Perceptual grouping, not covert attention, drives the connectedness effect in the ANS

Perceptual grouping, not covert attention, drives the connectedness effect in the ANS | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Perceptual grouping, not covert attention, drives the connectedness effect in the ANS Andrea Adriano, Michaël Vande Velde This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7767227/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Feb, 2026 Read the published version in Psychological Research → Version 1 posted 8 You are reading this latest preprint version Abstract A robust finding in numerical cognition is that connecting items within an array leads to systematic underestimation of numerosity. This provides evidence that approximate numerosity perception relies on discrete objects rather than on continuous variables (e.g., total area, density, convex hull). While this connectedness effect is often attributed to perceptual grouping, an alternative interpretation is that connected items may capture covert attention, thereby biasing the sampling of visual information. We tested these competing accounts by combining a numerosity estimation task with a target-detection task modeled after Posner’s cueing paradigm. On each trial, participants viewed dot arrays (14–20 items) that included two red lines, either connecting a pair of dots or terminating near unconnected dots. A target diamond could appear either near (congruent) or far (incongruent) from the quadrant containing the red lines. Participants first performed a go/no-go detection task, then estimated the array numerosity. Replicating prior work, connected arrays were consistently underestimated relative to unconnected ones. Crucially, detection performance showed no evidence of attentional capture: reaction times and accuracy did not differ as a function of connectedness or target position. These findings demonstrate that the underestimation effect cannot be attributed to covert attentional allocation. Instead, they support the view that perceptual grouping—rather than attentional biases—drives the connectedness effect in the Approximate Number System. More broadly, our results strengthen the case for segmentation-based mechanisms as a critical foundation of visual number perception. Numerosity perception Connectedness effect Perceptual grouping Covert attention Approximate Number System (ANS) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction There is broad consensus that humans and many animal species share a fundamental neurocognitive mechanism — the Approximate Number System (ANS) — which enables the extraction of non-symbolic, approximate numerical representations from large sets of objects (Dehaene et al., 1998 ; Nieder, 2016 ). Evidence for this system has been documented across a variety of species (e.g., Agrillo et al., 2009 ; Brannon & Terrace, 1998 ; Ditz & Nieder, 2015 ) and in early stages of human development (e.g., Brannon et al., 2004 ; Xu & Spelke, 2000 ; Xu et al., 2005 ). From an evolutionary perspective, this underscores the adaptive value of a specialized numerical mechanism for survival-relevant tasks, such as comparing group sizes of conspecifics or rivals, or selecting the larger food source (e.g., Agrillo et al., 2012 ; Benson-Amram et al., 2011 ; Perdue et al., 2012 ; Piantadosi & Cantlon, 2017 ). A hallmark behavioral property of the ANS is its compliance with Weber’s law, observed consistently across cultures, developmental stages, and species (e.g., Whalen et al., 1999 ). Weber’s law states that the just-noticeable difference between two stimuli scales with their magnitude, or more strictly, that discrimination accuracy depends on the ratio of their intensities (Brus et al., 2019 ; Dehaene, 2003 ). This has been extensively investigated using rapid numerical comparison tasks, in which participants choose the larger or smaller of two briefly presented arrays. In such tasks, error rates and reaction times increase as the numerical ratio approaches unity, indicating that non-symbolic number processing follows Weber’s law (e.g., Revkin et al., 2008 ). At the neural level, numerosity-selective responses have been identified in the parietal cortex of both humans and macaques (e.g., Castelli et al., 2006 ; Harvey et al., 2013 ; Nieder & Miller, 2004 ; Piazza et al., 2004 ). More recent findings suggest that a wider network, including early visual areas, may also contribute to numerosity processing (DeWind et al., 2019 ; Fornaciai et al., 2017 ; Fornaciai & Park, 2018 ; Park et al., 2015 ; Van Rinsveld et al., 2020 ). Although the existence of the ANS is widely accepted, the precise visual computations it relies on remain debated. Some models posit that numerosity is obtained through a segmentation-and-individuation process that counts discrete items regardless of their physical properties such as shape, size, or position (Burr & Ross, 2008 ; Dehaene & Changeux, 1993 ; Stoianov & Zorzi, 2012 ; Verguts & Fias, 2004 ). Strong support for this view comes from numerosity adaptation studies, where prolonged exposure to a set of a given numerosity biases the perceived numerosity of subsequent sets in the adapted location (Burr & Ross, 2008 ; Thompson & Burr, 2009 ). Typically, adaptation to a large number reduces the perceived numerosity of a smaller set, and adaptation to a small number increases the perceived numerosity of a larger set (Aagten-Murphy & Burr, 2016 ; Aulet & Lourenco, 2023 ). Such adaptation effects, observed across sensory modalities, have led to the proposal that numerosity functions as a primary sensory attribute, akin to colour, motion, or spatial frequency (Arrighi et al., 2014 ; Burr et al., 2025 , but see Yousif et al., 2024 , 2025 ). However, other psychophysical evidence challenges the notion of numerosity as a primary sense (e.g., Durgin, 2008 ). Alternative accounts suggest that numerical judgments are derived indirectly from continuous visual features correlated with numerosity, such as total occupied area, density, or luminance (Allik & Tuulmets, 1991 ; Dakin et al., 2011 ; Durgin, 2008 ; Gebuis & Reynvoet, 2012a , 2012b , 2012c ). The occupancy model (Allik & Tuulmets, 1991 ) proposes that numerosity is estimated by summing the “virtual” area occupied by items, with greater overlap leading to underestimation. Numerous studies have shown that item size, total surface area, convex hull, and density can all bias numerosity discrimination (e.g., Gebuis & Reynvoet, 2012a ; Hurewitz et al., 2006 ; Katzin et al., 2020 ). Given that it is physically impossible to create two sets differing in numerosity yet identical in all continuous features, it has been argued that the visual system may integrate one or more of these correlated cues to infer number, without requiring a dedicated discrete-number mechanism (Gebuis et al., 2016 ; Leibovich et al., 2017 ). In line with this, Durgin ( 2008 ) highlighted the role of texture-density statistics, while Dakin et al. ( 2011 ) proposed that density estimation could be achieved by analysing spatial-frequency content. Other biologically inspired models suggest that “contrast energy” could serve as a proxy for numerosity (Morgan et al., 2014 ). Still, recent work indicates that a dedicated density-processing system may operate for very large numerosities (≈ 100 items), where crowding prevents individual segmentation (Anobile et al., 2014 , 2016 ; cf. Portley et al., 2019). In such cases, Weber fractions remain constant at low numerosities but decrease with the square root of numerosity beyond a critical threshold (Anobile et al., 2014 ). This pattern suggests that, at least for moderate numerosities, visual number processing depends on item segmentation and cannot be fully reduced to texture-density mechanisms (Anobile et al., 2015 ; Pomè et al., 2019 ). Therefore, several investigations have employed innovative experimental approaches to directly test competing explanations, making use of visual illusions such as size illusions, illusory contours (ICs) and connectedness-based grouping (e.g., Adriano et al., 2021 , 2022 ; Franconeri et al., 2009 ; Picon et al., 2019 ). Consistent with the Gestalt principle of uniform connectedness (Palmer & Rock, 1994 ), a number of studies have reported that perceived numerosity is systematically underestimated when elements within an array are linked either by actual connecting lines (Anobile et al., 2017 ; Fornaciai & Park, 2018 ; Franconeri et al., 2009 ; He et al., 2009 , 2015 ; Pomè et al., 2022 ) or by task-irrelevant illusory connections (Adriano et al., 2021 , 2022 ; Adriano & Ciccione, 2024 ; Kirjakovski & Matsumoto, 2016 ), even when low-level visual attributes are held constant across connectedness conditions. Collectively, these results indicate that visual segmentation processes are central to the extraction of discrete numerical information. However, connected objects differ from unconnected ones not only in their grouping status but also in their visual salience: their “multi-part” structure can make them pop out from surrounding items, potentially attracting more attention to their location (He et al., 2009 ). Such attentional capture could reduce the processing time available for other items in the display, leading to their partial exclusion from the magnitude representation. In this view, the observed numerical underestimation reported with the connectedness illusion, might arise from differences in attentional allocation rather than from perceptual grouping per se. Previous studies have attempted to control for overt attentional shifts by using very brief stimulus presentations (e.g., 50 ms) to prevent eye movements (He et al., 2009 ). Paradoxically, these studies found that the underestimation effect was even larger at short exposure durations. Therefore, this leaves open the possibility that covert attention — the selective processing of visual information without eye movements (Posner, 1980 ) — could still play a role. If connected items automatically attract covert attention, they might draw processing resources away from other regions of the display, thereby biasing numerosity judgments through changes in the effective sampling of the scene. To the best of our knowledge, no previous study has accounted for this potential alternative explanation of the connectedness effect. To address this gap, we designed a novel task inspired by Posner’s classic attentional paradigm (1980). Similarly to the classic Posner cueing task, our paradigm required participants to identify a briefly flashed target (e.g., a diamond) that appeared either near (congruent) or far (incongruent) from the spatial position of two red lines acting as exogenous cues. The red lines were intermingled with a variable number of dots and could either connect or remain unconnected to two of them. Participants performed a go/no-go detection task, responding as quickly as possible when the target appeared. Immediately afterward, they reported the total number of objects displayed on the screen. We reasoned that, because the red line cues (connected or unconnected) should pop out among the surrounding objects and automatically attract covert attention to their location, detection times would be faster when the target appeared close (congruent) rather than far (incongruent) from the quadrant containing the red lines. Moreover, if connected multi-part objects (e.g., dumbbell objects) intrinsically capture more attention at their location, thereby reducing the resources available for other regions, the performance (RTs and accuracy) in the detection task should be better when the target appears spatially close to the connected, compared to unconnected, objects. Accordingly, a significant interaction between the spatial position of the target (close vs. far) and object type or connectedness level (connected vs. unconnected) would indicate that differences in covert attentional processing underlie the processing of connected objects, potentially explaining the numerosity underestimation driven by the connectedness effect. In this case, the underestimation effect could be attributed to attentional allocation rather than to perceptual grouping per se. Conversely, if no main effects or interactions emerged in the detection task, but connected objects were still underestimated in the estimation task, this would suggest that both connected and unconnected objects engage covert attention similarly, and that the underestimation effect cannot be primarily explained by attentional biases. 