There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.
Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.
Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach – that is, to incorporate prior knowledge when reasoning with incomplete information – in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli's Fallacy explains why something has gone wrong with how we use data – and how to fix it.
1. What Is Probability?
2. The Titular Fallacy
3. Adolphe Quetelet’s Bell Curve Bridge
4. The Frequentist Jihad
5. The Quote-Unquote Logic of Orthodox Statistics
6. The Replication Crisis/Opportunity
7. The Way Out
Aubrey Clayton is a mathematician who teaches the philosophy of probability and statistics at the Harvard Extension School. He holds a PhD from the University of California, Berkeley, and his writing has appeared in Pacific Standard, Nautilus, and the Boston Globe.
"An entertaining mix of history and science."
– Andrew Gelman, Columbia University
"I like it! Anything that gets people thinking about the uses and abuses of statistics is important and Clayton's book does just this. Fifty years ago E. T. Jaynes opened my eyes to the importance of Bayesian ideas in the real world and this readable account brings these ideas up to date."
– Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University
"This story of the 'statistics wars' is gripping, and Clayton is an excellent writer. He argues that scientists have been doing statistics all wrong, a case that should have profound ramifications for medicine, biology, psychology, the social sciences, and other empirical disciplines. Few books accessible to a broad audience lay out the Bayesian case so clearly."
– Eric-Jan Wagenmakers, coauthor of Bayesian Cognitive Modeling: A Practical Course
"The author writes with style and humor and tries to make the read minimally pedantic."
– Non-Stop Reader
"As well-written as it is fascinating, and for my money is the best single-volume work describing and contributing to the debates in modern statistics on the shelves today. It can be profitably read by those with no background in the field, but will surely contain new ideas for experts as well. Having read the book, I myself will never think about statistics the same way."
– Dominic Klyve, American Mathematical Monthly
"The book is highly accessible [...] Even readers who ultimately disagree with the author's position will still benefit from reading this text."