Journal articles: 'Numerosity effect'

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LIU, Wei, Zhi-Jun ZHANG, and Ya-Jun ZHAO. "Numerosity Adaptation Effect on the Basis of Perceived Numerosity." Acta Psychologica Sinica 44, no. 10 (April 16, 2013): 1297–308. http://dx.doi.org/10.3724/sp.j.1041.2012.01297.

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Gebuis, Titia, and Bert Reynvoet. "The Neural Mechanism Underlying Ordinal Numerosity Processing." Journal of Cognitive Neuroscience 26, no. 5 (May 2014): 1013–20. http://dx.doi.org/10.1162/jocn_a_00541.

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Changes in the sensory properties of numerosity stimuli have a direct effect on the outcomes of nonsymbolic number tasks. This suggests a prominent role of sensory properties in numerosity processing. However, the current consensus holds that numerosity is processed independent of its sensory properties. To investigate the role of sensory cues in ordinal number processes, we manipulated both dimensions orthogonally. Participants passively viewed the stimuli while their brain activity was measured using EEG. The results revealed an interaction between numerosity and its sensory properties in the absence of main effects. Different neural responses were present for trials where numerosity and sensory cues changed in the same direction compared with trials where they changed in opposite directions. These results show that the sensory cues are expected to change in concert with numerosity and support the notion that the visual cues are taken into account when judging numerosity.

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Valsecchi, Matteo, Natale Stucchi, and Lisa Scocchia. "Repulsive Serial Effects in Visual Numerosity Judgments." Perception 47, no. 7 (May 6, 2018): 780–88. http://dx.doi.org/10.1177/0301006618775235.

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We investigated how the approximate perceived numerosity of ensembles of visual elements is modulated by the numerosity of previously viewed ensembles depending on whether the first ensemble is held in visual working memory or not. We show that the numerosity of the previously seen ensemble has a repulsive effect, that is, a stimulus with high numerosity induces an underestimation of the following one and vice versa. This repulsive effect is present regardless of whether the first stimulus is memorized or not. While subtle changes of the experimental paradigm can have major consequences for the nature of interstimulus dependencies in perception, generally speaking the fact that we found such effects in a visual numerosity estimation task confirms that the process by which human observers produce estimates of the number of elements bears analogies to the processes that lead to the perception of visual dimensions such as orientation.

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Zhou, Xinlin, Chaoran Shen, Leinian Li, Dawei Li, and Jiaxin Cui. "Mental Numerosity Line in the Human’s Approximate Number System." Experimental Psychology 63, no. 3 (June 2016): 169–79. http://dx.doi.org/10.1027/1618-3169/a000324.

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Abstract. Previous studies have demonstrated existence of a mental line for symbolic numbers (e.g., Arabic digits). For nonsymbolic number systems, however, it remains unresolved whether a spontaneous spatial layout of numerosity exists. The current experiment investigated whether SNARC-like (Spatial-Numerical Association of Response Codes) effects exist in approximate processing of numerosity, as well as of size and density. Participants were asked to judge whether two serially presented stimuli (i.e., dot arrays, pentagons) were the same regarding numbers of dots, sizes of the pentagon, or densities of dots. Importantly, two confounds that were overlooked by most previous studies were controlled in this study: no ordered numerosity was presented, and only numerosity in the approximate number system (beyond the subitizing range) was used. The results demonstrated that there was a SNARC-like effect only in the numerosity-matching task. The results suggest that numerosity could be spontaneously aligned to a left-to-right oriented mental line according to magnitude information in human’s approximate number system.

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Anobile, Giovanni, Guido Marco Cicchini, Antonella Pomè, and David Charles Burr. "Connecting visual objects reduces perceived numerosity and density for sparse but not dense patterns." Journal of Numerical Cognition 3, no. 2 (December 22, 2017): 133–46. http://dx.doi.org/10.5964/jnc.v3i2.38.

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How is numerosity encoded by the visual system? – directly, or derived indirectly from texture density? We recently suggested that the numerosity of sparse patterns is encoded directly by dedicated mechanisms (which have been described as the “Approximate Number System” ANS). However, at high dot densities, where items become “crowded” and difficult to segregate, “texture-density” mechanisms come into play. Here we tested the importance of item segmentation on numerosity and density perception at various stimulus densities, by measuring the effect of connecting visual objects with thin lines. The results confirmed many previous studies showing that connecting items robustly reduces the apparent numerosity of patterns of moderate density. We further showed that the apparent density of moderate-density patterns is also reduced by connecting the dots. Crucially, we found that both these effects are strongly reduced at higher numerosities. Indeed for density judgments, the effect reverses, so connecting dots in dense patterns increases the apparent density (as expected from the physical characteristics). The results provide clear support for the three-regime framework of number perception, and suggest that for moderately sparse stimuli, numerosity – but not texture-density – is perceived directly.

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Simmons, Fiona, Thomas Gallagher-Mitchell, and Ruth S. Ogden. "Response-irrelevant number, duration, and extent information triggers the SQARC effect: Evidence from an implicit paradigm." Quarterly Journal of Experimental Psychology 72, no. 9 (April 3, 2019): 2261–71. http://dx.doi.org/10.1177/1747021819839413.