2. Methods 2.1. Participants An a priori power analysis was conducted using G*Power 3.1 (Faul et al., 2009 ) to estimate the required sample size. Based on previous findings from a study adopting a comparable design (Adriano & Vande Velde, 2025b ), which reported a partial eta-squared of 0.41 for the Connectedness factor, we calculated that a minimum of 18 participants would be necessary to achieve 80% power in a repeated-measures ANOVA with four conditions (Close Target Connected/Unconnected and Far Target Connected/Unconnected), assuming α = .05. Nineteen participants were recruited for the present study (mean age = 19.52 years, SD = 1.42; 16 females; 17 right-handed participants). All participants had normal or corrected-to-normal vision. The study was approved by the local Ethics Committee. 2.2. Stimuli The stimuli were generated offline using a custom Python/PsychoPy script (Peirce, 2007 ) and presented on a 19” LCD monitor (1280 × 960 pixels; 60 Hz) connected to a standard computer. Each stimulus consisted of a 12 × 12 black grid (cell size: 22 px; line width: 2 px; RGB: −1, − 1, −1). Within the grid, a variable number of white filled dots (radius: 6 px; RGB: 1, 1, 1) with a thin black outline (1 px; RGB: −1, − 1, −1) were placed on the grid intersections. The number of dots varied across four levels: 14, 16, 18, and 20. Each stimulus also included two parallel red lines oriented at 45° (width: 2 px; RGB: 1, 0, 0), randomly positioned in one of four predefined quadrants (upper-left, upper-right, lower-left, lower-right). The position of the lines was counterbalanced across quadrants. To manipulate connectedness, in half of the stimuli two pairs of dots were positioned at the endpoints of the lines, whereas in the other half the same spatial configuration was preserved, but the dots were placed on the opposite sides of the line terminations. In 50% of the trials, a black diamond (20 × 20 px; RGB: −1, − 1, −1) appeared in one of the four grid corners, while in the remaining trials the target was absent. Target position was counterbalanced across quadrants and could be either near (same corner) or far (opposite corner) relative to the quadrant containing the two lines (Fig. 1 ). Overall, the experiment comprised 64 conditions when the target was present (Go trials: 4 numerosities × 2 connectedness levels × 2 target positions × 4 quadrants) and 32 conditions when it was absent (No-Go trials: 4 numerosities × 2 connectedness levels × 4 quadrants). Each combination of quadrant position and numerosity was repeated 8 times (2 target positions × 2 connectedness levels × 2 Go/No-Go conditions). Each condition was presented with two unique visual patterns, resulting in a total of 256 stimuli. 2.3. Procedure The experiment was conducted in a quiet, dimly lit room, and participants were tested individually. The general procedure was explained to each participant before the experiment began, and detailed instructions were also presented on the screen. Participants were comfortably placed at about 50 cm from the screen. Subjects performed a dual task. First, they completed a go/no-go detection task : they had to press the space bar as quickly as possible if a target appeared in one of the corners (go) and withhold their response if it did not (no-go). Second, to ensure that their attention remained focused on the center of the display rather than the corners, participants also completed an estimation task , reporting as accurately as possible the number of objects in the array by typing their estimate on the numerical keypad of a standard PC keyboard. No information about the connectedness of the stimuli was provided to the participants. The participants were, in any case, instructed to provide a numerical estimate between 1 and 40. To familiarize participants with the procedure, the experimental phase was preceded by a short practice session (24 trials) with partial feedback (e.g., negative feedback was given only if the target was not correctly detected, and positive feedback was provided only if the exact number of items was reported in the estimation task). Each trial began with a fixation cross (500 ms), followed by a blank screen (500 ms). The stimulus array was then presented for 250 ms. At 200 ms after onset, a diamond target could appear for 50 ms in one of the four corners of the stimulus. When the target appeared, participants had a fixed response window of 2 seconds to press the space bar with their left hand. This time window was identical for go and no-go trials, regardless of whether a response was made. Immediately after the detection phase, a visual cue (“Estimation:”) prompted participants to enter their estimate of the numerosity on the numerical keypad using their right hand. After each estimation, participants pressed the space bar to proceed to the next trial (Fig. 2 ). The experimental phase consisted of 256 trials, with a self-paced break after half of the trials. The entire session lasted approximately 35 minutes. 3. Results 3.1. Estimation Task 3.1.1. Go vs. No-Go trials overall analysis Data analysis was performed with R/R-Studio (2018, v. 3.6.2; http://www.rstudio.com/ ) software. Individual subjective estimations were examined for the presence of possible aberrant responses (e.g., errors of typing, unrealistic estimations, etc). To exclude extreme values, we applied an outlier removal procedure based on Weber’s law. For each trial, an expected variability was computed as a function of numerosity (σ = w × Numerosity ), where w represents the Weber fraction. Upper and lower cutoffs were then defined as the target Numerosity ± k × σ, with k = 2.5 (number of standard deviations) and w = .18 (average Weber fraction calculated by Anobile et al., 2014 ) determining the tolerance range. Input values falling outside these bounds were discarded, thus ensuring that only responses consistent with the expected scalar variability were retained for further analyses. A repeated-measures ANOVA with Trial type (Go/No-Go), Connectedness (connected/unconnected), and Numerosity (14, 16, 18, 20) as within-subject factors revealed a robust main effect of Numerosity, F (3, 54) = 131.41, p < .001, η²ₚ = .88. Mauchly’s test indicated a violation of sphericity for this factor, therefore Greenhouse–Geisser correction was applied (ε = .50), which confirmed the significance of the effect, p < .001. Crucially, there was also a significant main effect of Connectedness, F (1, 18) = 12.25, p = .003, η²ₚ = .41, with connected arrays being systematically underestimated compared to unconnected ones. The main effect of Trial type was not significant, F (1, 18) = 1.16, p = .296, η²ₚ = .06. None of the two- or three-way interactions reached significance (all ps > .10), including Trial type × Numerosity ( F (3, 54) = 1.42, p = .247, η²ₚ = .07), Connectedness × Numerosity ( F (3, 54) = 1.87, p = .146, η²ₚ = .09), and the three-way interaction ( F (3, 54) = 2.18, p = .100, η²ₚ = .11, Fig. 3 A). Thus, the connectedness effect emerged consistently across numerosities and independently of the go/no-go detection task. To investigate scalar variability, a typical behavioral signature of numerosity estimation, a multiple linear regression was conducted to examine the effects of Numerosity, Connectedness, and Trial Type, as well as their interactions, on the Coefficient of Variation (CoV), used as an estimate of the Weber fraction (e.g., Halberda & Odic, 2014 ). The overall model was not significant, F (7, 8) = 0.52, p = .80, and explained a limited proportion of variance in the outcome ( R ² = .31, adj. R ² = −.29). Examination of individual predictors revealed that none of the main effects or interactions reached statistical significance. Specifically, Numerosity (β = 0.00059, p = .85), Connectedness (β = 0.0197, p = .79), and Trial Type (β = −0.0084, p = .91) did not significantly predict the dependent measure. Similarly, all two-way and the three-way interactions were non-significant (all p > .60, Fig. 3 B). These results indicate that, within the tested conditions, none of the factors or their interactions had a detectable effect on the CoV. 3.1.2. Go trials only analysis We further analysed subjective estimations for Go trials only, in function of the target distance. Then, we ran a repeated-measures ANOVA (2 × 2 × 4) with Target Position (far/close), Connectedness (connected/unconnected) and Numerosity (14, 16, 18, 20) as within-subject factors and the subjective estimation as dependent variable. The results revealed a robust main effect of Numerosity, F (3, 54) = 104.34, ε = .596, p < .001, η²ₚ = .85. A significant main effect of Connectedness was also observed, F (1, 18) = 4.63, p = .045, η²ₚ = .21, suggesting that connected arrays were systematically underestimated compared to unconnected ones. In contrast, the main effect of Target Position was not significant, F (1, 18) = 0.86, p = .367, η²ₚ = .05. None of the interaction effects reached significance (all p s > .20, Fig. 3 C). A multiple linear regression was conducted to examine the effects of Numerosity, Connectedness, and Target Position, as well as their interactions, on the coefficient of variation (CV). The overall model was not significant, F (7, 8) = 1.04, p = .475, indicating that the predictors explained little variance in CV ( R ² = .48, adj. R ² = .02). None of the predictors or interactions reached significance (all p s > .38, Fig. 3 D). In sum, these results replicate the results of the overall analysis. 