Distinct serial dependence between small and large numerosity processing

doi:10.21203/rs.3.rs-3633732/v1

Download PDF

Research Article

Distinct serial dependence between small and large numerosity processing

https://doi.org/10.21203/rs.3.rs-3633732/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

The serial dependence effect (SDE) is a bias in which the representation of current stimuli is attracted to previous stimuli. Although SDE has been observed in many substrates of visual processing, it remains unsolved whether humans adopt a similar SDE to achieve continuity and stability of numerosity processing in two distinct numerical ranges: subitizing (i.e., small numerosity processing, likely related to early object recognition) and estimation (i.e., large numerosity processing, likely related to ensemble numerosity extraction). Here, we demonstrate that subitizing and estimation are characterized by distinct SDEs, underpinned by different mechanisms: a temporal hysteresis-based perceptual mechanism for subitizing and a combination of perceptual and post-perceptual mechanisms for estimation. Critically, a novel type of SDE characterized by reduced processing precision is found in subitizing only, implying that the continuity and stability of numerical processing can be dissociable in dynamic situations where numerical information is integrated over time. Our findings reveal the multifaceted nature of SDE mechanisms and suggest their engagement with cognitive modules likely subserving different functionalities.

Serial dependence effect

numerosity

subitizing

estimation

temporal hysteresis

Humans dwell in an ever-changing environment. The dynamic nature of human information acquisition, characterized by frequent eye movements (Melcher, 2005), and the inherent susceptibility of cognitive processing to noise accumulation (Cheyette & Piantadosi, 2019), impose additional demands on our cognitive system. Consequently, humans must develop sophisticated brain networks (Ranieri et al., 2022) and implement complex strategies (Wutz et al., 2016) to maintain stabilities during information processing. A key cognitive strategy for maintaining continuity and stability in human cognition is to integrate information generated during one glance or moment with information generated during the next glance or moment in an attractive way, a phenomenon dubbed as the serial dependence effect (SDE).

SDE has been observed in many substrates of visual processing, from low-level features such as orientation, spatial location, and numerosity, to high-level attributes such as identity, attractiveness, and aesthetic judgment (Ceylan et al., 2021; Cicchini et al., 2021; Fischer & Whitney, 2014; Pascucci et al., 2023). In the domain of numerical processing, SDE has been widely observed across different paradigms, including numerosity discrimination (Fornaciai & Park, 2018b) and numerosity estimation (Fornaciai & Park, 2020b). However, the numerical range examined in these studies (Fornaciai & Park, 2018a; Fornaciai & Park, 2019a, 2022; Fornaciai et al., 2023) was exclusively focused on estimation, that is, numerosities greater than 3 or 4. Little is known about how the SDE influences numerosity perception in the other numerical range, subitizing (Jevons, 1871; Kaufman et al., 1949; Melcher et al., 2021), where numerosities are equal to or less than 3 or 4.

Whether small and large numerosity processing display comparable patterns of SDE is a key question in the ongoing debate on the underlying mechanisms and functionalities of subitizing and estimation. One view suggests that these two numerical ranges share a common underlying mechanism and functionality, targeting numerical processing specifically. Both subitizing and estimation involve the same numerosity estimation process, which becomes less precise as the numerosity increases (Cai et al., 2021; Dehaene & Changeux, 1993; Fornaciai & Park, 2021). In other words, subitizing is high-precision estimation. In line with this perspective, small and large numerosity processing should display analogous patterns of SDE.

Conversely, an alternative view posits that subitizing and estimation arise from distinct functionalities and possess separate mechanisms. Specifically, subitizing is thought to reflect a cross-domain, non-numerical mechanism that occurs in the early stages of object recognition and intrinsically involves object individuation (Trick & Pylyshyn, 1993), in which items are separated as individual entities with a particular identity and spatial location. According to the two-stage hypothesis of object recognition, the initial stage of object recognition, known as object individuation, is initiated by feedforward processing, followed by a second stage, object identification, which is likely driven by a combination of feedforward and feedback/reentrant processing (Thorpe et al., 1996; Wutz & Melcher, 2014; Xu & Chun, 2009). Object individuation is a relatively rapid process (around 100 ms; Wutz et al., 2012), primarily disrupted by forward and simultaneous masking stimuli (Wutz et al., 2012; Wutz & Melcher, 2014; Xu & Chun, 2009). Similarly, feedforward-driven object identification (Thorpe et al., 1996) is also a rapid process (less than 150ms; Hung et al., 2005; Isik et al., 2014). Conversely, feedback-driven object identification (Salinas & Abbott, 1996) is a slower process, unfolding over a time scale that can extend to several hundred milliseconds (Brincat & Connor, 2006; Cichy et al., 2014; Sugase et al., 1999), making it more susceptible to continuous interference from incoming stimuli in a stream. The capacity of object individuation resource is limited, which constrains how many objects can be encoded and used in subsequent tasks, such as enumeration (Wutz et al., 2012), visual working memory (VWM) (Luck & Vogel, 1997), multiple temporal processing (MTP) (Cheng et al., 2014), and multiple object track (MOT) (Pylyshyn & Storm, 1988). In contrast, estimation reflects a domain-specific mechanism, namely, the approximate numerical system (ANS), which represents numbers analogically and approximately to extract ensemble numerosity (Dantzig, 1967; Dehaene, 1997; Tall & Dehaene, 1998). The functional dissociation between subitizing and estimation is supported by evidence that later mathematical abilities in school children can be predicted by early estimation performance (Burr et al., 2018), but not by early subitizing performance (Anobile et al., 2019a). Assuming separate underlying mechanisms and functionalities, it follows that small and large numerosity processing would exhibit completely disparate patterns of SDE.

To investigate the potential SDE for small numerosities, two preconditions are required: (1) bias-susceptible numerical performance for small numerosities, since bias-free numerical reporting (e.g., performance in a typical subitizing paradigm where participants are asked to enumerate a single set of dots within the subitizing range; Melcher et al., 2021) carries no information about potential SDE; and (2) a stimulus stream consisting of two or more sets of dots, with each set within the subitizing range, to examine serial influence across neighboring numerical stimuli (as in SDE for estimation; Fornaciai & Park, 2020b). To meet these two preconditions, we developed a rapid serial visual presentation (RSVP)-based continuous numerical oddball paradigm that required participants to perform numerosity judgement on each item of the RSVP (see Method for more details). Critically, perceptual and post-perceptual interference (targeting the early stage of feedforward-initiated object individuation and late stage of feedforward and feedback/reentrant-driven object identification, respectively; (Wutz & Melcher, 2014; Xu & Chun, 2009) from neighboring items in the RSVP (Robinson et al., 2019) increased gradually with decreasing stimulus onset asynchrony (SOA).

