Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips

• 成果类型: Article; Early Access
• 署名作者: Bartos, Frantisek; Sarafoglou, Alexandra; Godmann, Henrik R.; Sahrani, Amir; Leunk, David Klein; Gui, Pierre Y.; Voss, David; Ullah, Kaleem; Zoubek, Malte; Nippold, Franziska; Aust, Frederik; Vieira, Felipe Fontana; Islam, Chris-Gabriel; Zoubek, Anton J.; Shabani, Sara; Petter, Jonas; Roos, Ingeborg B.; Finnemann, Adam; Lob, Aaron B.; Hoffstadt, Madlen F.; Nak, Jason; de Ron, Jill; Derks, Koen; Huth, Karoline; Terpstra, Sjoerd; Bastelica, Thomas; Matetovici, Magda; Ott, Vincent L.; Zetea, Andreea S.; Karnbach, Katharina; Donzallaz, Michelle C.; John, Arne; Moore, Roy M.; Assion, Franziska; van Bork, Riet; Leidinger, Theresa E.; Zhao, Xiaochang; Motaghi, Adrian Karami; Pan, Ting; Armstrong, Hannah; Peng, Tianqi; Bialas, Mara; Pang, Joyce Y. -C.; Fu, Bohan; Yang, Shujun; Lin, Xiaoyi; Sleiffer, Dana; Bognar, Miklos; Aczel, Balazs; Wagenmakers, Eric-Jan
• 署名单位: University of Amsterdam; University of Amsterdam; Universitat Kassel; KU Leuven; University of Gottingen; Hasselt University; Justus Liebig University Giessen; University of Amsterdam; University of Amsterdam; University of Zurich; Nyenrode Business University; University of Amsterdam; Vrije Universiteit Amsterdam; Utrecht University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Biology (INSB); Institut National de la Sante et de la Recherche Medicale (Inserm); Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Amsterdam; Vrije Universiteit Amsterdam; Radboud University Nijmegen; Eotvos Lorand University; Eotvos Lorand University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2516210
• 发表日期: 2025
• 关键词: Bias

摘要

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. We collected 350,757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Diaconis, Holmes, and Montgomery (DHM; 2007). The model asserts that when people flip an ordinary coin, it tends to land on the same side it started. Our data support this prediction: the coins landed on the same side more often than not, Pr(same side)=0.508, 95% credible interval (CI) [0.506, 0.509], BFsame-side bias=2359. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias. Our data also confirmed the generic prediction that when people flip an ordinary coin-with the initial side-up randomly determined-it is equally likely to land heads or tails:Pr(heads)=0.500, 95% CI [0.498, 0.502], BFheads-tails bias=0.182. Additional analyses revealed that the within-people same-side bias decreased as more coins were flipped, an effect that is consistent with the possibility that practice makes people flip coins in a less wobbly fashion. Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.