3.2. Detection Task To further examine potential differences in covert attentional demands between connected and unconnected arrays, we conducted a 2 × 2 × 4 repeated-measures ANOVA on RTs for correct Go-Trial responses (errors discarded: 2.17%), with Target Position (far/close), Connectedness (connected/unconnected), and Numerosity (14, 16, 18, 20) as within-subject factors. The ANOVA of mean RTs revealed no significant main effects of Target Position, F (1, 18) = 0.00003, p = .996, η²ₚ = .001, Connectedness, F (1, 18) = 0.010, p = .920, η²ₚ= .001, or Numerosity, F (3, 54) = 0.456, p = .714, η²ₚ = .025. None of the interactions reached significance: Target Position × Connectedness, F (1, 18) = 0.787, p = .387, η²ₚ = .042; Target Position × Numerosity, F (3, 54) = 1.324, p = .276, η²ₚ = .069; Connectedness × Numerosity, F (3, 54) = 2.727, p = .053, η²ₚ = .132; Target Position × Connectedness × Numerosity, F (3, 54) = 1.118, p = .350, η²ₚ = .058, Fig. 4 A. A further ANOVA with the same within factors was ran for the mean Accuracy in the Go-Trials only. The ANOVA of mean Accuracy revealed no significant main effects of Target Position, F (1, 18) = 0.411, p = .530, η²ₚ = .022, Connectedness, F (1, 18) = 3.119, p = .094, η²ₚ = .148, or Numerosity, F (3, 54) = 0.587, p = .626, η²ₚ = .032. No significant interactions emerged: Target Position × Connectedness, F (1, 18) = 3.195, p = .091, η²ₚ = .151; Target Position × Numerosity, F (3, 54) = 0.394, p = .758, η²ₚ = .021; Connectedness × Numerosity, F (3, 54) = 1.466, p = .234, η²ₚ = .075; Target Position × Connectedness × Numerosity, F (3, 54) = 0.072, p = .975, η²ₚ = .004, Fig. 4 B. To ensure that the absence of significant effects was not due to limited statistical power, we performed Bayesian repeated-measures analyses separately for both mean RTs and Accuracy. Bayesian model comparison for RTs data strongly favored the null model including only participant as a random factor (all BF₁₀ < 0.05), indicating that Target Position, Connectedness, Numerosity, and their interactions did not provide additional explanatory power. Evidence in favor of the null ranged from ~ 20:1 for the simplest models to several orders of magnitude for the more complex ones (Fig. 5 A). Similarly, Bayesian model comparison for mean Accuracy data strongly favored the null model including only participant as a random factor. All alternative models—including Target Position, Numerosity, Connectedness, and their interactions—showed BF₁₀ well below 1, ranging from 0.724 for Connectedness + participant to 1.46×10⁻¹¹ for the most complex model (Fig. 5 B). This indicates that none of the experimental manipulations reliably contributed to explaining response accuracy, with evidence in favor of the null ranging from roughly 1.4:1 for the simplest alternative to several orders of magnitude for the most complex models. 4. Discussion The present study examined whether the well-documented underestimation of numerosity in displays containing connected items (or connectedness illusion) is attributable to covert attentional biases rather than to perceptual grouping mechanisms. By integrating a detection task modeled after Posner’s ( 1980 ) spatial cueing paradigm with a standard numerosity estimation task, we tested the hypothesis that connected objects might preferentially capture attention, thereby altering performance independently of perceptual grouping. The results were straightforward: participants consistently underestimated the numerosity of connected arrays, replicating the classic connectedness effect (e.g., Adriano et al., 2021 , 2022 ; Anobile et al., 2017 ; Fornaciai & Park, 2018 ; Franconeri et al., 2009 ; He et al., 2009 , 2015 ; Pomè et al., 2022 ). Crucially, detection performance was unaffected by object connectedness or spatial congruency. This pattern of findings strongly suggests that the connectedness effect is not an attentional artifact. If attentional capture had played a role, targets appearing in the corner close to connected-object cues (or red lines) should have been detected more efficiently than those appearing farther away. That is, detection performance should have suffered in the presence of targets appearing far from connected items due to the automatic redeployment of attentional resources (attentional capture) triggered by multi-part objects. However, neither pattern was observed. Instead, the connectedness underestimation found supports a growing body of evidence indicating that the Approximate Number System (ANS) is shaped by perceptual segmentation mechanisms (e.g., Adriano & Vande Velde, 2025a ; Franconeri et al., 2009 ; He et al., 2009 , 2015 ), which define the units over which numerosity is computed. Another interesting finding of the current study is the absence of a significant difference in numerosity estimation between Go and No-Go trials, and within Go trials, between close and far target conditions. This result aligns with previous evidence suggesting that the Approximate Number System (ANS) operates independently of attentional engagement, particularly when estimating larger quantities. Such findings reinforce the notion that the ANS can support rapid, non-symbolic numerical judgments even under conditions of reduced attentional load (Burr et al., 2010 , 2011 ; Piazza et al., 2011 ). Indeed, Burr et al. ( 2010 ) using a dual task paradigm manipulating attentional load, demonstrated that subitizing—the precise apprehension of small numerosities (e.g., less than 4 items)—breaks down under high attentional load, whereas estimation of larger numerosities remains unaffected. This dissociation indicates that subitizing depends on focused attention, while estimation relies on more automatic or pre-attentive processes. Although the present study employed a Posner Go/No-Go paradigm, rather than an explicit dual-task manipulation, both approaches involve variations in attentional engagement. Indeed, in the Posner task, Go trials impose higher attentional demands than No-Go trials, as participants must detect a cue and respond rapidly pressing a key with the left hand, whereas No-Go trials require only response inhibition since no target is flashed. Notably, we found that within Go trials, numerosity estimation did not differ whether the target appeared close or far from the quadrant containing the connecting lines. Close trials likely imposed slightly higher attentional load because the target had to be discriminated from nearby connecting lines, increasing visual complexity and attentional load. The absence of differences between close and far trials further supports the idea that non-symbolic number perception is largely robust to variations in attentional engagement. Consistent with this view, the absence of differences between Go and No-Go and between close and far trials in the present study suggests that the Approximate Number System operates robustly even under reduced attentional resources (Burr et al., 2010 ). Hence neither the estimation task nor the detection task was affected by the target spatial position. Rather, connectedness seems to work as expected, reducing numerosity perception in line with Gestalt laws (Palmer & Rock, 1994 ), and cannot be explained by covert attentional biases. According to this view, connected elements are not encoded as separate items but as single grouped objects. This reduces the number of individuated entities available to numerical estimation, leading to systematic underestimation. Such an explanation is consistent with Gestalt principles of perceptual organization (Wagemans et., 2012; Wertheimer, 1923/1950) and recent demonstrations that several grouping cues such as proximity, symmetry, or color similarity can modulate approximate perceived numerosity (e.g., Adriano & Ciccione, 2024 ; Chakravarthi et al., 2023 ; He et al., 2009 ; Franconeri et al., 2009 ; Maldonado Moscoso et al., 2022 ). Our findings extend this literature by showing that the connectedness effect persists even when attentional capture is explicitly measured and ruled out as a potential confound. Hence, beyond ruling out attentional capture as an explanation, our findings strongly contribute to the broader debate about the nature of numerical perception. A central controversy concerns whether the Approximate Number System (ANS) reflects a dedicated perceptual mechanism for extracting numerosity (Burr & Ross, 2008 ), or whether apparent number sensitivity is instead a by-product of sensitivity to continuous visual dimensions such as density, total area, or spatial frequency content (Gebuis & Reynvoet, 2012a ; Leibovich et al., 2017 ). The persistence of the connectedness effect in our data suggests that underestimation is not reducible to attentional biases but rather arises from perceptual segmentation processes that alter the definition of discrete units over which either numerosity is computed. Crucially, this interpretation is also strongly suggested by the fact that manipulating connectedness did not vary the continuous features in the arrays. More broadly, these results reinforce the notion that visual number perception is therefore a direct read-out of discrete items in a scene, even though the discrete number of objects could be an emergent property of perceptual organization (Anobile et al., 2014 ; Burr & Ross, 2008 ; Franconeri et al., 2009 ). Segmentation and grouping principles appear to act at early perceptual stages, perhaps before or in parallel with the engagement of attentional mechanisms. Moreover, it remains an open question whether different grouping cues (e.g., symmetry, color similarity, etc.) exert additive, competitive, or interactive effects on numerosity perception (Adriano & Ciccione, 2024 ; Chakravarthi et al., 2023 ), and whether such effects are equally resistant to attentional load manipulations in Posner-like tasks, as tested in the present study for connectedness. Neuroimaging and electrophysiological approaches may also clarify whether grouping-induced underestimation reflects changes in early visual segmentation (V1–V4) or in higher-level parietal areas traditionally associated with numerosity processing (e.g., Harvey et al., 2013 ). Finally, the current results open avenues for developmental and clinical research. Children, individuals with dyscalculia, or patients with parietal lesions may exhibit altered sensitivity to grouping-induced biases and global shape organization, potentially shedding light on the role of perceptual organization in the development and maintenance of numerical cognition (e.g., Castaldi et al., 2020 ). Likewise, neuroimaging approaches combining population receptive field mapping with numerosity tasks could help disentangle whether grouping effects emerge primarily in early visual cortex or in parietal regions associated with number processing (Paul et al., 2022 ). In conclusion, the present findings provide strong evidence that the connectedness effect in numerosity perception arises from perceptual grouping rather than covert attentional biases. This supports the broader theoretical claim that object segmentation is a foundational constraint on the ANS and highlights the primacy of perceptual organization in shaping our experience of numerical quantity. Taken together, these findings highlight a crucial boundary condition for theories of numerical cognition: perceptual organization provides the input over which the ANS operates, and this segmentation step is fundamental to how humans perceive and evaluate numerical quantities in their environment. 