Crowding modulates time perception while controlling for valence and arousal

Crowding modulates time perception while controlling for valence and arousal | 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 Crowding modulates time perception while controlling for valence and arousal Youguo Chen, Yuanwei Xu, Gaomin Liang, Chunhua Peng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4008302/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Crowding has been found to slow down subjective time. This study aimed to investigate the modulation of crowding on time perception after excluding valence and arousal. In the pre-experiment, three types of crowding pictures (non-crowding, crowded objects, and crowded people) were screened, and the valence and arousal of the pictures were controlled. No significant difference in valence and arousal was found among the three types of pictures. Participants conducted a temporal bisection task with different types of pictures on sub-second (Experiment 1) and supra-second (Experiment 2) timescales. The results showed that crowding modulated time perception on the supra-second timescale rather than the sub-second. Linear mixing models and dominance analysis both confirmed that crowding, but not valence and arousal, can effectively predict subjective time on supra-second timescales. The results suggest that, excluding valence and arousal, crowding can modulate cognitively controlled timing on supra-second timescales. Both withdrawal motivation and cross-dimensional interference have been implicated in the modulation of crowding on time and need to be disentangled in future work. time perception crowding automatic timing cognitively controlled timing withdrawal motivation cross-dimension interference Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Over the past century, there has been an inexorable increase in the number of large urban agglomerations, as well as in the size and density of the population in the cities. The world’s urban population reached 4.2 billion in 2018 and is expected to grow to 6.7 billion by 2050. It is predicted that 68% of the world’s population will be living in cities by then (United Nations, 2019 ). Many countries will face challenges in meeting the needs of growing urban populations, including housing, transportation, energy systems and other infrastructure, as well as employment and basic services such as education and health care (United Nations, 2019 ). At the same time, the crowded environment also leads to the physical and mental health problem of individuals (Gray, 2001 ). Moreover, the crowded public transport can lead to passenger discomfort and increase the subjective perception of the traffic time (Haywood et al., 2017 ). The subjective perception of the traffic time has become an indicator to measure the subjective crowding of public transport (Lin et al., 2023 ; Wardman & Whelan, 2011 ). Therefore, it is of great value to study the relationship between subjective time and crowding for urban management and individual physical and mental health. There is an increasing body of evidence that suggests that individuals perceive time to pass more slowly (overestimate) in crowded settings compared to uncrowded. Fujimoto ( 2016 ) conducted a field experiment in which participants were asked to report their subjective perceived time in 13 different settings by filling out a questionnaire. Participants reported that the subjective time was longer in a crowded and noisy setting compared to a quiet and empty setting. Shimokawa and Sugimori ( 2019 ) further examined the effect of crowding on time estimation in virtual reality (VR) environments. Participants wore head-mounted VR displays and watched videos showing a cityscape and a countryside (Experiment 1), a crowded and uncrowded station (Experiment 2), and a crowded and uncrowded nature park (Experiment 3). Participants were asked to start the stopwatch and then stop it when they felt that 30 s or 60 s had passed, and the perceived time in the crowded settings was longer relative to the uncrowded settings in the three experiments. Sadeghi et al. ( 2023a , b ) conducted studies where participants experienced short (1–2 min) immersive virtual reality subway trips with different levels of public crowding. They found that increased crowding increased the unpleasantness of a trip and lengthened perceived trip duration (Sadeghi et al., 2023a , b ); the unpleasant emotional experience mediated the influence of crowding on subjective time (Sadeghi et al., 2023a ). Furthermore, the experience of withdrawal motivation, where individuals desire to terminate the trip sooner and escape the unpleasant environment, is one specific component related to the unpleasantness of crowding. Sadeghi et al. ( 2023a ) speculated that the extended perceived duration may stem from withdrawal motivation. However, it remains an open question whether crowding can modulate subjective time independently of affective valence. Crowding can influence subjective time perception through multiple factors. As previously mentioned, three dimensions of emotion, namely valence, arousal, and motivation, are closely linked to crowding (Sadeghi et al., 2023a ). A common naive theory is that “time flies when you’re having fun”, which suggests that events with positive valence pass especially quickly (Gable & Poole, 2012 ; Sackett et al., 2010 ; Tonietto et al., 2022 ). Conversely, negative events are perceived as passing slowly, and boredom overestimates time (Danckert & Allman, 2005 ; O’Brien et al., 2011 ; Tonietto et al., 2022 ). Arousal also modulates the perception of time, as the perceived time of an emotional picture increases with arousal level (Droit-Volet et al., 2004 , 2010 ; Gil & Droit-Volet, 2012 ). Gable et al. ( 2022 ) suggested that motivation directly modulates time perception, rather than being mediated by affective valence and arousal; specifically, approach motivation hastens the passing of time, whereas withdrawal motivation slows the passing of time, and motivation intensity is considered to enhance the effects of motivation direction (Gable et al., 2016 ; Gable & Poole, 2012 ). Furthermore, crowding is always accompanied by quantity processing, and quantity can modulate time perception, that is, larger magnitudes are perceived to last longer, resulting in cross-dimension interference (Oliveri et al., 2008 ; Xuan et al., 2007 , 2009 ). According to a theory of magnitude (ATOM), time, space, and quantity are part of a generalized magnitude system; external inputs of different dimensions are converted into a common magnitude representation; the cross-dimension interference results from the integration of representation of different dimensions in the generalized magnitude system; the parietal cortex is considered as the neural substrate of the magnitude system (Bueti & Walsh, 2009 ; Walsh, 2003b ). Crowding may modulate subjective time even after excluding emotional valence and arousal. An important finding in the field of time psychology is that the processing mechanism of temporal information is separate on different timescales (Buhusi & Meck, 2005 ). Time perception is the cognitive process of perceiving temporal information within a range of two to three seconds, and no more than five seconds, which is primarily related to perception. On the other hand, processing temporal information beyond this range is referred to as time estimation, which is mainly related to memory (Fraisse, 1984 ). Even the time intervals below and above one second are proven to be measured by separate neural timing systems. Automatic timing system measures sub-second intervals without attentional modulation, and rely primarily on motion circuits; cognitively controlled timing system is more involved in the measurement of supra-second intervals with attention and working memory, and depends upon prefrontal and parietal regions (Lewis & Miall, 2003b , 2003a , 2006 ). Crowding may have different influences on perception of time on sub-second and supra-second timescales. The purpose of the study was to investigate the correlation between crowding and time perception while controlling for the effects of valence and arousal. In the pre-experiment, three types of crowding pictures (non-crowding, crowded objects, and crowded people) were collected and evaluated. There was no significant difference in the valence and arousal scores among the three kinds of pictures. Participants performed a temporal bisection task with different types of crowding pictures on the sub-second (Experiment 1) and supra-second (Experiment 2) timescales. Given that time perception can be directly modulated by withdrawal motivation (Gable et al., 2016 , 2022 ; Gable & Poole, 2012 ) and quantity (Oliveri et al., 2008 ; Xuan et al., 2007 , 2009 ), we hypothesize that crowding can modulate time perception after the exclusion of valence and arousal. Time perception is mainly processed automatically on the sub-second timescales and is a cognitively controlled process on supra-second timescales (Lewis & Miall, 2003b , 2003a , 2006 ). Automatic timing is less susceptible to interference from non-temporal tasks, whereas cognitively controlled timing is susceptible to interference from non-temporal tasks (Hellström & Rammsayer, 2004 ; Rammsayer, 2006 ). Therefore, we hypothesized that crowding would modulate time perception on seconds rather than the sub-second. Pre-experiment: collecting and evaluating crowding pictures In the pre-experiment, we collected three types of pictures (non-crowding, crowded objects, and crowded people) from the internet. Participants rated the degree of crowding, valence, and arousal for each picture. To avoid the effect of valence and arousal on time perception in following experiments, we ensured that the valence and arousal of the three types of pictures were controlled so that there were no significant differences among the three types of pictures. This approach will help us to better understand the effect of crowding on time perception. Methods Participants The power analysis was performed using the PANGEA, which is specifically designed for analysis of variance (ANOVA), and available to the public at https://jakewestfall.shinyapps.io/pangea/ (Westfall et al., 2014). The study adopted a one-factor within-subject design with crowding as the factor, having three levels: non-crowding, crowded objects, and crowded people. Each treatment consisted of 30 trials. As the variances associated with the main effect of crowding could not be predicted in advance, the default variance parameters in PANGEA were used (var [error] = 0.5, var [participant × crowding] = 0.167). Given a recommended statistical power of 0.8, a medium effect size (Cohen’s d ) of 0.5, and a significance level of 0.05 (Clayson et al., 2019 ), the required a minimum of sample size is 23. Twenty-five undergraduate students volunteered to participate in the pre-experiment (18–24 years old, 15 females). All participants had normal or corrected vision, were right-handed, and had no history of color blindness, color weakness, or mental illness. The participants signed informed consent before the experiment, and received corresponding remuneration after the experiment. The experimental procedures followed the Declaration of Helsinki and are reviewed by the Ethics Committee of Southwest University. Stimuli and procedures Three types of pictures are collected on the Internet (Figure. 1A). Non-crowding pictures were mainly empty scenes, such as city streets, roads, parks, and residential gardens, and so on. The crowded objects pictures were mainly dense express boxes, books, toys, bicycles, fruits, and so on. The crowded people pictures were the crowded people in the station, street, swimming pool, and so on. The sizes of all the images were standardized using Photoshop (The Adobe, Inc.). The length of the picture was 30 cm and its width was 22.5 cm. The pictures were displayed in the middle of a 28-inch LCD screen with a black background. Participants assessed the crowding of pictures on a 9-point self-report rating scale (Vaske & Shelby, 2008 ). Crowding refers to the feeling of how crowded the area was when viewing the scene. The more crowded the scene, the closer the score is to 9, and the less crowded the scene, the closer the score is to 1. Participants also assessed the pictures in terms of valence and arousal on the 9-point self-assessment Manikin scale (Bradley & Lang, 1994 ). Valence refers to the degree of pleasure or unpleasant when viewing the scene. The higher the pleasant, the closer the rating is to 9, and the less pleasant, the closer the rating is to 1. Arousal refers to the degree of excitement or calm when viewing the scene. The higher the level of excitement, the closer the score is to 9, and the less excited, the closer the score is to 1. Participants were seated approximately 60 cm away from the screen. E-prime 2.0 (Psychology Software Tools, Inc.) was used to control the presentation of pictures, and record the responses of participants. The pictures were presented randomly, and the participants used a keyboard to rate the valence, arousal, and crowding of each picture. The order of rating the three dimensions was balanced among the participants. After the evaluation of the first dimension, all the pictures were randomly presented again for the next dimension, and all the pictures were presented for a total of three rounds. The rating time was determined by the participants themselves. In principle, the rating was based on the immediate feeling, and there was no long-term thinking. Data analysis There were 30 pictures per category: non-crowding, crowded objects, and crowded people) (Fig. 1 A). Raw ratings were averaged across pictures for each picture type and each participant. A one-way repeated-measures ANOVA was conducted on the scores of crowding (Fig. 1 B), valence (Fig. 1 C), and arousal (Fig. 1 D), respectively. The ANOVA factor was picture type (non-crowding, valence, and arousal). The Greenhouse-Geisser correction was employed to correct for any violations of sphericity (Greenhouse & Geisser, 1959 ), and the partial eta squared ( η p 2 ) was utilized to estimate the ANOVA effect size (Levine & Hullett, 2002 ). Results and discussion The ANOVA conducted on crowding scores revealed a significant main effect of picture type, F (2, 48) = 498.017, p < 0.001, η 2 p = 0.954. The post-hoc test using least significant difference (LSD) method showed that the crowding scores of the non-crowding pictures (1.765 ± 0.153) was lower than that of the crowded object pictures (6.188 ± 0.206, p < 0.001), and that of the crowded people (7.692 ± 0.118, p < 0.001); the crowding scores of the crowded object pictures was lower than that of the crowded people ( p < 0.001). According to previous studies, a score of 1–2 indicates not at all crowded, 3–4 indicates slightly crowded, 5–7 indicates moderately crowded, and 8–9 indicates extremely crowded (Vaske & Shelby, 2008 ). At a group-level, the non-crowding pictures were classified as “not at all crowded”, while the crowded objects and people pictures were classified as “moderately