Under review is a Dover reprint of a book originally published in 1969. That and the title immediately raise two concerns. Is the book sufficiently up to date? Is the book, like too many other books about applying statistics to subject X, a guide to how to commit the statistical errors that are a tradition in that field? A partial answer to both questions is that the authors appear to really know their statistics, and their advice is in many respects more up to date than the advice given in some recent introductory textbooks. However, the authors themselves admit that were they to revise this book today they would include more information on use of the computer and fewer of the old and numerically unstable "computational" formulae.

The text is intended for advanced undergraduate or graduate students. Topical coverage includes most of a first course in statistics, covered in about 150 pages. This seems too long for a review but too short for a first exposure to this material. Next come about 100 pages on analysis of variance followed by 60 pages on regression. Textbooks that cover all this material often run to 1000 pages or more, so it goes without saying that the present treatment is terse. But it is not quite as terse as the page counts suggest, especially in the sections that do not overlap an introductory course. There are no color pictures or wide margins full of decorations, no sections on software, nothing at the ends of chapters but a few exercises. On the other hand, a great deal of space is devoted to getting the arithmetic done with a basic scientific calculator. The most frightening of these is a five-page computation of a two-way analysis of variance. Many students will also be frightened by the algebraic expectations, with derivations and manipulations of single and double summations common.

There are a number of interesting exercises and examples that seem quite modern, as well as many real data sets from the biological sciences. Unfortunately, most of the data might almost as well be made up numbers. Very little context is given on the meaning of the data or the purpose of the study. Students are simply asked to carry out the latest procedure on the numbers given. Answers are provided for many problems but they usually consist of a number or two. There is no checking of assumptions or interpretation of the results in context. Experiments are treated as a type of sampling.

There are two areas where the authors deviate from what one sees in most textbooks. They suggest that simple linear regression is misapplied to situations where both variables are subject to error. They are essentially correct though their advice is fairly conservative. They also use what they call a "G test" in the contexts where most texts use chi-squared. Again they are technically correct, but the two methods differ only for samples small enough that today we can use software to get even more precise answers. However, if you are not using such software, G is a good alternative to chi-squared.

While this was no doubt an excellent text in 1969, it is hard to say just where it fits in today. The mathematical level is quite high for current American undergraduates who are not majoring in the mathematical sciences. There are several introductory statistics textbooks that do much better on technology and pedagogy. The book includes many real biological datasets, but they are so sketchily presented that about all they convince one of is that people gather biological data. Rarely is the data used to answer an interesting scientific question. Still, the book has many interesting insights. It would be an easy read for a mathematician and it does provide an inexpensive way to access some of the mathematics behind the introductory course and a few additional topics just beyond the introductory course. Recommended to mathematicians with little background in statistics who are teaching an introductory statistics course from an excellent modern textbook such as any of those by David Moore.

After a few years in industry, Robert W. Hayden (bob@statland.org) 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.