5. Conclusions The present study demonstrates that the well-known underestimation of numerosity in connected displays cannot be attributed to covert attentional biases. By integrating a spatial cueing paradigm with a numerosity estimation task, we showed that connectedness does not modulate detection performance, thereby ruling out attentional capture as a confounding factor. Instead, the persistence of the connectedness effect strongly supports the view that numerosity perception is constrained by perceptual grouping mechanisms. These findings reinforce the idea that the Approximate Number System (ANS) operates on the outputs of early segmentation processes, whereby connected elements are encoded as single units rather than distinct items. This highlights perceptual organization as a fundamental step in numerical cognition, shaping the very input over which the ANS computes. More broadly, our results point to object segmentation as a core constraint on number perception, with implications for theories of numerical cognition as well as for future developmental, clinical, and neuroimaging research. Declarations Conflicts of interest: The authors declare no conflict of interest. Ethics approval: The study was approved by the Local Ethical Committee and was conducted in accordance with the Declaration of Helsinki. Consent to participate: An informed consent document was signed before the experiment began. Consent for publication: An informed consent document was signed before the experiment began. Availability of data and material: The datasets generated during the current study are available from the authors upon request. Open Practice Statement The data for all experiments are available from the authors upon request. References Aagten-Murphy, D., & Burr, D. (2016). Adaptation to numerosity requires only brief exposures, and is determined by number of events, not exposure duration. Journal of Vision , 16 (10), 1–14. Adriano, A., & Ciccione, L. (2024). The interplay between spatial and non-spatial grouping cues over approximate number perception. 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R., Clarke, S., & Brannon, E. M. (2025). Seven reasons to (still) doubt the existence of number adaptation: A rebuttal to Burr et al. and Durgin Cognition , 254 , 105939. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Feb, 2026 Read the published version in Psychological Research → Version 1 posted Editorial decision: Revision requested 18 Jan, 2026 Reviews received at journal 16 Nov, 2025 Reviewers agreed at journal 20 Oct, 2025 Reviewers agreed at journal 18 Oct, 2025 Reviewers invited by journal 16 Oct, 2025 Editor assigned by journal 08 Oct, 2025 Submission checks completed at journal 03 Oct, 2025 First submitted to journal 02 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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1","display":"","copyAsset":false,"role":"figure","size":95171,"visible":true,"origin":"","legend":"\u003cp\u003eStimuli consisted of dot patterns (14–20 dots) displayed on a 12 × 12 grid, with two red parallel lines randomly placed in one quadrant. A black diamond target appeared in 50% of the trials, either near or far from the line quadrant.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/04e38c006f7930e429482332.png"},{"id":94761011,"identity":"0676cfa4-2a49-4ecb-888f-aa3730fdac0b","added_by":"auto","created_at":"2025-10-30 12:06:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":48034,"visible":true,"origin":"","legend":"\u003cp\u003eThe combined cue-detection \u0026amp; estimation task. Participants performed a dual task: (i) a go/no-go detection task, pressing the space bar if a diamond target appeared in a corner, and (ii) a numerosity estimation task, reporting the number of dots in the array. Each trial began with a fixation cross, followed by the stimulus (250 ms), with the target (when present) displayed for 50 ms. After detection, participants entered their estimate on the keypad.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/0493a47ece8be4d9dececcff.png"},{"id":94761012,"identity":"0730bf9b-7115-4a58-905b-5dcc981614fc","added_by":"auto","created_at":"2025-10-30 12:06:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":216932,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA) \u003c/strong\u003eMean estimation as a function of the target Numerosity, the Connectedness Level and the Trial type. \u003cstrong\u003eB) \u003c/strong\u003eMean\u003cstrong\u003e \u003c/strong\u003ecoefficient of variation as a function of the target Numerosity, the Connectedness Level and the Trial type. \u003cstrong\u003eC) \u003c/strong\u003eMean estimation as a function of the target Numerosity, the Connectedness Level and the Target Position. \u003cstrong\u003eD) \u003c/strong\u003eMean\u003cstrong\u003e \u003c/strong\u003ecoefficient of variation as a function of the target Numerosity, the Connectedness Level and the Target Position. Bars represent ±1 standard error of the mean (SEM).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/6b95fcfd0464f063c763674b.png"},{"id":94824568,"identity":"fe340f55-9c01-4f9d-abe7-e8c41b379c47","added_by":"auto","created_at":"2025-10-31 06:49:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":50905,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA) \u003c/strong\u003eMean RTs as a function of the Connectedness Level and the Target Position. \u003cstrong\u003eB) \u003c/strong\u003eMean Accuracy as a function of the Connectedness Level and the Target Position. Bars represent ±1 standard error of the mean (SEM).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/100f21bf181ed0d6b467896d.png"},{"id":94824434,"identity":"6c77a921-b4d6-44a9-99f3-9cd8ccaad4e8","added_by":"auto","created_at":"2025-10-31 06:49:00","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":923511,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA)\u003c/strong\u003e Results of the Bayesian model comparison for RTs data, showing the relative evidence for each model. \u003cstrong\u003eB)\u003c/strong\u003e Results of the Bayesian model comparison for Accuracy data, indicating the strength of evidence supporting alternative models. On the x-axis, the Bayes Factor (BF₁₀) values are shown for each model.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/c396f8845078452e40e5dbfa.jpeg"},{"id":103765555,"identity":"48df3f13-8756-4a35-8c55-5df35d05b7d7","added_by":"auto","created_at":"2026-03-02 16:04:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2007490,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7767227/v1/f67f2f57-4eea-4d7f-a9d8-204da532528b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Perceptual grouping, not covert attention, drives the connectedness effect in the ANS","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThere is broad consensus that humans and many animal species share a fundamental neurocognitive mechanism \u0026mdash; the \u003cem\u003eApproximate Number System\u003c/em\u003e (ANS) \u0026mdash; which enables the extraction of non-symbolic, approximate numerical representations from large sets of objects (Dehaene et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Nieder, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Evidence for this system has been documented across a variety of species (e.g., Agrillo et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Brannon \u0026amp; Terrace, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Ditz \u0026amp; Nieder, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and in early stages of human development (e.g., Brannon et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Xu \u0026amp; Spelke, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). From an evolutionary perspective, this underscores the adaptive value of a specialized numerical mechanism for survival-relevant tasks, such as comparing group sizes of conspecifics or rivals, or selecting the larger food source (e.g., Agrillo et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Benson-Amram et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Perdue et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Piantadosi \u0026amp; Cantlon, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA hallmark behavioral property of the ANS is its compliance with Weber\u0026rsquo;s law, observed consistently across cultures, developmental stages, and species (e.g., Whalen et al., \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Weber\u0026rsquo;s law states that the just-noticeable difference between two stimuli scales with their magnitude, or more strictly, that discrimination accuracy depends on the ratio of their intensities (Brus et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Dehaene, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). This has been extensively investigated using rapid numerical comparison tasks, in which participants choose the larger or smaller of two briefly presented arrays. In such tasks, error rates and reaction times increase as the numerical ratio approaches unity, indicating that non-symbolic number processing follows Weber\u0026rsquo;s law (e.g., Revkin et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAt the neural level, numerosity-selective responses have been identified in the parietal cortex of both humans and macaques (e.g., Castelli et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Harvey et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Nieder \u0026amp; Miller, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Piazza et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). More recent findings suggest that a wider network, including early visual areas, may also contribute to numerosity processing (DeWind et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Fornaciai et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Fornaciai \u0026amp; Park, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Park et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Van Rinsveld et al., \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAlthough the existence of the ANS is widely accepted, the precise visual computations it relies on remain debated. Some models posit that numerosity is obtained through a segmentation-and-individuation process that counts discrete items regardless of their physical properties such as shape, size, or position (Burr \u0026amp; Ross, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Dehaene \u0026amp; Changeux, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Stoianov \u0026amp; Zorzi, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Verguts \u0026amp; Fias, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Strong support for this view comes from \u003cem\u003enumerosity adaptation\u003c/em\u003e studies, where prolonged exposure to a set of a given numerosity biases the perceived numerosity of subsequent sets in the adapted location (Burr \u0026amp; Ross, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Thompson \u0026amp; Burr, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Typically, adaptation