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.

"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." - American Mathematical Monthly

"A timely story, well-told. It makes a compelling case for a shake-up in the world of statistics that may just be strident enough to spark change." - MAA Reviews

"The author writes with style and humor and tries to make the read minimally pedantic." - Non-Stop Reader

"The book is highly accessible. . . . Even readers who ultimately disagree with the author's position will still benefit from reading this text." - Choice

"Bernoulli’s Fallacy will be of use to readers of any mathematical background who wish to understand not only the math but also the motivations behind the rising Bayesian wave. It is a vivid, nontechnical look at the bees in the contemporary statistician’s bonnet." - H-Sci-Med_Tech

"Thrilling...The specialists and laymen alike will judge the value of the contents of the book, in the very affirmative." - zbMath