How to train your Bayesian: a problem-representation transfer rather than a format-representation shift explains training effects

People improve their Bayesian reasoning most when they are trained to represent single-event probabilities as natural frequencies; nevertheless, the underlying mechanism of this representational training remains unclear. Several authors suggested that people learn to shift the initial format to natural frequencies, and improve their reasoning because natural frequencies align with an evolutionary designed frequency-coding mechanism—the format-representation shift hypothesis. Alternatively, people may acquire a generic problem representation in terms of nested sets that is then transferred to similar problems—the problem-representation transfer hypothesis. To disentangle the effect of the format shift from problem representation transfer, we devised two types of training with problems featuring a nonfrequency format and a concealed nested-sets structure. Participants learnt the adequate problem representation in both training manipulations, but in only one did they learn, in addition, to shift the format to frequencies. Substantial evidence (BF01 = 5, where BF = Bayes factor) indicates that both types of training improved reasoning in an immediate and a one-week follow-up posttest to the same extent. Such findings support the problem-representation transfer hypothesis because learning an adequate nested-sets problem representation accounts for the performance improvement, whereas the frequency format per se confers no additional benefit. We discuss the implications of these findings for two dominant accounts of statistical reasoning.