To ensure that participants could subitize a single RSVP item composed of a dot set within the subitizing range, a 200-ms SOA was chosen in Experiment 1 (since the full capacity of subitizing requires a temporal window of around 100 ms, which is well below the chosen 200ms SOA; Wutz et al., 2012). However, when enumerating sequentially-presented multiple RSVP items within the subitizing range in the continuous numerical oddball paradigm, participants may experience a performance reduction (a required precondition for potential SDE for small numerosities). Given that subitizing of the current RSVP item is hypothesized to rely on object individuation, a rapid process that occurs in the early stages of object recognition (Wutz & Melcher, 2014; Xu & Chun, 2009), the decline in its performance is likely attributable to perceptual interference primarily induced by the immediately preceding RSVP item, rather than by post-perceptual interference induced primarily by the subsequent RSVP items (Robinson et al., 2019). Consequently, we anticipate that subitizing-based SDE will occur in Experiment 1, with an SOA of 200 ms, but will be eliminated in Experiment 2, with an SOA of 494 ms, by substantially reducing perceptual interference from the immediately preceding RSVP item. Conversely, we predict that subitizing-based SDE, if it exists, will remain unaffected by manipulating post-perceptual interference from the subsequent RSVP items in Experiment 4. Additionally, two control experiments (Experiments 3 and 5) will explore whether it is still robust when non-numerical continuous variables (e.g., convex hull) (Adriano et al., 2021; Fornaciai & Park, 2020a; Fornaciai & Park, 2022) and a forward mask (Robinson et al., 2019) are introduced, respectively.

Subjects

A two-tailed power analysis using G*power3.1 (Faul et al., 2007) indicated that a sample size of 28 subjects would afford 80% power to detect a SDE with an alpha level of 0.05 and a medium effect size (Cohen’s d = 0.55). A total of 164 undergraduate or postgraduate students from Central China Normal University (CCNU) participated in the study. Of these, 136 were female and the mean age was 20.66 ± 1.87 years. The participants were right-handed and had normal or corrected-to-normal vision. They were randomly assigned to one of five experiments, with 34, 33, 35, 32, and 30 participants in each experiment, respectively. They had no history of neurological disorders or color blindness. Each participant provided signed consent in accordance with the requirements of the Institutional Review Board of CCNU.

Stimuli

Stimuli in Experiment 1 to 4 were presented on a 17’’ CRT monitor with a resolution of 1280 × 1024 pixels at a refresh rate of 85 Hz. Stimuli in Experiment 5 were back-projected by a ProPixx projector (VPixx Technologies, Saint-Bruno, Quếbec, Canada) with a resolution of 1280 × 1024 pixels and a refresh rate of 100 Hz. We used the Psychophysics Toolbox (Brainard, 1997; Pelli & Denis, 1997) implemented on MATLAB (MathWorks Inc.) to generate stimuli. All stimuli were presented on a black background (luminance of 5.03cd/m², measured with a Minolta CS-200 Chromameter photometer). Participants’ responses were recorded using a keyboard connected to the PC while their heads were stabilized by a chin rest and their viewing distance was fixed at 57 cm.

Experiment 1

All experiments employed a continuous numerical oddball paradigm (an example see Fig. 1a upper panel). Each trial commenced with an Arabic numeral (e.g., ‘1’) presented at the center of the display, cueing a standard numerosity for 1000 ms, followed by a red fixation cross (line length: 0.18° visual angle [VA], line width: 0.06° VA) for 1496 ms. After a blank interval of 494 ms, a rapid serial visual presentation (RSVP) sequence consisting of 7 items was presented, followed by a colored noise mask. The stimuli were presented with a SOA of 200 ms in Experiment 1, which included a 47 ms item duration and a 153 ms inter-item blank.

Each item in the RSVP sequence consisted of randomly located dots (1.2° VA in diameter) featuring either the standard numerosity cued by the numeral or a new oddball numerosity. The dots were placed within an invisible square area (16° VA × 16° VA) centered around the display. The dots within an RSVP item and between any two neighboring RSVP items were never spatially overlapping, and were at least 0.375° VA away from the fixation cross. Any two dots within an RSVP item were at least 0.25° VA apart from each other. All dots within an RSVP item had the same color, which was randomly selected without replacement from a set of 7 discriminable colors (more details see the Supplementary Information (SI)). There was no color repetition across different RSVP items in a trial. The oddball was presented either not at all (with all items being standard numerosities) or only once (with six standard numerosities and one oddball numerosity) at a serial position out of the first to the sixth RSVP items (oddball position) with equal probability (the seventh RSVP item always contained a standard numerosity). The standard numerosity and oddball numerosity of a particular trial were both within the same numerosity range, namely either small (1, 2, 3) or large (5, 6, 7) numerosities. The mask was a mixture of noise patches (0.405° VA × 0.405° VA), randomly sampled from the 7 discriminable colors, and lasted for 494 ms. Participants were instructed to report whether they perceived a numerosity change (i.e., the oddball numerosity) or no numerosity change (i.e., the standard numerosity) after the mask was presented.

The relative oddball change (see Table S1) in numerosity between oddball numerosity and standard numerosity for a given trial was defined as follows:

$$\text{R}\text{e}\text{l}\text{a}\text{t}\text{i}\text{v}\text{e} \text{o}\text{d}\text{d}\text{b}\text{a}\text{l}\text{l} \text{c}\text{h}\text{a}\text{n}\text{g}\text{e}=\frac{Oddball-Standard}{Standard}$$

The positive relative change of oddball, indicating a larger oddball numerosity relative to standard numerosity, whereas the negative relative change of oddball, indicating a smaller oddball numerosity relative to standard numerosity. The small or large numerosities, oddball position (the first to the sixth RSVP items), and larger or smaller oddball were fully crossed, resulting in 24 key conditions that were randomly interleaved. The formal test comprised of 480 trials with oddballs (24 key conditions with 20 repetitions) and 120 padding trials without oddballs (in fully crossed conditions and excluded from analysis), resulting in a total of 600 trials.