crowded” and “extremely crowded”. We conducted a one-way repeated-measures ANOVA to examine the impact of picture type on valence and arousal, respectively. The results revealed that the main effect of picture type was not statistically significant for either valence [ F (2, 48) = 2.470, p > 0.05, η 2 p = 0.093] or arousal [ F (2, 48) = 3.344, p > 0.05, η 2 p = 0.122] (Fig. 1 C and 1 D). The findings serve as a foundation for further investigating the influence of crowding on time perception, while also eliminating potential confounding effects from valence and arousal. Experiment 1: Crowding and time perception on sub-second timescales Participants were presented with three types of pictures (non-crowding, crowded objects, and crowded people), while performed a temporal bisection task on sub-second timescales. Participants first learned with a short (0.2 s) and a long anchor duration (0.8 s). Then a series of pictures were presented with durations ranging from 0.2 s to 0.8 s. Participants should judge whether the duration of the pictures was closer to the short duration or closer to the long duration. Given that time perception primarily relies on automatic processing mechanisms on sub-second timescales (Lewis & Miall, 2003b , 2003a , 2006 ), we hypothesized that participants’ perception of sub-second duration would not be significantly modulated by crowding. Methods Participants The power analysis was performed using the PANGEA (Westfall et al., 2014). The study adopted a one-factor within-subject design with crowding as the factor, having three levels: non-crowding, crowded objects, and crowded people. Each level consisted of 210 trials (7 durations × 30 pictures). The default variance parameters in PANGEA were used (var [error] = 0.5, var [participant × crowding] = 0.167). Given a recommended statistical power of 0.8, a medium effect size (Cohen’s d ) of 0.5, and a significance level of 0.05 (Clayson et al., 2019 ), the required a minimum of sample size is 23. Thirty undergraduate students took part in the experiment (18–24 years old, 23 females). The other details were the same as the pre-experiment. Stimuli and procedures The visual stimuli were presented on a 28-inch LCD monitor. The visual stimuli consisted of white crosses, white circles, cyan question marks (R: 0, G: 255, B: 255), and pictures with varying degrees of crowding. The white circles had a diameter of 1 cm, the white crosses measured 1 cm in length, and the cyan question marks were approximately 0.8 cm in length. The images with different levels of crowding were measured 30 cm in length and 22.5 cm in width. We utilized E-prime 2.0 (Psychology Software Tools, Inc.) to control stimulus presentation and record participants’ responses. Participants were seated approximately 60 cm away from the screen. We conducted a temporal bisection task that consisted of a learning phase and a formal experiment phase (Fig. 2 ). In the learning phase, participants were presented with a small white circle in the center of the screen for either 200 ms or 800 ms (Fig. 2 A). Each duration was repeated five times to help participants learn and memorize the short and long anchor durations. Then, participants were presented with a small white circle for either 200 ms or 800 ms and were asked to judge whether the duration of the circle belonged to the short or long anchor duration (Fig. 2 B). Each duration was also repeated five times. Participants were provided with feedback on whether their response was correct or not. To proceed to the formal experiment, a correct rate of 90% or higher was required. In the formal experiment, participants performed the temporal bisection task with three types of pictures (Fig. 2 C). At the beginning of each trial, a white fixation was presented in the center of the screen for a random duration between 300 ms and 600 ms. Then, a picture was presented in the center of the screen. A total of 90 pictures were used, including 30 non-crowding, 30 crowded objects, and 30 crowded people pictures. The presentation time of each picture was selected from one of the following durations: 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, and 800 ms, each duration was presented once for each picture, and the order in which the pictures were presented was random. After a random interval of 500 ms to 800 ms, a question mark appeared on the screen, and the participants had 2 seconds to respond by pressing either the “F” key (closer to the long duration) or the “J” key (closer to the short duration) to determine whether the presentation time of the picture was closer to the short (200 ms) or long (800 ms) anchor durations. There was no feedback during the formal experiment, and after the participants pressed the key, they moved on to the next trial after a random interval of 500 ms to 800 ms. The experiment consisted of three picture types, each of seven durations, and each treatment was presented 30 times (30 pictures), comprising a total of 630 trials (3 × 7 × 30). Participants took one break after each 180 trials, for a total of three breaks. Participants had control over the duration of the break, which was limited to a maximum of 2 minutes. Data analysis Bisection point (BP) is defined as the point of subjective equality, which is the duration for which participants respond long (closer to the long duration) as often as they do short (percentage of choosing “closer to the long duration” = 0.5) (Fig. 3 A and 3 B). A smaller BP value for one stimulus than for another suggests a lengthening effect, with participants responding long more often for the former than for the latter, even though they are of the same physical duration. We obtained BP and standard deviation (SD) by fitting a cumulative normal distribution function to the data using MATLAB (The MathWorks, Inc.). Then we conducted a one-way repeated-measures ANOVA on the BP and SD, respectively (Fig. 3 B and 3 C). The factor was crowding type including non-crowding, crowded objects, and crowded people. The other details were the same as the pre-experiment. Results and discussion The ANOVA revealed that the main effect of crowding type was not statistically significant for either BP [ F (2, 58) = 1.825, p > 0.05, η 2 p = 0.043] or SD [ F (2, 58) = 1.184, p > 0.05, η 2 p = 0.039] (Fig. 3 B and 3 C). These findings are consistent with previous studies that used the dual-task paradigm, which suggest that temporal processing in the sub-second range is less susceptible to interference from non-time tasks (Hellström & Rammsayer, 2004 ; Rammsayer, 2006 ; Rammsayer & Ulrich, 2011 ). The results support our hypothesis that crowding does not modulate time perception on sub-second timescales, as the automatic timing system mainly measures time intervals on these scales (Lewis & Miall, 2003b , 2003a , 2006 ). Experiment 2: Crowding and time perception on supra-second timescales Participants were shown three types of pictures (non-crowding, crowded objects, and crowded people) and were asked to perform the temporal bisection task on supra-second timescales. The presentation time of the pictures ranged from 1 s to 4 s, instead of 0.2 s to 0.8 s as in Experiment 1. Given that cognitively controlled timing system is more involved in the measurement of supra-second time intervals with attention and working memory (Lewis & Miall, 2003b , 2003a , 2006 ), we hypothesized that crowding would modulate time perception on supra-second timescales. Methods Participants As in Experiment 1, the PANGEA (Westfall et al., 2014) determined that the minimum sample size required was 23. Thirty-seven undergraduate students, 20 of whom were female, aged between 18 and 24 years old, participated in Experiment 2. Four participants were excluded from further statistical analysis due to data fitting issues and large variability in the data (see results for details). The retained sample size was 33. The other details of participants were identical to those of the pre-experiment and Experiment 1. Stimuli and procedures In Experiment 2, participants performed a temporal bisection task on supra-second timescales. During the learning phase, the short anchor duration was 1 s, and the long anchor duration was 4 s. In the formal experiment, the presentation time of the pictures was chosen from 1 s, 1.5 s, 2 s, 2.5 s, 3 s, 3.5 s, and 4 s. After every 90 trials, participants were allowed to take a break. Other details of the procedures were identical to those of Experiment 1. After completing the temporal bisection task, participants rated the crowding, valence, and arousal of the 90 pictures respectively, as in the pre-experiment. Data analysis The bisection point (BP) and the standard deviation (SD) were obtained by fitting the psychometric curve as the same in Experiment 1. A one-way repeated-measures ANOVA was conducted on the BP and SD, respectively (Fig. 4 B and 4 C). The factor was crowding type including non-crowding, crowded objects, and crowded people. To test whether the valence and arousal of the three types of pictures were effectively controlled in experiment 2, we fitted a linear mixed model (LMM) to the BP using the lme4 (Bates et al., 2015 ) and lmerTest (Kuznetsova et al., 2017 ) in R (R Core Team, 2022 ). The LMM model included the crowding, valence and arousal as fixed effects, the participants’ intercept as the random effect, and the BP values as the dependent variable, respectively. The model formula was: BP ~ crowding + valence + arousal + (1| Participant ID ) 1 . In order to avoid the multicollinearity problem in multiple regression, dominance analysis was used to determine the relative importance of the crowding, valence, and arousal in predicting the BP (Table 1 ). The approach establishes the relative importance of predictors based on an examination of the R 2 values for all possible subset models (Budescu, 1993 ), and has been successfully applied in various psychological fields, such as cognition (Gellersen et al., 2021 ), personality (Duan et al., 2021 ), education (Lau & Yuen, 2016 ), customer satisfaction (Garver & Williams, 2019 ), and organization (Simonet et al., 2019 ). We adopted R&B R 1 2 to calculate the R 2 statistic for each variance component in the model (Raudenbush & Bryk, 2002 ), because R&B R 1 2 is appropriate for the individual-level (Level-1) variance component in hierarchical linear models (Luo & Azen, 2013 ). The dominance analysis was applied using the R package dominanceanalysis (Bustos Navarrete & Coutinho Soares, 2020 ). The columns labeled R 2 represented each subset model’s contribution relative to a null model that was: BP ~ (1| Participant ID ) (Luo & Azen, 2013 ). [1] In the pre-analysis, the slopes of crowding, valence, and arousal were also considered as random factors. However, the model failed to fit the data due to an excessive number of random effects. The error message was as follows: number of observations (=99) <= number of random effects (=99) for term (0 + crowding+ valence + arousal | Subject); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable. Results and discussion One participant’s data could not be fitted by a cumulative normal distribution function (Fig. 4 A). The proportions of “long” responses for different crowding types and different durations were all around 0.5, indicating that the participant randomly pressed the keys. The bisection points (BP) and standard deviations (SD) were obtained for the remaining participants under each crowding type. Three participants had SD values greater than 2 s and violated the two-sigma rule that SD values were two standard deviations above or below the mean of the SD values, and were therefore excluded from the following analyses. In comparison to normal participants (Fig. 5 A), the proportions of “long” responses of these participants tended to be closer to 0.5 and resulted in larger SD values (Fig. 4 B). An SD that is too large indicates that participants may not have performed the experimental task seriously. The data of 33 participants entered the further statistical analysis. The ANOVA conducted on BP (Fig. 5 B) revealed a significant main effect of crowding type, F (2, 64) = 3.459, p < 0.05, η 2 p = 0.098. The post-hoc test revealed that the BP was significantly greater for the non-crowding (2409.134 ± 85.492 ms) than that for the crowded people (2356.070 ± 92.970 ms) ( p 0.05), nor was the difference of BP between the crowded objects and the crowded people ( p > 0.05). The ANOVA conducted on SD (Fig. 5 C) revealed that the main effect of crowding type was not significant, F (2, 64) = 0.377, p > 0.05, η 2 p = 0.012. The results supports our hypothesis that crowding modulates time perception on supra-second timescales because of the cognitively controlled timing system employed on this timescale. LMM not only predicted the decline of BP with the increase of crowding (Fig. 6 A), but also took into account individual differences in BP, where greater individual BP corresponded to greater predicted values (Fig. 6 B). The LMM revealed that the BP decreased with increasing crowding [ β = -8.260, SE = 3.761, t (66.231) = -2.196, p 0.05], nor between BP and arousal [ β = 5.316, SE = 6.947, t (66.579) = 0.765, p > 0.05]. The results provide evidence that the linear relationship between BP and crowding was not confused by the effects of valence and arousal in Experiment 2. Additional contributions of crowding, valence, and arousal to each subset model were calculated according to the dominance analysis (Table 1 ). The crowding completely dominated valence and arousal as the additional contribution by crowding was higher than that by valence and arousal for every subset model (Azen & Budescu, 2003 ). When predicting the BP, the crowding, valence, and arousal account for 91.304%, 2.895%, and 5.797% of overall average additional contributions, respectively. Table 1 Relative importance of crowding, valence, and arousal in predicting bisection point (BP). Additional contribution of: R 2 crowding valence arousal Null and k = 0 average 0.000 0.060 0.003 0.000 crowding 0.060 0.001 0.009 valence 0.003 0.058 0.000 arousal 0.000 0.069 0.003 k = 1 average 0.063 0.002 0.004 crowding, valence 0.061 0.009 crowding, arousal 0.069 0.001 valence, arousal 0.003 0.067 k = 2 average 0.067 0.001 0.009 crowding, valence, arousal 0.070 Overall average 0.063 0.002 0.004 General Discussion The study conducted a temporal bisection task to investigate the effect of crowding on time perception, independent of valence and arousal. To eliminate their impact, we carefully chose three types of pictures: non-crowding, crowded objects, and crowded people, and observed no significant differences in valence and arousal scores among these picture types (Fig. 1 ). The results of Experiment 1 indicated that crowding did not affect time perception significantly on sub-second timescales. However, Experiment 2 demonstrated that crowding modulated time perception on supra-second timescales. Then we employed a linear mixed model (LMM) to examine the prediction of crowding, valence, and arousal to the bisection point (BP). The LMM revealed a significant linear relationship between crowding and BP, while