Figure 2. High threshold/signal-detection theory and the receiver operating characteristic.

aThe high threshold/signal-detection representation³⁰ of a strong memory condition that involves both recollection and familiarity. Recollection occurs with some discrete probability (R; in this example, R = 0.5). When a test item generates recollection, a ‘high confidence old’ decision (which is equivalent to a confidence rating of six on a six-point scale) is made. When a test item fails to generate recollection (a situation that occurs with probability equal to 1 − R), the decision is based on familiarity. Decisions based on familiarity are characterized by a signal-detection model in which the targets (the old items) and foils (the new items) are presumed to have different average levels of familiarity but equivalent variances. A test item that generates a familiarity value exceeding a criterion value (indicated by the solid vertical line labelled c) is declared to be ‘old’. Otherwise, the test item is declared to be ‘new’. Thus, whereas most confidence ratings of six are based on recollection in this example (the 50% of the targets that are recollected receive this rating), a few additional ratings of six are based on familiarity. The right-hand panel shows the predicted asymmetrical ROC curve, which is similar to the asymmetrical ROC curve predicted by the traditional signal-detection model when memory is strong (FIG. 1a). b. The high threshold/signal-detection representation of a condition in which recollection is not involved (that is, in which R = 0) but familiarity can be used to discriminate targets and foils. The right-hand panel shows the predicted symmetrical ROC curve, which is similar to the symmetrical ROC curve predicted by the traditional signal-detection model when memory is weak (FIG. 1b). Although the high-threshold/signal-detection model fits ROC data reasonably well, recent findings favour the traditional signal-detection model³⁴–³⁷.