Fig. 1.

ROCs in extant confidence-ratings recognition memory tasks show curvature. (A) Points are data from Slotnick and Dodson (9), where the task was yes/no memory recognition. Dashed and solid lines show the best fit of a discrete-state model with and without the certainty assumption, respectively. (B) Points are data from Qin et al. (27), where the task was 2AFC source-memory recognition. Dashed and solid lines show the best fit of a discrete-state model with and without the certainty assumption, respectively. (C) A discrete-threshold model with the certainty assumption. The figure shows the case for four response options: sure new, maybe new, maybe old, and sure old, and detection leads to highest-confidence responses (the certainty assumption). Parameters d_s and d_n denote the probability of detection for old and new items, respectively. Parameters γ₁, … , γ₄ denote the probability of making a response conditional on guessing. (D) A more general discrete-state model without the certainty assumption. Parameters α₁, … , α₄ and β₁, … , β₄ denote the probability of making a response conditional on detecting an old or new item, respectively.