Analysing 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-operator Keywords: metacognition; signal-detection theory; modeling; meta-d ′ ; confidence; discrimination 3 Metacognition, and in particular the ability to assess the accuracy of knowledge states, is fundamental to understanding executive processes (e.g. Koriat, 2007) that G is sensitive to bias (i.e. a priori disposition to respond in one way or another), and thus not ideal. They recommended a signal detection approach instead. Here we will pursue the use of signal detection theory (SDT) to determine the suitability of the different signal detection measures of association available for assessing metacognition.SDT has been a major innovation in psychology and neuroscience, proving extremely useful for measuring stimulus discrimination accuracy independently of response bias (Lau & Passingham, 2006;Lau, 2008;Macmillan & Creelman, 2005). In a typical stimulus discrimination study subjects encounter many trials, in each of which they make a forced-choice response, classifying a stimulus as either present versus absent, or as 'type A' versus 'type B'. SDT posits that the discrimination decision on this so-called 'type I' task is based on internally generated evidence that follows distinct Gaussian probability distributions in the respective scenarios of 'absent' and 'present' (see 4 Figure 1 and e.g. Macmillan & Creelman, 2005). The fundamental SDT measure of discrimination performance, 'type I d-prime', is defined theoretically as the difference between the means divided by the standard deviation of the 'absent' distribution. 1 SDT further assumes a decision threshold (or criterion) determining whether the subject responds 'absent' or 'present', allowing each trial to be classified as a hit, miss, false alarm, or correct rejection. On this model, type I d-prime is by definition independent of this decision threshold and is therefore insensitive to response bias.Given the success of SDT in measuring type I stimulus discrimination, there has been a natural motivation to apply it also to the so-called type II, or metacognitive, task We first consider 'type II d-prime', which is computed from type II hit and false alarm rates using the directly analogous formula to type I d-prime (a type II hit [false An alternative to type II d-prime that has received some support (Kolb & Braun, 1995;Wilimzig, Tsuchiya, Fahle, Einhuser, & Koch, 2008;Clifford, Arabzadeh & Harris, 2008;Masson & Rotello, 2009) is the use of receiver operating characteristic (ROC) curves to assess type II behaviour. A type I ROC curve charact...