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Spatial–Numerical Association of Response Codes (SNARC) and Spatial–Quantity Association of Response Codes (SQARC) effects are evident when people produce faster left-sided responses to smaller numbers, sizes, and durations and faster right-sided responses to larger numbers, sizes, and durations. SQARC effects have typically been demonstrated in paradigms where the explicit processing of quantity information is required for successful task completion. The current study tested whether the implicit presentation of task-irrelevant magnitude information could trigger a SQARC effect as has been demonstrated previously when task-irrelevant information triggers a SNARC effect. In Experiment 1, participants ( n = 20) made orientation judgements for triangles varying in numerosity and physical extent. In Experiment 2, participants ( n = 20) made orientation judgements for triangles varying in numerosity and for a triangle preceded by a delay of varying duration. SNARC effects were observed for the numerosity conditions of Experiments 1 and 2 replicating Mitchell et al. SQARC effects were also demonstrated for physical extent and for duration. These findings demonstrate that SQARC effects can be implicitly triggered by the presentation of the task-irrelevant magnitude.

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Zhang, Jinbo, Zehua Wu, Jiashuang Wu, Yi Mou, and Zhenzhu Yue. "The effects of auditory numerosity and magnitude on visual numerosity representation: An ERP study." Journal of Numerical Cognition 6, no. 2 (September 9, 2020): 164–85. http://dx.doi.org/10.5964/jnc.v6i2.234.

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Numerical representation is not restricted to sensory modalities. It remains unclear how numerosity processing in different modalities interacts within the brain. Moreover, the effect of continuous magnitudes presented in one modality on the representation of numerosity in another modality has not been well studied. By using event-related potential (ERP) and source localization analyses, the present study examined whether there was an interaction between auditory numerosity and continuous magnitude on visual numerosity representation. A visual dot array (visual standard stimulus) was preceded by sound in which numerosity (Multiple-tone vs. One-tone conditions) and magnitude (Loud-tone vs. Soft-tone conditions) information were manipulated. Then, another visual dot array (visual comparison stimulus) was presented, and participants were required to compare the numerosities of the visual dots. Behavioural results revealed that participants showed smaller just-noticeable differences (JNDs) when visual stimuli were preceded by multiple tones than those when visual stimuli were preceded by one tone. The subsequent ERP analysis of visual standard stimuli revealed that the peak amplitude of N1 was more negative under the Loud-tone condition than that under the Soft-tone condition, which could be related to better preparatory attention. Moreover, a significant interaction between auditory numerosity and magnitude was found within the P2p time window for the standard stimuli. Further source localization analysis identified the effect of N1 and P2p to be in the right middle frontal gyrus (MFG) and left inferior parietal lobule (IPL). The present study suggests that numerosity information presented in one sensory modality could spontaneously affect the numerical representation in another modality.

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Petrizzo, Irene, Giovanni Anobile, Eleonora Chelli, Roberto Arrighi, and David Charles Burr. "Visual Duration but Not Numerosity Is Distorted While Running." Brain Sciences 12, no. 1 (January 5, 2022): 81. http://dx.doi.org/10.3390/brainsci12010081.

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There is increasing evidence that action and perception interact in the processing of magnitudes such as duration and numerosity. Sustained physical exercise (such as running or cycling) increases the apparent duration of visual stimuli presented during the activity. However, the effect of exercise on numerosity perception has not yet been investigated. Here, we asked participants to make either a temporal or a numerical judgment by comparing the duration or numerosity of standard stimuli displayed at rest with those presented while running. The results support previous reports in showing that physical activity significantly expands perceived duration; however, it had no effect on perceived numerosity. Furthermore, the distortions of the perceived durations vanished soon after the running session, making it unlikely that physiological factors such as heart rate underlie the temporal distortion. Taken together, these results suggest a domain-selective influence of the motor system on the perception of time, rather than a general effect on magnitude.

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Burr, David, Giovanni Anobile, and Marco Turi. "Adaptation Affects Both High and Low (Subitized) Numbers Under Conditions of High Attentional Load." Seeing and Perceiving 24, no. 2 (2011): 141–50. http://dx.doi.org/10.1163/187847511x570097.

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AbstractIt has recently been reported that, like most sensory systems, numerosity is subject to adaptation. However, the effect seemed to be limited to numerosity estimation outside the subitizing range. In this study we show that low numbers, clearly in the subitizing range, are adaptable under conditions of high attentional load. These results support the idea that numerosity is detected by a perceptual mechanism that operates over the entire range of numbers, supplemented by an attention-based system for small numbers (subitizing).

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Ginsburg, Norman, and Laraine Pringle. "Haptic Numerosity Perception: Effect of Item Arrangement." American Journal of Psychology 101, no. 1 (1988): 131. http://dx.doi.org/10.2307/1422798.

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Kenenbaeva, G. M., and S. B. Tagaeva. "ON CONSTANTS RELATED TO EFFECT OF "NUMEROSITY"." Herald of Institute Mathematics of the National Academy of Sciences of the Kyrgyz Republic, no. 1 (2021): 10–16. http://dx.doi.org/10.52448/16948173_2021_1_10.

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He, Lixia, Ke Zhou, Tiangang Zhou, Sheng He, and Lin Chen. "Topology-defined units in numerosity perception." Proceedings of the National Academy of Sciences 112, no. 41 (September 28, 2015): E5647—E5655. http://dx.doi.org/10.1073/pnas.1512408112.

