scholarly journals Modeling response times in the size-congruity effect: Early versus late interaction

2020 ◽  
Author(s):  
Kristen Bowman ◽  
Thomas J. Faulkenberry
Keyword(s):  
Drift Rate ◽  
Response Times ◽  
Decision Time ◽  
Congruity Effect ◽  
Response Threshold ◽  
Numerical Magnitude ◽  
Comparison Task ◽  
Single Digit ◽  
Paired Samples ◽  
Size Congruity Effect

The size-congruity effect occurs when numerical magnitude interferes with judgments of physical size. Various accounts propose that this interference is either encoding-related or decision-related, though at present a clear consensus is lacking. In our study, we administered a single-digit physical comparison task (i.e., which digit is physically larger?) and applied four different mathematical models (ex-Gaussian, ex-Wald, shifted Wald and EZ-diffusion) to the observed response times. The aim of this modeling was to index the underlying cognitive processes via estimates of drift rate, response threshold, and non-decision time. The collection of estimates for each individual was then subjected to Bayesian paired samples t-tests. We found that the drift rate for incongruent trials was smaller than for congruent trials, indicating that congruent trials had a faster rate of information uptake. The response threshold for incongruent trials was generally larger than for congruent trials, indicating that for incongruent trials more information needed to be accumulated before a response could be initiated. Critically, we found evidence of an invariance in non-decision times between incongruent and congruent trials. This combination of results provides support for a late interaction account of the size-congruity effect, shedding further light onto models of decision making in number processing.

scholarly journals Modeling the latent structure of individual differences in the numerical size-congruity effect

2020 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Kristen Bowman
Keyword(s):  
Individual Differences ◽  
Numerical Cognition ◽  
Congruity Effect ◽  
Numerical Magnitude ◽  
Data Sets ◽  
Comparison Task ◽  
Physical Size ◽  
The Individual ◽  
Size Congruity Effect ◽  
Individual Size

When people are asked to choose the physically larger of a pair of numerals, they are often slower when relative physical size is incongruent with numerical magnitude. This size-congruity effect is usually assumed as evidence for automatic activation of numerical magnitude. In this paper, we apply the methods of Haaf and Rouder (2017) to look at the size-congruity effect through the lens of individual differences. Here, we simply ask whether everyone exhibits the effect. We develop a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual size- congruity effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. We then apply this modeling technique to three data sets. In all three data sets, the winning model was one in which the size-congruity effect was constrained to be positive. This indicates that, at least in a physical comparison task with numerals, everyone exhibits a positive size-congruity effect. We discuss these results in the context of measurement fidelity and theory-building in numerical cognition.

EXPRESS: Sometimes nothing is simply nothing: Automatic processing of empty sets

2021 ◽  
pp. 174702182110664
Author(s):  
Yam Zagury ◽  
Rut Zaks-Ohayon ◽  
Joseph Tzelgov ◽  
Michal Pinhas
Keyword(s):  
Visual Cues ◽  
Automatic Processing ◽  
Congruity Effect ◽  
Numerical Magnitude ◽  
Numerical Comparison ◽  
Comparison Task ◽  
Numerical Comparisons ◽  
Perceptual Dominance ◽  
Size Congruity Effect

Previous work using the numerical comparison task has shown that an empty set, the nonsymbolic manifestation of zero, can be represented as the smallest quantity of the numerical magnitude system. In the present study, we examined whether an empty set can be represented as such under conditions of automatic processing in which deliberate processing of stimuli magnitudes is not required by the task. In Experiment 1, participants performed physical and numerical comparisons of empty sets (i.e., empty frames) and of other numerosities presented as framed arrays of 1 to 9 dots. The physical sizes of the frames varied within pairs. Both tasks revealed a size congruity effect (SCE) for comparisons of non-empty sets. In contrast, comparisons to empty sets produced an inverted SCE in the physical comparison task, while no SCE was found for comparisons to empty sets in the numerical comparison task. In Experiment 2, participants performed an area comparison task using the same stimuli as Experiment 1 to examine the effect of visual cues on the automatic processing of empty sets. The results replicated the findings of the physical comparison task in Experiment 1. Taken together, our findings indicate that empty sets are not perceived as “zero”, but rather as “nothing”, when processed automatically. Hence, the perceptual dominance of empty sets seems to play a more important role under conditions of automatic processing, making it harder to abstract the numerical meaning of zero from empty sets.

