''Combinatorics of Experimental Design'' is a textbook on the

design of experiments The design of experiments (DOE), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. ...

, a subject that connects applications in

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

to the theory of

combinatorial mathematics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

. It was written by mathematician

Anne Penfold Street Anne Penfold Street (1932–2016) was one of Australia's leading mathematicians, specialising in combinatorics. She was the third woman to become a mathematics professor in Australia, following Hanna Neumann and Cheryl Praeger. She was the auth ...

and her daughter, statistician Deborah Street, and published in 1987 by the

Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

under their

Clarendon Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

imprint.

Topics

The book has 15 chapters. Its introductory chapter covers the history and applications of experimental designs, it has five chapters on balanced incomplete block designs and their existence, and three on

Latin square Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion o ...

s and

mutually orthogonal Latin squares In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are ...

. Other chapters cover resolvable block designs,

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

, symmetric and asymmetric factorial designs, and partially balanced incomplete block designs. After this standard material, the remaining two chapters cover less-standard material. The penultimate chapter covers miscellaneous types of designs including circular block designs, incomplete Latin squares, and serially balanced sequences. The final chapter describes specialized designs for agricultural applications. The coverage of the topics in the book includes examples, clearly written proofs, historical references, and exercises for students.

Audience and reception

Although intended as an advanced undergraduate textbook, this book can also be used as a graduate text, or as a reference for researchers. Its main prerequisites are some knowledge of

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

and

linear model In statistics, the term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, t ...

s, but some topics touch on

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

as well. Although disappointed by the omission of some topics, reviewer D. V. Chopra writes that the book "succeeds remarkably well" in connecting the separate worlds of combinatorics and statistics. And Marshall Hall, reviewing the book, called it "very readable" and "very satisfying".

Related books

Other books on the combinatorics of experimental design include ''Statistical Design and Analysis of Experiments'' (John, 1971), ''Constructions and Combinatorial Problems in Design of Experiments'' (Rao, 1971), ''Design Theory'' (Beth, Jungnickel, and Lenz, 1985), and ''Combinatorial Theory and Statistical Design'' (Constantine, 1987). Compared to these, ''Combinatorics of Experimental Design'' makes the combinatorial aspects of the subjects more accessible to statisticians, and its last two chapters contain material not covered by the other books. However, it omits several other topics that were included in Rao's more comprehensive text.

References

{{reflist, refs= {{citation, first=D. V., last=Chopra, title=Review of ''Combinatorics of Experimental Design'', journal=

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

, zbl=0622.05001 {{citation, first=William I., last=Notz, year=1988, title=Review of ''Combinatorics of Experimental Design'', journal=

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

, mr=0908490 {{citation, last=Hall, first=Marshall Jr., authorlink=Marshall Hall (mathematician), date=January–February 1989, issue=1, journal=

American Scientist ''American Scientist'' (informally abbreviated ''AmSci'') is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Honor Society. In the beginning of 2000s the headquarters was moved to ...

, jstor=27855619, page=91, title=Review of ''Combinatorics of Experimental Design'', volume=77 {{citation, last=Iyer, first=Hari K., date=March 1989, doi=10.2307/2289885, issue=405, journal=

Journal of the American Statistical Association The ''Journal of the American Statistical Association'' is a quarterly peer-reviewed scientific journal published by Taylor & Francis on behalf of the American Statistical Association. It covers work primarily focused on the application of statis ...

, jstor=2289885, page=333, title=Review of ''Combinatorics of Experimental Design'', volume=84 Design of experiments Mathematics textbooks Statistics books 1987 non-fiction books Clarendon Press books

Topics

Audience and reception

Related books

See also

References