Experiment 2

Experiment 2 (see Fig. 1b) had an SOA of 494 ms with substantially reducing perceptual interference from the immediately preceding RSVP item (Robinson et al., 2019). This was achieved by using a 47 ms item duration and a 447 ms inter-item blank. All other aspects of Experiment 2 were identical to those of Experiment 1.

Experiment 3

In Experiment 3, all stimuli and procedures were the same as Experiment 1, except that the non-numerical magnitudes of the dot arrays were controlled. We used the GeNEsIS toolbox (Zanon et al., 2022), following the approach in Potrich et al. (2022), to control the non-numerical magnitudes (Fig. 2, more details see the SI).

Experiment 4

In Experiment 4, all stimuli and procedures were the same as Experiment 3, except that each RSVP sequence contained only three RSVP items. Oddballs were introduced solely in the first or the second RSVP item, while the third RSVP item (maintained to match equivalent backward masking for the first and the second RSVP items) consistently displayed a standard numerosity. The removal after the third RSVP items would primarily mitigate post-perceptual (rather than perceptual) interference on the first and the second RSVP item caused by the subsequent RSVP items.

Experiment 5

A recent study (Robinson et al., 2019) suggested that object representations are attenuated due to forward and backward masking from neighboring RSVP items. An abrupt onset of the first RSVP item might enhance its representation relative to the second one. To rule out the potential unmatched processing between the first and the second RSVP items, we conducted Experiment 5. Here, all stimuli and procedures were the same as Experiment 3, except that a forward mask was added before the first RSVP item to eliminate its abrupt onset. Since we focused on the SDE between the first and second RSVP positions, all the positions after the position 2 were used as foil trials and excluded from data analysis.

Data Analysis

As our study focuses on accuracy-based SDEs, we primarily used accuracy and precision to evaluate numerical performance. Additionally, error rate was employed to validate the effectiveness of our SOA manipulation. In this context, accuracy was operationally defined as the mean numerosity responses, which reflects the overall accuracy of participants' numerosity discrimination. Precision was operationally defined as the coefficient of variation (CoV), which is the standard deviation of numerical responses divided by mean response (The calculation formula for CoV can be found from the SI). CoVs illustrate overall precision of underlying numerical processing (Revkin et al., 2008; Véronique et al., 2008). A CoV that is zero or close to it indicates the highest stability or repeatability of a response. A stable CoV across numerosities indicates that the reporting of magnitudes adheres to Weber's law and is a property of the scalar of underlying numerical processing (Véronique et al., 2008; Whalen et al., 1999). Accuracy fluctuations between neighboring oddball positions, i.e., accuracy-based SDEs, reflects the continuity of numerical processing. Similarly, precision changes between neighboring oddball positions indicates the stability of numerical processing.

Throughout our study, we used a measurement called the SDE _Ratio to quantify the magnitude of the SDE. The SDE _Ratio was operationally defined as an oddball numerical response in the position 2 condition (with a history of a standard numerosity presented at the first RSVP item) divided by an oddball numerical response in the position 1 condition (without a history of a standard numerosity presented at the first RSVP item), as illustrated below:

$${\text{S}\text{D}\text{E}}_{\text{R}\text{a}\text{t}\text{i}\text{o}} = \frac{\text{R}\text{e}\text{p}\text{o}\text{r}\text{t}\text{e}\text{d} \text{o}\text{d}\text{d}\text{b}\text{a}\text{l}\text{l} \text{n}\text{u}\text{m}\text{e}\text{r}\text{o}\text{s}\text{i}\text{t}\text{y} \text{a}\text{t} \text{p}\text{o}\text{s}\text{i}\text{t}\text{i}\text{o}\text{n} 2}{\text{R}\text{e}\text{p}\text{o}\text{r}\text{t}\text{e}\text{d} \text{o}\text{d}\text{d}\text{b}\text{a}\text{l}\text{l} \text{n}\text{u}\text{m}\text{e}\text{r}\text{o}\text{s}\text{i}\text{t}\text{y} \text{a}\text{t} \text{p}\text{o}\text{s}\text{i}\text{t}\text{i}\text{o}\text{n} 1}$$

Accuracy

Experiment 1: A SOA of 200ms

To directly evaluate the SDE that is based on analysis on accuracy results (Fig. 3a & 3b; see the SI for ANOVA analysis), we used the slope as the index of SDE. We found that for small numerosities (see Fig. 3c), the SDE _Ratio was significantly larger than one in the smaller oddball condition (t (33) = 5.107, p < 0.001, d’ = 0.876, mean = 1.248, SD = 0.283) but not significantly different from one in the larger oddball condition (t (33) = -0.237, p = 0.814, mean = 0.998, SD = 0.055). In contrast, for large numerosities (see Fig. 3d), the SDE _Ratio was significantly larger than one in the smaller oddball condition (t (33) = 5.113, p = 0.001, d’ = 0.875, mean = 1.056, SD = 0.064) but smaller than one in the larger oddball condition (t (33) = -3.286, p = 0.002, d’ =0.561, mean = 0.977, SD = 0.041). These analyses clearly indicated differences in SDEs between small and large numerosities.

Experiment 2: A SOA of 494 ms

The accuracy results in Experiment 2 (Fig. 4) diverged from those observed in Experiment 1. In particular, the SDE was not observed for subitizing in terms of both ANOVA (See Fig. 4a) and the SDE _Ratio analysis (See Fig. 4c). For estimation, the ANOVA analysis showed a complex pattern (See Fig. 4b). Further SDE _Ratio analysis (See Fig. 4d) showed that there was no significant SDE in the larger oddball condition (t (32) = 0.373, p = 0.712, mean = 1.003, SD = 0.040) but a non-significant trend of SDE in the smaller oddball condition (t (32) = 2.331, p = 0.026, Bonferroni-corrected p value threshold for statistical significance is 0.05/4 = 0.0125, d’ = 0.406, mean = 1.024, SD = 0.058).

Experiment 3: Balancing Continuous Variables

The accuracy results in Experiment 3 (Fig. 5) replicated and extended the findings of Experiment 1 (Fig. 3), demonstrating that the SDE was asymmetric for small numerosity and symmetric for large numerosity (more details see the SI) even after controlling non-numerical magnitudes. These results suggest that the different dimensions of non-numerical magnitude in the stimulus, including inter-distance, convex hull, total perimeter, total area, and radius (see Fig. 2), did not substantially influence SDEs in numerosity perception. The asymmetrical SDEs for small numerosity were also not attributable to differences in absolute values of the relative oddball changes between the smaller and the larger oddball conditions (see Table S1 in the SI), as the asymmetrical SDEs remained largely unchanged in a sub-analysis after matching absolute values of the relative oddball changes (see Fig. S1 in the SI for more details).

