Measures of metacognition on signal-detection theoretic models

Analyzing metacognition, specifically knowledge of accuracy of internal perceptual, memorial, or other knowledge states, is vital for many strands of psychology, including determining the accuracy of feelings of knowing and discriminating conscious from unconscious cognition. Quantifying metacognitive sensitivity is however more challenging than quantifying basic stimulus sensitivity. Under popular signal-detection theory (SDT) models for stimulus classification tasks, approaches based on Type II receiver-operating characteristic (ROC) curves or Type II d-prime risk confounding metacognition with response biases in either the Type I (classification) or Type II (metacognitive) tasks. A new approach introduces meta-d': The Type I d-prime that would have led to the observed Type II data had the subject used all the Type I information. Here, we (a) further establish the inconsistency of the Type II d-prime and ROC approaches with new explicit analyses of the standard SDT model and (b) analyze, for the first time, the behavior of meta-d' under nontrivial scenarios, such as when metacognitive judgments utilize enhanced or degraded versions of the Type I evidence. Analytically, meta-d' values typically reflect the underlying model well and are stable under changes in decision criteria; however, in relatively extreme cases, meta-d' can become unstable. We explore bias and variance of in-sample measurements of meta-d' and supply MATLAB code for estimation in general cases. Our results support meta-d' as a useful measure of metacognition and provide rigorous methodology for its application. Our recommendations are useful for any researchers interested in assessing metacognitive accuracy.