valence and arousal failed to predict BP. Finally, we used dominance analysis to reveal the relative importance of crowding, valence, and arousal in predicting the BP, and found that crowding completely outperformed valence and arousal, with crowding explaining more than 91% of overall average additional contributions while valence and arousal together explaining less than 9%. In summary, the findings provide evidence that crowding significantly modulates time perception on supra-second timescales, even when valence and arousal are controlled for three types of pictures. Crowding and motivation are closely intertwined. High crowd density can be a source of mental stress and too much information can lead to a negative mood state (Schmidt & Keating, 1979 ). For instance, in crowded public transport, passengers’ discomfort can arise from standing instead of being seated, less opportunities to use time during the journey, and the physical closeness of other travelers (Haywood et al., 2017 ). This can lead to negative emotions and stress (Bruins & Barber, 2000 ; Evans & Wener, 2007 ). Furthermore, crowding can also reduce an individual’s sense of autonomy, increase the sense of personal space invasion (Lawrence & Andrews, 2004 ; Maeng et al., 2013 ; Maeng & Tanner, 2013 ; Nieuwenhuijsen & de Waal, 1982 ), and reduce individuals’ freedom of activity and control over the environment (Consiglio et al., 2018 ; Rompay et al., 2008 ; Stokols, 1972 ). Therefore, individuals often hope to end the crowded travel and escape from the unpleasant environment as soon as possible (Sadeghi et al., 2023a ), which is known as the withdrawal motivation of individuals in the crowded environment (Maeng et al., 2013 ; Maeng & Tanner, 2013 ). We found that crowding can modulate time perception, independent of the valence and arousal (Fig. 5 and Table 1 ). Given that the crowding is accompanied by the withdrawal motivation (Maeng et al., 2013 ; Maeng & Tanner, 2013 ), out results are consistent with the motivation dimension model of time perception, in which withdrawal motivation should slow down the subjective time, and the motivation directly modulates time perception, rather than being mediated by affective valence and arousal (Gable et al., 2016 , 2022 ; Gable & Poole, 2012 ). Supporting for the motivation dimension model of time perception, Yin et al. ( 2021 ) reported that approach and withdrawal motivations modulate time perception after controlling for valence and arousal of emotional images. More evidence suggests that emotion and motivation induce attention biases (Cisler & Koster, 2010 ) and further modulate time perception (J. Liu & Li, 2020 ; Yin et al., 2023 ). Electrophysiological evidence has been obtained to support that emotion modulates time perception through the attention system (Tamm et al., 2014 ; Vallet et al., 2019 ). Especially, Yin et al. ( 2021 ) employed contingent negative variation (CNV) to examine the processing mechanism of different motivations affecting time perception. CNV is a well-known event-related potential (ERP) component that has been shown to be associated with temporal encoding (Wiener et al., 2012 ), and more attention assigned to temporal information leads to a longer perceived duration and a larger CNV (Chen et al., 2007 ; Y. Liu et al., 2013 ). Angry expressions are negative stimuli with approach motivation, and fearful expressions are also negative stimuli but with withdrawal motivation. According to the attentional perspective of temporal processing (Coull et al., 2004 ; Macar et al., 1994 ; Zakay & Block, 1997 ), approach motivation attract more attention than withdrawal motivation, less attention was paid on time in the angry condition than that in the fear condition, therefore, the perceived time of angry expression is shorter than that of fear expression, and the amplitude of CNV induced by angry expression is lower than that of fear expression (Yin, Cui, et al., 2021 ). Therefore, compared with uncrowded conditions, withdrawal motivation allows participants allocate more attention to time and less attention to crowded images, resulting in longer perceptual time in crowded conditions. According to the theory of magnitude (ATOM), time, space, and quantity are all part of a generalized magnitude system, which can lead to cross-dimension interference; the parietal cortex is believed to be the locus of this magnitude system (Bueti & Walsh, 2009 ; Walsh, 2003a ). The parietal cortex is a region of the brain that has been implicated in working memory (Chai et al., 2018 ). For instance, Jonides et al. ( 1998 ) found that parietal regions are part of a network of brain areas that mediate the short-term storage and retrieval of phonologically coded verbal material. Koenigs et al. ( 2009 ) also found that the superior parietal cortex is critical for the manipulation of information in working memory. Cui et al. ( 2022 ) used event-related potentials (ERPs) to identify the neural basis of cross-dimension interference. They found that the parietal P2 and P3b component index updates a common magnitude representation of spatiotemporal information in working memory, and the neural source of P2 and P3b was located in the parietal cortex. Based on the above theoretical considerations and empirical evidence, it can be inferred that the cross-dimension interference of quantity on time may occur in working memory. We found that crowding modulated time perception on the supra-second timescales rather than the sub-second timescales. An automatic timing system measures sub-second intervals without attentional modulation, and a cognitively controlled timing system is more involved in the measurement of supra-second intervals with attention and working memory (Lewis & Miall, 2003b , 2003a , 2006 ). Behavioral evidence also supports the idea that processing shorter intervals depends on sensory or automatic processing while processing longer intervals requires cognitive resources (Hellström & Rammsayer, 2004 ; Rammsayer, 2006 ). Taken together, these findings suggest that the cognitive mechanisms underlying time perception are different for sub-second and supra-second intervals. As previously mentioned, after controlling for emotional valence and arousal, crowding may modulate time perception through withdrawal motivation and cross-dimension interference. The impact of withdrawal motivation on time perception may involve the allocation of attention between temporal and non-temporal information in the attention system (Coull et al., 2004 ; Macar et al., 1994 ; Yin, Cui, et al., 2021 ; Yin et al., 2023 ; Zakay & Block, 1997 ); the impact of quantitative information on time involves the mutual interference of different dimensional information in a generalized magnitude system located in parietal cortex (Bueti & Walsh, 2009 ; Walsh, 2003a ), which is has been implicated in working memory (Chai et al., 2018 ). Therefore, the finding that crowding modulates time perception on supra-second timescales rather than the sub-second timescales is consistent with the theory of automatic and cognitively controlled timing systems. This study has the following advantages and limitations. Firstly, the study effectively controlled for the impacts of valence and arousal on time perception. We carefully selected three types of crowding pictures so that there was no significant difference in valence and arousal scores among the three crowding types. Then, we used LMM and dominance analysis to confirm that valence and arousal did not affect subjective time. The study provided strong evidence that crowding can modulate time perception even after valence and arousal were excluded. Secondly, the study examined the influence of crowding on sub-second and supra-second timescales, respectively, based on the theory of automatic and cognitively controlled timing systems. We found that crowding modulated time perception on the supra-second timescales rather than the sub-second, which helps to establish a connection between crowding and existing theories in the psychology of time. However, one limitation of this study is that it does not distinguish the influence of withdrawal motivation on time perception from that of quantity. Crowding is accompanied by withdrawal motivation and quantity, but the mechanisms of their impacts on time are different. The withdrawal motivation modulates time through attention, and the cross-dimensional interference of quantity on time may occur in working memory. Further research on these two mechanisms in crowded situations can not only provide answers to how withdrawal motivation and magnitude processing affect time perception but also deepen our understanding of the interaction between cognition and motivation. Future studies could combine behavioral experiments with cognitive neuroscience techniques to separate the mechanism of withdrawal motivation and quantity in the modulation of time perception in a crowded environment. In summary, this study controlled the valence and arousal of three types of crowding pictures, and investigate the effect of crowding on time perception on sub-second and supra-second timescales. We found that crowding modulated time perception on the supra-second rather than the sub-second timescales. The LMM and dominance analysis verified that valence and arousal did not significantly modulate time perception. Crowding includes withdrawal motivation and quantity, which are considered to be influencing factors of time perception after excluding valence and arousal. Withdrawal motivation modulates time perception through attention system, and the cross-dimension interference of quantity on time may occur in working memory. These explanations are consistent with the idea that automatic timing systems measure sub-second time intervals without attentional modulation, while cognitively controlled timing systems are more involved in supra-second interval measurements with attention and working memory. Declarations Data availability Behavioral data have been deposited at Zenodo: https://www.zenodo.org/record/10683927 (DOI:10.5281/zenodo.10683927) and are publicly available as of the date of publication. Declaration of interest The authors declare that there are no competing interests. Credit authorship contribution statement Youguo Chen: Conceptualization, Methodology, Formal analysis, Visualization, Writing – review & editing. Yuanwei Xu: Investigation, Formal analysis, Writing – original draft. Gaomin Liang and Chunhua Peng: Writing – review & editing. Author Contribution C: Conceptualization, Methodology, Formal analysis, Visualization, Writing – review & editing.X: Investigation, Formal analysis, Writing – original draft. L and P: Writing – review & editing. Acknowledgements This study was supported by General Program of the Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-msxmX0758) and Humanities and Social Science Youth Foundation of Ministry of Education of China (Grant No. 19YJC190002). References Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods , 8 (2), 129–148. https://doi.org/10.1037/1082-989x.8.2.129 . Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software , 67 (1), 1–48. https://doi.org/10.18637/jss.v067.i01 . Bradley, M. M., & Lang, P. J. (1994). Measuring emotion: The self-assessment manikin and the semantic differential. Journal of Behavior Therapy and Experimental Psychiatry , 25 (1), 49–59. https://doi.org/10.1016/0005-7916(94)90063-9 . Bruins, J., & Barber, A. (2000). Crowding, Performance, and Affect: A Field Experiment Investigating Mediational Processes. Journal of Applied Social Psychology , 30 (6), 1268–1280. https://doi.org/10.1111/j.1559-1816.2000.tb02520.x . Budescu, D. V. (1993). Dominance Analysis: A New Approach to the Problem of Relative Importance of Predictors in Multiple Regression. Psychological Bulletin , 114 (3), 542–551. https://doi.org/10.1037/0033-2909.114.3.542 . Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions Of The Royal Society Of London. Series B, Biological Sciences , 364 (1525), 1831–1840. https://doi.org/10.1098/rstb.2009.0028 . Buhusi, C. V., & Meck, W. H. (2005). What makes us tick? Functional and neural mechanisms of interval timing. Nature Reviews Neuroscience , 6 (10), 755–765. Bustos Navarrete, C., & Coutinho Soares, F. (2020). R-package: Dominanceanalysis (2.0.0) [Computer software]. https://cran.r-project.org/src/contrib/Archive/dominanceanalysis/ . Chai, W. J., Hamid, A., A. I., & Abdullah, J. M. (2018). Working Memory From the Psychological and Neurosciences Perspectives: A Review. Frontiers in Psychology . 10.3389/fpsyg.2018.00401 . 9 https://www.frontiersin.org/articles/ . Chen, Y. G., Zhang, Z. J., Huang, X. T., Guo, X. Y., Yuan, H., & Zhang, T. (2007). Attentional Modulation of Time Perception: An ERP Study. Acta Psychologica Sinica , 39 (06), 1002–1011. Cisler, J. M., & Koster, E. H. W. (2010). Mechanisms of attentional biases towards threat in anxiety disorders: An integrative review. Clinical Psychology Review , 30 (2), 203–216. https://doi.org/10.1016/j.cpr.2009.11.003 . Clayson, P. E., Carbine, K. A., Baldwin, S. A., & Larson, M. J. (2019). Methodological reporting behavior, sample sizes, and statistical power in studies of event-related potentials: Barriers to reproducibility and replicability. Psychophysiology , 56 (11), e13437. https://doi.org/10.1111/psyp.13437 . Consiglio, I., De Angelis, M., & Costabile, M. (2018). The Effect of Social Density on Word of Mouth. Journal of Consumer Research , 45 (3), 511–528. https://doi.org/10.1093/jcr/ucy009 . Coull, J. T., Vidal, F., Nazarian, B., & Macar, F. (2004). Functional anatomy of the attentional modulation of time estimation. Science , 303 (5663), 1506–1508. https://doi.org/10.1126/science.1091573 . Cui, M. H., Peng, C. H., Huang, M., & Chen, Y. G. (2022). Electrophysiological Evidence for a Common Magnitude Representation of Spatiotemporal Information in Working Memory. Cerebral Cortex , 32 (18), 4068–4079. https://doi.org/10.1093/cercor/bhab466 . Danckert, J. A., & Allman, A. A. A. (2005). Time flies when you’re having fun: Temporal estimation and the experience of boredom. Brain and Cognition , 59 (3), 236–245. https://doi.org/10.1016/j.bandc.2005.07.002 . Droit-Volet, S., Bigand, E., Ramos, D., & Bueno, J. L. (2010). Time flies with music whatever its emotional valence. Acta Psychol (Amst) , 135 (2), 226–232. https://doi.org/10.1016/j.actpsy.2010.07.003 . Droit-Volet, S., Brunot, S., & Niedenthal, P. M. (2004). Perception of the duration of emotional events. Cognition & Emotion , 18 (6), 849–858. https://doi.org/10.1080/02699930341000194 . Duan, J., Yang, Z., Zhang, F., Zhou, Y., & Yin, J. (2021). Aggressive behaviors in highly sadistic and highly impulsive individuals. Personality and Individual Differences , 178 , 110875. https://doi.org/10.1016/j.paid.2021.110875 . Evans, G. W., & Wener, R. E. (2007). Crowding and personal space invasion on the train: Please don’t make me sit in the middle. Journal of Environmental Psychology , 27 (1), 90–94. https://doi.org/10.1016/j.jenvp.2006.10.002 . Fraisse, P. (1984). Perception and estimation of time. Annual Review of Psychology , 35 , 1–36. Fujimoto, M. (2016). A fundamental study on the interaction of people with their surrounding space and sense of time in a rest. Journal of Home Economics of Japan , 67 (7), 382–396. https://doi.org/10.11428/jhej.67.382 . Gable, P. A., Neal, L. B., & Poole, B. D. (2016). Sadness speeds and disgust drags: Influence of motivational direction on time perception in negative affect. Motivation Science , 2 (4), 238–255. https://doi.org/10.1037/mot0000044 . Gable, P. A., & Poole, B. D. (2012). Time flies when you’re having approach-motivated fun: Effects of motivational intensity on time perception. Psychological Science , 23 (8), 879–886. https://doi.org/10.1177/0956797611435817 . Gable, P. A., Wilhelm, A. L., & Poole, B. D. (2022). How Does Emotion Influence Time Perception? A Review of Evidence Linking Emotional Motivation and Time Processing. Frontiers in Psychology , 13 , 848154. https://doi.org/10.3389/fpsyg.2022.848154 . Garver, M. S., & Williams, Z. (2019). Utilizing relative weight analysis in customer satisfaction research. International Journal of Market Research , 62 (2), 158–175. https://doi.org/10.1177/1470785319859794 . Gellersen, H. M., Trelle, A. N., Henson, R. N., & Simons, J. S. (2021). Executive function and high ambiguity perceptual discrimination contribute to individual differences in mnemonic discrimination in older adults. Cognition , 209 , 104556. https://doi.org/10.1016/j.cognition.2020.104556 . Gil, S., & Droit-Volet, S. (2012). Emotional time distortions: The fundamental role of arousal. Cognition And Emotion , 26 (5), 847–862. https://doi.org/10.1080/02699931.2011.625401 . Gray, A. (2001). Definitions of crowding and the effects of crowding on health: A literature review . Ministry of Social Policy. Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika , 24 (2), 95–112. https://doi.org/10.1007/BF02289823 . Haywood, L., Koning, M., & Monchambert, G. (2017). Crowding in public transport: Who cares and why? Transportation Research Part A: Policy and Practice , 100 , 215–227. https://doi.org/10.1016/j.tra.2017.04.022 . Hellström, Å., & Rammsayer, T. H. (2004). Effects of time-order, interstimulus interval, and feedback in duration discrimination of noise bursts in the 50- and 1000-ms ranges. Acta Psychologica , 116 (1), 1–20. https://doi.org/10.1016/j.actpsy.2003.11.003 . Jonides, J., Schumacher, E. H., Smith, E. E., Koeppe, R. A., Awh, E., Reuter-Lorenz, P. A., Marshuetz, C., & Willis, C. R. (1998). The role of parietal cortex in verbal working memory. Journal of Neuroscience , 18 (13), 5026–5034. Koenigs, M., Barbey, A. K., Postle, B. R., & Grafman, J. (2009). Superior Parietal Cortex Is Critical for the Manipulation of Information in Working Memory. Journal of Neuroscience , 29 (47), 14980–14986. https://doi.org/10.1523/JNEUROSCI.3706-09.2009 . Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. B. (2017). lmerTest Package: Tests in Linear Mixed Effects Models. Journal of Statistical Software , 82 , 1–26. https://doi.org/10.18637/jss.v082.i13 . Lau, W. W. F., & Yuen, A. H. K. (2016). The relative importance of paternal and maternal parenting as predictors of adolescents’ home Internet use and usage. Computers & Education , 102 , 224–233. https://doi.org/10.1016/j.compedu.2016.09.002 . Lawrence, C., & Andrews, K. (2004). The influence of perceived prison crowding on male inmates’ perception of aggressive events. Aggressive Behavior , 30 (4), 273–283. https://doi.org/10.1002/ab.20024 . Levine, T. R., & Hullett, C. R. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research , 28 (4), 612–625. https://doi.org/10.1111/j.1468-2958.2002.tb00828.x . Lewis, P. A., & Miall, R. C. (2003a). Brain activation patterns during measurement of sub- and supra-second intervals. Neuropsychologia , 41 (12), 1583–1592. Lewis, P. A., & Miall, R. C. (2003b). Distinct systems for automatic and cognitively controlled time measurement: Evidence from neuroimaging. Current Opinion in Neurobiology , 13 (2), 250–255. https://doi.org/10.1016/S0959-4388(03)00036-9 . Lewis, P. A., & Miall, R. C. (2006). Remembering the time: A continuous clock. Trends in Cognitive Sciences , 10 (9), 401–406. Lin, J. Y. J., Jenelius, E., Cebecauer, M., Rubensson, I., & Chen, C. (2023). The equity of public transport crowding exposure. Journal of Transport Geography , 110 , 103631. https://doi.org/10.1016/j.jtrangeo.2023.103631 . Liu, J., & Li, H. (2020). How individuals perceive time in an anxious state: The mediating effect of attentional bias. Emotion , 20 (5), 761–772. https://doi.org/10.1037/emo0000586 . Liu, Y., Zhang, D., Ma, J., Li, D., Yin, H., & Luo, Y. (2013). The attention modulation on timing: An event-related potential study. PLOS ONE , 8 (6), e66190. https://doi.org/10.1371/journal.pone.0066190 . Luo, W., & Azen, R. (2013). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. Journal of Educational and Behavioral Statistics , 38 (1), 3–31. https://doi.org/10.3102/1076998612458319 . Macar, F., Grondin, S., & Casini, L. (1994). Controlled attention sharing influences time estimation. Memory & Cognition , 22 (6), 673–686. Maeng, A., & Tanner, R. J. (2013). Construing in a crowd: The effects of social crowding on mental construal. Journal of Experimental Social Psychology , 49 (6), 1084–1088. https://doi.org/10.1016/j.jesp.2013.07.010 . Maeng, A., Tanner, R. J., & Soman, D. (2013). Conservative When Crowded: Social Crowding and Consumer Choice. Journal of Marketing Research , 50 (6), 739–752. https://doi.org/10.1509/jmr.12.0118 . Nieuwenhuijsen, K., & de Waal, F. B. M. (1982). Effects of spatial crowding on social behavior in a chimpanzee colony. Zoo Biology , 1 (1), 5–28. https://doi.org/10.1002/zoo.1430010103 . O’Brien, E. H., Anastasio, P. A., & Bushman, B. J. (2011). Time Crawls When You’re Not Having Fun: Feeling Entitled Makes Dull Tasks Drag On. Personality and Social Psychology Bulletin , 37 (10), 1287–1296. https://doi.org/10.1177/0146167211408922 . Oliveri, M., Vicario, C. M., Salerno, S., Koch, G., Turriziani, P., Mangano, R., Chillemi, G., & Caltagirone, C. (2008). Perceiving numbers alters time perception. Neuroscience Letters , 438 (3), 308–311. R Core Team (2022). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. https://www.R-project.org/ . Rammsayer, T. (2006). Effects of pharmacologically induced changes in NMDA receptor activity on human timing and sensorimotor performance. Brain Research , 1073 , 407–416. Rammsayer, T., & Ulrich, R. (2011). Elaborative rehearsal of nontemporal information interferes with temporal processing of durations in the range of seconds but not milliseconds. Acta Psychologica , 137 (1), 127–133. https://doi.org/10.1016/j.actpsy.2011.03.010 . Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Sage. van Rompay, T. J. L., Galetzka, M., Pruyn, A. T. H., & Garcia, J. M. (2008). Human and spatial dimensions of retail density: Revisiting the role of perceived control. Psychology & Marketing , 25 (4), 319–335. https://doi.org/10.1002/mar.20211 . Sackett, A. M., Meyvis, T., Nelson, L. D., Converse, B. A., & Sackett, A. L. (2010). You’re having fun when time flies: The hedonic consequences of subjective time progression. Psychological Science , 21 (1), 111–117. Sadeghi, S., Daziano, R., Yoon, S. Y., & Anderson, A. K. (2023a). Affective experience in a virtual crowd regulates perceived travel time. Virtual Reality , 27 (2), 1051–1061. https://doi.org/10.1007/s10055-022-00713-8 . Sadeghi, S., Daziano, R., Yoon, S. Y., & Anderson, A. K. (2023b). Crowding and Perceived Travel Time in Public Transit: Virtual Reality Compared With Stated Choice Surveys. Transportation Research Record , 2677 (5), 296–307. https://doi.org/10.1177/03611981221130346 . Schmidt, D. E., & Keating, J. P. (1979). Human crowding and personal control: An integration of the research. Psychological Bulletin , 86 (4), 680–700. Shimokawa, K., & Sugimori, E. (2019). Using Virtual Reality to Study Subjective Time in Crowded Versus Uncrowded Environments. Perceptual and Motor Skills , 126 (5), 737–752. https://doi.org/10.1177/0031512519857869 . Simonet, D. V., Miller, K. E., Luu, S., Askew, K. L., Narayan, A., Cunningham, S., Pena, C., Attar, A., Fonseca, R., & Kobezak, H. M. (2019). Who is empowered? Relative importance of dispositional and situational sources to psychological empowerment. European Journal of Work and Organizational Psychology , 28 (4), 536–554. https://doi.org/10.1080/1359432X.2019.1624532 . Stokols, D. (1972). On the distinction between density and crowding: Some implications for future research. Psychological Review , 79 (3), 275–277. https://doi.org/10.1037/h0032706 . Tamm, M., Uusberg, A., Allik, J., & Kreegipuu, K. (2014). Emotional modulation of attention affects time perception: Evidence from event-related potentials. Acta Psychologica , 149 , 148–156. https://doi.org/10.1016/j.actpsy.2014.02.008 . Tonietto, G. N., VanEpps, E. M., Malkoc, S. A., & Maglio, S. J. (2022). Time Will Fly During Future Fun (But Drag Until Then). Journal of Consumer Psychology , 32 (3), 475–483. https://doi.org/10.1002/jcpy.1247 . United Nations. (2019). World Urbanization Prospects: The 2018 Revision (ST/ESA/SER.A/420) . United Nations, Department of Economic and Social Affairs. Vallet, W., Laflamme, V., & Grondin, S. (2019). An EEG investigation of the mechanisms involved in the perception of time when expecting emotional stimuli. Biological Psychology , 148 , 107777. https://doi.org/10.1016/j.biopsycho.2019.107777 . Vaske, J. J., & Shelby, L. B. (2008). Crowding as a Descriptive Indicator and an Evaluative Standard: Results from 30 Years of Research. Leisure Sciences , 30 (2), 111–126. https://doi.org/10.1080/01490400701881341 . Walsh, V. (2003a). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences , 7 (11), 483–488. https://doi.org/10.1016/j.tics.2003.09.002 . Walsh, V. (2003b). Time: The back-door of perception. Trends in Cognitive Sciences , 7 (8), 335–338. Wardman, M., & Whelan, G. (2011). Twenty Years of Rail Crowding Valuation Studies: Evidence and Lessons from British Experience. Transport Reviews , 31 (3), 379–398. https://doi.org/10.1080/01441647.2010.519127 . Wiener, M., Kliot, D., Turkeltaub, P. E., Hamilton, R. H., Wolk, D. A., & Coslett, H. B. (2012). Parietal influence on temporal encoding indexed by simultaneous transcranial magnetic stimulation and electroencephalography. Journal of Neuroscience , 32 (35), 12258–12267. https://doi.org/10.1523/JNEUROSCI.2511-12.2012 . Xuan, B., Chen, X. C., He, S., & Zhang, D. R. (2009). Numerical magnitude modulates temporal comparison: An ERP study. Brain Research , 1269 , 135–142. Xuan, B., Zhang, D., He, S., & Chen, X. (2007). Larger stimuli are judged to last longer. Journal Of Visualization , 7 (10), 1–5. https://doi.org/10.1167/7.10.2 . Yin, H. Z., Bai, Y. L., Liu, S. G., & Li, D. (2021). The influence of motivation direction and intensity on time perception in positive and negative emotions. Journal of Psychological Science , 44 (6), 1313–1321. Yin, H. Z., Cui, X. B., Bai, Y. L., Cao, G., Zhang, L., Ou, Y. H., Li, D., & Liu, J. P. (2021). The Effects of Angry Expressions and Fearful Expressions on Duration Perception: An ERP Study. Frontiers in Psychology , 12 , 10.3389/fpsyg.2021.570497 . https://www.frontiersin.org/articles/ . Yin, H. Z., Zhang, L., Liu, P. Y., & Li, D. (2023). How the dimension of negative emotional motivation influences time perception: The mediating role of attention control and attention bias. Acta Psychologica Sinica, 55(12), 1917. https://doi.org/10.3724/SP.J.1041.2023.01917 . Zakay, D., & Block, R. A. (1997). Temporal Cognition. Current Directions in Psychological Science , 6 (1), 12–16. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4008302","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":276470376,"identity":"119ddde3-568a-423d-b416-ca6f01a1652f","order_by":0,"name":"Youguo Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYHACNiC2YeZnbwDSBhZEa0ljl+w5ANIiQbSWw/wGMxJAHCK0GJxf/OzBxx3M0gaSz69u+FEgwcDf3p2AX8uNZ+aGM8+wGZtL55Td7AE6TOLM2Q0EtJxhk+Zt40m2nJ2TdoMHqMVAIpcILX/bJOo33DyTdvMPUVrO97BJM7YZMBvcYD92myhbJG+wmUn2tiUwS/bksN2WMZDgIegXvvOHn0n8bPsPjMrjz26++WMjx9/ei1+Lwo0EGJPHAEziVQ4C8v0HYEz2BwRVj4JRMApGwcgEAE4uSSSNLJbfAAAAAElFTkSuQmCC","orcid":"","institution":"Southwest University","correspondingAuthor":true,"prefix":"","firstName":"Youguo","middleName":"","lastName":"Chen","suffix":""},{"id":276470377,"identity":"abe4f9ab-a480-422f-9098-e4de2c5bce7f","order_by":1,"name":"Yuanwei Xu","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"prefix":"","firstName":"Yuanwei","middleName":"","lastName":"Xu","suffix":""},{"id":276470378,"identity":"11bd7a27-b346-4c24-b76b-10889673d730","order_by":2,"name":"Gaomin Liang","email":"","orcid":"","institution":"Southwest University","correspondingAuthor":false,"prefix":"","firstName":"Gaomin","middleName":"","lastName":"Liang","suffix":""},{"id":276470379,"identity":"55b68d77-de30-45ef-9489-dae57c3dbfac","order_by":3,"name":"Chunhua Peng","email":"","orcid":"","institution":"Chongqing University of Arts and Sciences","correspondingAuthor":false,"prefix":"","firstName":"Chunhua","middleName":"","lastName":"Peng","suffix":""}],"badges":[],"createdAt":"2024-03-03 10:46:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4008302/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4008302/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52191399,"identity":"69f79497-1194-4677-9c2c-33b2a45fdde2","added_by":"auto","created_at":"2024-03-07 19:30:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":4015552,"visible":true,"origin":"","legend":"\u003cp\u003ePicture types and dimensional ratings. (A) Examples of three types of pictures. (B) Mean crowding scores of all participants for three types of pictures. (C) Mean valence scores of all participants for three types of pictures. (D) Mean arousal scores of all participants for three types of pictures. NC: non-crowding, CO: crowded objects, and CP: crowded people. Error bars represent standard error of mean across all participants. ***\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001.\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/21a831ee8a40cda7cbac4f3f.png"},{"id":52191403,"identity":"e8926d8c-5fe8-4368-9bc3-b396bb7171bf","added_by":"auto","created_at":"2024-03-07 19:30:03","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":250945,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental procedures. (A) Learning without response. (B) Learning with response and feedback. (C) Formal experiment.\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/adb5d3e9672951548dfea034.png"},{"id":52191398,"identity":"79816b58-03d6-48d7-ad34-580c9339b3fa","added_by":"auto","created_at":"2024-03-07 19:30:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":145554,"visible":true,"origin":"","legend":"\u003cp\u003eBehavior responses in Experiment 1. (A) Mean proportion of “long” responses of all participants plotted against stimulus durations. (B) Mean bisection point (BP) of all participants under three crowding types. (C) Mean standard deviation (SD) of all participants under three crowding types. NC: non-crowding, CO: crowded objects, and CP: crowded people. Error bars represent standard error of mean across all participants.