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What is a number? The number sense hypothesis suggests that numerosity is “a primary visual property” like color, contrast, or orientation. However, exactly what attribute of a stimulus is the primary visual property and determines numbers in the number sense? To verify the invariant nature of numerosity perception, we manipulated the numbers of items connected/enclosed in arbitrary and irregular forms while controlling for low-level features (e.g., orientation, color, and size). Subjects performed discrimination, estimation, and equality judgment tasks in a wide range of presentation durations and across small and large numbers. Results consistently show that connecting/enclosing items led to robust numerosity underestimation, with the extent of underestimation increasing monotonically with the number of connected/enclosed items. In contrast, grouping based on color similarity had no effect on numerosity judgment. We propose that numbers or the primitive units counted in numerosity perception are influenced by topological invariants, such as connectivity and the inside/outside relationship. Beyond the behavioral measures, neural tuning curves to numerosity in the intraparietal sulcus were obtained using functional MRI adaptation, and the tuning curves showed that numbers represented in the intraparietal sulcus were strongly influenced by topology.

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Dormal, Valérie, Nathanaël Larigaldie, Nathalie Lefèvre, Mauro Pesenti, and Michael Andres. "Effect of perceived length on numerosity estimation: Evidence from the Müller-Lyer illusion." Quarterly Journal of Experimental Psychology 71, no. 10 (January 1, 2018): 2142–51. http://dx.doi.org/10.1177/1747021817738720.

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Previous studies showed that the magnitude information conveyed by sensory cues, such as length or surface, influences the ability to compare the numerosity of sets of objects. However, the perceptual nature of this representation and how it interacts with the processes involved in numerical judgements remain unclear. This study aims to address these issues by studying the interference of length on numerosity under different perceptual and response conditions. The first experiment shows that the influence of length does not depend on the actual length but on subjective values reflecting the way length is perceived in a given visual context. The Müller-Lyer illusion was used to manipulate the perceived length of two dot arrays independently of their actual length. When the length of two dot arrays was equal but perceived as different due to the illusion, participants erroneously reported differences in the number of dots contained in each array, evidencing a similar effect of Müller-Lyer illusion on length and numerosity comparison. This finding was replicated in a second experiment where participants had to give a verbal estimate of the number of dots contained in a given array, thereby eliminating the choice between a small or large response. Compared with a neutral condition, estimations were systematically larger than the actual number of dots as the illusory length increased. These results demonstrate that the illusory-induced experience of length influences numerosity estimation over and beyond objective cues and that this influence is not a response selection bias.

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Gheorghiu, Elena, and Dirk Goldschmitt. "Spatial and chromatic properties of numerosity estimation in isolation and context." PLOS ONE 17, no. 9 (September 15, 2022): e0274564. http://dx.doi.org/10.1371/journal.pone.0274564.

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Numerosity estimation around the subitizing range is facilitated by a shape-template matching process and shape-coding mechanisms are selective to visual features such as colour and luminance contrast polarity. Objects in natural scenes are often embedded within other objects or textured surfaces. Numerosity estimation is improved when objects are grouped into small clusters of the same colour, a phenomenon termed groupitizing, which is thought to leverage on the subitizing system. Here we investigate whether numerosity mechanisms around the subitizing range are selective to colour, luminance contrast polarity and orientation, and how spatial organisation of context and target elements modulates target numerosity estimation. Stimuli consisted of a small number (3-to-6) of target elements presented either in isolation or embedded within context elements. To examine selectivity to colour, luminance polarity and orientation, we compared target-only conditions in which all elements were either the same or different along one of these feature dimensions. We found comparable performance in the same and different feature conditions, revealing that subitizing mechanism do not depend on ‘on-off’ luminance-polarity, colour or orientation channel interactions. We also measured the effect of varying spatial organisation of (i) context, by arranging the elements either in a grid, mirror-symmetric, translation-symmetric or random; (ii) target, by placing the elements either mirror-symmetric, on the vertices of simple shapes or random. Our results indicate higher accuracy and lower RTs in the grid compared to all other context types, with mirror symmetric, translation and random arrangements having comparable effects on target numerosity. We also found improved performance with shape-target followed by symmetric and random target arrangements in the absence and presence of context. These findings indicate that numerosity mechanisms around the subitizing range are not selective to colour, luminance polarity and orientation, and that symmetric, translation and random contexts organisations inhibit target-numerosity encoding stronger than regular/grid context.

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Wilcox, Keith, and Sonja Prokopec. "Restraint That Blinds: Attention Narrowing and Consumers’ Response to Numerosity in Self-Control Decisions." Journal of Consumer Research 46, no. 2 (December 13, 2018): 371–87. http://dx.doi.org/10.1093/jcr/ucy078.

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Abstract A significant amount of research on numerosity demonstrates that product perceptions are often influenced by the scale on which numerical attribute information is presented. However, fewer studies have examined how self-control is influenced by the numerosity of cost information (e.g., price, nutritional content) in situations that may violate a personal goal. The present research demonstrates that, in such situations, the numerosity of cost information has a stronger influence on self-control when consumers are highly focused on restraint. Because restrained consumers regulate their behavior by anticipating the negative emotions from violating their goals, they experience a narrowing of attention during self-control decisions that makes them more reliant on numerosity as a cue for judgment. The results of eight experiments demonstrate that consumers who are primed or predisposed to be high in restraint display less self-control when cost information is presented on a contracted scale with small numbers compared to an expanded scale with large numbers. When consumers are less focused on restraint, numerosity has less of an effect on self-control because unrestrained consumers do not experience an analogous narrowing of attention.