to a large number reduces the perceived numerosity of a smaller set, and adaptation to a small number increases the perceived numerosity of a larger set (Aagten-Murphy \u0026amp; Burr, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Aulet \u0026amp; Lourenco, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Such adaptation effects, observed across sensory modalities, have led to the proposal that numerosity functions as a primary sensory attribute, akin to colour, motion, or spatial frequency (Arrighi et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Burr et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e, but see Yousif et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2024\u003c/span\u003e, \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eHowever, other psychophysical evidence challenges the notion of numerosity as a primary sense (e.g., Durgin, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Alternative accounts suggest that numerical judgments are derived indirectly from continuous visual features correlated with numerosity, such as total occupied area, density, or luminance (Allik \u0026amp; Tuulmets, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Dakin et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Durgin, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Gebuis \u0026amp; Reynvoet, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2012a\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2012b\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2012c\u003c/span\u003e). The \u003cem\u003eoccupancy model\u003c/em\u003e (Allik \u0026amp; Tuulmets, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) proposes that numerosity is estimated by summing the \u0026ldquo;virtual\u0026rdquo; area occupied by items, with greater overlap leading to underestimation. Numerous studies have shown that item size, total surface area, convex hull, and density can all bias numerosity discrimination (e.g., Gebuis \u0026amp; Reynvoet, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2012a\u003c/span\u003e; Hurewitz et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Katzin et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Given that it is physically impossible to create two sets differing in numerosity yet identical in all continuous features, it has been argued that the visual system may integrate one or more of these correlated cues to infer number, without requiring a dedicated discrete-number mechanism (Gebuis et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Leibovich et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn line with this, Durgin (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) highlighted the role of texture-density statistics, while Dakin et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) proposed that density estimation could be achieved by analysing spatial-frequency content. Other biologically inspired models suggest that \u0026ldquo;contrast energy\u0026rdquo; could serve as a proxy for numerosity (Morgan et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Still, recent work indicates that a dedicated density-processing system may operate for very large numerosities (\u0026asymp;\u0026thinsp;100 items), where crowding prevents individual segmentation (Anobile et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; cf. Portley et al., 2019). In such cases, Weber fractions remain constant at low numerosities but decrease with the square root of numerosity beyond a critical threshold (Anobile et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This pattern suggests that, at least for moderate numerosities, visual number processing depends on item segmentation and cannot be fully reduced to texture-density mechanisms (Anobile et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Pom\u0026egrave; et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTherefore, several investigations have employed innovative experimental approaches to directly test competing explanations, making use of visual illusions such as size illusions, illusory contours (ICs) and connectedness-based grouping (e.g., Adriano et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Picon et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Consistent with the Gestalt principle of uniform connectedness (Palmer \u0026amp; Rock, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1994\u003c/span\u003e), a number of studies have reported that perceived numerosity is systematically underestimated when elements within an array are linked either by actual connecting lines (Anobile et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Fornaciai \u0026amp; Park, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Pom\u0026egrave; et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) or by task-irrelevant illusory connections (Adriano et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Adriano \u0026amp; Ciccione, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Kirjakovski \u0026amp; Matsumoto, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), even when low-level visual attributes are held constant across connectedness conditions. Collectively, these results indicate that visual segmentation processes are central to the extraction of discrete numerical information.\u003c/p\u003e\u003cp\u003eHowever, connected objects differ from unconnected ones not only in their grouping status but also in their visual salience: their \u0026ldquo;multi-part\u0026rdquo; structure can make them pop out from surrounding items, potentially attracting more attention to their location (He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Such attentional capture could reduce the processing time available for other items in the display, leading to their partial exclusion from the magnitude representation. In this view, the observed numerical underestimation reported with the connectedness illusion, might arise from differences in attentional allocation rather than from perceptual grouping per se.\u003c/p\u003e\u003cp\u003ePrevious studies have attempted to control for \u003cem\u003eovert\u003c/em\u003e attentional shifts by using very brief stimulus presentations (e.g., 50 ms) to prevent eye movements (He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Paradoxically, these studies found that the underestimation effect was even larger at short exposure durations. Therefore, this leaves open the possibility that \u003cem\u003ecovert\u003c/em\u003e attention \u0026mdash; the selective processing of visual information without eye movements (Posner, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e1980\u003c/span\u003e) \u0026mdash; could still play a role. If connected items automatically attract covert attention, they might draw processing resources away from other regions of the display, thereby biasing numerosity judgments through changes in the effective sampling of the scene.\u003c/p\u003e\u003cp\u003eTo the best of our knowledge, no previous study has accounted for this potential alternative explanation of the connectedness effect. To address this gap, we designed a novel task inspired by Posner\u0026rsquo;s classic attentional paradigm (1980).\u003c/p\u003e\u003cp\u003e Similarly to the classic Posner cueing task, our paradigm required participants to identify a briefly flashed target (e.g., a diamond) that appeared either near (congruent) or far (incongruent) from the spatial position of two red lines acting as exogenous cues. The red lines were intermingled with a variable number of dots and could either connect or remain unconnected to two of them. Participants performed a go/no-go detection task, responding as quickly as possible when the target appeared. Immediately afterward, they reported the total number of objects displayed on the screen.\u003c/p\u003e\u003cp\u003eWe reasoned that, because the red line cues (connected or unconnected) should pop out among the surrounding objects and automatically attract covert attention to their location, detection times would be faster when the target appeared close (congruent) rather than far (incongruent) from the quadrant containing the red lines. Moreover, if connected multi-part objects (e.g., dumbbell objects) intrinsically capture more attention at their location, thereby reducing the resources available for other regions, the performance (RTs and accuracy) in the detection task should be better when the target appears spatially close to the connected, compared to unconnected, objects.\u003c/p\u003e\u003cp\u003eAccordingly, a significant interaction between the spatial position of the target (close vs. far) and object type or connectedness level (connected vs. unconnected) would indicate that differences in covert attentional processing underlie the processing of connected objects, potentially explaining the numerosity underestimation driven by the connectedness effect. In this case, the underestimation effect could be attributed to attentional allocation rather than to perceptual grouping per se. Conversely, if no main effects or interactions emerged in the detection task, but connected objects were still underestimated in the estimation task, this would suggest that both connected and unconnected objects engage covert attention similarly, and that the underestimation effect cannot be primarily explained by attentional biases.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Participants\u003c/h2\u003e\u003cp\u003eAn a priori power analysis was conducted using G*Power 3.1 (Faul et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) to estimate the required sample size. Based on previous findings from a study adopting a comparable design (Adriano \u0026amp; Vande Velde, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025b\u003c/span\u003e), which reported a partial eta-squared of 0.41 for the Connectedness factor, we calculated that a minimum of 18 participants would be necessary to achieve 80% power in a repeated-measures ANOVA with four conditions (Close Target Connected/Unconnected and Far Target Connected/Unconnected), assuming α\u0026thinsp;=\u0026thinsp;.05. Nineteen participants were recruited for the present study (mean age\u0026thinsp;=\u0026thinsp;19.52 years, SD\u0026thinsp;=\u0026thinsp;1.42; 16 females; 17 right-handed participants). All participants had normal or corrected-to-normal vision. The study was approved by the local Ethics Committee.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Stimuli\u003c/h2\u003e\u003cp\u003eThe stimuli were generated offline using a custom Python/PsychoPy script (Peirce, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) and presented on a 19\u0026rdquo; LCD monitor (1280 \u0026times; 960 pixels; 60 Hz) connected to a standard computer. Each stimulus consisted of a 12 \u0026times; 12 black grid (cell size: 22 px; line width: 2 px; RGB: \u0026minus;1, \u0026minus;\u0026thinsp;1, \u0026minus;1). Within the grid, a variable number of white filled dots (radius: 6 px; RGB: 1, 1, 1) with a thin black outline (1 px; RGB: \u0026minus;1, \u0026minus;\u0026thinsp;1, \u0026minus;1) were placed on the grid intersections. The number of dots varied across four levels: 14, 16, 18, and 20.