Fair coins tend to land on the same side they started: Evidence from 350,757 flips
Abstrak
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 -- DHM estimated the probability of a same-side outcome to be about 51\%. Our data lend strong support to this precise prediction: the coins landed on the same side more often than not, $\text{Pr}(\text{same side}) = 0.508$, 95\% credible interval (CI) [$0.506$, $0.509$], $\text{BF}_{\text{same-side bias}} = 2359$. 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: $\text{Pr}(\text{heads}) = 0.500$, 95\% CI [$0.498$, $0.502$], $\text{BF}_{\text{heads-tails bias}} = 0.182$. Furthermore, this lack of heads-tails bias does not appear to vary across coins. 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.
Topik & Kata Kunci
Penulis (50)
František Bartoš
Alexandra Sarafoglou
Henrik R. Godmann
Amir Sahrani
David Klein Leunk
Pierre Y. Gui
David Voss
Kaleem Ullah
Malte J. Zoubek
Franziska Nippold
Frederik Aust
Felipe F. Vieira
Chris-Gabriel Islam
Anton J. Zoubek
Sara Shabani
Jonas Petter
Ingeborg B. Roos
Adam Finnemann
Aaron B. Lob
Madlen F. Hoffstadt
Jason Nak
Jill de Ron
Koen Derks
Karoline Huth
Sjoerd Terpstra
Thomas Bastelica
Magda Matetovici
Vincent L. Ott
Andreea S. Zetea
Katharina Karnbach
Michelle C. Donzallaz
Arne John
Roy M. Moore
Franziska Assion
Riet van Bork
Theresa E. Leidinger
Xiaochang Zhao
Adrian Karami Motaghi
Ting Pan
Hannah Armstrong
Tianqi Peng
Mara Bialas
Joyce Y. -C. Pang
Bohan Fu
Shujun Yang
Xiaoyi Lin
Dana Sleiffer
Miklos Bognar
Balazs Aczel
Eric-Jan Wagenmakers
Akses Cepat
- Tahun Terbit
- 2023
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