Is The Weber Fraction a Function of Physical or Perceived Input?

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.

Duration discrimination: A diffusion decision modeling approach

The human ability to discriminate the duration of two subsequently presented stimuli is often studied with tasks that involve a comparison between a standard stimulus (with fixed duration) and comparison stimuli (with varying durations). The performance in such tasks is influenced by the presentation order of these successively presented stimuli. The so-called Type A effect refers to the impact of presentation order on the point of subjective equality. The Type B effect describes effects of presentation order on the just-noticeable-difference. Cognitive models that account for these context effects assume that participants' duration estimation is influenced by the history of previously encountered stimuli. For example, the internal reference model assumes that the magnitude of a "typical" stimulus is represented by an internal reference. This internal reference evolves throughout an experiment and is updated on every trial. Different recent models have in common that they describe how the internal reference is computed but are agnostic to the decision process itself. In this study, we develop a new model that incorporates the mechanisms of perceptual discrimination models into a diffusion model. The diffusion model focuses on the dynamics of the decision process itself and accounts for choice and response times based on a set of latent cognitive variables. We show that our model accurately predicts the accuracy and response time distribution in a classical duration discrimination task. Further, model parameters were sensitive to the Type A and B effect. The proposed model opens up new opportunities for studying human discrimination performance (e.g., individual differences).

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.

The number-weight illusion

When objects are manually lifted to compare their weight, then smaller objects are judged to be heavier than larger objects of the same physical weights: the classical size-weight illusion (Gregory, 2004). It is also well established that increasing numerical magnitude is strongly associated with increasing physical size: the number-size congruency effect e.g., (Besner & Coltheart Neuropsychologia, 17, 467-472 1979); Henik & Tzelgov Memory & Cognition, 10, 389-395 1982). The present study investigates the question suggested by combining these two classical effects: if smaller numbers are associated with smaller size, and objects of smaller size appear heavier, then are numbered objects (balls) of equal weight and size also judged as heavier when they carry smaller numbers? We present two experiments testing this hypothesis for weight comparisons of numbered (1 to 9) balls of equal size and weight, and report results which largely conform to an interpretation in terms of a new "number-weight illusion".

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.

Weight illusions and weight discrimination-a revised hypothesis

The results of several experiments are reported most of which suggest that there is an optimum density for weight discrimination. This density corresponds to the “non-illusory” density, as determined by the density at which a visible weight is correctly matched with a hidden weight. The greater the illusion (whether of heaviness or lightness) the poorer the discrimination.

It is pointed out that similar changes in discrimination occur as a result of peripheral sensory adaptation in many modalities; but that the size-weight illusion, and the associated discrimination changes, must be due to a central scaling process. A theoretical model is suggested.

Are thresholds reduced by illusions? An attempt at replication

Three experiments are reported, which are attempts to replicate the finding of Ross and Gregory (1964) that difference thresholds for weights can be lowered by means of the size-weight illusion. Three different procedures were used, the first one (experiment I) being designed to show whether or not changes in a subject's judgement criterion could account for apparent changes in sensitivity. The second method (Experiment II) was a replication of Ross and Gregory's first procedure, in which the standard weight was judged before the comparison. In Experiments I and II a larger illusion was induced than in the original studies, but in Experiment III both the weights and container sizes were practically identical to those used by Ross and Gregory. The procedure was also the same as their most successful procedure (number 3) in which standard and comparison were judged simultaneously. The findings were uniformly negative: there was no evidence of criterion shift when the size-weight illusion was induced nor did we find the lowering of threshold previously reported.

Arm weight, adaptation,and weight discrimination

The addition of a large weight to the forearm impairs weight discrimination by an amount which is small by Weber's Law but which could affect skilled tasks. When time is allowed for adaptation to the forearm weight, discrimination with the weight is improved and discrimination without the weight is impaired. Implications for pilots and astronauts under varying g are discussed.