Experiment 4: Removal of RSVP Items after the third one

Compared with Experiment 3, the accuracy results in Experiment 4 (see Fig. 6) showed a similar pattern in subitizing, but a different pattern in estimation. In terms of SDE _Ratio analysis, for small numerosities (see Fig. 6c), the SDE _Ratio was significantly larger than one in the smaller oddball condition (t (31) = 5.831, p < 0.001, d’ = 1.035, mean = 1.209, SD = 0.202) but not significantly different from one in the larger oddball condition (t (31) = -0.919, p = 0.365, mean = 0.996, SD = 0.025). For large numerosities, the SDE _Ratio analysis (See Fig. 6d) showed that there was significant SDE in the smaller oddball condition (t (31) = 5.086, p < 0.001, d’ = 0.909, mean = 1.050, SD = 0.055) but a non-significant trend of SDE in the larger oddball condition (t (31) = -2.102, p = 0.044, Bonferroni-corrected p value threshold for statistical significance is 0.05/4 = 0.0125, d’ =0.367, mean = 0.982, SD = 0.049). The results indicated that the removal of the RSVP items after the third one had an impact on the SDE of estimation, while it did not appear to affect SDE in subitizing.

Experiment 5: Matched processing by adding a forward-mask

We added a forward-mask before the first RSVP item in this experiment (see Fig. 7). The accuracy results in Experiment 5 (see Fig. 8) confirmed the findings of Experiment 1 and 3 (see Fig. 3 and Fig. 5), showing that the SDE was asymmetric for small numerosity and symmetric for large numerosity (more details see the SI), even after eliminating the abrupt onset of the first RSVP item. These results suggest that the observed SDEs in the present study were not due to unmatched processing between the first and the second RSVP items, but rather due to an attractive effect from the first RSVP item to the second one.

Precision

Experiment 1–3: CoV Analysis: no influence on processing prevision for estimation

Collectively, the CoV results (see Methods and Fig. 9) demonstrated that large numerosities adhered to Weber's law regardless of the smaller / larger oddball, oddball positions, or SOA conditions. However, the precision of small numerosity processing was more likely to be influenced by the smaller / larger oddball and temporal window. Specifically, within the 200 ms SOA (i.e., Experiment 1, 3 See Fig. 9a & 9e), the CoVs for small numerosity processing increased with oddball positions, particularly under the smaller oddball condition, indicating an elevated variance, whereas the CoVs largely remained constant under the larger oddball condition.

Experiment 4–5: CoV Analysis: little influence on processing precision for estimation

Both the smaller / larger oddball conditions for small numerosities and the larger oddball condition for large numerosities had similar CoV patterns between Experiment 4 & 5 and Experiment 1 & 3. However, CoVs in the smaller oddball condition for large numerosities decreased slightly with oddball positions in Experiment 4 & 5, indicating an increased processing precision (See Fig. 9h & 9l; more details see the SI). It is worth noting that the magnitudes of the precision change between position 1 and position 2 (ΔCoV = CoV at position 2 - CoV at position 1) were significantly larger (t (29) = 7.406, p < 0.001, d’ = 1.206) for small numerosities (Mean(ΔCoV) = 0.173, SD(ΔCoV) = 0.141, relatively large and an impaired processing precision) than that for large numerosities (Mean(ΔCoV) = -0.027, SD(ΔCoV) = 0.034, relatively little or no influence on processing precision) in the smaller oddball condition. This was also true for Experiment 4.

Error rate

The error rate results demonstrated that our SOA manipulation is successful: extending the temporal window decreased the error rates for both small and large numerosities (i.e., E1 vs E2, ps < 0.001, Fig. 10; more details see the SI).

Our study showed different mechanisms of SDEs between subitizing and estimation. Experiment 1, with an SOA of 200 ms, showed significant SDE only when the current magnitude was smaller than the previous magnitude (smaller oddball), but not when it was larger (larger oddball). In contrast, symmetrical SDEs were observed in estimation. Experiment 2 showed that SDE was eliminated for subitizing and reduced for estimation when perceptual interference from the immediately preceding RSVP item was greatly reduced by prolonging SOA to 494 ms. Experiment 4, on the other hand, showed that SDE was intact for subitizing and substantially reduced for estimation when post-perceptual interference to the first and second RSVP items was greatly reduced by removing RSVP items after the third one. These independent manipulations suggest that subitizing-related SDE is likely due to perceptual processing, while estimation-related SDE is due to a combination of perceptual and post-perceptual processing. Additionally, asymmetrical SDEs for subitizing and symmetrical ones for estimation were still observed even when non-numerical, continuous magnitude variables were controlled in Experiment 3 and when processing between the first and the second RSVP items was matched by adding a forward-mask in Experiment 5.

Different mechanisms of SDE between small and large numerosities

The present study suggested that the SDE mechanisms seem to be different between the two numerosity ranges. In estimation, over- and under-estimations of the mean numerical response between the first and the second oddball positions were accompanied by either a constant processing precision (in Experiment 1 & 3) or a very small increase of processing precision (in Experiment 4 & 5, negligible relative to the decreased processing precision in subitizing) across oddball positions. This dissociation between accuracy and precision for SDE on large numerosities is consistent with previous numerical literature indicating that SDE in estimation essentially introduces bias, with little or no influence on the precision of numerical discriminability (Fornaciai & Park, 2018a; Fornaciai & Park, 2019b). More generally, this is also consistent with the consensus view in the current SDE literature that SDE is a mechanism to achieve processing continuity and stability by integrating information over time (Cicchini et al., 2021; Fischer & Whitney, 2014). However, in subitizing, all experiments with 200ms SOA revealed similar patterns of changes in accuracy and precision, i.e., different from that in estimation. This finding reveals a novel type of SDE, whereby perceptual appearance drifts towards recent information along with decreased processing precision. Our findings thus reveal the diverse nature of SDE mechanisms. We identified at least two qualitatively different SDE types: one characterized by decreased processing precision, prioritizing processing continuity at the expense of processing stability, and the other characterized by stable processing precision, enabling the concurrent achievement of processing continuity and processing stability. These two types of SDEs manifest differentially in the small and large numerosity ranges, respectively.

