Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations

Participant recruitment methods and statistical reasoning performance

Optimal Bayesian reasoning performance has reportedly been elusive, and a variety of explanations have been suggested for this situation. In a series of experiments, it is demonstrated that these difficulties with replication can be accounted for by differences in participant-sampling methodologies. Specifically, the best performances are obtained with students from top-tier, national universities who were paid for their participation. Performance drops significantly as these conditions are altered regarding inducements (e.g., using unpaid participants) or participant source (e.g., using participants from a second-tier, regional university). Honours-programme undergraduates do better than regular undergraduates within the same university, paid participation creates superior performance, and top-tier university students do better than students from lower ranked universities. Pictorial representations (supplementing problem text) usually have a slight facilitative effect across these participant manipulations. These results indicate that studies should take account of these methodological details and focus more on relative levels of performance rather than absolute performance