Reviewed by David R. Cordie (Edgewood College)
Downey, A.B. 2023. Probably Overthinking It: How to Use Data to Answer Questions, Avoid Statistical Traps, and Make Better Decisions. Univ. of Chicago Press, Chicago, IL. 256 pp. ($14.40 cloth, $14.39 paper/e-book with 40% PS discount.)
Many of us are familiar with the phrase “there are lies, damn lies, and statistics” as a dismissive expression about statistics. The power, and potential misuse, of statistical inference has become all too common in modern social discourse. I think many of us are already cautious of blindly accepting numerical arguments because we are aware of the many paradoxes and traps that statistics can bring. As the subtitle of Allen Downey’s book Probably Overthinking It suggests, we do not need to avoid statistics, just understand them better before acting.
What I liked most about Probably Overthinking It was its singular focus on one thing: statistical paradoxes. After an initial chapter introducing basic concepts, the author summarily describes and breaks down numerous statistical paradoxes that we encounter every day. This is not a work about the nuances of high-end mathematical research, but rather about the counterintuitive statistical results we see in everything from marathon running to COVID tests. The author spends two, sometimes three, chapters on each paradox in roughly the same format. First, introducing a real-life event with a counterintuitive statistical trend. Second, dissecting the problem using current data and step-by-step analysis. And finally, returning to the original example, with the readers renewed understanding of the phenomenon, to explain the results. I found this format easy to follow and relevant to my life. By the end, Downey exemplified multiple cases of the inspection paradox, Preston’s paradox, Berkson’s paradox, base rate fallacy, Simpson’s paradox, as well as others.
As paleontologists, one might think that a book on statistical paradoxes is nice, but what does it have to do with the fossil record? I admit that my interest in this book was not necessarily connected to being a paleontologist. I just like stats. However, after reading it, I see there are many connections to paleontology. One that came to mind was the Berkson paradox and evolution. The Berkson paradox is an observation where a subset of a population has a negative correlation between two values, despite there being a positive correlation in the population overall. The example given in the book is of professional volleyball players and the correlation between height and jumping ability. In the general population, it is not surprising that taller people can jump higher. However, if you look at professional athletes, the opposite is true. Often the tallest players are poor jumpers compared to shorter players. The answer to this paradox is actually very simple. If you were both a poor jumper and short, you probably are not a professional athlete. While it is possible that you could be a giant as well as a fantastic jumper, it is unlikely that you are the best at both traits. Rather, if you are a professional athlete who is short, it makes sense that you are also an amazing jumper.
When reflecting on this paradox, I realized it is very relevant to evolution and ecological tradeoffs. We often see organisms that sacrifice fitness for higher sexual selection rates (think peacocks – lots of pretty feathers but cannot fly well). It might seem strange that there is a negative correlation between these traits because, in general, one is more likely to be alive today if they have higher fitness and more successful reproductive events. But the paradox is resolved when we consider that we are looking only at organisms that have passed the filter of natural selection. Natural selection is like the condition of being a professional athlete while the traits of fitness and sexual selection are analogous to jumping ability and height. If an organism were bad at both, it probably does not exist, but if you are good at one trait, that is often enough for you to survive.
As a teacher, I enjoyed how each explanation of a paradox was accompanied by data and examples from many different fields (sociology, criminology, epidemiology) making it easy to pick an example that fits your interests. Further, Downey meticulously documents where he gets his data for each analysis and has a GitHub repository to reproduce each figure. This might sound like details better left for a peer-reviewed journal, but the presentation is simple and easy to read. In truth, this was a very quick read. I do not consider myself a fast reader, yet I finished this in just two sittings.
I truly enjoyed Allen Downey’s book. It is a refreshing way to look at everyday occurrences and a confidence builder for me as we head into political ad season, which will be rife with statistics. Probably Overthinking It provides a timely message that it is not always the responsibility of statisticians and academics to untangle the chaos of the world. Rather, with a bit of background, we can too.