title: Now you Bayes, now you don't: effects of set-problem and frequency-format mental representations on statistical reasoning.
abstract: People appear to be Bayesian when statistical information is presented in terms of natural frequencies and non-Bayesian when presented in terms of single-event probabilities, unless the probabilities resemble natural frequencies, for example, as chances. The isomorphic format of chances, however, does not always facilitate performance to the extent that the format of natural frequencies does. Prior research has not addressed the underlying mechanism that accounts for this gap despite its theoretical significance. The mechanism explaining this external format gap could lie in the interpretation of the problem as a set-problem, which cues relevant problem model and arithmetic operations (the problem interpretation hypothesis) and/or in the interpretation of the format as frequencies, which may be easier to process (the format interpretation hypothesis). In two parallel experiments, we found support for the problem interpretation hypothesis only: set representations mediated solely the isomorphic format gap (Experiment 1: part A) and accounted for the transfer effect to natural frequencies (Experiment 1: part B); priming set representations improved performance with chances (Experiment 2). We discuss how the supported explanation corroborates the nested-sets rather than the ecological rationality account of statistical reasoning and how it helps explain individual differences in Bayesian reasoning.
authors.affiliation: Department of Psychology, Kingston University, Penrhyn Road, Kingston upon Thames, Surrey, KT1 2EE, London, UK. miroslav.sirota@kingston.ac.uk.
authors.forename: Miroslav
authors.initials: M
authors.lastname: Sirota
authors.affiliation: Institute of Experimental Psychology, Slovak Academy of Sciences, Bratislava, Slovakia.
authors.forename: Lenka
authors.initials: L
authors.lastname: Kostovičová
authors.affiliation: Department of Psychology, Kingston University, Penrhyn Road, Kingston upon Thames, Surrey, KT1 2EE, London, UK.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Vallée-Tourangeau
mesh_terms: D000293:Adolescent; D000328:Adult; D001499:Bayes Theorem; D032882:Comprehension; D005260:Female; D006801:Humans; D008297:Male; D010364:Pattern Recognition, Visual / Q000502:physiology; D011337:Probability Learning; D011340:Problem Solving; D011897:Random Allocation; D060865:Repetition Priming; D012718:Set, Psychology; D014163:Transfer, Psychology; D055815:Young Adult
keywords: Bayesian reasoning; Chances; Format mental representation; Natural frequencies; Problem mental representation