§14 Signal Detection Theory — d', Criterion, and ROC
d' = z(H) - z(FA)
c = -½(z(H) + z(FA))
AUC = Φ(d' / √2)
c = -½(z(H) + z(FA))
AUC = Φ(d' / √2)
Signal detection theory separates perceptual sensitivity (d') from response bias (criterion c). d' reflects the intrinsic signal-to-noise ratio; c reflects how high or low the decision criterion is set. The ROC curve plots hit rate vs FA rate across criteria, and the AUC quantifies overall sensitivity.
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