There is currently a lively debate in the literature regarding the underlying mechanisms of SDE (Ceylan et al., 2021; Cicchini et al., 2017; Fischer & Whitney, 2014; Fornaciai & Park, 2018a). Initially, SDE was thought to originate from and act on early perceptual processing (Fischer & Whitney, 2014). However, recent studies have shown that SDE can instead originate from a high-level, post-perceptual processing of the previous trial and act on a low-level, perceptual processing of the current trial (Fornaciai & Park, 2019b, 2022; Schwiedrzik et al., 2014; St John-Saaltink et al., 2016). For example, Fornaciai and Park (2022) found that abstract information (symbolic numerosity) successfully yielded attractive serial dependence biases, and that external information at the level of judgment (by providing feedback of responses) significantly modulated the magnitude of SDEs. These findings align with our proposal that SDE of estimation may involve a combination of both perceptual and post-perceptual processing. Further studies are required to elucidate at which stage (origin or target) and how estimation-based SDEs combine perceptual and post-perceptual processing.

It remains unclear whether and how the neural substrates differ between subitizing- and estimation-based SDEs. Prior research by Fornaciai and Park (2018a) reported a neural signature of attractive SDEs emerging early in the visual stream in estimation. Recent studies (Fornaciai & Park, 2020a; Fornaciai et al., 2023) confirmed this early neural signature and demonstrated that this biased neural representation was preserved for a relatively long period and can be reactivated by reactivating hidden memory states (Wolff et al., 2015). Our study showed that subitizing-based SDEs primarily involve perceptual components, lacking post-perceptual components. Therefore, an interesting question arises as to whether the neural signature of subitizing-based SDE is limited to early stages and cannot be retained as a hidden memory state. This hypothesis merits further investigation.

The present study contributes to the ongoing debate on whether subitizing and estimation involve the same mechanisms (Dantzig, 1967; Dehaene, 1997). In terms of sensitivity and dependence on contextual information, it appears that small and large numerosities operate via distinct mechanisms. Critically, our findings demonstrated the multifaceted nature of SDE mechanisms in supporting continuity and/or stability of visual processing (Cicchini et al., 2021; Fischer & Whitney, 2014). As an active process integrating past and present information, SDE can be differentially engaged with cognitive modules subserving different functionalities, such as cognitive scenarios closely-related with early object recognition in subitizing (Trick & Pylyshyn, 1993) and ensemble numerosity extraction in estimation (Dantzig, 1967; Dehaene, 1997), respectively.

An object individuation-based 'temporal hysteresis' account for SDE in subitizing

We provide evidence for the first time that SDE can occur in subitizing. The SDE in small numerosities shows an asymmetrical pattern, different from the SDEs in large numerosities (Fornaciai & Park, 2018b, 2022). The asymmetrical SDEs in subitizing are unlikely be explained by several well-established effects such as difference of signal strength (Pascucci et al., 2019), persistence of vision (Coltheart, 1980), postdiction (Eagleman & Sejnowski, 2000), central tendency (Anobile et al., 2012), or ensemble representation (Manassi et al., 2017) (more details see the SI). Here, we propose a 'temporal hysteresis' account based on object individuation (Pylyshyn, 1989; Trick & Pylyshyn, 1993; Xu & Chun, 2009) to explain SDE in subitizing. Specifically, we propose that the asymmetrical SDE in subitizing reflects the disposition of temporal hysteresis (a delayed offset) in object individuation (Wutz et al., 2012; Wutz & Melcher, 2013, 2014). That is, object individuation resource has a tendency to be easy to open but difficult to close. In other words, within its limited capacity, the allocation of new object individuation resource is rapid and efficient. However, the reclamation of previously-occupied object individuation resource is relatively slow and inefficient. Therefore, the SDE observed in the smaller oddball condition (i.e., standard numerosity > oddball numerosity) of subitizing, that is, numerical overestimation of the position 2 relative to the position 1, is likely due to the residual activity of the net object individuation resource elicited by the previous standard numerosity. These resources are no longer required by the current oddball numerosity and cannot be immediately reclaimed by the object individuation system. In contrast, in the larger oddball condition (i.e., standard numerosity < oddball numerosity) of subitizing, there is no net object individuation resource elicited by the previous standard numerosity. Instead, the extra object individuation resource required by the current oddball numerosity can be efficiently opened and allocated by the object individuation system, leaving no bias in numerical processing between the first and the second positions, i.e., no SDE.

The object individuation-based 'temporal hysteresis' account received further support from the analysis of CoV, an index of the precision of underlying numerical processing (Revkin et al., 2008; Véronique et al., 2008). All experiments with a 200ms SOA showed an asymmetrical pattern of CoV in subitizing, where CoVs significantly increased with oddball positions in the smaller oddball conditions but remained stable and constant in the larger oddball conditions. These findings were consistent with the 'temporal hysteresis' account, in that the residual activity of the net object individuation resource, which was only present in the smaller oddball but not the larger oddball conditions, contributed to numerical processing in two ways: leading to an inflation of mean numerical response and a deterioration of processing precision by introducing extra noise into the object individuation system.

Hysteresis-like effects have been frequently observed across various aspects of human cognition, including motion direction perception (Williams et al., 1986), apparent motion (Hock et al., 1993), occluded object recognition (Ernst et al., 2021), spatial frequency integration during active perception (Brady & Oliva, 2012), contrast change-driven visual letter recognition (Kleinschmidt et al., 2002), and judgment of auditory pitch shift (Chambers & Pressnitzer, 2014; Giangrand et al., 2003). The present study provides new evidence for the ubiquity of hysteresis-like effects in human cognition. In light of recent research (Ernst et al., 2021) proposing that recurrent connectivity in the brain and its associated feedback/re-entrant processing may be key to understanding perceptual hysteresis for both auditory and visual stimuli (Buckthought et al., 2008; You et al., 2011), future studies investigating the role of feedback/re-entrant processing in the hysteresis-like SDE for subitizing would be of great interest. In particular, it would be intriguing to examine whether ’the residual activity of the net object individuation resource’ acting on current stimuli in the object individuation-based 'temporal hysteresis' account is linked with feedback/re-entrant processing (Ernst et al., 2021) of immediately preceding stimuli.

