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Association Schemes: Designed Experiments, Algebra and Combinatorics.

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Association Schemes: Designed Experiments, Algebra and Combinatorics.

Rosemary BAILEY. New York: Cambridge University Press, 2004. ISBN 0-521-82446-X. xviii + 387 pp. $70.00.

A book review frequently tells you what the Preface should but often fails to muster: the coverage of the book, precisely and transparently, so that those who do not know can know what they will know, should they choose to read. That is not necessary here, for Bailey's preface is exactly a conceptual outline of content and interrelationships. Spend 10 minutes reading her preface (available online at http://www.maths.qmw.ac.uk/~rab/Asbook/), and you will know what you are getting. We are free to spend our time discussing who the book is for (and who it is not), the reach of the book's methods (and what they fail to grasp), its placement relative to current trends in statistics, and of course the requisite nitpicking.

Most JASA readers will have completed at least one course in experimental design at the graduate level, with a selection of topics from a standard list including completely randomized designs, randomized complete-block designs, Latin squares, split-plots, fractional factorials, and confounding of factorials into incomplete blocks. For incomplete block designs other than confounded factorials, coverage is typically balanced incomplete block designs (BIBDs), and, if pursued further, partially balanced incomplete block designs (PBIBDs). It is the notion of partial balance that this book explores, thoroughly and exhaustively, for simple and complex block structures with crossing, nesting, and more. However, do not think you...

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