Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. In a preregistered study 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 exploratory 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. Our data provide compelling statistical support for the DHM physics model of coin tossing.
The relation between religiosity and well-being is one of the most researched topics in the psychology of religion, yet the directionality and robustness of the effect remains debated. Here, we ...adopted a many-analysts approach to assess the robustness of this relation based on a new cross-cultural dataset (
participants from 24 countries). We recruited 120 analysis teams to investigate (1) whether religious people self-report higher well-being, and (2) whether the relation between religiosity and self-reported well-being depends on perceived cultural norms of religion (i.e., whether it is considered normal and desirable to be religious in a given country). In a two-stage procedure, the teams first created an analysis plan and then executed their planned analysis on the data. For the first research question, all but 3 teams reported positive effect sizes with credible/confidence intervals excluding zero (median reported
). For the second research question, this was the case for 65% of the teams (median reported
). While most teams applied (multilevel) linear regression models, there was considerable variability in the choice of items used to construct the independent variables, the dependent variable, and the included covariates.
In Germany, package holidays are an important driver of consumer prices. Several challenges arise when measuring the price development of these bundled travel and accommodation services, such as the ...quality of accommodation and the timing of booking. Statistical practices are currently based on sampling offer prices. By using actual bookings, this paper analyses the possibilities and challenges in compiling a price index out of transaction data for flight package holidays. Our dataset comprises both online bookings and bookings made via stationary travel agencies on a daily basis. The large sample size allows for a disaggregation by individual holiday destination. Several methodological issues such as product definition, the grouping of unstructured text information, and weighting are addressed. Moreover, various index aggregation methods are analysed, which include hedonic regressions, stratification, and also a multilateral index method. Applied to six major holiday destinations for German travellers, all transaction-based methods under consideration exhibit similar price dynamics, pointing to robust results for destinationbased price indicators for package holidays.
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