Extended Data Fig. 1: Differences between observed and predicted choice probabilities.

These plots represent for each participant, the difference between the observed and predicted probability of choosing ‘right’ in the second decision, expressed as standardized Pearson residuals. Positive values indicate that the model underestimates the probability, and negative values indicate overestimation. Panel a shows the average residuals after a wrong first decision and panel b after a correct first decision. Blue bars represent the the discrete model (with 2 confidence levels) and the orange bars represent the biased-Bayesian model. Error bands represent bootstrapped standard errors. To facilitate interpretation, blue dots on the bottom denote participants for which the average residuals of the discrete model are smaller than that of the biased-Bayesian model, indicating that the discrete model made predictions that were on average closer to the observed probability. Note that individual data display the same pattern seen in the group data (Fig. 2, Main text), in which the biased-Bayesian model provides a poorer fit to the data, because it tends to more severely underestimate the probability of choosing ‘right’ after a wrong response.