The effects of mental steps and compatibility on Bayesian reasoning

Four laboratory studies were conducted to test the hypothesis that correct Bayesian reasoning can be predicted by two factors of task complexity --- the number of mental steps required to reach the normative solution, and the compatibility between the framing of data presented and the framing of the question posed. The findings show that participants performed better on frequency format questions only when one mental step was required to solve the task and when the data were in a compatible frequency format. By contrast, participants performed more poorly on more complicated tasks which required more mental steps (in a compatible frequency or probability format) or when the data and question formats were incompatible (Studies 1 and 2). Incompatibility between data and question formats was also associated with higher reaction times (Study 2b). Furthermore, on problems that incorporated incompatibility between the data sample size and the target (question) sample size, participants performed better on the probability question than the frequency question, regardless of data format (Study 3). The latter findings highlight the ecological advantage of translating data into probability terms, which are normalized in a range between 0 and 1, and thus can be transferred from one situation to another.