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Scientific Inference: Learning from Data

Simon Vaughan
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Robert W. Hayden
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On offer is everything physics majors need to know about statistics in about 200 pages. This consists of bits and pieces snatched from an introductory statistics course and a mathematical statistics course — perhaps three semesters of material. Included are most of the tests and intervals from a first course as well as lots of multiple integrals and maximum likelihood estimators. It sounds like a questionable enterprise, but the physicists do have a point. The most common introductory statistics course offered in mathematics departments is populated with students shaky in basic algebra. Too often these courses degenerate into a struggle to get through the arithmetic. Since few physics majors struggle with arithmetic, physics faculty may well be reluctant to devote three credit hours to that task.

On the other hand, tossing together bits and pieces and focusing primarily on computations runs the risk of ignoring the rudiments of statistical thinking. On that count, the text at hand is a curious mix of success and failure.

Prerequisites are multivariable calculus and linear algebra (as well as a fair amount of physics to follow the examples). The book is written in a fairly clear but telegraphic style. This keeps the page count down, but perhaps at the expense of readers skimming along the surface of the subject. Likewise, there are no statistical exercises save things left to the student to complete. The book does include an introduction to the statistical programing language R which is used effectively throughout, again with a cost: even fewer pages devoted to the statistics. There are some exercises in using R.

Chapters end with a summary and brief reference list. Within the chapters are a few examples. These often use historical datasets from physics and the quality is excellent but the number too few to provide a broad understanding. Many minor examples or asides live in “boxes” which get laid out like figures, meaning that they can be far from the discussion they exemplify. As a result, managing the actual figures becomes even more difficult, resulting in considerable interruption of flow. There are some distressing errors. Already on page 4 there is a botched attempt to prove there are infinitely many prime numbers. We are not talking about Bourbaki rigor here — Euclid got this right 2400 years ago. Elsewhere open intervals include their endpoints, significance level is equated to confidence level, and so on.

The biggest loss is in the development of underlying concepts. Sampling distributions are a difficult idea even for students who can do arithmetic. In this book they are covered by a few sentences here and there. Being sketchy about where the techniques come from results in being sketchy about underlying assumptions and the interpretation of results. Assumption checking is hit-or-miss, with normal errors usually assumed without question or investigation.

On smaller issues the book has many virtues. There is extensive coverage of different types of graphical display with unusually good advice on when to use each type. There are many bits of advice on how to think about things that introductory texts could well adopt, such as seeing a standard deviation as a typical deviation from the mean. This perhaps reflects a physicist’s prejudice that numbers should mean something! There are similar bits on the connections between various methods such as pointing out how the test for a single mean is a special case of comparing the means of two independent samples, which is in turn a special case of regression. The book is worth reading for these alone.

Perhaps the best reason for mathematicians and statisticians to read this book is to get an idea of what physicists think they want in the way of statistics. Theirs is a mix of misguided and legitimate demands. Generally, mathematics departments offering introductory statistics courses serve a wide range of disciplines, many of whom question whether a single course can be right for all the majors served. When those perceptions are not addressed, those disciplines are likely to demand their own course with a textbook similar to the one at hand.

Finally, on a personal note, your reviewer was constantly reminded in reading this book that he began college as an engineering major. That required four semesters of physics. Wouldn’t it have been great if someone had put all an engineer needed to know about physics into a 200 page book covered in one course in an engineering department? If nothing else, such a possibility might help the author of this book to understand its getting mixed reviews from statisticians or mathematicians.

After a few years in industry, Robert W. Hayden ( 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 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.

1. Science and statistical data analysis
2. Statistical summaries of data
3. Simple statistical inferences
4. Probability theory
5. Random variables
6. Estimation and maximum likelihood
7. Significance tests and confidence intervals
8. Monte Carlo methods