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Fornaciai, Michele, and Joonkoo Park. "Early Numerosity Encoding in Visual Cortex Is Not Sufficient for the Representation of Numerical Magnitude." Journal of Cognitive Neuroscience 30, no. 12 (December 2018): 1788–802. http://dx.doi.org/10.1162/jocn_a_01320.

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Recent studies have demonstrated that the numerosity of visually presented dot arrays is represented in low-level visual cortex extremely early in latency. However, whether or not such an early neural signature reflects the perceptual representation of numerosity remains unknown. Alternatively, such a signature may indicate the raw sensory representation of the dot-array stimulus before becoming the perceived representation of numerosity. Here, we addressed this question by using the connectedness illusion, whereby arrays with pairwise connected dots are perceived to be less numerous compared with arrays containing isolated dots. Using EEG and fMRI in two independent experiments, we measured neural responses to dot-array stimuli comprising 16 or 32 dots, either isolated or pairwise connected. The effect of connectedness, which reflects the segmentation of the visual stimulus into perceptual units, was observed in the neural activity after 150 msec post stimulus onset in the EEG experiment and in area V3 in the fMRI experiment using a multivariate pattern analysis. In contrast, earlier neural activity before 100 msec and in area V2 was strictly modulated by numerosity regardless of connectedness, suggesting that this early activity reflects the sensory representation of a dot array before perceptual segmentation. Our findings thus demonstrate that the neural representation for numerosity in early visual cortex is not sufficient for visual number perception and suggest that the perceptual encoding of numerosity occurs at or after the segmentation process that takes place later in area V3.

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OYAMA, TADASU. "The effect of stimulus organization on numerosity discrimination." Japanese Psychological Research 28, no. 2 (1986): 77–86. http://dx.doi.org/10.4992/psycholres1954.28.77.

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Dehaene, Stanislas, and Jean-Pierre Changeux. "Development of Elementary Numerical Abilities: A Neuronal Model." Journal of Cognitive Neuroscience 5, no. 4 (October 1993): 390–407. http://dx.doi.org/10.1162/jocn.1993.5.4.390.

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Despite their lack of language, human infants and several animal species possess some elementary abilities for numerical processing. These include the ability to recognize that a given numerosity is being presented visually or auditorily, and, at a later stage of development, the ability to compare two nume-rosities and to decide which is larger. We propose a model for the development of these abilities in a formal neuronal network. Initially, the model is equipped only with unordered numerosity detectors. It can therefore detect the numerosity of an input set and can be conditioned to react accordingly. In a later stage, the addition of a short-term memory network is shown to be sufficient for number comparison abilities to develop. Our computer simulations account for several phenomena in the numerical domain, including the distance effect and Fechner's law for numbers. They also demonstrate that infants' numerosity detection abilities may be explained without assuming that infants can count. The neurobiological bases of the critical components of the model are discussed.

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Overvliet, Krista E., Kim Verlaers, Ralf T. Krampe, and Johan Wagemans. "The effect of perceptual grouping on haptic numerosity perception." Seeing and Perceiving 25 (2012): 183. http://dx.doi.org/10.1163/187847612x648134.

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In order to investigate the effect of perceptual grouping on haptic numerosity perception, we asked participants to explore tangible dot patterns and report the number of dots present in the display. We hypothesized that when there are subsets of dots that can be grouped together, exploration time will be shorter as compared to a display where no grouping takes place. The base display consists of dots that are equally spaced on a straight line. We manipulated subset grouping by using both proximity and configurational cues. By placing subsets of dots closer together or placing them in a spatial configuration (e.g., in a triangular shape with three dots, or a rectangular shape with four dots), while keeping the total exploration distance constant, we expected to find shorter exploration times as compared to the base display. The results indeed show that both these cues yield faster exploration. We therefore conclude that both proximity and configurational information can influence haptic grouping for numerosity judgments.

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Verlaers, K., J. Wagemans, and K. E. Overvliet. "The effect of perceptual grouping on haptic numerosity perception." Attention, Perception, & Psychophysics 77, no. 1 (September 24, 2014): 353–67. http://dx.doi.org/10.3758/s13414-014-0770-8.

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Adriano, Andrea, Luca Rinaldi, and Luisa Girelli. "Nonsymbolic numerosity in sets with illusory-contours exploits a context-sensitive, but contrast-insensitive, visual boundary formation process." Attention, Perception, & Psychophysics 84, no. 1 (October 17, 2021): 205–20. http://dx.doi.org/10.3758/s13414-021-02378-y.

