title: Natural frequencies improve Bayesian reasoning in simple and complex inference tasks.
abstract: Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions-three cue values, three hypotheses, two cues, or three cues-by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought.
authors.affiliation: Faculty of Business and Economics (HEC Lausanne), University of Lausanne Lausanne, Switzerland.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Hoffrage
authors.affiliation: Mathematics Education, Faculty of Mathematics, University of Regensburg Regensburg, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Krauss
authors.affiliation: Institute of Mathematics, Ludwigsburg University of Education Ludwigsburg, Germany.
authors.forename: Laura
authors.initials: L
authors.lastname: Martignon
authors.affiliation: Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development Berlin, Germany.
authors.forename: Gerd
authors.initials: G
authors.lastname: Gigerenzer
keywords: Bayesian inference; fast-and-frugal trees; instruction; natural frequencies; representation of information; task complexity; visualization