Variance SDT Model

Previously we have proposed a signal detection theory (SDT) methodology for measuring metacognitive sensitivity (Maniscalco and Lau, Conscious Cogn 21:422–430, 2012). Our SDT measure, meta-d0, provides a response-bias free measure of how well confidence ratings track task accuracy. Here we provide an overview of standard SDT and an extended formal treatment of metad0. However, whereas meta-d0 characterizes an observer’s sensitivity in tracking overall accuracy, it may sometimes be of interest to assess metacognition for a particular kind of behavioral response. For instance, in a perceptual detection task, we may wish to characterize metacognition separately for reports of stimulus presence and absence. Here we discuss the methodology for computing such a ‘‘response-specific’’ meta-d0 and provide corresponding Matlab code. This approach potentially offers an alternative explanation for data that are typically taken to support the unequal variance SDT (UV-SDT) model. We demonstrate that simulated data generated from UV-SDT can be well fit by an equal variance SDT model positing different metacognitive ability for each kind of behavioral response, and likewise that data generated by the latter model can be captured by UV-SDT. This ambiguity entails that caution is needed in interpreting the processes underlying relative operating characteristic (ROC) curve properties. Type 1 ROC curves generated by combining type 1 and type 2 judgments, traditionally interpreted in B. Maniscalco (&) National Institute of Neurological Disorders and Stroke, National Institutes of Health, 10 Center Drive, Building 10, Room B1D728, MSC 1065, Bethesda, MD 20892-1065, USA e-mail: [email protected] B. Maniscalco H. Lau Department of Psychology, Columbia University, 406 Schermerhorn Hall, 1190 Amsterdam Avenue MC 5501, New York, NY 10027, USA e-mail: [email protected] H. Lau Department of Psychology, UCLA, 1285 Franz Hall, Box 951563 Los Angeles, CA 90095-1563, USA S. M. Fleming and C. D. Frith (eds.), The Cognitive Neuroscience of Metacognition, DOI: 10.1007/978-3-642-45190-4_3, Springer-Verlag Berlin Heidelberg 2014 25 terms of low-level processes (UV), can potentially be interpreted in terms of high-level processes instead (response-specific metacognition). Similarly, differences in area under response-specific type 2 ROC curves may reflect the influence of low-level processes (UV) rather than high-level metacognitive processes.