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AbstractThe visual mechanisms underlying approximate numerical representation are still intensely debated because numerosity information is often confounded with continuous sensory cues (e.g., texture density, area, convex hull). However, numerosity is underestimated when a few items are connected by illusory contours (ICs) lines without changing other physical cues, suggesting in turn that numerosity processing may rely on discrete visual input. Yet, in these previous works, ICs were generated by black-on-gray inducers producing an illusory brightness enhancement, which could represent a further continuous sensory confound. To rule out this possibility, we tested participants in a numerical discrimination task in which we manipulated the alignment of 0, 2, or 4 pairs of open/closed inducers and their contrast polarity. In Experiment 1, aligned open inducers had only one polarity (all black or all white) generating ICs lines brighter or darker than the gray background. In Experiment 2, open inducers had always opposite contrast polarity (one black and one white inducer) generating ICs without strong brightness enhancement. In Experiment 3, reverse-contrast inducers were aligned but closed with a line preventing ICs completion. Results showed that underestimation triggered by ICs lines was independent of inducer contrast polarity in both Experiment 1 and Experiment 2, whereas no underestimation was found in Experiment 3. Taken together, these results suggest that mere brightness enhancement is not the primary cause of the numerosity underestimation induced by ICs lines. Rather, a boundary formation mechanism insensitive to contrast polarity may drive the effect, providing further support to the idea that numerosity processing exploits discrete inputs.

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Zhou, Cihua, Wei Xu, Yujie Liu, Zhichao Xue, Rui Chen, Ke Zhou, and Jia Liu. "Numerosity representation in a deep convolutional neural network." Journal of Pacific Rim Psychology 15 (January 2021): 183449092110126. http://dx.doi.org/10.1177/18344909211012613.

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Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.

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Saiu, Salvatore, Francesco Massara, and Daniele Porcheddu. "Super-Items Created by Mere Presence of Visual Material on Retail Displays." International Business Research 13, no. 5 (April 2, 2020): 1. http://dx.doi.org/10.5539/ibr.v13n5p1.

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This study focuses on the perception of numerosity of item sets placed in retail displays. Previous studies have demonstrated that the item sets’ perceived numerosity decreases as the number of polygonal shapes placed in a panel behind a display increases. Such a result was explained by a non-spatial clustering phenomenon exerted by the shapes. Our research reveals the perceptual mechanisms underlying the described effect. Using an eye-tracking procedure, we highlight that upon augmenting the number of polygonal shapes in the decision-making context: (a) there is a significant decrease in the number of total fixations per display; (b) there is an underestimation of the perceived numerosity of item sets involved. The findings suggest that the mere presence of visual shapes can alter perception generating complex objects or “super-items”, which tend to perceptually replace entire item sets. We also propose managerial implications in terms of category management and merchandising.

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Palomares, Melanie, Paul R. Smith, and Holley C. Pitts. "Enumeration of Small and Large Numerosities: The Effect of Element Visibility." Quarterly Journal of Experimental Psychology 65, no. 6 (June 2012): 1185–94. http://dx.doi.org/10.1080/17470218.2011.648647.

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Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1–8) or by tens (10–80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.

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김혜진 and Sang Chul Chong. "The Effect of Density and Size Variance on Numerosity Estimation." Korean Journal of Cognitive and Biological Psychology 29, no. 2 (April 2017): 173–80. http://dx.doi.org/10.22172/cogbio.2017.29.2.005.

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Luwel, Koen, Lieven Verschaffel, Patrick Onghena, and Erik De Corte. "Strategic Aspects of Numerosity Judgment: The Effect of Task Characteristics." Experimental Psychology (formerly "Zeitschrift für Experimentelle Psychologie") 50, no. 1 (January 1, 2003): 63–75. http://dx.doi.org/10.1026//1618-3169.50.1.63.

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Luwel, Koen, Lieven Verschaffel, Patrick Onghena, and Erik De Corte. "Strategic Aspects of Numerosity Judgment: The Effect of Task Characteristics." Experimental Psychology 50, no. 1 (January 2003): 63–75. http://dx.doi.org/10.1027//1618-3169.50.1.63.

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In previous investigations we documented that people use several strategies to determine different numerosities of blocks that are presented in a square grid. One of these strategies is the clever subtraction strategy, wherein the number of empty squares in the grid is subtracted from the total number of squares in the grid. In the present study we investigated participants’ flexibility in strategy use when varying the shape of the grid. Analysis of the results in terms of the theoretical framework of Lemaire and Siegler (1995 ) regarding strategic change shows that this contextual variable affected the frequency, execution time, and accuracy of subjects’ use of the subtraction strategy. The usefulness of this framework for analyzing the nature of the adaptation to contextual variations is discussed. From a methodological point of view, this study documents the potential of Beem’s (1993 , 1999) segmented linear regression models for assessing subjects’ strategy use in cognitive tasks.

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Nejad, Mona Rahimi, and Selçuk Onay. "Numerosity and Cognitive Complexity as Moderators of the Medium Effect." Procedia Economics and Finance 14 (2014): 445–53. http://dx.doi.org/10.1016/s2212-5671(14)00733-3.

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Speelman, Craig P., and Emma Shadbolt. "The role of awareness of repetition during the development of automaticity in a dot-counting task." PeerJ 6 (January 31, 2018): e4329. http://dx.doi.org/10.7717/peerj.4329.