In conclusion, employing a novel continuous numerical oddball paradigm, we unveiled two distinct types of SDEs in numerical cognition: subitizing-based and estimation-based SDEs. The divergent patterns and underlying mechanisms of these SDEs imply that the continuity and stability of numerical processing can be dissociable in dynamic situations where numerical information is integrated over time. Our findings also provide additional empirical support for the functional dissociation between two numerical ranges: subitizing, likely linked to early object recognition, and estimation, likely associated with ensemble numerosity extraction.

Supplementary Information

Additional supplemental material can be found at https://osf.io/yna72/.

Acknowledgments

This work was supported by a grant from The National Social Science Fund of China (BBA210036).

Author contributions

Conceptualization: Yue Huang, Haokun Li, Xianfeng Ding; Data curation: Yue Huang, Shiming Qiu; Formal analysis: Yue Huang; Funding Acquisition: Zhao Fan, Xiaorong Cheng; Investigation: Yue Huang, Min Li, Wangjuan Liu; Project administration: Zhao Fan, Yue Huang; Resources: Xiaorong Cheng; Software: Haokun Li, Shiming Qiu; Supervision: Zhao Fan; Visualization: Yue Huang; Writing – original draft: Yue Huang, Shiming Qiu; Writing – review & editing: Yue Huang, Zhao Fan, Xianfeng Ding, Xiaorong Cheng

Open Practice Statement

The study was not preregistered. The processed data analyzed during the study and the Matlab code for generating the figures are available at https://osf.io/yna72/.

Declaration of interests

Conflict of interest The authors declare no competing interests.

Ethical approval Allprocedures performed in studies involving human participants were in accordance with ethical standards of the institutional and/or national research committee, the American Psychological Association (APA) standards and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed consent Informed consent was obtained from all the individual participants included in the study.

