Signal detection theory (SDT) sensory discrimination analysis using A-Not A with a two-step rating is an efficient approach to in-house sensory quality management in the food industry. For such sensory analysis using an internal panel, the panels' ability to use stable decision criteria and provide a consistent response distribution responding to "A" vs "Not A" is critical for guaranteeing the data quality. This study examined the effects of the familiarization procedure (FP) and reference presentation probability (RPP) in the SDT A-Not A rating protocol on the panels' sensory learning of samples and stability of decision criteria using SDT parameters, recognition d' (d'Rec),criteria location (c), and discrimination d' indices. Three different protocols were compared using ice-tea samples with small differences: Control, 0.25 RPP with repeated reference tasting (FPR); Modified-1, 0.25 RPP with reference categorization (FPC); Modified-2, 0.5 RPP with reference categorization (FPC). An independent sample design with three groups having equal sensitivity was used to identify the differences among the protocols. For each protocol, two sub-groups with similar decision criteria (response bias) were formed according to the results obtained from the pre-test and used for the main-test analysis. SDT analysis results indicated that the Modified-2 protocol with a higher RPP (0.5) induced the most efficient sensory learning of the reference. The protocol improved the subjects' recognition of the reference and test samples, better differentiating from the reference and stabilizing the decision criterion, resulting in higher discrimination performance (larger d'). The results showed that d'Rec analysis, together with d' analysis using a sensory panel, is a useful tool for monitoring the panel performance and checking for the sensory data quality of the sensory difference tests. In the present paper, a detailed illustration of the A-Not A sensory test procedure and examples of how to apply the SDT indices for different business decision-making is also introduced using the design and results of the present experiment.

Signal detection theory (SDT) is used to analyze yes/no judgment accuracy in many research domains of psychology. SDT yields separate estimates for response bias/criterion (c) and for sensitivity/discriminability (d'). Discrimination performance can be displayed in Receiver Operating Characteristics (ROCs) plotting hit and false alarm rates at various levels of confidence. We provide formal proof and simulations showing that asymmetric ROCs in Gaussian SDT are not exclusively diagnostic of unequal residual variance but may as well result from equal-variance models with c and d' systematically varying across subjects and/or items. Falsely attributing zROC slopes to unequal residual variance while neglecting true group-level variability introduces systematic and unsystematic statistical error. We show that ordinal regression models minimize such errors while estimating all SDT parameters and statistical criteria in a single model.