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This study examined whether being aware of the repetition of stimuli in a simple numerosity task could aid the development of automaticity. The numerosity task used in this study was a simple counting task. Thirty-four participants were divided into two groups. One group was instructed that the stimuli would repeat many times throughout the experiment. The results showed no significant differences in the way automatic processing developed between the groups. Similarly, there was no correlation between the point at which automatic processing developed and the point at which participants felt they benefitted from the repetition of stimuli. These results suggest that extra-trial features of a task may have no effect on the development of automaticity, a finding consistent with the instance theory of automatisation.

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Cleland, Alexandra A., Kathryn Corsico, Kirstin White, and Rebecca Bull. "Non-symbolic numerosities do not automatically activate spatial–numerical associations: Evidence from the SNARC effect." Quarterly Journal of Experimental Psychology 73, no. 2 (September 9, 2019): 295–308. http://dx.doi.org/10.1177/1747021819875021.

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The SNARC (spatial–numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards vs. pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitising range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards/inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2, and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range or within the subset of the subitising range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical–spatial associations.

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Battaglini, Luca, Federica Mena, and Clara Casco. "Improving motion detection via anodal transcranial direct current stimulation." Restorative Neurology and Neuroscience 38, no. 5 (November 13, 2020): 395–405. http://dx.doi.org/10.3233/rnn-201050.

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Background: To study motion perception, a stimulus consisting of a field of small, moving dots is often used. Generally, some of the dots coherently move in the same direction (signal) while the rest move randomly (noise). A percept of global coherent motion (CM) results when many different local motion signals are combined. CM computation is a complex process that requires the integrity of the middle-temporal area (MT/V5) and there is evidence that increasing the number of dots presented in the stimulus makes such computation more efficient. Objective: In this study, we explored whether anodal direct current stimulation (tDCS) over MT/V5 would increase individual performance in a CM task at a low signal-to-noise ratio (SNR, i.e. low percentage of coherent dots) and with a target consisting of a large number of moving dots (high dot numerosity, e.g. >250 dots) with respect to low dot numerosity (<60 dots), indicating that tDCS favour the integration of local motion signal into a single global percept (global motion). Method: Participants were asked to perform a CM detection task (two-interval forced-choice, 2IFC) while they received anodal, cathodal, or sham stimulation on three different days. Results: Our findings showed no effect of cathodal tDCS with respect to the sham condition. Instead, anodal tDCS improves performance, but mostly when dot numerosity is high (>400 dots) to promote efficient global motion processing. Conclusions: The present study suggests that tDCS may be used under appropriate stimulus conditions (low SNR and high dot numerosity) to boost the global motion processing efficiency, and may be useful to empower clinical protocols to treat visual deficits.

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Bertamini, Marco, Michele Zito, Nicholas E. Scott-Samuel, and Johan Hulleman. "Spatial clustering and its effect on perceived clustering, numerosity, and dispersion." Attention, Perception, & Psychophysics 78, no. 5 (May 3, 2016): 1460–71. http://dx.doi.org/10.3758/s13414-016-1100-0.

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Krishna, Aradhna, and Priya Raghubir. "The effect of line configuration on perceived numerosity of dotted lines." Memory & Cognition 25, no. 4 (July 1997): 492–507. http://dx.doi.org/10.3758/bf03201125.

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Lopiccolo, Dominique, and Charles B. Chang. "Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates." PLOS ONE 16, no. 12 (December 16, 2021): e0261146. http://dx.doi.org/10.1371/journal.pone.0261146.

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Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures—namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates’ results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates’ results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates’. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing—each involved at varying levels depending on individual and task factors.

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Liu, Hsin-Hsien, and Hsuan-Yi Chou. "Attribute specification effect on hedonic and utilitarian options." Australian Journal of Management 47, no. 2 (October 29, 2021): 322–41. http://dx.doi.org/10.1177/03128962211054236.

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Integrating ideas and theories from the numerosity effect and utilitarian/hedonic consumption, this research explores how hedonic and utilitarian attributes specified with contracted and expanded specifications affect consumer preferences. Results from two experiments indicate an expanded utilitarian attribute enhances consumer preference for choosing the utilitarian option. However, an expanded hedonic attribute does not influence preference for choosing the hedonic option. The relative perceived guilt of the hedonic option and the perceived attractiveness of the utilitarian option mediate the effect. Acquisition format (purchase vs windfall) moderates this effect by influencing consumers’ perceived guilt from choosing the hedonic option. JEL Classification: C91, D12, M31

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Broze, Yuri, Brandon T. Paul, Erin T. Allen, and Kathleen M. Guarna. "Polyphonic Voice Multiplicity, Numerosity, and Musical Emotion Perception." Music Perception 32, no. 2 (December 1, 2014): 143–59. http://dx.doi.org/10.1525/mp.2014.32.2.143.

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Three experimental studies suggest that music with more musical voices (higher voice multiplicity) tends to be perceived more positively. In the first experiment, participants heard brief extracts from polyphonic keyboard works representing conditions of one, two, three, or four concurrent musical voices. Two basic emotions (happiness and sadness) and two social emotions (pride and loneliness) were rated on a continuous scale. Listeners rated excerpts with higher voice multiplicity as sounding more happy, less sad, less lonely, and more proud. Results from a second experiment indicate that this effect might extend to positive and negative emotions more generally. In a third experiment, participants were asked to count (denumerate) the number of musical voices in the same stimuli. Denumeration responses corresponded closely with ratings for both positive and negative emotions, suggesting that a single musical feature or percept might play a role in both. Possible roles for both symbolic and psychoacoustic musical features are discussed.

