Fig. 3: The relationship between Type-I bound efficiency and Type-II efficiency.

a Average proportion correct in each condition of the Stopping task. The horizontal red lines subtend the target performance level in each condition. Error bars show 95% within-subjects (thick) and between-subjects (thin) confidence intervals n = 20. The red circles show the predicted performance based on the fitted parameters of the model. b Average proportion of trials by the number of samples the observers chose to respond to in each condition of the Stopping task. Vertical dashed lines show the average median number of samples. Red circles show the predicted median number of samples based on the fitted parameters of the model. c Proportion correct (top), decision evidence (bottom left) and number of samples (bottom right) by confidence rating in the Replay task. Error bars show 95% within-subjects confidence intervals (n = 20), and red circles show the predicted performance at each confidence level based on the fitted parameters of the model. d Each observer’s bound efficiency (x-axis) by their Type-II efficiency (y-axis) and the line minimising the perpendicular distance from these points, here shown excluding two outlier participants (open circles) whose optimal bound was estimated using maximum performance rather than 85% correct (y = 1.5× + 0.2, p-value for slope = 0.026, one-sided, based on bootstrapping, with outlier participants removed).