In the rating-scale version of SDT, observers respond with confidence ratings rather than binary yes/no decisions. This is equivalent to placing multiple criteria along the internal evidence axis, with each criterion separating adjacent confidence categories. The advantage is that a complete ROC curve can be constructed from a single experimental condition, rather than requiring manipulation of bias across conditions.
Multiple Criteria
P(rating ≥ j | signal) = Φ(d′/2 − cⱼ)
P(rating ≥ j | noise) = Φ(−d′/2 − cⱼ)
Each criterion yields one ROC point
Constructing the ROC
Each criterion divides responses into "would have said yes" and "would have said no." Using criterion j, the hit rate is P(rating ≥ j | signal) and the false alarm rate is P(rating ≥ j | noise). This produces k−1 ROC points, tracing out the ROC curve. More extreme criteria produce conservative points (low hit rate, low false alarm rate); lenient criteria produce liberal points.
Rating-scale data are typically analyzed by fitting signal detection models (equal- or unequal-variance) to the full set of ROC points using maximum likelihood estimation. This provides more precise estimates of sensitivity and the variance ratio than binary data, and allows the researcher to assess the fit of the underlying distributional assumptions.