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Hajnal, Alen, Jennifer Vonk, and Virgil Zeigler-Hill. "Peer influence on conformity and confidence in a perceptual judgment task." Psihologija 53, no. 1 (2020): 101–13. http://dx.doi.org/10.2298/psi190107018h.

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Undergraduate college students were presented with two arrays of dots varying in numerosity on a computer screen and asked to indicate if the arrays differed in number. They also rated their level of confidence in their responses. Trials varied in difficulty based on the size of the arrays. On half of the trials, participants were shown the ostensible responses of confederates to test the effect of peer influence on numerosity judgments and participant confidence. On the other half of the trials, participants received no information about the responses of the confederates to provide a measure of baseline performance. Higher levels of conformity were observed for the difficult trials, on which participants were both less accurate and less confident. However, confidence ratings were influenced by peer judgments for easy trials but not for difficult trials. These data suggest that task difficulty influences conformity when making perceptual judgments.

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Takeshima, Y., and J. Gyoba. "Differential effect of visual and auditory spatial cues on visual numerosity judgment." Journal of Vision 14, no. 10 (August 22, 2014): 428. http://dx.doi.org/10.1167/14.10.428.

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Cohen, Zahira, and Avishai Henik. "Visual and Tactile Enumeration and the Effect of Numerosity Range on Enumeration." Journal of Vision 16, no. 12 (September 1, 2016): 155. http://dx.doi.org/10.1167/16.12.155.

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Reynvoet, Bert, Helene Vos, and Avishai Henik. "Comparative Judgment of Familiar Objects Is Modulated by Their Size." Experimental Psychology 65, no. 6 (November 2018): 353–59. http://dx.doi.org/10.1027/1618-3169/a000418.

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Abstract. Perceptual decisions such as that we have more strawberries than apples left in our fruit basket seem to be made effortlessly. However, it is not examined yet whether such decisions are also biased by the size of the objects, just like numerosity comparisons with meaningless dot arrays. We presented two homogeneous sets of larger and smaller fruits (e.g., three apples and four strawberries), and participants had to indicate which set was more numerous. Although accuracy was nearly perfect, a strong congruency effect was found in reaction times, showing it is more difficult to compare the numerosities of sets of 2 apples and 3 strawberries than the opposite, that is, 3 apples and 2 strawberries. Because the stimuli were selected to simulate everyday conditions as much as possible, the present results suggest that most likely also comparative numerosity judgment in daily life is biased by nonnumerical cues such as size of the objects.

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Lindemann, Oliver, and Michael D. Tira. "Operational Momentum in Numerosity Production Judgments of Multi-Digit Number Problems." Zeitschrift für Psychologie 219, no. 1 (January 2011): 50–57. http://dx.doi.org/10.1027/2151-2604/a000046.

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The current study demonstrates a numerosity production task and investigates approximate mental calculations with two-digit numbers. Participants were required to produce random dot patterns to indicate the size of two-digit numbers and the results of addition and subtraction problems. The stimuli in the calculation task consisted of problems requiring a carry operation (e.g., 24 + 18) or no-carry problems (e.g., 24 + 53) or zero problems (e.g., 24 + 0). Our analysis revealed that the outcomes of additions were estimated to be larger than the outcomes of subtractions. Interestingly, this judgment bias was present for no-carry and zero problems but not for carry problems. Taken together, the presented data provide empirical support for the presence of an operational momentum effect (OM effect) in multi-digit number arithmetic. These findings and the dissociation of the OM effect for carry and no-carry problems are discussed in the context of recent models on multi-digit number processing.

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Lõoke, Miina, Lieta Marinelli, Carla Jade Eatherington, Christian Agrillo, and Paolo Mongillo. "Do Domestic Dogs (Canis lupus familiaris) Perceive Numerosity Illusions?" Animals 10, no. 12 (December 4, 2020): 2304. http://dx.doi.org/10.3390/ani10122304.

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Recent studies have showed that domestic dogs are only scantly susceptible to visual illusions, suggesting that the perceptual mechanisms might be different in humans and dogs. However, to date, none of these studies have utilized illusions that are linked to quantity discrimination. In the current study, we tested whether dogs are susceptible to a linear version of the Solitaire illusion, a robust numerosity illusion experienced by most humans. In the first experiment, we tested dogs’ ability to discriminate items in a 0.67 and 0.75 numerical ratio. The results showed that dogs’ quantity discrimination abilities fall in between these two ratios. In Experiment 2, we presented the dogs with the Solitaire illusion pattern using a spontaneous procedure. No evidence supporting any numerosity misperception was found. This conclusion was replicated in Experiment 3, where we manipulated dogs’ initial experience with the stimuli and their contrast with the background. The lack of dogs’ susceptibility to the Solitaire illusion suggests that numerical estimation of dogs is not influenced by the spatial arrangement of the items to be enumerated. In view of the existing evidence, the effect may be extended to dogs’ quantitative abilities at large.

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Adriano, Andrea, Luisa Girelli, and Luca Rinaldi. "The ratio effect in visual numerosity comparisons is preserved despite spatial frequency equalisation." Vision Research 183 (June 2021): 41–52. http://dx.doi.org/10.1016/j.visres.2021.01.011.

