In 34 short chapters, Prof. Robert Matthews provides an engaging tour of practically relevant topics whose treatment benefits from a little “common sense expressed in numbers”. These topics include lotteries, insurance, casinos, and the law.
This book distinguishes itself favorably from others in its genre. The chapters are well written and relatively concise, making the work ideally suited for readers who prefer to peruse books in the privacy of their restroom. In addition, the work is very much up-to-date: the paperback edition came out in 2017, and many references acknowledge work that was published in the last few years. It is evident that Matthews knows his stuff. It is also refreshing to see that Matthews does not pull any punches; fittingly, his ire is drawn by the multitudes who repeatedly violate and misapply probability theory.
My only misgiving about this book is that it sometimes shuns statistical details. This certainly spurs sales but leaves the statistically savvy reader wanting more. Nevertheless, readers of all backgrounds will find that the book helps them better understand uncertainty.
To provide an idea of Matthews’ lively writing style I’ll provide two representative excerpts. First, in the chapter “A scandal of significance”, Matthews summarizes the plight of the p-value:
“Fisher’s loathing was visceral, although he often tried to disguise this using seemingly dispassionate technical reasons for rejecting Bayesian methods.(9) Having done so, Fisher had no choice but to concoct some non-Bayesian measure of use to researchers trying to make sense of their findings. The result was the p-value, whose notoriously contrived definition reflects its origins: as a doomed attempt to avoid the unavoidable. It’s simply not possible to gauge the probability of a result being the result of a fluke solely by using p-values.”
(p. 170)
footnote 9: J. Aldrich, ‘R A Fisher on Bayes and Bayes’ Theorem’, Bayesian Analysis, 3(1), 2008, pp. 161-70.
And in the chapter “I’m sorry, professor, I just don’t buy it”, Matthews doubles down:
“Since their invention in the 1920s, significance testing and p-values have been confusing students, fooling researchers and misleading the rest of us into seeing ‘significance’ in results that are anything but significant. Ironically, having been invented as a gentle way of weeding out obvious flukes, they have been transformed into the Amazing Baloney Machine, which claims to reveal what to take seriously, but in fact cannot. Whether it’s the results from the latest investigation of a widely studied medical treatment, or an out-of-the-blue claim about something no one’s studied before, it’s all the same to the machine. It just takes the data in, ignores everything else – and gives its pronouncement: either ‘gold dust’ or ‘garbage’. Such an approach is inimical to scientific progress.”
(p. 190)
Before those few notorious p-value apologists saddle up to chastize Matthews for his unkind words, they should realize that his statements echo those from the American Statistical Association, who came out last year to say that “The widespread use of ‘statistical significance’ (generally interpreted as ‘p <= 0.05') as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process." (Wasserstein & Lazar, 2016, p. 131) and that "a p-value near 0.05 taken by itself offers only weak evidence against the null hypothesis" (Wasserstein & Lazar, 2016, p. 132). This last statement is quantified by the Vovk-Sellke maximum p-ratio implemented in JASP.
In sum, this is an insightful book about statistical reasoning – highly recommended.
References
Matthews, R. (2017). Chancing it: The laws of chance and how they can work for you. London: Profile Books.
Wasserstein, R. L., & Lazar, N. A. (2016). The ASA’s statement on p-values: Context, process, and purpose. The American Statistician, 70, 129-133.
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