Adriano, A., Rinaldi, L., & Girelli, L. (2021, Mar). Visual illusions as a tool to hijack numerical perception: Disentangling nonsymbolic number from its continuous visual properties. J Exp Psychol Hum Percept Perform, 47(3), 423-441. https://doi.org/10.1037/xhp0000844
Anobile, G., Arrighi, R., & Burr, D. C. (2019a, 2019/02/01/). Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities. Journal of Experimental Child Psychology, 178, 86-103. https://doi.org/https://doi.org/10.1016/j.jecp.2018.09.017
Anobile, G., Cicchini, G. M., & Burr, D. C. (2012, Mar). Linear mapping of numbers onto space requires attention. Cognition, 122(3), 454-459. https://doi.org/10.1016/j.cognition.2011.11.006
Brady, T. F., & Oliva, A. (2012). Spatial frequency integration during active perception: perceptual hysteresis when an object recedes. Front Psychol, 3, 462. https://doi.org/10.3389/fpsyg.2012.00462
Brainard, D. H. (1997). The Psychophysics Toolbox. Spat Vis, 10.
Brincat, S. L., & Connor, C. E. (2006, Jan 5). Dynamic shape synthesis in posterior inferotemporal cortex. Neuron, 49(1), 17-24. https://doi.org/10.1016/j.neuron.2005.11.026
Buckthought, A., Kim, J., & Wilson, H. R. (2008, Mar). Hysteresis effects in stereopsis and binocular rivalry. Vision Res, 48(6), 819-830. https://doi.org/10.1016/j.visres.2007.12.013
Burr, D. C., Anobile, G., & Arrighi, R. (2018). Psychophysical evidence for the number sense. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1740), 20170045. https://doi.org/doi:10.1098/rstb.2017.0045
Cai, Y., Hofstetter, S., van Dijk, J., Zuiderbaan, W., van der Zwaag, W., Harvey, B. M., & Dumoulin, S. O. (2021, 2021/06/07). Topographic numerosity maps cover subitizing and estimation ranges. Nature Communications, 12(1), 3374. https://doi.org/10.1038/s41467-021-23785-7
Ceylan, G., Herzog, M. H., & Pascucci, D. (2021, 2021/07/01/). Serial dependence does not originate from low-level visual processing. Cognition, 212, 104709. https://doi.org/https://doi.org/10.1016/j.cognition.2021.104709
Chambers, C., & Pressnitzer, D. (2014, Jul). Perceptual hysteresis in the judgment of auditory pitch shift. Atten Percept Psychophys, 76(5), 1271-1279. https://doi.org/10.3758/s13414-014-0676-5
Cheng, X., Yang, Q., Han, Y., Ding, X., & Fan, Z. (2014). Capacity limit of simultaneous temporal processing: how many concurrent ‘clocks’ in vision? PLoS One, 9(3), e91797. https://doi.org/10.1371/journal.pone.0091797
Cheyette, S. J., & Piantadosi, S. T. (2019, Sep 3). A primarily serial, foveal accumulator underlies approximate numerical estimation. Proc Natl Acad Sci U S A, 116(36), 17729-17734. https://doi.org/10.1073/pnas.1819956116
Cicchini, G. M., Benedetto, A., & Burr, D. C. (2021, 2021/03/22/). Perceptual history propagates down to early levels of sensory analysis. Current Biology, 31(6), 1245-1250.e1242. https://doi.org/https://doi.org/10.1016/j.cub.2020.12.004
Cicchini, G. M., Mikellidou, K., & Burr, D. (2017). Serial dependencies act directly on perception. Journal of Vision, 17(14), 6-6. https://doi.org/10.1167/17.14.6
Cichy, R. M., Pantazis, D., & Oliva, A. (2014, Mar). Resolving human object recognition in space and time. Nat Neurosci, 17(3), 455-462. https://doi.org/10.1038/nn.3635
Coltheart, M. (1980). The persistences of vision. Philos Trans R Soc Lond B Biol Sci, 8:290(1038), 57-69. https://doi.org/10.1098/rstb.1980.0082
Dantzig, T. (1967). Number: The language of science (4th ed. ). New York: The Free Press.
Dehaene, S. (1997). The number sense Oxford University Press. New York.
Dehaene, S., & Changeux, J.-P. (1993). Development of Elementary Numerical Abilities: A Neuronal Model. Journal of Cognitive Neuroscience, 5(4), 390-407. https://doi.org/10.1162/jocn.1993.5.4.390
Eagleman, D. M., & Sejnowski, T. J. (2000, Mar 17). Motion integration and postdiction in visual awareness. Science, 287(5460), 2036-2038. https://doi.org/10.1126/science.287.5460.2036
Ernst, M. R., Burwick, T., & Triesch, J. (2021, Dec 1). Recurrent processing improves occluded object recognition and gives rise to perceptual hysteresis. J Vis, 21(13), 6. https://doi.org/10.1167/jov.21.13.6
Fischer, J., & Whitney, D. (2014, May). Serial dependence in visual perception. Nat Neurosci, 17(5), 738-743. https://doi.org/10.1038/nn.3689
Fornaciai, M., & Park, J. (2018a, 2018/03/01). Attractive Serial Dependence in the Absence of an Explicit Task. Psychological Science, 29(3), 437-446. https://doi.org/10.1177/0956797617737385
Fornaciai, M., & Park, J. (2018b, Sep 4). Serial dependence in numerosity perception. J Vis, 18(9), 15. https://doi.org/10.1167/18.9.15
Fornaciai, M., & Park, J. (2019a, Jul). Serial dependence generalizes across different stimulus formats, but not different sensory modalities. Vision Res, 160, 108-115. https://doi.org/10.1016/j.visres.2019.04.011
Fornaciai, M., & Park, J. (2019b, May 1). Spontaneous repulsive adaptation in the absence of attractive serial dependence. J Vis, 19(5), 21. https://doi.org/10.1167/19.5.21
Fornaciai, M., & Park, J. (2020a). Neural Dynamics of Serial Dependence in Numerosity Perception. Journal of Cognitive Neuroscience, 32(1), 141-154. https://doi.org/10.1162/jocn_a_01474
Fornaciai, M., & Park, J. (2020b, Jul). Attractive serial dependence between memorized stimuli. Cognition, 200, 104250. https://doi.org/10.1016/j.cognition.2020.104250
Fornaciai, M., & Park, J. (2021, Jul 1). Decoding of Electroencephalogram Signals Shows No Evidence of a Neural Signature for Subitizing in Sequential Numerosity. J Cogn Neurosci, 33(8), 1535-1548. https://doi.org/10.1162/jocn_a_01734
Fornaciai, M., & Park, J. (2022, Jul). The effect of abstract representation and response feedback on serial dependence in numerosity perception. Atten Percept Psychophys, 84(5), 1651-1665. https://doi.org/10.3758/s13414-022-02518-y
Fornaciai, M., Togoli, I., & Bueti, D. (2023, Apr 19). Perceptual history biases are predicted by early visual-evoked activity. J Neurosci. https://doi.org/10.1523/JNEUROSCI.1451-22.2023
Giangrand, J., Tuller, B., & Kelso, J. A. S. (2003). Perceptual Dynamics of Circular Pitch. Music Perception, 20(3), 241-262. https://doi.org/10.1525/mp.2003.20.3.241
Hock, H. S., Kelso, J. A., & Schöner, G. (1993, Feb). Bistability and hysteresis in the organization of apparent motion patterns. J Exp Psychol Hum Percept Perform, 19(1), 63-80. https://doi.org/10.1037//0096-1523.19.1.63
Hung, C. P., Kreiman, G., Poggio, T., & DiCarlo, J. J. (2005, Nov 4). Fast readout of object identity from macaque inferior temporal cortex. Science, 310(5749), 863-866. https://doi.org/10.1126/science.1117593
Isik, L., Meyers, E. M., Leibo, J. Z., & Poggio, T. (2014, Jan). The dynamics of invariant object recognition in the human visual system. J Neurophysiol, 111(1), 91-102. https://doi.org/10.1152/jn.00394.2013
Jevons, W. S. (1871, February 01, 1871). The Power of Numerical Discrimination. Nature, 3, 281. https://doi.org/10.1038/003281a0
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The Discrimination of Visual Number. The American Journal of Psychology, 62(4), 498-525. https://doi.org/10.2307/1418556
Kleinschmidt, A., Büchel, C., Hutton, C., Friston, K. J., & Frackowiak, R. S. (2002, May 16). The neural structures expressing perceptual hysteresis in visual letter recognition. Neuron, 34(4), 659-666. https://doi.org/10.1016/s0896-6273(02)00694-3
Luck, S. J., & Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature, 390(6657), 279-281. https://doi.org/10.1038/36846
Manassi, M., Liberman, A., Chaney, W., & Whitney, D. (2017, May 16). The perceived stability of scenes: serial dependence in ensemble representations. Sci Rep, 7(1), 1971. https://doi.org/10.1038/s41598-017-02201-5
Melcher, D. (2005, Oct 11). Spatiotopic transfer of visual-form adaptation across saccadic eye movements. Curr Biol, 15(19), 1745-1748. https://doi.org/10.1016/j.cub.2005.08.044
Melcher, D., Huber-Huber, C., & Wutz, A. (2021, Apr). Enumerating the forest before the trees: The time courses of estimation-based and individuation-based numerical processing. Atten Percept Psychophys, 83(3), 1215-1229. https://doi.org/10.3758/s13414-020-02137-5
Pascucci, D., Mancuso, G., Santandrea, E., Della Libera, C., Plomp, G., & Chelazzi, L. (2019). Laws of concatenated perception: Vision goes for novelty, decisions for perseverance. PLoS Biol 17(3), e3000144. https://doi.org/10.1101/229187
Pascucci, D., Tanrikulu, O. D., Ozkirli, A., Houborg, C., Ceylan, G., Zerr, P., Rafiei, M., & Kristjansson, A. (2023, Jan 3). Serial dependence in visual perception: A review. J Vis, 23(1), 9. https://doi.org/10.1167/jov.23.1.9
Pelli, & Denis, G. (1997). The VideoToolbox software for visual psychophysics: transforming numbers into movies. Spatial Vision, 10(4), 437.
Potrich, D., Zanon, M., & Vallortigara, G. (2022, 2022/01/10). Archerfish number discrimination. eLife, 11, e74057. https://doi.org/10.7554/eLife.74057
Pylyshyn, Z. W. (1989, Jun). The role of location indexes in spatial perception: a sketch of the FINST spatial-index model. Cognition, 32(1), 65-97. https://doi.org/10.1016/0010-0277(89)90014-0
Pylyshyn, Z. W., & Storm, R. W. (1988). Tracking multiple independent targets: evidence for a parallel tracking mechanism. Spat Vis, 3(3), 179-197. https://doi.org/10.1163/156856888x00122
Ranieri, G., Benedetto, A., Ho, H. T., Burr, D. C., & Morrone, M. C. (2022, Nov 23). Evidence of Serial Dependence from Decoding of Visual Evoked Potentials. J Neurosci, 42(47), 8817-8825. https://doi.org/10.1523/JNEUROSCI.1879-21.2022
Revkin, S. K., Piazza, M., Izard, V., Cohen, L., & Dehaene, S. (2008). Does Subitizing Reflect Numerical Estimation? Psychological Science, 19(6), 607-614. https://doi.org/10.1111/j.1467-9280.2008.02130.x
Robinson, A. K., Grootswagers, T., & Carlson, T. A. (2019, Aug 15). The influence of image masking on object representations during rapid serial visual presentation. Neuroimage, 197, 224-231. https://doi.org/10.1016/j.neuroimage.2019.04.050
Salinas, E., & Abbott, L. F. (1996, Oct 15). A model of multiplicative neural responses in parietal cortex. Proc Natl Acad Sci U S A, 93(21), 11956-11961. https://doi.org/10.1073/pnas.93.21.11956
Schwiedrzik, C. M., Ruff, C. C., Lazar, A., Leitner, F. C., Singer, W., & Melloni, L. (2014, May). Untangling perceptual memory: hysteresis and adaptation map into separate cortical networks. Cereb Cortex, 24(5), 1152-1164. https://doi.org/10.1093/cercor/bhs396
St John-Saaltink, E., Kok, P., Lau, H. C., & de Lange, F. P. (2016, Jun 8). Serial Dependence in Perceptual Decisions Is Reflected in Activity Patterns in Primary Visual Cortex. J Neurosci, 36(23), 6186-6192. https://doi.org/10.1523/JNEUROSCI.4390-15.2016
Sugase, Y., Yamane, S., Ueno, S., & Kawano, K. (1999, Aug 26). Global and fine information coded by single neurons in the temporal visual cortex. Nature, 400(6747), 869-873. https://doi.org/10.1038/23703
Tall, D., & Dehaene, S. (1998). The Number Sense: How the Mind Creates Mathematics. The Mathematical Gazette, 82(495), 528.
Thorpe, S., Fize, D., & Marlot, C. (1996, Jun 6). Speed of processing in the human visual system. Nature, 381(6582), 520-522. https://doi.org/10.1038/381520a0
Trick, L. M., & Pylyshyn, Z. W. (1993, 05/01). What Enumeration Studies Can Show Us About Spatial Attention: Evidence for Limited Capacity Preattentive Processing. Journal of experimental psychology. Human perception and performance, 19, 331-351. https://doi.org/10.1037//0096-1523.19.2.331
Véronique, Izard, and, Stanislas, & Dehaene. (2008). Calibrating the mental number line. Cognition, 106(3), 1221-1247. https://doi.org/10.1016/j.cognition.2007.06.004
Whalen, J., Gallistel, C. R., & Gelman, R. (1999, 1999/03/01). Nonverbal Counting in Humans: The Psychophysics of Number Representation. Psychological Science, 10(2), 130-137. https://doi.org/10.1111/1467-9280.00120
Williams, D., Phillips, G., & Sekuler, R. (1986, Nov 20-26). Hysteresis in the perception of motion direction as evidence for neural cooperativity. Nature, 324(6094), 253-255. https://doi.org/10.1038/324253a0
Wolff, M. J., Ding, J., Myers, N. E., & Stokes, M. G. (2015). Revealing hidden states in visual working memory using electroencephalography. Front Syst Neurosci, 9, 123. https://doi.org/10.3389/fnsys.2015.00123
Wutz, A., Caramazza, A., & Melcher, D. (2012). Rapid enumeration within a fraction of a single glance: The role of visible persistence in object individuation capacity. Visual Cognition, 20(6), 717-732. https://doi.org/10.1080/13506285.2012.686460
Wutz, A., & Melcher, D. (2013, Jul). Temporal buffering and visual capacity: the time course of object formation underlies capacity limits in visual cognition. Atten Percept Psychophys, 75(5), 921-933. https://doi.org/10.3758/s13414-013-0454-9
Wutz, A., & Melcher, D. (2014). The temporal window of individuation limits visual capacity. Front Psychol, 5, 952. https://doi.org/10.3389/fpsyg.2014.00952
Wutz, A., Muschter, E., van Koningsbruggen, M. G., Weisz, N., & Melcher, D. (2016, Jul 11). Temporal Integration Windows in Neural Processing and Perception Aligned to Saccadic Eye Movements. Curr Biol, 26(13), 1659-1668. https://doi.org/10.1016/j.cub.2016.04.070
Xu, Y., & Chun, M. M. (2009, 2009/04/01/). Selecting and perceiving multiple visual objects. Trends in Cognitive Sciences, 13(4), 167-174. https://doi.org/10.1016/j.tics.2009.01.008
You, H., Meng, Y., Huan, D., & Wang, D.-H. (2011, 2011/10/01/). The neural dynamics for hysteresis in visual perception. Neurocomputing, 74(17), 3502-3508. https://doi.org/https://doi.org/10.1016/j.neucom.2011.06.004
Zanon, M., Potrich, D., Bortot, M., & Vallortigara, G. (2022, Feb). Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli. Behav Res Methods, 54(1), 146-157. https://doi.org/10.3758/s13428-021-01580-y

