Children's quantitative Bayesian inferences from natural frequencies and number of chances

- Children's capacity to draw quantitative Bayesian inferences appears to be limited.
- Children perform equally well with natural frequencies and number of chances.
- Children's Bayesian inferences can be improved by fostering extensional reasoning.

Zhu and Gigerenzer (2006) showed that an appreciable number of Chinese children aged between 9 and 12 years old made correct quantitative Bayesian inferences requiring the integration of priors and likelihoods as long as they were presented with numerical information phrased in terms of natural frequencies. In this study, we sought to replicate this finding and extend the investigation of children's Bayesian reasoning to a different numerical format (chances) and other probability questions (distributive and relative). In Experiment 1, a sample of Italian children was presented with the natural frequency version of five Bayesian inference problems employed by Zhu and Gigerenzer (2006), but only a tiny minority of them were able to produce correct responses. In Experiment 2, we found that the children's accuracy, as well as the coherence between their probability judgments, depended on the type of question but not on the format (natural frequency vs. chance) in which information was presented. We conclude that children's competence in drawing quantitative Bayesian inferences is lower than suggested by Zhu and Gigerenzer (2006) and, similarly to what happens with adults, it relies more on a problem representation that fosters an extensional evaluation of possibilities than on a specific numerical format.