scholarly journals Effects of attentional shifts along the vertical axis on number processing: an eye-tracking study with optokinetic stimulation

2021 ◽  
Author(s):  
Arianna Felisatti ◽  
Mariagrazia Ranzini ◽  
Elvio Blini ◽  
Matteo Lisi ◽  
Marco Zorzi
Keyword(s):  
Eye Tracking ◽  
Numerical Cognition ◽  
Response Times ◽  
Eye Gaze ◽  
Distance Effect ◽  
Vertical Axis ◽  
Number Processing ◽  
Numerical Magnitude ◽  
Optokinetic Stimulation ◽  
Comparison Task

Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, downward attentional displacement increased the Magnitude effect (slower responses for large numbers) and reduced the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a parity by magnitude interaction that was amplified by downward OKS. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of numbers 1-2 as compared to 8-9; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.

scholarly journals Bottom-up and top-down attentional contributions to the size congruity effect

2016 ◽  
Vol 78 (5) ◽  
pp. 1324-1336 ◽  
Author(s):  
Kenith V. Sobel ◽  
Amrita M. Puri ◽  
Thomas J. Faulkenberry
Keyword(s):  
Congruity Effect ◽  
Top Down ◽  
Bottom Up ◽  
Size Congruity Effect

scholarly journals Same model, different conclusions: An identifiability issue in the linear ballistic accumulator model of decision-making

2020 ◽  
Author(s):  
Nathan J. Evans
Keyword(s):  
Decision Making ◽  
Diffusion Model ◽  
Large Scale ◽  
Drift Rate ◽  
Decision Time ◽  
Measurement Properties ◽  
Decision Threshold ◽  
Experimental Conditions ◽  
Model Application ◽  
Linear Ballistic Accumulator

Evidence accumulation models (EAMs) – the dominant modelling framework for speeded decision-making – have become an important tool for model application. Model application involves using specific model to estimate parameter values that relate to different components of the cognitive process, and how these values differ over experimental conditions and/or between groups of participants. In this context, researchers are often agnostic to the specific theoretical assumptions made by different EAM variants, and simply desire a model that will provide them with an accurate measurement of the parameters that they are interested in. However, recent research has suggested that the two most commonly applied EAMs – the diffusion model and the linear ballistic accumulator (LBA) – come to fundamentally different conclusions when applied to the same empirical data. The current study provides an in-depth assessment of the measurement properties of the two models, as well as the mapping between, using two large scale simulation studies and a reanalysis of Evans (2020a). Importantly, the findings indicate that there is a major identifiability issue within the standard LBA, where differences in decision threshold between conditions are practically unidentifiable, which appears to be caused by a tradeoff between the threshold parameter and the overall drift rate across the different accumulators. While this issue can be remedied by placing some constraint on the overall drift rate across the different accumulators – such as constraining the average drift rate or the drift rate of one accumulator to have the same value in each condition – these constraints can qualitatively change the conclusions of the LBA regarding other constructs, such as non-decision time. Furthermore, all LBA variants considered in the current study still provide qualitatively different conclusions to the diffusion model. Importantly, the current findings suggest that researchers should not use the unconstrained version of the LBA for model application, and bring into question the conclusions of previous studies using the unconstrained LBA.

scholarly journals Perceptual decision-making in children: Age-related differences and EEG correlates

2020 ◽  
Author(s):  
Catherine Manning ◽  
Eric-Jan Wagenmakers ◽  
Anthony Norcia ◽  
Gaia Scerif ◽  
Udo Boehm
Keyword(s):  
Decision Making ◽  
Drift Rate ◽  
Decision Time ◽  
Diffusion Models ◽  
Perceptual Task ◽  
Model Parameters ◽  
Older Children ◽  
Perceptual Decision Making ◽  
Boundary Separation ◽  
Age Related

Children make faster and more accurate decisions about perceptual information as they get older, but it is unclear how different aspects of the decision-making process change with age. Here, we used hierarchical Bayesian diffusion models to decompose performance in a perceptual task into separate processing components, testing age-related differences in model parameters and links to neural data. We collected behavioural and EEG data from 96 six- to twelve-year-olds and 20 adults completing a motion discrimination task. We used a component decomposition technique to identify two response-locked EEG components with ramping activity preceding the response in children and adults: one with activity that was maximal over centro-parietal electrodes and one that was maximal over occipital electrodes. Younger children had lower drift rates (reduced sensitivity), wider boundary separation (increased response caution) and longer non-decision times than older children and adults. Yet model comparisons suggested that the best model of children’s data included age effects only on drift rate and boundary separation (not non-decision time). Next we extracted the slope of ramping activity in our EEG components and covaried these with drift rate. The slopes of both EEG components related positively to drift rate, but the best model with EEG covariates included only the centro-parietal component. By decomposing performance into distinct components and relating them to neural markers, diffusion models have the potential to identify the reasons why children with developmental conditions perform differently to typically developing children - and to uncover processing differences inapparent in the response time and accuracy data alone.

