Datasets and Codebook for three studies on "Bayesian reasoning without numbers: Are proportions more natural than probabilities?"

Bayesian reasoning requires the processing of data in probabilistic situations to revise risk estimations. Research has shown that this is difficult when data is presented as single-event probabilities; the multiplicative combination of priors and likelihoods often is disregarded, resulting in erroneous strategies such as prior neglect or averaging. Proportions (relative frequencies) are computationally equivalent to probabilities: they also require a multiplicative combination. However, proportions are connected to natural mental representations (ratio sense). More specifically, mental representations of nested proportions (e.g., 70% of 20%) allow for mental operations that correspond to multiplicative combinations. In three experimental studies, we avoided numerical calculations and focused on the conceptual understanding underlying Bayesian reasoning by administering tasks with bar chart representations without numbers. In all studies, we compared two conditions: the tasks were either verbally framed in terms of proportions or in terms of single-event probabilities. The studies revealed that the framing had no substantial effect on whether participants combined priors and likelihoods or neglecting part of the information. However, the findings supported our hypothesis that the framing impacts how the information is combined. In line with our hypothesis, proportions increased the correct Bayesian judgment and reduced an incorrect averaging strategy – a strategy for combining information that was predominant with single-event probabilities. Thus, proportions appear as a natural view on combining information in Bayesian situations. peerReviewed