1989/12/01 by Persi Diaconis, Frederick Mosteller · 192 citations
Psychology · Decision Sciences · Mathematics · #Social Representations and Identity #Decision-Making and Behavioral Economics #Cognitive Abilities and Testing #Computer science #Statistical physics #Mathematics #Physics
paper · doi:10.2307/2290058
published in Journal of the American Statistical Association 84(408), 853
openalex publication_date 1989/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
This article illustrates basic statistical techniques for studying coincidences. These include data-gathering methods (informal anecdotes, case studies, observational studies, and experiments) and methods of analysis (exploratory and confirmatory data analysis, special analytic techniques, and probabilistic modeling, both general and special purpose). We develop a version of the birthday problem general enough to include dependence, inhomogeneity, and almost and multiple matches. We review Fisher's techniques for giving partial credit for close matches. We develop a model for studying coincidences involving newly learned words. Once we set aside coincidences having apparent causes, four principles account for large numbers of remaining coincidences: hidden cause; psychology, including memory and perception; multiplicity of endpoints, including the counting of “close” or nearly alike events as if they were identical; and the law of truly large numbers, which says that when enormous numbers of events and people and their interactions cumulate over time, almost any outrageous event is bound to occur. These sources account for much of the force of synchronicity.