No competing interests reported.

SupplementaryInformation.docx

Download PDF

Editorial decision: Revision requested
30 Jul, 2024
Reviews received at journal
01 Jan, 2024
Reviewers agreed at journal
15 Dec, 2023
Reviewers agreed at journal
10 Dec, 2023
Reviewers invited by journal
10 Dec, 2023
Editor assigned by journal
23 Nov, 2023
Submission checks completed at journal
22 Nov, 2023
First submitted to journal
19 Nov, 2023

You are reading this latest preprint version

Distinct serial dependence between small and large numerosity processing

Status:

Version 1

Abstract

Figures

Introduction

Methods

Subjects

Stimuli

Experiment 1

Experiment 2

Experiment 3

Experiment 4

Experiment 5

Data Analysis

Results

Accuracy

Experiment 1: A SOA of 200ms

Experiment 2: A SOA of 494 ms

Experiment 3: Balancing Continuous Variables

Experiment 4: Removal of RSVP Items after the third one

Experiment 5: Matched processing by adding a forward-mask

Precision

Experiment 1–3: CoV Analysis: no influence on processing prevision for estimation

Experiment 4–5: CoV Analysis: little influence on processing precision for estimation

Error rate

General Discussion

Different mechanisms of SDE between small and large numerosities

An object individuation-based 'temporal hysteresis' account for SDE in subitizing

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1