This article reviews methods for quantitatively measuring metacognition, focusing on the relationship between trial-by-trial accuracy and confidence. Metacognition refers to the ability to assess one's own cognitive processing, such as in perceptual or memory tasks. The authors discuss various measures, including correlation coefficients like phi and gamma, and signal detection theory (SDT) based measures like type 2 d' and ROC analysis. They emphasize that measures of metacognitive sensitivity should be bias-free and distinguish between metacognitive sensitivity (ability to discriminate correct from incorrect judgments), metacognitive bias (overall confidence level), and metacognitive efficiency (sensitivity given task performance). The authors argue that simple correlation measures like phi and gamma do not separate sensitivity from bias, while non-parametric methods like AUROC2 provide bias-free sensitivity measures. They also discuss the importance of controlling for task performance when measuring metacognition and highlight the meta-d' measure as a promising bias-free method. The article also addresses the distinction between metacognitive sensitivity and awareness, noting that metacognitive sensitivity does not necessarily reflect conscious experience. Finally, the authors emphasize the need for bias-free measures in future studies of metacognition and conscious awareness.This article reviews methods for quantitatively measuring metacognition, focusing on the relationship between trial-by-trial accuracy and confidence. Metacognition refers to the ability to assess one's own cognitive processing, such as in perceptual or memory tasks. The authors discuss various measures, including correlation coefficients like phi and gamma, and signal detection theory (SDT) based measures like type 2 d' and ROC analysis. They emphasize that measures of metacognitive sensitivity should be bias-free and distinguish between metacognitive sensitivity (ability to discriminate correct from incorrect judgments), metacognitive bias (overall confidence level), and metacognitive efficiency (sensitivity given task performance). The authors argue that simple correlation measures like phi and gamma do not separate sensitivity from bias, while non-parametric methods like AUROC2 provide bias-free sensitivity measures. They also discuss the importance of controlling for task performance when measuring metacognition and highlight the meta-d' measure as a promising bias-free method. The article also addresses the distinction between metacognitive sensitivity and awareness, noting that metacognitive sensitivity does not necessarily reflect conscious experience. Finally, the authors emphasize the need for bias-free measures in future studies of metacognition and conscious awareness.