Signal detection theory (SDT) has long provided the field of psychology with a simple but powerful model of how observers make decisions under uncertainty. SDT can distinguish sensitivity from response bias and characterize optimal decision strategies. Whereas classical SDT pertains to "type 1" judgments about the world, recent work has extended SDT to quantify sensitivity for metacognitive or "type 2" judgments about one's own type 1 processing, e.g. confidence ratings. Here we further advance the application of SDT to the study of metacognition by providing a formal account of normative metacognitive decision strategies - i.e., type 2 (confidence) criterion setting - for ideal observers. Optimality is always defined relative to a given objective. We use SDT to derive formulae for optimal type 2 criteria under four distinct objectives: maximizing type 2 accuracy, maximizing type 2 reward, calibrating confidence to accuracy, and maximizing the difference between type 2 hit rate and false alarm rate. Where applicable, we consider these optimization contexts alongside their type 1 counterparts (e.g. maximizing type 1 accuracy) to deepen understanding. We examine the different strategies implied by these formulae and further consider how optimal type 2 criterion setting differs when metacognitive sensitivity deviates from SDT expectation. The theoretical framework provided here can be used to better understand the metacognitive decision strategies of real observers. Possible applications include characterizing observers' spontaneously chosen metacognitive decision strategies, assessing their ability to fine-tune metacognitive decision strategies to optimize a given outcome when instructed, determining over- or under-confidence relative to an optimal standard, and more. This framework opens new avenues for enriching our understanding of metacognition. Keywords: Metacognition, Decision-making, Signal detection theory, Computational modelling status released display-pdf yes is-in-collection-domain yes is-olf no is-manuscript no is-preprint no is-journal-matter no is-scanned no is-retracted no Accepted 2024 Mar 28; Issue date 2025. Introduction Signal detection theory (SDT) has long provided the field of psychology with a simple but powerful model of how observers make decisions under uncertainty (Green & Swets, 1966 ; Macmillan & Creelman, 2004 ). Central to SDT is the distinction between sensitivity and criterion setting. Sensitivity corresponds to an observer’s overall ability to distinguish different states of the world (e.g. Importantly, although type 2 criterion setting is a central aspect of modelling confidence judgments using signal detection theory, it remains less studied and poorly understood (Sherman et al., 2018 ). In particular, it remains unclear how the demands of the decision-making context affect the confidence criterion-setting strategy for both ideal 2 and actual observers (Fleming & Dolan, 2010 ; Lebreton et al., 2018 ; Locke et al., 2020 ), and to what extent actual observers’ strategies resemble ideal strategies for optimizing various outcome measures of metacognitive performance. Optimizing criterion setting for different tasks and goals The following discussion assumes the reader is familiar with classical signal detection theory and its extension to response-specific type 2 decision making. To briefly review, type 1 SDT models how an observer performs the task of discriminating whether a stimulus (e.g. a grating) belongs to class S1 (e.g. left tilt) or S2 (e.g. right tilt). The model assumes that on each trial, the observer perceives a certain magnitude of evidence associated with the stimulus (e.g. evidence for left vs right tilt), with lower and higher values being more associated with S1 and S2, respectively. The type 2 SDT model posits that confidence ratings for “S1” and “S2” responses are similarly produced using additional type 2 decision criteria on either side of the type 1 criterion (Figure 1 C), which can capture empirical patterns in type 2 ROC curves (Figure 1 D). For a more in-depth review of type 1 and type 2 SDT, please see Supplementary Material S1 . Fig. 1 Type 1 and type 2 criterion in Signal Detection Theory. (A) The standard type 1 signal detection model. The observer discriminates between two stimuli S1 and S2. General discussion An observer’s strategy for rating confidence in their decisions depends highly on that observer’s goal: just as with type 1 decisions, the optimal strategy for producing type 2 ratings of confidence changes whether the observer wishes to maximize type 2 accuracy, type 2 reward, the correspondence between confidence and accuracy, or the difference between type 2 hit and false alarm rates. In this paper, we explored the different strategies an observer can adopt to optimize these various outcomes using the framework of type 2 signal detection theory. To facilitate this exploration and derivation of optimal strategies, we first reviewed how, according to classic signal detection theory, the decision criterion can be set to optimize a particular outcome measure following the experimenter’s instructions and stimuli presented. We then explored how such optimization could apply to confidence judgments, evaluating how different outcome measures at the type 2 level could be optimized, and how this would affect the position of the criteria for reporting high confidence. Closing remarks Here, we have used type 2 signal detection theory to derive optimal metacognitive criterion setting strategies under four optimization contexts: type 2 accuracy, type 2 reward, calibration of confidence to accuracy, and maximizing the difference between type 2 hit rate and false alarm rate. Our formal derivation approach provides both theoretical and practical contribution to the study of decision-making and metacognition. Further, our simulation code provides a practical tool by which researchers in the field may explore the impact of

Perception is biased by expectations and previous actions. Pre-stimulus brain oscillations are a potential candidate for implementing biases in the brain. In two EEG studies (43 and 39 participants) on somatosensory near-threshold detection, we investigated the pre-stimulus neural correlates of an (implicit) previous choice bias and an explicit bias. The explicit bias was introduced by informing participants about stimulus probability on a single-trial level (volatile context) or block-wise (stable context). Behavioural analysis confirmed adjustments in the decision criterion and confidence ratings according to the cued probabilities and previous choice-induced biases. Pre-stimulus beta power with distinct sources in sensory and higher-order cortical areas predicted explicit and implicit biases, respectively, on a single subject level and partially mediated the impact of previous choice and stimulus probability on the detection response. We suggest pre-stimulus beta oscillations in distinct brain areas as a neural correlate of explicit and implicit biases in somatosensory perception.