\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/90282c3617a5f9ed7f22c94b.png"},{"id":52193744,"identity":"4577d11b-2a14-4306-b5de-a58bd40e3f33","added_by":"auto","created_at":"2024-03-07 19:38:03","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":114671,"visible":true,"origin":"","legend":"\u003cp\u003eProportion of “long” responses of excluded participants. (A) Proportion of “long” responses of the participant with failure in data fitting. (B) Mean proportion of “long” responses of three participants with too large variability in data. NC: non-crowding, CO: crowded objects, and CP: crowded people.\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/d053eb6a9057dd042a977609.png"},{"id":52193743,"identity":"bcd31023-0ff4-468d-9473-b90d46b83917","added_by":"auto","created_at":"2024-03-07 19:38:03","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":119458,"visible":true,"origin":"","legend":"\u003cp\u003eBehavior responses in Experiment 2. (A) Mean proportion of “long” responses of all participants. (B) Mean bisection point (BP) of all participants for three crowding types. (C) Mean standard deviation (SD) of all participants for three crowding types. NC: non-crowding, CO: crowded objects, and CP: crowded people. Error bars represent standard error of mean across all participants. *\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05.\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/8765b07fc85cb4ad13302bf4.png"},{"id":52191401,"identity":"d0fa8439-128c-40f6-987b-01314c6d2a9d","added_by":"auto","created_at":"2024-03-07 19:30:03","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":109231,"visible":true,"origin":"","legend":"\u003cp\u003eBisection points and predictions. (A) Mean bisection points and corresponding predictions of linear mixed model (LMM) for three crowding types. (B) Scatter plots between bisection points and predictions for each participant and each crowding type. NC: non-crowding, CO: crowded objects, and CP: crowded people. Error bars and shadows represent standard error of mean across all participants.\u003c/p\u003e","description":"","filename":"Fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/a37dcef9521163af343e9c0d.png"},{"id":53562600,"identity":"27f7b9d2-3d38-46c2-b180-ed8720dcf805","added_by":"auto","created_at":"2024-03-27 13:53:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1470195,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4008302/v1/3dbd8d5a-de0a-4cce-b26c-7e81cc37a142.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Crowding modulates time perception while controlling for valence and arousal","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOver the past century, there has been an inexorable increase in the number of large urban agglomerations, as well as in the size and density of the population in the cities. The world’s urban population reached 4.2\u0026nbsp;billion in 2018 and is expected to grow to 6.7\u0026nbsp;billion by 2050. It is predicted that 68% of the world’s population will be living in cities by then (United Nations, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Many countries will face challenges in meeting the needs of growing urban populations, including housing, transportation, energy systems and other infrastructure, as well as employment and basic services such as education and health care (United Nations, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). At the same time, the crowded environment also leads to the physical and mental health problem of individuals (Gray, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). Moreover, the crowded public transport can lead to passenger discomfort and increase the subjective perception of the traffic time (Haywood et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The subjective perception of the traffic time has become an indicator to measure the subjective crowding of public transport (Lin et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wardman \u0026amp; Whelan, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Therefore, it is of great value to study the relationship between subjective time and crowding for urban management and individual physical and mental health.\u003c/p\u003e \u003cp\u003eThere is an increasing body of evidence that suggests that individuals perceive time to pass more slowly (overestimate) in crowded settings compared to uncrowded. Fujimoto (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) conducted a field experiment in which participants were asked to report their subjective perceived time in 13 different settings by filling out a questionnaire. Participants reported that the subjective time was longer in a crowded and noisy setting compared to a quiet and empty setting. Shimokawa and Sugimori (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) further examined the effect of crowding on time estimation in virtual reality (VR) environments. Participants wore head-mounted VR displays and watched videos showing a cityscape and a countryside (Experiment 1), a crowded and uncrowded station (Experiment 2), and a crowded and uncrowded nature park (Experiment 3). Participants were asked to start the stopwatch and then stop it when they felt that 30 s or 60 s had passed, and the perceived time in the crowded settings was longer relative to the uncrowded settings in the three experiments. Sadeghi et al. (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003eb\u003c/span\u003e) conducted studies where participants experienced short (1–2 min) immersive virtual reality subway trips with different levels of public crowding. They found that increased crowding increased the unpleasantness of a trip and lengthened perceived trip duration (Sadeghi et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003eb\u003c/span\u003e); the unpleasant emotional experience mediated the influence of crowding on subjective time (Sadeghi et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e). Furthermore, the experience of withdrawal motivation, where individuals desire to terminate the trip sooner and escape the unpleasant environment, is one specific component related to the unpleasantness of crowding. Sadeghi et al. (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e) speculated that the extended perceived duration may stem from withdrawal motivation. However, it remains an open question whether crowding can modulate subjective time independently of affective valence.\u003c/p\u003e \u003cp\u003eCrowding can influence subjective time perception through multiple factors. As previously mentioned, three dimensions of emotion, namely valence, arousal, and motivation, are closely linked to crowding (Sadeghi et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e). A common naive theory is that “time flies when you’re having fun”, which suggests that events with positive valence pass especially quickly (Gable \u0026amp; Poole, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Sackett et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Tonietto et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Conversely, negative events are perceived as passing slowly, and boredom overestimates time (Danckert \u0026amp; Allman, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; O’Brien et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Tonietto et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Arousal also modulates the perception of time, as the perceived time of an emotional picture increases with arousal level (Droit-Volet et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2004\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Gil \u0026amp; Droit-Volet, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Gable et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) suggested that motivation directly modulates time perception, rather than being mediated by affective valence and arousal; specifically, approach motivation hastens the passing of time, whereas withdrawal motivation slows the passing of time, and motivation intensity is considered to enhance the effects of motivation direction (Gable et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Gable \u0026amp; Poole, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Furthermore, crowding is always accompanied by quantity processing, and quantity can modulate time perception, that is, larger magnitudes are perceived to last longer, resulting in cross-dimension interference (Oliveri et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Xuan et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). According to a theory of magnitude (ATOM), time, space, and quantity are part of a generalized magnitude system; external inputs of different dimensions are converted into a common magnitude representation; the cross-dimension interference results from the integration of representation of different dimensions in the generalized magnitude system; the parietal cortex is considered as the neural substrate of the magnitude system (Bueti \u0026amp; Walsh, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Walsh, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e). Crowding may modulate subjective time even after excluding emotional valence and arousal.\u003c/p\u003e \u003cp\u003eAn important finding in the field of time psychology is that the processing mechanism of temporal information is separate on different timescales (Buhusi \u0026amp; Meck, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Time perception is the cognitive process of perceiving temporal information within a range of two to three seconds, and no more than five seconds, which is primarily related to perception. On the other hand, processing temporal information beyond this range is referred to as time estimation, which is mainly related to memory (Fraisse, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). Even the time intervals below and above one second are proven to be measured by separate neural timing systems. Automatic timing system measures sub-second intervals without attentional modulation, and rely primarily on motion circuits; cognitively controlled timing system is more involved in the measurement of supra-second intervals with attention and working memory, and depends upon prefrontal and parietal regions (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Crowding may have different influences on perception of time on sub-second and supra-second timescales.\u003c/p\u003e \u003cp\u003eThe purpose of the study was to investigate the correlation between crowding and time perception while controlling for the effects of valence and arousal. In the pre-experiment, three types of crowding pictures (non-crowding, crowded objects, and crowded people) were collected and evaluated. There was no significant difference in the valence and arousal scores among the three kinds of pictures. Participants performed a temporal bisection task with different types of crowding pictures on the sub-second (Experiment 1) and supra-second (Experiment 2) timescales. Given that time perception can be directly modulated by withdrawal motivation (Gable et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gable \u0026amp; Poole, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and quantity (Oliveri et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Xuan et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), we hypothesize that crowding can modulate time perception after the exclusion of valence and arousal. Time perception is mainly processed automatically on the sub-second timescales and is a cognitively controlled process on supra-second timescales (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Automatic timing is less susceptible to interference from non-temporal tasks, whereas cognitively controlled timing is susceptible to interference from non-temporal tasks (Hellström \u0026amp; Rammsayer, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Rammsayer, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Therefore, we hypothesized that crowding would modulate time perception on seconds rather than the sub-second.\u003c/p\u003e\n\n\n\n \n\n \n\n \n\n\n\n \n\n \n\n \u003cp\u003e \u003c/p\u003e\n\n\n\n \n\n \n\n\n \u003cp\u003e\u003c/p\u003e\n\n "},{"header":"Pre-experiment: collecting and evaluating crowding pictures","content":"\u003cp\u003eIn the pre-experiment, we collected three types of pictures (non-crowding, crowded objects, and crowded people) from the internet. Participants rated the degree of crowding, valence, and arousal for each picture. To avoid the effect of valence and arousal on time perception in following experiments, we ensured that the valence and arousal of the three types of pictures were controlled so that there were no significant differences among the three types of pictures. This approach will help us to better understand the effect of crowding on time perception.\u003c/p\u003e\u003ch3\u003eMethods\u003c/h3\u003e\u003cp\u003e \u003cb\u003eParticipants\u003c/b\u003e \u003c/p\u003e\u003cp\u003eThe power analysis was performed using the PANGEA, which is specifically designed for analysis of variance (ANOVA), and available to the public at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://jakewestfall.shinyapps.io/pangea/\u003c/span\u003e\u003cspan address=\"https://jakewestfall.shinyapps.io/pangea/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (Westfall et al., 2014). The study adopted a one-factor within-subject design with crowding as the factor, having three levels: non-crowding, crowded objects, and crowded people. Each treatment consisted of 30 trials. As the variances associated with the main effect of crowding could not be predicted in advance, the default variance parameters in PANGEA were used (var [error] = 0.5, var [participant × crowding] = 0.167). Given a recommended statistical power of 0.8, a medium effect size (Cohen’s \u003cem\u003ed\u003c/em\u003e) of 0.5, and a significance level of 0.05 (Clayson et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), the required a minimum of sample size is 23.\u003c/p\u003e\u003cp\u003eTwenty-five undergraduate students volunteered to participate in the pre-experiment (18–24 years old, 15 females). All participants had normal or corrected vision, were right-handed, and had no history of color blindness, color weakness, or mental illness. The participants signed informed consent before the experiment, and received corresponding remuneration after the experiment. The experimental procedures followed the Declaration of Helsinki and are reviewed by the Ethics Committee of Southwest University.\u003c/p\u003e\u003ch3\u003eStimuli and procedures\u003c/h3\u003e\u003cp\u003eThree types of pictures are collected on the Internet (Figure. 1A). Non-crowding pictures were mainly empty scenes, such as city streets, roads, parks, and residential gardens, and so on. The crowded objects pictures were mainly dense express boxes, books, toys, bicycles, fruits, and so on. The crowded people pictures were the crowded people in the station, street, swimming pool, and so on. The sizes of all the images were standardized using Photoshop (The Adobe, Inc.). The length of the picture was 30 cm and its width was 22.5 cm. The pictures were displayed in the middle of a 28-inch LCD screen with a black background.