Fair coins tend to land on the same side they started: Evidence from 350,757 flips
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912430356955136 |
|---|---|
| author | Bartoš, František Sarafoglou, Alexandra Godmann, Henrik R. Sahrani, Amir Leunk, David Klein Gui, Pierre Y. Voss, David Ullah, Kaleem Zoubek, Malte J. Nippold, Franziska Aust, Frederik Vieira, Felipe F. 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 |
| author_facet | Bartoš, František Sarafoglou, Alexandra Godmann, Henrik R. Sahrani, Amir Leunk, David Klein Gui, Pierre Y. Voss, David Ullah, Kaleem Zoubek, Malte J. Nippold, Franziska Aust, Frederik Vieira, Felipe F. 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 |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fair coins tend to land on the same side they started: Evidence from 350,757 flips Bartoš, František Sarafoglou, Alexandra Godmann, Henrik R. Sahrani, Amir Leunk, David Klein Gui, Pierre Y. Voss, David Ullah, Kaleem Zoubek, Malte J. Nippold, Franziska Aust, Frederik Vieira, Felipe F. 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 History and Overview Data Analysis, Statistics and Probability Other Statistics 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. |
| title | Fair coins tend to land on the same side they started: Evidence from 350,757 flips |
| topic | History and Overview Data Analysis, Statistics and Probability Other Statistics |
| url | https://arxiv.org/abs/2310.04153 |