Neuroscientific theories hypothesize that arousal fluctuations influence human perception and behavior in two functionally distinct ways: through variations in baseline state (tonic arousal) and by transient task-evoked bursts (phasic arousal). We combined causal (pharmacology) and correlational (pupillometry) methods to test the hypothesis that tonic and phasic arousal differentially influence decision biases in human male participants performing a yes/no visual detection task. Computational modeling of choice behavior and analyses of neural data (EEG) revealed that experimentally induced shifts in decision bias were associated with changes in preparatory activity over motor cortex resembling a starting-point bias in the decision formation. The behavioral, computational, and neural effects of strategic shifts in decision bias were weakest on trials with high phasic pupil-linked arousal, but did not relate to tonic pupil-linked arousal or pharmacology. In sharp contrast, tonic pupil-linked arousal and pharmacological interventions were associated with more liberal decision-making (increased proportion of "yes" choices) independent of task context. Thus, in line with the hypothesized functional distinction, tonic arousal was associated with inherent decision bias, whereas phasic arousal was related to context-dependent strategic shifts in decision bias.

Humans can subjectively yet quantitatively assess choice confidence based on perceptual precision even when a perceptual decision is made without an immediate reward or feedback. However, surprisingly little is known about choice confidence. Here we investigate the dynamics of choice confidence by merging two parallel conceptual frameworks of decision making, signal detection theory and sequential analyses (i.e., drift-diffusion modeling). Specifically, to capture end-point statistics of binary choice and confidence, we built on a previous study that defined choice confidence in terms of psychophysics derived from signal detection theory. At the same time, we augmented this mathematical model to include accumulator dynamics of a drift-diffusion model to characterize the time dependence of the choice behaviors in a standard forced-choice paradigm in which stimulus duration is controlled by the operator. Human subjects performed a subjective visual vertical task, simultaneously reporting binary orientation choice and probabilistic confidence. Both binary choice and confidence experimental data displayed statistics and dynamics consistent with both signal detection theory and evidence accumulation, respectively. Specifically, the computational simulations showed that the unbounded evidence accumulator model fits the confidence data better than the classical bounded model, while bounded and unbounded models were indistinguishable for binary choice data. These results suggest that

Receiver operating characteristic (ROC) analysis is a widely used evaluation tool in signal processing and communications, and medical diagnosis for performance analysis. It utilizes 2-D curves plotted by detection rate (P D) against false alarm rate (P F) to assess effectiveness of a detector, sensor/device for detection. However, P D and P F are actually dependent parameters resulting from a more crucial but implicit parameter hidden in the ROC curves, threshold ? , which is determined by the cost of implementing a detector or sensor/device, except only the case that when the Bayes theory is used for detection, ? is completely determined by the Bayes cost. This paper extends the traditional ROC analysis for single-signal detection to detection and classification of multiple signals. It also explores relationships among the three parameters, P D, P F, and ? , and further develops a new concept of multiparameter ROC analysis, which uses 3-D ROC curves plotted by three parameters, P D, P F, and ?, to evaluate effectiveness of detection performance based on interrelationship among P D, P F, and ?, rather then only P D and P F used by 2-D ROC analysis. As a result of a 3-D ROC curve, three 2-D ROC curves can be also derived: the conventional 2-D ROC curve plotted by P D versus P F and two new 2-D ROC curves plotted based on P D versus ? and P F versus ?. In order to demonstrate the utility of 3-D ROC analysis, four applications are considered: hyperspectral target detection, med