\u003c/p\u003e\u003cp\u003eParticipants assessed the crowding of pictures on a 9-point self-report rating scale (Vaske \u0026amp; Shelby, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Crowding refers to the feeling of how crowded the area was when viewing the scene. The more crowded the scene, the closer the score is to 9, and the less crowded the scene, the closer the score is to 1. Participants also assessed the pictures in terms of valence and arousal on the 9-point self-assessment Manikin scale (Bradley \u0026amp; Lang, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Valence refers to the degree of pleasure or unpleasant when viewing the scene. The higher the pleasant, the closer the rating is to 9, and the less pleasant, the closer the rating is to 1. Arousal refers to the degree of excitement or calm when viewing the scene. The higher the level of excitement, the closer the score is to 9, and the less excited, the closer the score is to 1.\u003c/p\u003e\u003cp\u003eParticipants were seated approximately 60 cm away from the screen. E-prime 2.0 (Psychology Software Tools, Inc.) was used to control the presentation of pictures, and record the responses of participants. The pictures were presented randomly, and the participants used a keyboard to rate the valence, arousal, and crowding of each picture. The order of rating the three dimensions was balanced among the participants. After the evaluation of the first dimension, all the pictures were randomly presented again for the next dimension, and all the pictures were presented for a total of three rounds. The rating time was determined by the participants themselves. In principle, the rating was based on the immediate feeling, and there was no long-term thinking.\u003c/p\u003e\u003ch2\u003eData analysis\u003c/h2\u003e\u003cp\u003eThere were 30 pictures per category: non-crowding, crowded objects, and crowded people) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA). Raw ratings were averaged across pictures for each picture type and each participant. A one-way repeated-measures ANOVA was conducted on the scores of crowding (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB), valence (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC), and arousal (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD), respectively. The ANOVA factor was picture type (non-crowding, valence, and arousal). The Greenhouse-Geisser correction was employed to correct for any violations of sphericity (Greenhouse \u0026amp; Geisser, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1959\u003c/span\u003e), and the partial eta squared (\u003cem\u003eη\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e) was utilized to estimate the ANOVA effect size (Levine \u0026amp; Hullett, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e\u003ch3\u003eResults and discussion\u003c/h3\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eThe ANOVA conducted on crowding scores revealed a significant main effect of picture type, \u003cem\u003eF\u003c/em\u003e (2, 48) = 498.017, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.954. The post-hoc test using least significant difference (LSD) method showed that the crowding scores of the non-crowding pictures (1.765 ± 0.153) was lower than that of the crowded object pictures (6.188 ± 0.206, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001), and that of the crowded people (7.692 ± 0.118, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001); the crowding scores of the crowded object pictures was lower than that of the crowded people (\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001). According to previous studies, a score of 1–2 indicates not at all crowded, 3–4 indicates slightly crowded, 5–7 indicates moderately crowded, and 8–9 indicates extremely crowded (Vaske \u0026amp; Shelby, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). At a group-level, the non-crowding pictures were classified as “not at all crowded”, while the crowded objects and people pictures were classified as “moderately crowded” and “extremely crowded”.\u003c/p\u003e\u003cp\u003eWe conducted a one-way repeated-measures ANOVA to examine the impact of picture type on valence and arousal, respectively. The results revealed that the main effect of picture type was not statistically significant for either valence [\u003cem\u003eF\u003c/em\u003e (2, 48) = 2.470, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.093] or arousal [\u003cem\u003eF\u003c/em\u003e (2, 48) = 3.344, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.122] (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD). The findings serve as a foundation for further investigating the influence of crowding on time perception, while also eliminating potential confounding effects from valence and arousal.\u003c/p\u003e"},{"header":"Experiment 1: Crowding and time perception on sub-second timescales","content":"\u003cp\u003eParticipants were presented with three types of pictures (non-crowding, crowded objects, and crowded people), while performed a temporal bisection task on sub-second timescales. Participants first learned with a short (0.2 s) and a long anchor duration (0.8 s). Then a series of pictures were presented with durations ranging from 0.2 s to 0.8 s. Participants should judge whether the duration of the pictures was closer to the short duration or closer to the long duration. Given that time perception primarily relies on automatic processing mechanisms on sub-second timescales (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), we hypothesized that participants’ perception of sub-second duration would not be significantly modulated by crowding.\u003c/p\u003e\u003ch3\u003eMethods\u003c/h3\u003e\u003cp\u003e \u003cb\u003eParticipants\u003c/b\u003e \u003c/p\u003e\u003cp\u003eThe power analysis was performed using the PANGEA (Westfall et al., 2014). The study adopted a one-factor within-subject design with crowding as the factor, having three levels: non-crowding, crowded objects, and crowded people. Each level consisted of 210 trials (7 durations × 30 pictures). The default variance parameters in PANGEA were used (var [error] = 0.5, var [participant × crowding] = 0.167). Given a recommended statistical power of 0.8, a medium effect size (Cohen’s \u003cem\u003ed\u003c/em\u003e) of 0.5, and a significance level of 0.05 (Clayson et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), the required a minimum of sample size is 23.\u003c/p\u003e\u003cp\u003eThirty undergraduate students took part in the experiment (18–24 years old, 23 females). The other details were the same as the pre-experiment.\u003c/p\u003e\u003ch3\u003eStimuli and procedures\u003c/h3\u003e\u003cp\u003eThe visual stimuli were presented on a 28-inch LCD monitor. The visual stimuli consisted of white crosses, white circles, cyan question marks (R: 0, G: 255, B: 255), and pictures with varying degrees of crowding. The white circles had a diameter of 1 cm, the white crosses measured 1 cm in length, and the cyan question marks were approximately 0.8 cm in length. The images with different levels of crowding were measured 30 cm in length and 22.5 cm in width. We utilized E-prime 2.0 (Psychology Software Tools, Inc.) to control stimulus presentation and record participants’ responses.\u003c/p\u003e\u003cp\u003eParticipants were seated approximately 60 cm away from the screen. We conducted a temporal bisection task that consisted of a learning phase and a formal experiment phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In the learning phase, participants were presented with a small white circle in the center of the screen for either 200 ms or 800 ms (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA). Each duration was repeated five times to help participants learn and memorize the short and long anchor durations. Then, participants were presented with a small white circle for either 200 ms or 800 ms and were asked to judge whether the duration of the circle belonged to the short or long anchor duration (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). Each duration was also repeated five times. Participants were provided with feedback on whether their response was correct or not. To proceed to the formal experiment, a correct rate of 90% or higher was required.\u003c/p\u003e\u003cp\u003eIn the formal experiment, participants performed the temporal bisection task with three types of pictures (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). At the beginning of each trial, a white fixation was presented in the center of the screen for a random duration between 300 ms and 600 ms. Then, a picture was presented in the center of the screen. A total of 90 pictures were used, including 30 non-crowding, 30 crowded objects, and 30 crowded people pictures. The presentation time of each picture was selected from one of the following durations: 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, and 800 ms, each duration was presented once for each picture, and the order in which the pictures were presented was random. After a random interval of 500 ms to 800 ms, a question mark appeared on the screen, and the participants had 2 seconds to respond by pressing either the “F” key (closer to the long duration) or the “J” key (closer to the short duration) to determine whether the presentation time of the picture was closer to the short (200 ms) or long (800 ms) anchor durations. There was no feedback during the formal experiment, and after the participants pressed the key, they moved on to the next trial after a random interval of 500 ms to 800 ms.\u003c/p\u003e\u003cp\u003eThe experiment consisted of three picture types, each of seven durations, and each treatment was presented 30 times (30 pictures), comprising a total of 630 trials (3 × 7 × 30). Participants took one break after each 180 trials, for a total of three breaks. Participants had control over the duration of the break, which was limited to a maximum of 2 minutes.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003ch2\u003eData analysis\u003c/h2\u003e\u003cp\u003eBisection point (BP) is defined as the point of subjective equality, which is the duration for which participants respond long (closer to the long duration) as often as they do short (percentage of choosing “closer to the long duration” = 0.5) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). A smaller BP value for one stimulus than for another suggests a lengthening effect, with participants responding long more often for the former than for the latter, even though they are of the same physical duration. We obtained BP and standard deviation (SD) by fitting a cumulative normal distribution function to the data using MATLAB (The MathWorks, Inc.). Then we conducted a one-way repeated-measures ANOVA on the BP and SD, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC). The factor was crowding type including non-crowding, crowded objects, and crowded people. The other details were the same as the pre-experiment.\u003c/p\u003e\u003ch3\u003eResults and discussion\u003c/h3\u003e\u003cp\u003eThe ANOVA revealed that the main effect of crowding type was not statistically significant for either BP [\u003cem\u003eF\u003c/em\u003e(2, 58) = 1.825, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.043] or SD [\u003cem\u003eF\u003c/em\u003e(2, 58) = 1.184, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.039] (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC). These findings are consistent with previous studies that used the dual-task paradigm, which suggest that temporal processing in the sub-second range is less susceptible to interference from non-time tasks (Hellström \u0026amp; Rammsayer, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Rammsayer, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Rammsayer \u0026amp; Ulrich, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The results support our hypothesis that crowding does not modulate time perception on sub-second timescales, as the automatic timing system mainly measures time intervals on these scales (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e"},{"header":"Experiment 2: Crowding and time perception on supra-second timescales","content":"\u003cp\u003eParticipants were shown three types of pictures (non-crowding, crowded objects, and crowded people) and were asked to perform the temporal bisection task on supra-second timescales. The presentation time of the pictures ranged from 1 s to 4 s, instead of 0.2 s to 0.8 s as in Experiment 1. Given that cognitively controlled timing system is more involved in the measurement of supra-second time intervals with attention and working memory (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), we hypothesized that crowding would modulate time perception on supra-second timescales.\u003c/p\u003e\u003ch3\u003eMethods\u003c/h3\u003e\u003cp\u003e \u003cb\u003eParticipants\u003c/b\u003e \u003c/p\u003e\u003cp\u003eAs in Experiment 1, the PANGEA (Westfall et al., 2014) determined that the minimum sample size required was 23. Thirty-seven undergraduate students, 20 of whom were female, aged between 18 and 24 years old, participated in Experiment 2. Four participants were excluded from further statistical analysis due to data fitting issues and large variability in the data (see results for details). The retained sample size was 33. The other details of participants were identical to those of the pre-experiment and Experiment 1.\u003c/p\u003e\u003ch3\u003eStimuli and procedures\u003c/h3\u003e\u003cp\u003eIn Experiment 2, participants performed a temporal bisection task on supra-second timescales. During the learning phase, the short anchor duration was 1 s, and the long anchor duration was 4 s. In the formal experiment, the presentation time of the pictures was chosen from 1 s, 1.5 s, 2 s, 2.5 s, 3 s, 3.5 s, and 4 s. After every 90 trials, participants were allowed to take a break. Other details of the procedures were identical to those of Experiment 1.\u003c/p\u003e\u003cp\u003eAfter completing the temporal bisection task, participants rated the crowding, valence, and arousal of the 90 pictures respectively, as in the pre-experiment.\u003c/p\u003e\u003ch2\u003eData analysis\u003c/h2\u003e\u003cp\u003eThe bisection point (BP) and the standard deviation (SD) were obtained by fitting the psychometric curve as the same in Experiment 1. A one-way repeated-measures ANOVA was conducted on the BP and SD, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC). The factor was crowding type including non-crowding, crowded objects, and crowded people.