Most readers of this review will be familiar with statistical inference for random sampling based on the Central Limit Theorem and friends. While these techniques sometimes offer reasonable approximations for data from experiments, it is worth knowing what we are approximating. There are exact tests based on permuting the observations to mimic random assignment of treatments, which is the form of randomness relevant to experiments. This has been known since R. A. Fisher’s early work in the last century, but Fisher lacked the computing power to carry out such tests. Their theory was developed anyway, however, and now we so have the computing power to use them.
Today, many college introductory statistics courses include permutation methods. The Common Core Standards adopted for the schools in most states treat inference for experiments via “simulations” which some interpret to indicate some form of permutation test. We can expect these methods to be much more widely used and discussed in the near future.
The word “chronicle” in the title of the book is well-chosen. We find a broadly chronological account of the history of permutation methods. The emphasis is on volume of information rather than on identifying the most important contributions. For instance, the reference list cites 1498 publications.
The authors divide the time period covered into five intervals. Within each interval, they try to identify the main trends of research at that time, and group their reporting accordingly. This can be useful to the person seeking a thorough treatment of a particular research trend, but for individual topics there seems to be little consistency in what gets reported. In some cases there are detailed mathematical explanations and concrete examples, while elsewhere entire paragraphs are but lists of references. One consistency is that there are thumbnail biographies of many of the people who have done research in this area. Your reviewer found many of these interesting, but at times these do seem to take us far afield. Although the book wisely covers developments in computing that made permutation methods practical, it seems a bit of a stretch to include biographies of Bill Gates and the founders of Google. Perhaps the most extravagant digression is a five-page history of the property where Fisher did his early research. On the whole one gets the feeling the authors included everything they unearthed during their research. They are also very generous in citing their own work.
So, we have here a huge amount of information that does not appear to have been critically chosen or interpreted. Still the volume of information to be found here may trump that consideration. The information is not readily available elsewhere. This book would be a great asset to anyone about to do a literature search on some aspect of permutation methods. Despite the claim on the book’s cover, this is for the specialist and not the general reader. In short, a book of great value to a narrow audience.
After a few years in industry, Robert W. Hayden (email@example.com) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.