Bernoulli’s Fallacy
Statistical Illogic and the Crisis of Modern Science, Columbia University Press (excerpt)
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There is a catastrophic error in the logic of the standard statistical methods in almost all the sciences. As science has become increasingly data-driven, this foundational crack has spread into a reproducibility crisis threatening to bring down entire disciplines of research. Outside of science, we see the same fallacies in medicine, law, and public policy, often with disastrous consequences.
At the heart of the problem is a misunderstanding of the quantification of chance — that is, probability — and its role in drawing inferences from data, a mistake that was present from probability’s beginnings in the seminal work of 17th century mathematician Jacob Bernoulli. If statistics never quite made sense to you, Bernoulli’s Fallacy might be why.
How did we get here? The story of probability is one of politics, theology, and feuds between competing schools. For the last hundred years, the wrong school has won. This was a victory not on mathematical merits but due to historical time and place, grand personalities, and some of our worst human tendencies. In service to a sociopolitical agenda, the most influential statisticians of the 19th and 20th centuries claimed statistics as purely objective, a promise it simply couldn’t deliver on, and we’re still paying the price.
Bernoulli’s Fallacy is the story of this mistaken idea of probability, how it became embedded in modern statistics, and the ramifications it has in science, social justice, and everywhere else we use data to draw conclusions about the world. Which is to say, almost everywhere.
Praise
An entertaining mix of history and science.
/Andrew Gelman, Higgins Professor of Statistics, Professor of Political Science and director of the Applied Statistics Center, Columbia University
Bernoulli’s Fallacy is 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, Central Washington University, in The American Mathematical Monthly
Aubrey Clayton’s “Bernoulli’s Fallacy” is not here to make friends;… 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.
/Sara Stoudt, Bucknell University, in MAA Reviews, Mathematical Association of America
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, Professor of Psychology, University of Amsterdam, Coauthor of Bayesian Cognitive Modeling: A Practical Course
