Beyond the primary (type 1) decision of whether a signal is present, observers can also rate their confidence in that decision. These confidence ratings provide a window into metacognition — the ability to monitor and evaluate one's own cognitive processes. Type 2 SDT provides the mathematical framework for analyzing the relationship between confidence and accuracy.
Type 2 SDT and Meta-d′
Type 2: discriminating correct from incorrect responses → meta-d′
Metacognitive efficiency: M_ratio = meta-d′ / d′
M_ratio = 1: metacognitively optimal
M_ratio < 1: metacognitive loss
The meta-d′ framework (Maniscalco & Lau, 2012) provides a signal detection measure of metacognitive sensitivity that is expressed in the same units as type 1 d′. The ratio meta-d′/d′ measures metacognitive efficiency: a ratio of 1 indicates that the observer uses all available perceptual information for confidence judgments; ratios below 1 indicate metacognitive loss.
Applications
The meta-d′ framework has been widely applied to study metacognition in perception, memory, and clinical populations. It has revealed that metacognitive efficiency is relatively stable within individuals across tasks but varies across clinical conditions — patients with lesions to prefrontal cortex show impaired metacognition (low meta-d′/d′) despite intact perceptual sensitivity.