Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

Cybersecurity research often describes people as understanding internet security in terms of metaphorical mental models (e.g., disease risk, physical security risk, or criminal behavior risk). However, little research has directly evaluated if this is an accurate or productive framework. To assess this question, two experiments asked participants to respond to a statistical reasoning task framed in one of four different contexts (cybersecurity, plus the above alternative models). Each context was also presented using either percentages or natural frequencies, and these tasks (...) were followed by a behavioral likelihood rating. As in previous research, consistent use of natural frequencies promoted correct Bayesian reasoning. There was little indication, however, that any of the alternative mental models generated consistently better understanding or reasoning over the actual cybersecurity context. There was some evidence that different models had some effects on patterns of responses, including the behavioral likelihood ratings, but these effects were small, as compared to the effect of the numerical format manipulation. This points to a need to improve the content of actual internet security warnings, rather than working to change the models users have of warnings. (shrink)