How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled?

Tokita, Midori; Ishiguchi, Akira

doi:10.3758/app.72.7.1839

Cited by 54 publications

(78 citation statements)

References 38 publications

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“…Participants were slower to respond to incongruent trials than to congruent trials, suggesting that although irrelevant to the task, the physical size of the number was automatically processed. Similar effects were also found for nonsymbolic stimuli-when participants were asked to ignore the size of dots and the area of an array, their results were still affected by those dimensions (e.g., Gebuis & Reynvoet, 2011;Tokita & Ishiguchi, 2010), suggesting possible interaction between the subsystem for processing discrete magnitudes and the subsystem for processing continuous magnitudes (Arrow 1 in the model).…”

Section: Suggested Modelsupporting

confidence: 64%

Comparing Performance in Discrete and Continuous Comparison Tasks

Leibovich

Henik

2014

Quarterly Journal of Experimental Psychology

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The approximate number system (ANS) theory suggests that all magnitudes, discrete (i.e., number of items) or continuous (i.e., size, density, etc.), are processed by a shared system and comply with Weber's law. The current study reexamined this notion by comparing performance in discrete (comparing numerosities of dot arrays) and continuous (comparisons of area of squares) tasks. We found that: (a) threshold of discrimination was higher for continuous than for discrete comparisons; (b) while performance in the discrete task complied with Weber's law, performance in the continuous task violated it; and (c) performance in the discrete task was influenced by continuous properties (e.g., dot density, dot cumulative area) of the dot array that were not predictive of numerosities or task relevant. Therefore, we propose that the magnitude processing system (MPS) is actually divided into separate (yet interactive) systems for discrete and continuous magnitude processing. Further subdivisions are discussed. We argue that cooperation between these systems results in a holistic comparison of magnitudes, one that takes into account continuous properties in addition to numerosities. Considering the MPS as two systems opens the door to new and important questions that shed light on both normal and impaired development of the numerical system.

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Section: Suggested Modelsupporting

confidence: 64%

Comparing Performance in Discrete and Continuous Comparison Tasks

Leibovich

Henik

2014

Quarterly Journal of Experimental Psychology

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“…2C), but that observers still make systematic errors such that larger test patches appear more numerous (replicating ref. 8). Thresholds for the two tasks are shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Several previous studies have reported that this manipulation does not greatly influence the precision of number discrimination (6)(7)(8). However, in addition to expressing the usual concern about negative results, we note first that some studies have used relatively small numbers of elements (∼30) (6,8), which are less effective at engaging approximate number processing. Furthermore, the study by Ross and Burr (7) required observers to make either number or density comparisons within different blocks of trials.…”

mentioning

confidence: 88%

A common visual metric for approximate number and density

Dakin¹,

Tibber²,

Greenwood³

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

277

404

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There is considerable interest in how humans estimate the number of objects in a scene in the context of an extensive literature on how we estimate the density (i.e., spacing) of objects. Here, we show that our sense of number and our sense of density are intertwined. Presented with two patches, observers found it more difficult to spot differences in either density or numerosity when those patches were mismatched in overall size, and their errors were consistent with larger patches appearing both denser and more numerous. We propose that density is estimated using the relative response of mechanisms tuned to low and high spatial frequencies (SFs), because energy at high SFs is largely determined by the number of objects, whereas low SF energy depends more on the area occupied by elements. This measure is biased by overall stimulus size in the same way as human observers, and by estimating number using the same measure scaled by relative stimulus size, we can explain all of our results. This model is a simple, biologically plausible common metric for perceptual number and density.psychophysics | vision | texture | numerical cognition

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“…Many prior studies have found that non-numerical visual stimulus features influence numerosity discrimination performance, thus interfering with precise estimates of ANS acuity (e.g. DeWind & Brannon, 2012; Frith & Frith, 1972; Gebuis & Gevers, 2011; Ginsburg, 1976; Sophian, 2007; Tokita & Ishiguchi, 2010). …”

Section: Introductionmentioning

confidence: 99%

Modeling the approximate number system to quantify the contribution of visual stimulus features

et al. 2015

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The approximate number system (ANS) subserves estimation of the number of items in a set. Typically, ANS function is assessed by requiring participants to compare the number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant’s Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spacing of dots. Current models of numerosity comparison do not account for these effects and consequently lead to different estimates of w depending on the methods used to control for non-numerical features. Here we proffer a new model that teases apart the effects of ANS acuity from the effects of non-numerical stimulus features. The result is an estimate of w that is a more theoretically valid representation of numerical acuity and novel terms that denote the degree to which a participant’s perception of number is affected by non-numerical features. We tested this model in a sample of 20 adults and found that, by correctly attributing errors due to non-numerical stimulus features, the w obtained was more reliable across different stimulus conditions. We found that although non-numerical features biased numerosity discriminations in all participants, number was the primary feature driving discriminations in most of them. Our findings support the idea that, while numerosity is a distinct visual quantity, the internal representation of number is tightly bound to the representation of other magnitudes. This tool for identifying the different effects of the numerical and non-numerical features of a stimulus has important implications not only for the behavioral investigation of the ANS, but also for the collection and analyses of neural data sets associated with ANS function.

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How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled?

Cited by 54 publications

References 38 publications

Comparing Performance in Discrete and Continuous Comparison Tasks

Comparing Performance in Discrete and Continuous Comparison Tasks

A common visual metric for approximate number and density

Modeling the approximate number system to quantify the contribution of visual stimulus features

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