Type 2 receiver operating characteristic ($(P(C\ge t\mid Y=0),P(C\ge t\mid Y=1))$)

A receiver operating characteristic treating high confidence as a prediction that a first-order answer was correct. Varying confidence threshold $t$ traces the false-positive and true-positive probabilities in the displayed expression. Raw discrimination can depend on first-order task performance; it is not automatically a performance-independent measure of monitoring quality.