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Tricoche, Leslie, Elisabetta Monfardini, Amélie J. Reynaud, Justine Epinat-Duclos, Denis Pélisson, Jérôme Prado, and Martine Meunier. "Peer Presence Effect on Numerosity and Phonological Comparisons in 4th Graders: When Working with a SchoolMate Makes Children More Adult-like." Biology 10, no. 9 (September 12, 2021): 902. http://dx.doi.org/10.3390/biology10090902.

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Little is known about how peers’ mere presence may, in itself, affect academic learning and achievement. The present study addresses this issue by exploring whether and how the presence of a familiar peer affects performance in a task assessing basic numeracy and literacy skills: numerosity and phonological comparisons. We tested 99 fourth-graders either alone or with a classmate. Ninety-seven college-aged young adults were also tested on the same task, either alone or with a familiar peer. Peer presence yielded a reaction time (RT) speedup in children, and this social facilitation was at least as important as that seen in adults. RT distribution analyses indicated that the presence of a familiar peer promotes the emergence of adult-like features in children. This included shorter and less variable reaction times (confirmed by an ex-Gaussian analysis), increased use of an optimal response strategy, and, based on Ratcliff’s diffusion model, speeded up nondecision (memory and/or motor) processes. Peer presence thus allowed children to at least narrow (for demanding phonological comparisons), and at best, virtually fill in (for unchallenging numerosity comparisons) the developmental gap separating them from adult levels of performance. These findings confirm the influence of peer presence on skills relevant to education and lay the groundwork for exploring how the brain mechanisms mediating this fundamental social influence evolve during development.

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Leo, Fabrizio, Sara Nataletti, and Luca Brayda. "Non-informative vision improves spatial tactile discrimination on the shoulder but does not influence detection sensitivity." Experimental Brain Research 238, no. 12 (October 13, 2020): 2865–75. http://dx.doi.org/10.1007/s00221-020-05944-2.

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Abstract Vision of the body has been reported to improve tactile acuity even when vision is not informative about the actual tactile stimulation. However, it is currently unclear whether this effect is limited to body parts such as hand, forearm or foot that can be normally viewed, or it also generalizes to body locations, such as the shoulder, that are rarely before our own eyes. In this study, subjects consecutively performed a detection threshold task and a numerosity judgment task of tactile stimuli on the shoulder. Meanwhile, they watched either a real-time video showing their shoulder or simply a fixation cross as control condition. We show that non-informative vision improves tactile numerosity judgment which might involve tactile acuity, but not tactile sensitivity. Furthermore, the improvement in tactile accuracy modulated by vision seems to be due to an enhanced ability in discriminating the number of adjacent active electrodes. These results are consistent with the view that bimodal visuotactile neurons sharp tactile receptive fields in an early somatosensory map, probably via top-down modulation of lateral inhibition.

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Norris, Jade Eloise, Sarah Clayton, Camilla Gilmore, Matthew Inglis, and Julie Castronovo. "The measurement of approximate number system acuity across the lifespan is compromised by congruency effects." Quarterly Journal of Experimental Psychology 72, no. 5 (June 4, 2018): 1037–46. http://dx.doi.org/10.1177/1747021818779020.

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Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults’ ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.

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Celeghin, Alessia, Silvia Savazzi, Marissa Barabas, Matteo Bendini, and Carlo A. Marzi. "Blindsight is sensitive to stimulus numerosity and configuration: evidence from the redundant signal effect." Experimental Brain Research 233, no. 5 (February 25, 2015): 1617–23. http://dx.doi.org/10.1007/s00221-015-4236-6.

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Chau, Edwin, Carolyn A. Murray, and Ladan Shams. "Hierarchical drift diffusion modeling uncovers multisensory benefit in numerosity discrimination tasks." PeerJ 9 (October 27, 2021): e12273. http://dx.doi.org/10.7717/peerj.12273.

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Studies of accuracy and reaction time in decision making often observe a speed-accuracy tradeoff, where either accuracy or reaction time is sacrificed for the other. While this effect may mask certain multisensory benefits in performance when accuracy and reaction time are separately measured, drift diffusion models (DDMs) are able to consider both simultaneously. However, drift diffusion models are often limited by large sample size requirements for reliable parameter estimation. One solution to this restriction is the use of hierarchical Bayesian estimation for DDM parameters. Here, we utilize hierarchical drift diffusion models (HDDMs) to reveal a multisensory advantage in auditory-visual numerosity discrimination tasks. By fitting this model with a modestly sized dataset, we also demonstrate that large sample sizes are not necessary for reliable parameter estimation.

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Smets, Karolien, Delphine Sasanguie, Dénes Szücs, and Bert Reynvoet. "The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison." Journal of Cognitive Psychology 27, no. 3 (January 3, 2015): 310–25. http://dx.doi.org/10.1080/20445911.2014.996568.

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Luwel, Koen, and Lieven Verschaffel. "Adapting Strategy Choices to Situational Factors: The Effect of Time Pressure on Children’s Numerosity Judgement Strategies." Psychologica Belgica 43, no. 4 (January 1, 2003): 269. http://dx.doi.org/10.5334/pb.1013.

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Journal articles on the topic 'Numerosity effect'

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