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Statistics in Medicine

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MAA Review

Mathematicians who teach statistics are most likely to teach an introductory course for a broad audience. They may rarely see members of the textbook genus “Statistics for _______.” Such texts are usually used in the _______ Department. As a group, they have characteristic strengths and weaknesses. The arguments in favor of the courses that use them include the idea that students will see the specific techniques used in that field, learn how to apply the techniques in that field, and be motivated to learn those techniques by seeing numerous applications to their area of interest. On the other side, such courses run the risk of being taught by people with limited statistical training who are far from the current state of the art in both statistics and statistics pedagogy. (The current state in pedagogy is summarized in the GAISE Report, endorsed by the American Statistical Association.) At their worst, such books may serve as the instrument by which the characteristic statistical misunderstandings and errors of a field are passed on to the next generation. A review of a textbook of this genus needs to evaluate how well it avoids these pitfalls. The book at hand can claim in its favor an author with extensive medical research experience who has also chaired a department of statistics at a large university and been named a fellow of both the American Statistical Association and the Royal Statistical Society.

The first 40 or so pages give excellent (if terse) guidance to the design and planning of a study — topics slighted in many texts. Alas, the remainder of the text feels like a race to cover as many different hypothesis tests as possible. The template is a very brief description of a medical study followed by the computations of a hypothesis test. All issues of how the design or data gathering process might nuance our conclusions are ignored, rending those first 40 pages somewhat moot.

Assumptions are stated for most of the tests but handled inconsistently in examples. As one instance, the regression assumptions include the rarely stated one that the independent variable is measured without error (which is why the least squares method minimizes the errors in the dependent variable). Yet a few pages later an example appears with data that clearly violate the stated assumption that the variance of y does not depend on x. (One could rightly argue that assumption is needed only for inference, not merely fitting a line, but the text does not make that distinction.) In many other places, nonparametric tests are used when data appear to violate the normality assumption, which is valid, but nearly doubles the number of tests the reader has to contend with.

On the whole, the bulk of the text is reminiscent of a college bookstore study guide that focuses on crunching the numbers, but with far more topics covered and far fewer examples and exercises per topic. The frequent appearance of formulae with numbers plugged in suggests a hand calculator is the technology of choice, though software is mentioned for the scarier techniques.

Mathematics majors may learn something from working through a numerical example, but it seems unlikely that those to whom this text is directed would find the arithmetic enlightening. The examples do frequently use real data with brief context. Although the book claims to require no prerequisites, the reader with no foundation in the concepts of statistics or the complex logic of inference will not gain it here.

So, given such a mixed review, is there a place for this text? That place would seem to be as a reference for someone in medicine who has a sound knowledge of basic statistics (say a course matching the GAISE Report) and a good software package and who needs to look up an unfamiliar test or find a medical example. If one teaches a general course with a significant number of students with medical interests, this book could also provide supplementary readings or examples. (Note that the many medical examples are not explained in layperson’s terms, so those without a medical background may need some assistance.) Recommended as a reference but not as a text for beginners.

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.

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