Estimating discrimination performance in two-alternative forced choice tasks: Routines for MATLAB and R

Order effects in stimulus discrimination challenge established models of comparative judgement: A meta-analytic review of the Type B effect

This paper provides a comprehensive review of the Type B effect (TBE), a phenomenon reflected in the observation that discrimination sensitivity varies with the order of stimuli in comparative judgment tasks, such as the two-alternative forced-choice (2AFC) paradigm. Specifically, when the difference threshold is lower (higher) with the constant standard preceding rather than following the variable comparison, one speaks of a negative (positive) TBE. Importantly, prominent psychophysical difference models such as signal detection theory (Green & Swets, 1966) cannot easily account for the TBE, and are hence challenged by it. The present meta-analysis provides substantial evidence for the TBE across various stimulus attributes, suggesting that the TBE is a general feature of discrimination experiments when standard and comparison are presented successively. Thus, inconsistent with psychophysical difference models, subjective differences between stimuli are not merely a function of their physical differences but rather also depend on their temporal order. From the literature, we identify four classes of potential candidate theories explaining the origin of the TBE, namely (1) differential weighting of the stimulus magnitudes at the two positions (e.g., Hellström, Psychological Research, 39, 345-388 1977), (2) internal reference formation (e.g., Dyjas, Bausenhart, & Ulrich, Attention, Perception, & Psychophysics, 74, 1819-1841 2012), (3) Bayesian updating (e.g., de Jong, Akyürek, & van Rijn, Psychonomic Bulletin and Review, 28, 1183-1190 2021), and (4) biased threshold estimation (García-Pérez & Alcalá-Quintana, Attention, Perception & Psychophysics, 72, 1155-1178 2010). As these models, to some extent, make differential predictions about the direction of the TBE, investigating the respective boundary conditions of positive and negative TBEs might be a valuable perspective for diagnostic future research.

The Do's and Don'ts of Psychophysical Methods for Interpretability of Psychometric Functions and Their Descriptors

Many areas of research require measuring psychometric functions or their descriptors (thresholds, slopes, etc.). Data for this purpose are collected with psychophysical methods of various types and justification for the interpretation of results arises from a model of performance grounded in signal detection theory. Decades of research have shown that psychophysical data display features that are incompatible with such framework, questioning the validity of interpretations obtained under it and revealing that psychophysical performance is more complex than this framework entertains. This paper describes the assumptions and formulation of the conventional framework for the two major classes of psychophysical methods (single- and dual-presentation methods) and presents various lines of empirical evidence that the framework is inconsistent with. An alternative framework is then described and shown to account for all the characteristics that the conventional framework regards as anomalies. This alternative process model explicitly separates the sensory, decisional, and response components of performance and represents them via parameters whose estimation characterizes the corresponding processes. Retrospective and prospective evidence of the validity of the alternative framework is also presented. A formal analysis also reveals that some psychophysical methods and response formats are unsuitable for separation of the three components of observed performance. Recommendations are thus given regarding practices that should be avoided and those that should be followed to ensure interpretability of the psychometric function, or descriptors (detection threshold, difference limen, point of subjective equality, etc.) obtained with shortcut methods that do not require estimation of psychometric functions.

Decay of internal reference information in duration discrimination: Intertrial interval modulates the Type B effect

Psychophysical evidence suggests that human perception of a stimulus is assimilated towards previous stimuli. The internal reference model (IRM) explains such assimilation through an internal reference (IR), which integrates past and present stimulus representations and thus might be conceived as a form of perceptual memory. In this study, we investigated whether the IR decays with time, as previously shown for perceptual memory representations in general. One specific prediction of IRM is higher discrimination sensitivity when a constant standard precedes rather than follows a variable comparison in a two-alternative forced-choice (2AFC) discrimination task. Furthermore, the magnitude of this so-called negative Type B effect should decrease with decreasing weighting of past stimulus information in the integration process. Therefore, decay of the IR should result in a reduced Type B effect. To examine this prediction, we carried out a 2AFC duration discrimination experiment with a short (1,600 ms) and a long (3,200 ms) intertrial interval (ITI). As expected, a reduced negative Type B effect was observed at the long compared with the short ITI, consistent with the idea that humans rely on the immediate past when evaluating current sensory input, however, less so when the IR incorporating the perceptual short-term memory representation of these past stimuli has already decayed.