\u003c/p\u003e\u003cp\u003eTo test whether the valence and arousal of the three types of pictures were effectively controlled in experiment 2, we fitted a linear mixed model (LMM) to the BP using the lme4 (Bates et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and lmerTest (Kuznetsova et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) in R (R Core Team, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The LMM model included the crowding, valence and arousal as fixed effects, the participants’ intercept as the random effect, and the BP values as the dependent variable, respectively. The model formula was: \u003cem\u003eBP\u003c/em\u003e ~ \u003cem\u003ecrowding\u003c/em\u003e + \u003cem\u003evalence\u003c/em\u003e + \u003cem\u003earousal\u003c/em\u003e + (1|\u003cem\u003eParticipant ID\u003c/em\u003e)\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e1\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eIn order to avoid the multicollinearity problem in multiple regression, dominance analysis was used to determine the relative importance of the crowding, valence, and arousal in predicting the BP (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The approach establishes the relative importance of predictors based on an examination of the \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e values for all possible subset models (Budescu, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1993\u003c/span\u003e), and has been successfully applied in various psychological fields, such as cognition (Gellersen et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), personality (Duan et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), education (Lau \u0026amp; Yuen, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), customer satisfaction (Garver \u0026amp; Williams, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and organization (Simonet et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). We adopted \u003cem\u003eR\u0026amp;B R\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e to calculate the \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e statistic for each variance component in the model (Raudenbush \u0026amp; Bryk, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), because \u003cem\u003eR\u0026amp;B R\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e is appropriate for the individual-level (Level-1) variance component in hierarchical linear models (Luo \u0026amp; Azen, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The dominance analysis was applied using the R package dominanceanalysis (Bustos Navarrete \u0026amp; Coutinho Soares, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The columns labeled \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e represented each subset model’s contribution relative to a null model that was: \u003cem\u003eBP\u003c/em\u003e ~ (1|\u003cem\u003eParticipant ID\u003c/em\u003e) (Luo \u0026amp; Azen, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e[1] In the pre-analysis, the slopes of crowding, valence, and arousal were also considered as random factors. However, the model failed to fit the data due to an excessive number of random effects. The error message was as follows: number of observations (=99) \u0026lt;= number of random effects (=99) for term (0 + crowding+ valence + arousal | Subject); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\u003ch3\u003eResults and discussion\u003c/h3\u003e\u003cp\u003eOne participant’s data could not be fitted by a cumulative normal distribution function (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA). The proportions of “long” responses for different crowding types and different durations were all around 0.5, indicating that the participant randomly pressed the keys. The bisection points (BP) and standard deviations (SD) were obtained for the remaining participants under each crowding type. Three participants had SD values greater than 2 s and violated the two-sigma rule that SD values were two standard deviations above or below the mean of the SD values, and were therefore excluded from the following analyses. In comparison to normal participants (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA), the proportions of “long” responses of these participants tended to be closer to 0.5 and resulted in larger SD values (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB). An SD that is too large indicates that participants may not have performed the experimental task seriously. The data of 33 participants entered the further statistical analysis.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eThe ANOVA conducted on BP (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB) revealed a significant main effect of crowding type, \u003cem\u003eF\u003c/em\u003e (2, 64) = 3.459, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.098. The post-hoc test revealed that the BP was significantly greater for the non-crowding (2409.134 ± 85.492 ms) than that for the crowded people (2356.070 ± 92.970 ms) (\u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05). The difference of BP between the non-crowding and the crowded objects (2368.234 ± 95.427 ms) was not significant (\u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05), nor was the difference of BP between the crowded objects and the crowded people (\u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05). The ANOVA conducted on SD (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC) revealed that the main effect of crowding type was not significant, \u003cem\u003eF\u003c/em\u003e (2, 64) = 0.377, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003ep\u003c/sub\u003e = 0.012. The results supports our hypothesis that crowding modulates time perception on supra-second timescales because of the cognitively controlled timing system employed on this timescale.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eLMM not only predicted the decline of BP with the increase of crowding (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA), but also took into account individual differences in BP, where greater individual BP corresponded to greater predicted values (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB). The LMM revealed that the BP decreased with increasing crowding [\u003cem\u003eβ\u003c/em\u003e = -8.260, \u003cem\u003eSE\u003c/em\u003e = 3.761, \u003cem\u003et\u003c/em\u003e(66.231) = -2.196, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05]. The study did not find a significant linear relationship between BP and valence [\u003cem\u003eβ\u003c/em\u003e = -1.830, \u003cem\u003eSE\u003c/em\u003e = 5.753, \u003cem\u003et\u003c/em\u003e(66.701) = -0.318, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05], nor between BP and arousal [\u003cem\u003eβ\u003c/em\u003e = 5.316, \u003cem\u003eSE\u003c/em\u003e = 6.947, \u003cem\u003et\u003c/em\u003e(66.579) = 0.765, \u003cem\u003ep\u003c/em\u003e \u0026gt; 0.05]. The results provide evidence that the linear relationship between BP and crowding was not confused by the effects of valence and arousal in Experiment 2.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eAdditional contributions of crowding, valence, and arousal to each subset model were calculated according to the dominance analysis (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The crowding completely dominated valence and arousal as the additional contribution by crowding was higher than that by valence and arousal for every subset model (Azen \u0026amp; Budescu, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). When predicting the BP, the crowding, valence, and arousal account for 91.304%, 2.895%, and 5.797% of overall average additional contributions, respectively.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRelative importance of crowding, valence, and arousal in predicting bisection point (BP).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eAdditional contribution of:\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ecrowding\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003evalence\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003earousal\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNull and \u003cem\u003ek\u003c/em\u003e = 0 average\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecrowding\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003evalence\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.058\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003earousal\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.069\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e = 1 average\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.063\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecrowding, valence\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecrowding, arousal\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.069\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003evalence, arousal\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.067\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e = 2 average\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.067\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecrowding, valence, arousal\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.070\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOverall average\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.063\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e"},{"header":"General Discussion","content":"\u003cp\u003eThe study conducted a temporal bisection task to investigate the effect of crowding on time perception, independent of valence and arousal. To eliminate their impact, we carefully chose three types of pictures: non-crowding, crowded objects, and crowded people, and observed no significant differences in valence and arousal scores among these picture types (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The results of Experiment 1 indicated that crowding did not affect time perception significantly on sub-second timescales. However, Experiment 2 demonstrated that crowding modulated time perception on supra-second timescales. Then we employed a linear mixed model (LMM) to examine the prediction of crowding, valence, and arousal to the bisection point (BP). The LMM revealed a significant linear relationship between crowding and BP, while valence and arousal failed to predict BP. Finally, we used dominance analysis to reveal the relative importance of crowding, valence, and arousal in predicting the BP, and found that crowding completely outperformed valence and arousal, with crowding explaining more than 91% of overall average additional contributions while valence and arousal together explaining less than 9%. In summary, the findings provide evidence that crowding significantly modulates time perception on supra-second timescales, even when valence and arousal are controlled for three types of pictures.\u003c/p\u003e\u003cp\u003eCrowding and motivation are closely intertwined. High crowd density can be a source of mental stress and too much information can lead to a negative mood state (Schmidt \u0026amp; Keating, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1979\u003c/span\u003e). For instance, in crowded public transport, passengers’ discomfort can arise from standing instead of being seated, less opportunities to use time during the journey, and the physical closeness of other travelers (Haywood et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This can lead to negative emotions and stress (Bruins \u0026amp; Barber, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Evans \u0026amp; Wener, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Furthermore, crowding can also reduce an individual’s sense of autonomy, increase the sense of personal space invasion (Lawrence \u0026amp; Andrews, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Maeng et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Maeng \u0026amp; Tanner, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Nieuwenhuijsen \u0026amp; de Waal, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e1982\u003c/span\u003e), and reduce individuals’ freedom of activity and control over the environment (Consiglio et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Rompay et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Stokols, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e1972\u003c/span\u003e). Therefore, individuals often hope to end the crowded travel and escape from the unpleasant environment as soon as possible (Sadeghi et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e), which is known as the withdrawal motivation of individuals in the crowded environment (Maeng et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Maeng \u0026amp; Tanner, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWe found that crowding can modulate time perception, independent of the valence and arousal (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Given that the crowding is accompanied by the withdrawal motivation (Maeng et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Maeng \u0026amp; Tanner, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), out results are consistent with the motivation dimension model of time perception, in which withdrawal motivation should slow down the subjective time, and the motivation directly modulates time perception, rather than being mediated by affective valence and arousal (Gable et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gable \u0026amp; Poole, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Supporting for the motivation dimension model of time perception, Yin et al. (\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) reported that approach and withdrawal motivations modulate time perception after controlling for valence and arousal of emotional images. More evidence suggests that emotion and motivation induce attention biases (Cisler \u0026amp; Koster, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and further modulate time perception (J. Liu \u0026amp; Li, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Electrophysiological evidence has been obtained to support that emotion modulates time perception through the attention system (Tamm et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Vallet et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Especially, Yin et al. (\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) employed contingent negative variation (CNV) to examine the processing mechanism of different motivations affecting time perception. CNV is a well-known event-related potential (ERP) component that has been shown to be associated with temporal encoding (Wiener et al., \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), and more attention assigned to temporal information leads to a longer perceived duration and a larger CNV (Chen et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Y. Liu et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Angry expressions are negative stimuli with approach motivation, and fearful expressions are also negative stimuli but with withdrawal motivation. According to the attentional perspective of temporal processing (Coull et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Macar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Zakay \u0026amp; Block, \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), approach motivation attract more attention than withdrawal motivation, less attention was paid on time in the angry condition than that in the fear condition, therefore, the perceived time of angry expression is shorter than that of fear expression, and the amplitude of CNV induced by angry expression is lower than that of fear expression (Yin, Cui, et al., \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Therefore, compared with uncrowded conditions, withdrawal motivation allows participants allocate more attention to time and less attention to crowded images, resulting in longer perceptual time in crowded conditions.