*Combinatorics of Experimental Design*

*https://en.wikipedia.org/wiki/Combinatorics_of_Experimental_Design*

* Combinatorics of Experimental Design* is a textbook on the
design of experiments, a subject that connects applications in
statistics to the theory of
combinatorial mathematics. It was written by mathematician
Anne Penfold Street and her daughter, statistician
Deborah Street, and published in 1987 by the
Oxford University Press under their
Clarendon Press 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 squares and
mutually orthogonal Latin squares. Other chapters cover
resolvable block designs,
finite geometry, symmetric and asymmetric factorial designs, and partially balanced incomplete block designs.^{
[1]}^{
[2]}

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.^{
[1]}^{
[2]} The coverage of the topics in the book includes examples, clearly written proofs,^{
[3]} historical references,^{
[2]} and exercises for students.^{
[4]}

## 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 and
linear models, but some topics touch on
abstract algebra and
number theory as well.^{
[1]}^{
[2]}^{
[4]}

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.^{
[2]}
And
Marshall Hall, reviewing the book, called it "very readable" and "very satisfying".^{
[3]}

## 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.^{
[1]} However, it omits several other topics that were included in Rao's more comprehensive text.^{
[4]}

## See also

*The Design of Experiments*(1935), by Ronald Fisher

## References

- ^
^{a}^{b}^{c}^{d}Iyer, Hari K. (March 1989), "Review of*Combinatorics of Experimental Design*",*Journal of the American Statistical Association*,**84**(405): 333, doi: 10.2307/2289885, JSTOR 2289885 - ^
^{a}^{b}^{c}^{d}^{e}Chopra, D. V., "Review of*Combinatorics of Experimental Design*",*zbMATH*, Zbl 0622.05001 - ^
^{a}^{b}Hall, Marshall Jr. (January–February 1989), "Review of*Combinatorics of Experimental Design*",*American Scientist*,**77**(1): 91, JSTOR 27855619 - ^
^{a}^{b}^{c}Notz, William I. (1988), "Review of*Combinatorics of Experimental Design*",*Mathematical Reviews*, MR 0908490