title: Natural frequencies facilitate diagnostic inferences of managers.
abstract: In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in terms of probabilities or percentages. Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates. The present research replicates the beneficial effect of natural frequencies with four tasks from the domain of management, and with management students as well as experienced executives as participants. The percentage of Bayesian responses was almost twice as high when information was presented in natural frequencies compared to a presentation in terms of percentages. In contrast to most tasks previously studied, the majority of numerical responses were lower than the Bayesian solutions. Having heard of Bayes' rule prior to the study did not affect Bayesian performance. An implication of our work is that textbooks explaining Bayes' rule should teach how to represent information in terms of natural frequencies instead of how to plug probabilities or percentages into a formula.
authors.affiliation: Department of Organizational Behavior, Faculty of Business and Economics, University of Lausanne , Lausanne, Switzerland.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Hoffrage
authors.affiliation: Department of Organizational Behavior, Faculty of Business and Economics, University of Lausanne , Lausanne, Switzerland.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Hafenbrädl
authors.affiliation: International Institute for Management Development , Lausanne, Switzerland.
authors.forename: Cyril
authors.initials: C
authors.lastname: Bouquet
keywords: applied business statistics; bayesian inference; executives; management; natural frequency; representation format; updating beliefs