Time and Consistency as Measures of Psychological Distance

1972 ◽  
Vol 35 (2) ◽  
pp. 635-645 ◽  
Author(s):  
Joan Gay Snodgrass ◽  
Ruth Kass
Keyword(s):  
Paired Comparison ◽  
Psychological Distance ◽  
Decision Time ◽  
Single Stimulus ◽  
Paired Comparisons ◽  
Comparison Task ◽  
Stimulus Distance ◽  
Ideal Points ◽  
Decision Times ◽  
Study Stimulus

Decision times, consistency measures, and their relationships were used to study stimulus-stimulus and subject-stimulus distance for two types of responses—single stimulus and paired comparisons, and two types of tasks—preference and judged complexity. Two assumptions based on Coombs' (1964) theory of data—that decision time is inversely related to distance and that both stimulus and ideal points have variability—led to the following predictions: (1) stimulus ordering from paired comparison judgments will be predictable from the ordering of decision times in single stimulus judgments; (2) more intransitive triads will occur in paired comparison preference judgments than paired comparison complexity judgments; and (3) complexity judgments will exhibit greater concordance than preference judgments. All three predictions were supported by data. Of three latency transformations investigated, standardized reciprocal times showed the highest correlation with difference in ranks in the paired comparison task.

scholarly journals Qualitative speed-accuracy tradeoff effects that cannot be explained by the diffusion model under the selective influence assumption

2020 ◽  
Author(s):  
Farshad Rafiei ◽  
Dobromir Rahnev
Keyword(s):  
Diffusion Model ◽  
Discrimination Task ◽  
Drift Rate ◽  
Response Times ◽  
Perceptual Discrimination ◽  
The Difference ◽  
Speed Accuracy ◽  
Selective Influence ◽  
Accuracy Tradeoff ◽  
Rt Distributions

It is often thought that the diffusion model explains all effects related to the speed-accuracy tradeoff (SAT) but this has previously been examined with only a few SAT conditions or only a few subjects. Here we collected data from 20 subjects who performed a perceptual discrimination task with five different difficulty levels and five different SAT conditions (5,000 trials/subject). We found that the five SAT conditions produced robustly U-shaped curves for (i) the difference between error and correct response times (RTs), (ii) the ratio of the standard deviation and mean of the RT distributions, and (iii) the skewness of the RT distributions. Critically, the diffusion model where only drift rate varies with contrast and only boundary varies with SAT could not account for any of the three U-shaped curves. Further, allowing all parameters to vary across conditions revealed that both the SAT and difficulty manipulations resulted in substantial modulations in every model parameter, while still providing imperfect fits to the data. These findings demonstrate that the diffusion model cannot fully explain the effects of SAT and establishes three robust but challenging effects that models of SAT should account for.

scholarly journals Bayesian confidence for drift diffusion observers in dynamic stimuli tasks

2020 ◽  
Author(s):  
Joshua Calder-Travis ◽  
Rafal Bogacz ◽  
Nick Yeung
Keyword(s):  
Diffusion Model ◽  
Drift Rate ◽  
Response Times ◽  
Time Dependent ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Dynamic Stimuli ◽  
Computationally Expensive ◽  
Insight Into ◽  
Confidence Data

AbstractMuch work has explored the possibility that the drift diffusion model, a model of response times and choices, could be extended to account for confidence reports. Many methods for making predictions from such models exist, although these methods either assume that stimuli are static over the course of a trial, or are computationally expensive, making it difficult to capitalise on trial-by-trial variability in dynamic stimuli. Using the framework of the drift diffusion model with time-dependent thresholds, and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of “pipeline” evidence which has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli which change over the course of a trial with normally distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions only contain a small number of standard functions, and only require evaluating once per trial, making trial-by-trial modelling of confidence data in dynamic stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

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