\u003c/p\u003e\u003cp\u003eEach stimulus also included two parallel red lines oriented at 45\u0026deg; (width: 2 px; RGB: 1, 0, 0), randomly positioned in one of four predefined quadrants (upper-left, upper-right, lower-left, lower-right). The position of the lines was counterbalanced across quadrants. To manipulate connectedness, in half of the stimuli two pairs of dots were positioned at the endpoints of the lines, whereas in the other half the same spatial configuration was preserved, but the dots were placed on the opposite sides of the line terminations.\u003c/p\u003e\u003cp\u003eIn 50% of the trials, a black diamond (20 \u0026times; 20 px; RGB: \u0026minus;1, \u0026minus;\u0026thinsp;1, \u0026minus;1) appeared in one of the four grid corners, while in the remaining trials the target was absent. Target position was counterbalanced across quadrants and could be either near (same corner) or far (opposite corner) relative to the quadrant containing the two lines (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eOverall, the experiment comprised 64 conditions when the target was present (Go trials: 4 numerosities \u0026times; 2 connectedness levels \u0026times; 2 target positions \u0026times; 4 quadrants) and 32 conditions when it was absent (No-Go trials: 4 numerosities \u0026times; 2 connectedness levels \u0026times; 4 quadrants). Each combination of quadrant position and numerosity was repeated 8 times (2 target positions \u0026times; 2 connectedness levels \u0026times; 2 Go/No-Go conditions). Each condition was presented with two unique visual patterns, resulting in a total of 256 stimuli.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Procedure\u003c/h2\u003e\u003cp\u003eThe experiment was conducted in a quiet, dimly lit room, and participants were tested individually. The general procedure was explained to each participant before the experiment began, and detailed instructions were also presented on the screen. Participants were comfortably placed at about 50 cm from the screen.\u003c/p\u003e\u003cp\u003eSubjects performed a dual task. First, they completed a \u003cem\u003ego/no-go detection task\u003c/em\u003e: they had to press the space bar as quickly as possible if a target appeared in one of the corners (go) and withhold their response if it did not (no-go). Second, to ensure that their attention remained focused on the center of the display rather than the corners, participants also completed an \u003cem\u003eestimation task\u003c/em\u003e, reporting as accurately as possible the number of objects in the array by typing their estimate on the numerical keypad of a standard PC keyboard. No information about the connectedness of the stimuli was provided to the participants. The participants were, in any case, instructed to provide a numerical estimate between 1 and 40. To familiarize participants with the procedure, the experimental phase was preceded by a short practice session (24 trials) with partial feedback (e.g., negative feedback was given only if the target was not correctly detected, and positive feedback was provided only if the exact number of items was reported in the estimation task).\u003c/p\u003e\u003cp\u003eEach trial began with a fixation cross (500 ms), followed by a blank screen (500 ms). The stimulus array was then presented for 250 ms. At 200 ms after onset, a diamond target could appear for 50 ms in one of the four corners of the stimulus. When the target appeared, participants had a fixed response window of 2 seconds to press the space bar with their left hand. This time window was identical for go and no-go trials, regardless of whether a response was made. Immediately after the detection phase, a visual cue (\u0026ldquo;Estimation:\u0026rdquo;) prompted participants to enter their estimate of the numerosity on the numerical keypad using their right hand. After each estimation, participants pressed the space bar to proceed to the next trial (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe experimental phase consisted of 256 trials, with a self-paced break after half of the trials. The entire session lasted approximately 35 minutes.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Estimation Task\u003c/h2\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e3.1.1. Go vs. No-Go trials overall analysis\u003c/h2\u003e\u003cp\u003eData analysis was performed with R/R-Studio (2018, v. 3.6.2; \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.rstudio.com/\u003c/span\u003e\u003cspan address=\"http://www.rstudio.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) software. Individual subjective estimations were examined for the presence of possible aberrant responses (e.g., errors of typing, unrealistic estimations, etc). To exclude extreme values, we applied an outlier removal procedure based on Weber\u0026rsquo;s law. For each trial, an expected variability was computed as a function of numerosity (σ\u0026thinsp;=\u0026thinsp;\u003cem\u003ew\u003c/em\u003e \u0026times; \u003cem\u003eNumerosity\u003c/em\u003e), where \u003cem\u003ew\u003c/em\u003e represents the Weber fraction. Upper and lower cutoffs were then defined as the target \u003cem\u003eNumerosity\u003c/em\u003e\u0026thinsp;\u0026plusmn;\u0026thinsp;k\u0026thinsp;\u0026times;\u0026thinsp;σ, with k\u0026thinsp;=\u0026thinsp;2.5 (number of standard deviations) and \u003cem\u003ew\u0026thinsp;=\u003c/em\u003e\u0026thinsp;.18 (average Weber fraction calculated by Anobile et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) determining the tolerance range. Input values falling outside these bounds were discarded, thus ensuring that only responses consistent with the expected scalar variability were retained for further analyses. A repeated-measures ANOVA with Trial type (Go/No-Go), Connectedness (connected/unconnected), and Numerosity (14, 16, 18, 20) as within-subject factors revealed a robust main effect of Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;131.41, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u0026sup2;ₚ = .88. Mauchly\u0026rsquo;s test indicated a violation of sphericity for this factor, therefore Greenhouse\u0026ndash;Geisser correction was applied (ε\u0026thinsp;=\u0026thinsp;.50), which confirmed the significance of the effect, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001. Crucially, there was also a significant main effect of Connectedness, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;12.25, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.003, η\u0026sup2;ₚ = .41, with connected arrays being systematically underestimated compared to unconnected ones. The main effect of Trial type was not significant, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;1.16, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.296, η\u0026sup2;ₚ = .06. None of the two- or three-way interactions reached significance (all \u003cem\u003eps\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;.10), including Trial type \u0026times; Numerosity (\u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;1.42, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.247, η\u0026sup2;ₚ = .07), Connectedness \u0026times; Numerosity (\u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;1.87, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.146, η\u0026sup2;ₚ = .09), and the three-way interaction (\u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;2.18, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.100, η\u0026sup2;ₚ = .11, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA). Thus, the connectedness effect emerged consistently across numerosities and independently of the go/no-go detection task.\u003c/p\u003e\u003cp\u003eTo investigate scalar variability, a typical behavioral signature of numerosity estimation, a multiple linear regression was conducted to examine the effects of Numerosity, Connectedness, and Trial Type, as well as their interactions, on the Coefficient of Variation (CoV), used as an estimate of the Weber fraction (e.g., Halberda \u0026amp; Odic, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). The overall model was not significant, \u003cem\u003eF\u003c/em\u003e(7, 8)\u0026thinsp;=\u0026thinsp;0.52, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.80, and explained a limited proportion of variance in the outcome (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = .31, adj. \u003cem\u003eR\u003c/em\u003e\u0026sup2; = \u0026minus;.29). Examination of individual predictors revealed that none of the main effects or interactions reached statistical significance. Specifically, Numerosity (β\u0026thinsp;=\u0026thinsp;0.00059, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.85), Connectedness (β\u0026thinsp;=\u0026thinsp;0.0197, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.79), and Trial Type (β = \u0026minus;0.0084, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.91) did not significantly predict the dependent measure. Similarly, all two-way and the three-way interactions were non-significant (all \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;.60, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). These results indicate that, within the tested conditions, none of the factors or their interactions had a detectable effect on the CoV.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e3.1.2. Go trials only analysis\u003c/h2\u003e\u003cp\u003eWe further analysed subjective estimations for Go trials only, in function of the target distance. Then, we ran a repeated-measures ANOVA (2 \u0026times; 2 \u0026times; 4) with Target Position (far/close), Connectedness (connected/unconnected) and Numerosity (14, 16, 18, 20) as within-subject factors and the subjective estimation as dependent variable. The results revealed a robust main effect of Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;104.34, ε\u0026thinsp;=\u0026thinsp;.596, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u0026sup2;ₚ = .85. A significant main effect of Connectedness was also observed, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;4.63, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.045, η\u0026sup2;ₚ = .21, suggesting that connected arrays were systematically underestimated compared to unconnected ones. In contrast, the main effect of Target Position was not significant, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;0.86, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.367, η\u0026sup2;ₚ = .05. None of the interaction effects reached significance (all \u003cem\u003ep\u003c/em\u003es\u0026thinsp;\u0026gt;\u0026thinsp;.20, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC).\u003c/p\u003e\u003cp\u003eA multiple linear regression was conducted to examine the effects of Numerosity, Connectedness, and Target Position, as well as their interactions, on the coefficient of variation (CV). The overall model was not significant, \u003cem\u003eF\u003c/em\u003e(7, 8)\u0026thinsp;=\u0026thinsp;1.04, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.475, indicating that the predictors explained little variance in CV (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = .48, adj. \u003cem\u003eR\u003c/em\u003e\u0026sup2; = .02). None of the predictors or interactions reached significance (all \u003cem\u003ep\u003c/em\u003es\u0026thinsp;\u0026gt;\u0026thinsp;.38, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD). In sum, these results replicate the results of the overall analysis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Detection Task\u003c/h2\u003e\u003cp\u003eTo further examine potential differences in covert attentional demands between connected and unconnected arrays, we conducted a 2 \u0026times; 2 \u0026times; 4 repeated-measures ANOVA on RTs for correct Go-Trial responses (errors discarded: 2.17%), with Target Position (far/close), Connectedness (connected/unconnected), and Numerosity (14, 16, 18, 20) as within-subject factors.\u003c/p\u003e\u003cp\u003eThe ANOVA of mean RTs revealed no significant main effects of Target Position, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;0.00003, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.996, η\u0026sup2;ₚ = .001, Connectedness, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;0.010, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.920, η\u0026sup2;ₚ= .001, or Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;0.456, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.714, η\u0026sup2;ₚ = .025. None of the interactions reached significance: Target Position \u0026times; Connectedness, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;0.787, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.387, η\u0026sup2;ₚ = .042; Target Position \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;1.324, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.276, η\u0026sup2;ₚ = .069; Connectedness \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;2.727, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.053, η\u0026sup2;ₚ = .132; Target Position \u0026times; Connectedness \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;1.118, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.350, η\u0026sup2;ₚ = .058, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA.\u003c/p\u003e\u003cp\u003eA further ANOVA with the same within factors was ran for the mean Accuracy in the Go-Trials only. The ANOVA of mean Accuracy revealed no significant main effects of Target Position, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;0.411, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.530, η\u0026sup2;ₚ = .022, Connectedness, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;3.119, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.094, η\u0026sup2;ₚ = .148, or Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;0.587, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.626, η\u0026sup2;ₚ = .032. No significant interactions emerged: Target Position \u0026times; Connectedness, \u003cem\u003eF\u003c/em\u003e(1, 18)\u0026thinsp;=\u0026thinsp;3.195, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.091, η\u0026sup2;ₚ = .151; Target Position \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;0.394, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.758, η\u0026sup2;ₚ = .021; Connectedness \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;1.466, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.234, η\u0026sup2;ₚ = .075; Target Position \u0026times; Connectedness \u0026times; Numerosity, \u003cem\u003eF\u003c/em\u003e(3, 54)\u0026thinsp;=\u0026thinsp;0.072, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.975, η\u0026sup2;ₚ = .004, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB.\u003c/p\u003e\u003cp\u003eTo ensure that the absence of significant effects was not due to limited statistical power, we performed Bayesian repeated-measures analyses separately for both mean RTs and Accuracy. Bayesian model comparison for RTs data strongly favored the null model including only participant as a random factor (all \u003cem\u003eBF₁₀\u003c/em\u003e \u0026lt; 0.05), indicating that Target Position, Connectedness, Numerosity, and their interactions did not provide additional explanatory power. Evidence in favor of the null ranged from ~\u0026thinsp;20:1 for the simplest models to several orders of magnitude for the more complex ones (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA). Similarly, Bayesian model comparison for mean Accuracy data strongly favored the null model including only participant as a random factor. All alternative models\u0026mdash;including Target Position, Numerosity, Connectedness, and their interactions\u0026mdash;showed \u003cem\u003eBF₁₀\u003c/em\u003e well below 1, ranging from 0.724 for Connectedness\u0026thinsp;+\u0026thinsp;participant to 1.46\u0026times;10⁻\u0026sup1;\u0026sup1; for the most complex model (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB). This indicates that none of the experimental manipulations reliably contributed to explaining response accuracy, with evidence in favor of the null ranging from roughly 1.4:1 for the simplest alternative to several orders of magnitude for the most complex models.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe present study examined whether the well-documented underestimation of numerosity in displays containing connected items (or connectedness illusion) is attributable to covert attentional biases rather than to perceptual grouping mechanisms. By integrating a detection task modeled after Posner\u0026rsquo;s (\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e1980\u003c/span\u003e) spatial cueing paradigm with a standard numerosity estimation task, we tested the hypothesis that connected objects might preferentially capture attention, thereby altering performance independently of perceptual grouping. The results were straightforward: participants consistently underestimated the numerosity of connected arrays, replicating the classic connectedness effect (e.g., Adriano et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Anobile et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Fornaciai \u0026amp; Park, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Pom\u0026egrave; et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Crucially, detection performance was unaffected by object connectedness or spatial congruency. This pattern of findings strongly suggests that the connectedness effect is not an attentional artifact.\u003c/p\u003e\u003cp\u003eIf attentional capture had played a role, targets appearing in the corner close to connected-object cues (or red lines) should have been detected more efficiently than those appearing farther away. That is, detection performance should have suffered in the presence of targets appearing far from connected items due to the automatic redeployment of attentional resources (attentional capture) triggered by multi-part objects. However, neither pattern was observed. Instead, the connectedness underestimation found supports a growing body of evidence indicating that the Approximate Number System (ANS) is shaped by perceptual segmentation mechanisms (e.g., Adriano \u0026amp; Vande Velde, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2025a\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), which define the units over which numerosity is computed.\u003c/p\u003e\u003cp\u003eAnother interesting finding of the current study is the absence of a significant difference in numerosity estimation between Go and No-Go trials, and within Go trials, between close and far target conditions. This result aligns with previous evidence suggesting that the Approximate Number System (ANS) operates independently of attentional engagement, particularly when estimating larger quantities. Such findings reinforce the notion that the ANS can support rapid, non-symbolic numerical judgments even under conditions of reduced attentional load (Burr et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Piazza et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Indeed, Burr et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) using a dual task paradigm manipulating attentional load, demonstrated that subitizing\u0026mdash;the precise apprehension of small numerosities (e.g., less than 4 items)\u0026mdash;breaks down under high attentional load, whereas estimation of larger numerosities remains unaffected. This dissociation indicates that subitizing depends on focused attention, while estimation relies on more automatic or pre-attentive processes.\u003c/p\u003e\u003cp\u003eAlthough the present study employed a Posner Go/No-Go paradigm, rather than an explicit dual-task manipulation, both approaches involve variations in attentional engagement. Indeed, in the Posner task, Go trials impose higher attentional demands than No-Go trials, as participants must detect a cue and respond rapidly pressing a key with the left hand, whereas No-Go trials require only response inhibition since no target is flashed. Notably, we found that within Go trials, numerosity estimation did not differ whether the target appeared close or far from the quadrant containing the connecting lines. Close trials likely imposed slightly higher attentional load because the target had to be discriminated from nearby connecting lines, increasing visual complexity and attentional load. The absence of differences between close and far trials further supports the idea that non-symbolic number perception is largely robust to variations in attentional engagement. Consistent with this view, the absence of differences between Go and No-Go and between close and far trials in the present study suggests that the Approximate Number System operates robustly even under reduced attentional resources (Burr et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eHence neither the estimation task nor the detection task was affected by the target spatial position. Rather, connectedness seems to work as expected, reducing numerosity perception in line with Gestalt laws (Palmer \u0026amp; Rock, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1994\u003c/span\u003e), and cannot be explained by covert attentional biases.\u003c/p\u003e\u003cp\u003eAccording to this view, connected elements are not encoded as separate items but as single grouped objects. This reduces the number of individuated entities available to numerical estimation, leading to systematic underestimation. Such an explanation is consistent with Gestalt principles of perceptual organization (Wagemans et., 2012; Wertheimer, 1923/1950) and recent demonstrations that several grouping cues such as proximity, symmetry, or color similarity can modulate approximate perceived numerosity (e.g., Adriano \u0026amp; Ciccione, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chakravarthi et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; He et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Maldonado Moscoso et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Our findings extend this literature by showing that the connectedness effect persists even when attentional capture is explicitly measured and ruled out as a potential confound.