On the interplay of visuospatial and audiotemporal dominance: Evidence from a multimodal kappa effect

When participants judge multimodal audiovisual stimuli, the auditory information strongly dominates temporal judgments, whereas the visual information dominates spatial judgments. However, temporal judgments are not independent of spatial features. For example, in the kappa effect, the time interval between two marker stimuli appears longer when they originate from spatially distant sources rather than from the same source. We investigated the kappa effect for auditory markers presented with accompanying irrelevant visual stimuli. The spatial sources of the markers were varied such that they were either congruent or incongruent across modalities. In two experiments, we demonstrated that the spatial layout of the visual stimuli affected perceived auditory interval duration. This effect occurred although the visual stimuli were designated to be task-irrelevant for the duration reproduction task in Experiment 1, and even when the visual stimuli did not contain sufficient temporal information to perform a two-interval comparison task in Experiment 2. We conclude that the visual and auditory marker stimuli were integrated into a combined multisensory percept containing temporal as well as task-irrelevant spatial aspects of the stimulation. Through this multisensory integration process, visuospatial information affected even temporal judgments, which are typically dominated by the auditory modality.

The Indecision Model of Psychophysical Performance in Dual-Presentation Tasks: Parameter Estimation and Comparative Analysis of Response Formats

Psychophysical data from dual-presentation tasks are often collected with the two-alternative forced-choice (2AFC) response format, asking observers to guess when uncertain. For an analytical description of performance, psychometric functions are then fitted to data aggregated across the two orders/positions in which stimuli were presented. Yet, order effects make aggregated data uninterpretable, and the bias with which observers guess when uncertain precludes separating sensory from decisional components of performance. A ternary response format in which observers are also allowed to report indecision should fix these problems, but a comparative analysis with the 2AFC format has never been conducted. In addition, fitting ternary data separated by presentation order poses serious challenges. To address these issues, we extended the indecision model of psychophysical performance to accommodate the ternary, 2AFC, and same-different response formats in detection and discrimination tasks. Relevant issues for parameter estimation are also discussed along with simulation results that document the superiority of the ternary format. These advantages are demonstrated by fitting the indecision model to published detection and discrimination data collected with the ternary, 2AFC, or same-different formats, which had been analyzed differently in the sources. These examples also show that 2AFC data are unsuitable for testing certain types of hypotheses. matlab and R routines written for our purposes are available as Supplementary Material, which should help spread the use of the ternary format for dependable collection and interpretation of psychophysical data.

Effects of Stimulus Order on Discrimination Processes in Comparative and Equality Judgements: Data and Models

In typical discrimination experiments, participants are presented with a constant standard and a variable comparison stimulus and their task is to judge which of these two stimuli is larger (comparative judgement). In these experiments, discrimination sensitivity depends on the temporal order of these stimuli (Type B effect) and is usually higher when the standard precedes rather than follows the comparison. Here, we outline how two models of stimulus discrimination can account for the Type B effect, namely the weighted difference model (or basic Sensation Weighting model) and the Internal Reference Model. For both models, the predicted psychometric functions for comparative judgements as well as for equality judgements, in which participants indicate whether they perceived the two stimuli to be equal or not equal, are derived and it is shown that the models also predict a Type B effect for equality judgements. In the empirical part, the models’ predictions are evaluated. To this end, participants performed a duration discrimination task with comparative judgements and with equality judgements. In line with the models’ predictions, a Type B effect was observed for both judgement types. In addition, a time-order error, as indicated by shifts of the psychometric functions, and differences in response times were observed only for the equality judgement. Since both models entail distinct additional predictions, it seems worthwhile for future research to unite the two models into one conceptual framework.

Trial-by-trial updating of an internal reference in discrimination tasks: evidence from effects of stimulus order and trial sequence

In psychophysics, participants are often asked to discriminate between a constant standard and a variable comparison. Previous studies have shown that discrimination performance is better when the comparison follows, rather than precedes, the standard. Prominent difference models of psychophysics and decision making cannot easily explain this order effect. However, a simple extension of this model class involving dynamical updating of an internal reference accounts for this order effect. In addition, this Internal Reference Model (IRM) predicts sequential response effects. We examined the predictions of IRM in two duration discrimination experiments. The obtained results are in agreement with the predictions of IRM, suggesting that participants update their internal reference on every trial. Additional simulations show that IRM also accounts for the negative sequential effects observed in single-stimulus paradigms.