author index, and a subject index. The required background to use this book is modest, some elementary matrix theory on the math side and exposure to mathematical statistics and experimental design on the statistical side.

The authors have succeeded in their objective and the new book should be on the desk of any researcher or teacher in statistical analysis or user of block designs. If the first book can be said to have emphasized the mathematical aspects of the constructions, this book can be characterized as emphasizing statistical applications of the constructions. Indeed, an important purpose of the book is to lead the statistical student into more sophisticated areas of the usage of block designs for a very wide range of applications. The book would be very suitable for a seminar or special topics course in the subject.

The chapters are titled: (1) Linear estimation and tests for linear hypotheses; (2) General analysis of block designs; (3) Randomized block designs; (4) Balanced incomplete block designs-analysis and combinatorics; (5) Balanced incomplete block designs – applications; (6) \(t\)-designs; (7) Linked block designs; (8) Partially balanced incomplete block designs; (9) lattice designs; (10) Miscellaneous designs. There are 23 pages of references, an author index, and a subject index. The required background to use this book is modest, some elementary matrix theory on the math side and exposure to mathematical statistics and experimental design on the statistical side.

Reviewer: Spencer P. Hurd (Charleston)