\u003c/p\u003e\u003cp\u003eHence, beyond ruling out attentional capture as an explanation, our findings strongly contribute to the broader debate about the nature of numerical perception. A central controversy concerns whether the Approximate Number System (ANS) reflects a dedicated perceptual mechanism for extracting numerosity (Burr \u0026amp; Ross, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), or whether apparent number sensitivity is instead a by-product of sensitivity to continuous visual dimensions such as density, total area, or spatial frequency content (Gebuis \u0026amp; Reynvoet, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2012a\u003c/span\u003e; Leibovich et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The persistence of the connectedness effect in our data suggests that underestimation is not reducible to attentional biases but rather arises from perceptual segmentation processes that alter the definition of discrete units over which either numerosity is computed. Crucially, this interpretation is also strongly suggested by the fact that manipulating connectedness did not vary the continuous features in the arrays. More broadly, these results reinforce the notion that visual number perception is therefore a direct read-out of discrete items in a scene, even though the discrete number of objects could be an emergent property of perceptual organization (Anobile et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Burr \u0026amp; Ross, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Franconeri et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Segmentation and grouping principles appear to act at early perceptual stages, perhaps before or in parallel with the engagement of attentional mechanisms.\u003c/p\u003e\u003cp\u003eMoreover, it remains an open question whether different grouping cues (e.g., symmetry, color similarity, etc.) exert additive, competitive, or interactive effects on numerosity perception (Adriano \u0026amp; Ciccione, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chakravarthi et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and whether such effects are equally resistant to attentional load manipulations in Posner-like tasks, as tested in the present study for connectedness. Neuroimaging and electrophysiological approaches may also clarify whether grouping-induced underestimation reflects changes in early visual segmentation (V1\u0026ndash;V4) or in higher-level parietal areas traditionally associated with numerosity processing (e.g., Harvey et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Finally, the current results open avenues for developmental and clinical research. Children, individuals with dyscalculia, or patients with parietal lesions may exhibit altered sensitivity to grouping-induced biases and global shape organization, potentially shedding light on the role of perceptual organization in the development and maintenance of numerical cognition (e.g., Castaldi et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Likewise, neuroimaging approaches combining population receptive field mapping with numerosity tasks could help disentangle whether grouping effects emerge primarily in early visual cortex or in parietal regions associated with number processing (Paul et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn conclusion, the present findings provide strong evidence that the connectedness effect in numerosity perception arises from perceptual grouping rather than covert attentional biases. This supports the broader theoretical claim that object segmentation is a foundational constraint on the ANS and highlights the primacy of perceptual organization in shaping our experience of numerical quantity. Taken together, these findings highlight a crucial boundary condition for theories of numerical cognition: perceptual organization provides the input over which the ANS operates, and this segmentation step is fundamental to how humans perceive and evaluate numerical quantities in their environment.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThe present study demonstrates that the well-known underestimation of numerosity in connected displays cannot be attributed to covert attentional biases. By integrating a spatial cueing paradigm with a numerosity estimation task, we showed that connectedness does not modulate detection performance, thereby ruling out attentional capture as a confounding factor. Instead, the persistence of the connectedness effect strongly supports the view that numerosity perception is constrained by perceptual grouping mechanisms.\u003c/p\u003e\u003cp\u003eThese findings reinforce the idea that the Approximate Number System (ANS) operates on the outputs of early segmentation processes, whereby connected elements are encoded as single units rather than distinct items. This highlights perceptual organization as a fundamental step in numerical cognition, shaping the very input over which the ANS computes. More broadly, our results point to object segmentation as a core constraint on number perception, with implications for theories of numerical cognition as well as for future developmental, clinical, and neuroimaging research.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eConflicts of interest:\u0026nbsp;\u003c/strong\u003eThe authors declare no conflict of interest.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eEthics approval:\u0026nbsp;\u003c/strong\u003eThe study was approved by the Local Ethical Committee and was conducted in accordance with the Declaration of Helsinki.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eConsent to participate:\u0026nbsp;\u003c/strong\u003eAn informed consent document was signed before the experiment began.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eConsent for publication:\u0026nbsp;\u003c/strong\u003eAn informed consent document was signed before the experiment began.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eAvailability of data and material:\u0026nbsp;\u003c/strong\u003eThe datasets generated during the current study are available from the authors upon request.\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eOpen Practice Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data for all experiments are available from the authors upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAagten-Murphy, D., \u0026amp; Burr, D. 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Seven reasons to (still) doubt the existence of number adaptation: A rebuttal to Burr et al. \u003cem\u003eand Durgin Cognition\u003c/em\u003e, \u003cem\u003e254\u003c/em\u003e, 105939.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"psychological-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"prpf","sideBox":"Learn more about [Psychological Research](http://link.springer.com/journal/426)","snPcode":"426","submissionUrl":"https://submission.nature.com/new-submission/426/3","title":"Psychological Research","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Numerosity perception, Connectedness effect, Perceptual grouping, Covert attention, Approximate Number System (ANS)","lastPublishedDoi":"10.21203/rs.3.rs-7767227/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7767227/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA robust finding in numerical cognition is that connecting items within an array leads to systematic underestimation of numerosity. This provides evidence that approximate numerosity perception relies on discrete objects rather than on continuous variables (e.g., total area, density, convex hull). While this \u003cem\u003econnectedness effect\u003c/em\u003e is often attributed to perceptual grouping, an alternative interpretation is that connected items may capture covert attention, thereby biasing the sampling of visual information. We tested these competing accounts by combining a numerosity estimation task with a target-detection task modeled after Posner\u0026rsquo;s cueing paradigm. On each trial, participants viewed dot arrays (14\u0026ndash;20 items) that included two red lines, either connecting a pair of dots or terminating near unconnected dots. A target diamond could appear either near (congruent) or far (incongruent) from the quadrant containing the red lines. Participants first performed a go/no-go detection task, then estimated the array numerosity. Replicating prior work, connected arrays were consistently underestimated relative to unconnected ones. Crucially, detection performance showed no evidence of attentional capture: reaction times and accuracy did not differ as a function of connectedness or target position. These findings demonstrate that the underestimation effect cannot be attributed to \u003cem\u003ecovert\u003c/em\u003e attentional allocation. Instead, they support the view that perceptual grouping\u0026mdash;rather than attentional biases\u0026mdash;drives the connectedness effect in the Approximate Number System. More broadly, our results strengthen the case for segmentation-based mechanisms as a critical foundation of visual number perception.\u003c/p\u003e","manuscriptTitle":"Perceptual grouping, not covert attention, drives the connectedness effect in the ANS","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-30 12:06:34","doi":"10.21203/rs.3.rs-7767227/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-18T12:26:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-16T05:58:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"172141267948078532636253341508474948792","date":"2025-10-20T08:11:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"52380364288068544331393816082169218339","date":"2025-10-18T18:38:59+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-16T14:05:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-08T08:52:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-03T13:27:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Psychological Research","date":"2025-10-02T14:13:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"psychological-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"prpf","sideBox":"Learn more about [Psychological Research](http://link.springer.com/journal/426)","snPcode":"426","submissionUrl":"https://submission.nature.com/new-submission/426/3","title":"Psychological Research","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1ff74d30-0382-4192-8a1b-705ee17e2e30","owner":[],"postedDate":"October 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-02T16:01:23+00:00","versionOfRecord":{"articleIdentity":"rs-7767227","link":"https://doi.org/10.1007/s00426-026-02255-z","journal":{"identity":"psychological-research","isVorOnly":false,"title":"Psychological Research"},"publishedOn":"2026-02-24 15:58:10","publishedOnDateReadable":"February 24th, 2026"},"versionCreatedAt":"2025-10-30 12:06:34","video":"","vorDoi":"10.1007/s00426-026-02255-z","vorDoiUrl":"https://doi.org/10.1007/s00426-026-02255-z","workflowStages":[]},"version":"v1","identity":"rs-7767227","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7767227","identity":"rs-7767227","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}