\u003c/p\u003e\u003cp\u003eAccording to the theory of magnitude (ATOM), time, space, and quantity are all part of a generalized magnitude system, which can lead to cross-dimension interference; the parietal cortex is believed to be the locus of this magnitude system (Bueti \u0026amp; Walsh, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Walsh, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e). The parietal cortex is a region of the brain that has been implicated in working memory (Chai et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). For instance, Jonides et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) found that parietal regions are part of a network of brain areas that mediate the short-term storage and retrieval of phonologically coded verbal material. Koenigs et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) also found that the superior parietal cortex is critical for the manipulation of information in working memory. Cui et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) used event-related potentials (ERPs) to identify the neural basis of cross-dimension interference. They found that the parietal P2 and P3b component index updates a common magnitude representation of spatiotemporal information in working memory, and the neural source of P2 and P3b was located in the parietal cortex. Based on the above theoretical considerations and empirical evidence, it can be inferred that the cross-dimension interference of quantity on time may occur in working memory.\u003c/p\u003e\u003cp\u003eWe found that crowding modulated time perception on the supra-second timescales rather than the sub-second timescales. An automatic timing system measures sub-second intervals without attentional modulation, and a cognitively controlled timing system is more involved in the measurement of supra-second intervals with attention and working memory (Lewis \u0026amp; Miall, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2003b\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Behavioral evidence also supports the idea that processing shorter intervals depends on sensory or automatic processing while processing longer intervals requires cognitive resources (Hellström \u0026amp; Rammsayer, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Rammsayer, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Taken together, these findings suggest that the cognitive mechanisms underlying time perception are different for sub-second and supra-second intervals. As previously mentioned, after controlling for emotional valence and arousal, crowding may modulate time perception through withdrawal motivation and cross-dimension interference. The impact of withdrawal motivation on time perception may involve the allocation of attention between temporal and non-temporal information in the attention system (Coull et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Macar et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Yin, Cui, et al., \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zakay \u0026amp; Block, \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e1997\u003c/span\u003e); the impact of quantitative information on time involves the mutual interference of different dimensional information in a generalized magnitude system located in parietal cortex (Bueti \u0026amp; Walsh, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Walsh, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2003a\u003c/span\u003e), which is has been implicated in working memory (Chai et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Therefore, the finding that crowding modulates time perception on supra-second timescales rather than the sub-second timescales is consistent with the theory of automatic and cognitively controlled timing systems.\u003c/p\u003e\u003cp\u003eThis study has the following advantages and limitations. Firstly, the study effectively controlled for the impacts of valence and arousal on time perception. We carefully selected three types of crowding pictures so that there was no significant difference in valence and arousal scores among the three crowding types. Then, we used LMM and dominance analysis to confirm that valence and arousal did not affect subjective time. The study provided strong evidence that crowding can modulate time perception even after valence and arousal were excluded. Secondly, the study examined the influence of crowding on sub-second and supra-second timescales, respectively, based on the theory of automatic and cognitively controlled timing systems. We found that crowding modulated time perception on the supra-second timescales rather than the sub-second, which helps to establish a connection between crowding and existing theories in the psychology of time. However, one limitation of this study is that it does not distinguish the influence of withdrawal motivation on time perception from that of quantity. Crowding is accompanied by withdrawal motivation and quantity, but the mechanisms of their impacts on time are different. The withdrawal motivation modulates time through attention, and the cross-dimensional interference of quantity on time may occur in working memory. Further research on these two mechanisms in crowded situations can not only provide answers to how withdrawal motivation and magnitude processing affect time perception but also deepen our understanding of the interaction between cognition and motivation. Future studies could combine behavioral experiments with cognitive neuroscience techniques to separate the mechanism of withdrawal motivation and quantity in the modulation of time perception in a crowded environment.\u003c/p\u003e\u003cp\u003eIn summary, this study controlled the valence and arousal of three types of crowding pictures, and investigate the effect of crowding on time perception on sub-second and supra-second timescales. We found that crowding modulated time perception on the supra-second rather than the sub-second timescales. The LMM and dominance analysis verified that valence and arousal did not significantly modulate time perception. Crowding includes withdrawal motivation and quantity, which are considered to be influencing factors of time perception after excluding valence and arousal. Withdrawal motivation modulates time perception through attention system, and the cross-dimension interference of quantity on time may occur in working memory. These explanations are consistent with the idea that automatic timing systems measure sub-second time intervals without attentional modulation, while cognitively controlled timing systems are more involved in supra-second interval measurements with attention and working memory.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBehavioral data have been deposited at Zenodo: https://www.zenodo.org/record/10683927 (DOI:10.5281/zenodo.10683927) and are publicly available as of the date of publication.\u003c/p\u003e\u003cp\u003e \u003ch2\u003eDeclaration of interest\u003c/h2\u003e \u003cp\u003eThe authors declare that there are no competing interests.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eCredit authorship contribution statement\u003c/h2\u003e \u003cp\u003eYouguo Chen: Conceptualization, Methodology, Formal analysis, Visualization, Writing \u0026ndash; review \u0026amp; editing. Yuanwei Xu: Investigation, Formal analysis, Writing \u0026ndash; original draft. Gaomin Liang and Chunhua Peng: Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eC: Conceptualization, Methodology, Formal analysis, Visualization, Writing \u0026ndash; review \u0026amp; editing.X: Investigation, Formal analysis, Writing \u0026ndash; original draft. L and P: Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis study was supported by General Program of the Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-msxmX0758) and Humanities and Social Science Youth Foundation of Ministry of Education of China (Grant No. 19YJC190002).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAzen, R., \u0026amp; Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. \u003cem\u003ePsychological Methods\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e(2), 129\u0026ndash;148. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1037/1082-989x.8.2.129\u003c/span\u003e\u003cspan address=\"10.1037/1082-989x.8.2.129\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBates, D., M\u0026auml;chler, M., Bolker, B., \u0026amp; Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. \u003cem\u003eJournal of Statistical Software\u003c/em\u003e, \u003cem\u003e67\u003c/em\u003e(1), 1\u0026ndash;48. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18637/jss.v067.i01\u003c/span\u003e\u003cspan address=\"10.18637/jss.v067.i01\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBradley, M. M., \u0026amp; Lang, P. J. (1994). Measuring emotion: The self-assessment manikin and the semantic differential. \u003cem\u003eJournal of Behavior Therapy and Experimental Psychiatry\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e(1), 49\u0026ndash;59. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0005-7916(94)90063-9\u003c/span\u003e\u003cspan address=\"10.1016/0005-7916(94)90063-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBruins, J., \u0026amp; Barber, A. (2000). Crowding, Performance, and Affect: A Field Experiment Investigating Mediational Processes. \u003cem\u003eJournal of Applied Social Psychology\u003c/em\u003e, \u003cem\u003e30\u003c/em\u003e(6), 1268\u0026ndash;1280. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1559-1816.2000.tb02520.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1559-1816.2000.tb02520.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBudescu, D. V. (1993). Dominance Analysis: A New Approach to the Problem of Relative Importance of Predictors in Multiple Regression. \u003cem\u003ePsychological Bulletin\u003c/em\u003e, \u003cem\u003e114\u003c/em\u003e(3), 542\u0026ndash;551. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1037/0033-2909.114.3.542\u003c/span\u003e\u003cspan address=\"10.1037/0033-2909.114.3.542\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBueti, D., \u0026amp; Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. \u003cem\u003ePhilosophical Transactions Of The Royal Society Of London. Series B, Biological Sciences\u003c/em\u003e, \u003cem\u003e364\u003c/em\u003e(1525), 1831\u0026ndash;1840. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1098/rstb.2009.0028\u003c/span\u003e\u003cspan address=\"10.1098/rstb.2009.0028\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBuhusi, C. V., \u0026amp; Meck, W. H. (2005). What makes us tick? Functional and neural mechanisms of interval timing. \u003cem\u003eNature Reviews Neuroscience\u003c/em\u003e, \u003cem\u003e6\u003c/em\u003e(10), 755\u0026ndash;765.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBustos Navarrete, C., \u0026amp; Coutinho Soares, F. (2020). R-package: Dominanceanalysis (2.0.0) [Computer software]. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cran.r-project.org/src/contrib/Archive/dominanceanalysis/\u003c/span\u003e\u003cspan address=\"https://cran.r-project.org/src/contrib/Archive/dominanceanalysis/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChai, W. J., Hamid, A., A. I., \u0026amp; Abdullah, J. M. (2018). Working Memory From the Psychological and Neurosciences Perspectives: A Review. \u003cem\u003eFrontiers in Psychology\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3389/fpsyg.2018.00401\u003c/span\u003e\u003cspan address=\"10.3389/fpsyg.2018.00401\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. 9\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.frontiersin.org/articles/\u003c/span\u003e\u003cspan address=\"https://www.frontiersin.org/articles/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen, Y. G., Zhang, Z. J., Huang, X. T., Guo, X. Y., Yuan, H., \u0026amp; Zhang, T. (2007). Attentional Modulation of Time Perception: An ERP Study. \u003cem\u003eActa Psychologica Sinica\u003c/em\u003e, \u003cem\u003e39\u003c/em\u003e(06), 1002\u0026ndash;1011.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCisler, J. M., \u0026amp; Koster, E. H. W. (2010). Mechanisms of attentional biases towards threat in anxiety disorders: An integrative review. \u003cem\u003eClinical Psychology Review\u003c/em\u003e, \u003cem\u003e30\u003c/em\u003e(2), 203\u0026ndash;216. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cpr.2009.11.003\u003c/span\u003e\u003cspan address=\"10.1016/j.cpr.2009.11.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eClayson, P. E., Carbine, K. A., Baldwin, S. A., \u0026amp; Larson, M. J. (2019). Methodological reporting behavior, sample sizes, and statistical power in studies of event-related potentials: Barriers to reproducibility and replicability. \u003cem\u003ePsychophysiology\u003c/em\u003e, \u003cem\u003e56\u003c/em\u003e(11), e13437. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/psyp.13437\u003c/span\u003e\u003cspan address=\"10.1111/psyp.13437\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eConsiglio, I., De Angelis, M., \u0026amp; Costabile, M. (2018). The Effect of Social Density on Word of Mouth. \u003cem\u003eJournal of Consumer Research\u003c/em\u003e, \u003cem\u003e45\u003c/em\u003e(3), 511\u0026ndash;528. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/jcr/ucy009\u003c/span\u003e\u003cspan address=\"10.1093/jcr/ucy009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCoull, J. T., Vidal, F., Nazarian, B., \u0026amp; Macar, F. (2004). Functional anatomy of the attentional modulation of time estimation. \u003cem\u003eScience\u003c/em\u003e, \u003cem\u003e303\u003c/em\u003e(5663), 1506\u0026ndash;1508. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.1091573\u003c/span\u003e\u003cspan address=\"10.1126/science.1091573\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCui, M. H., Peng, C. H., Huang, M., \u0026amp; Chen, Y. G. (2022). Electrophysiological Evidence for a Common Magnitude Representation of Spatiotemporal Information in Working Memory. \u003cem\u003eCerebral Cortex\u003c/em\u003e, \u003cem\u003e32\u003c/em\u003e(18), 4068\u0026ndash;4079. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/cercor/bhab466\u003c/span\u003e\u003cspan address=\"10.1093/cercor/bhab466\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDanckert, J. A., \u0026amp; Allman, A. A. A. (2005). Time flies when you\u0026rsquo;re having fun: Temporal estimation and the experience of boredom. \u003cem\u003eBrain and Cognition\u003c/em\u003e, \u003cem\u003e59\u003c/em\u003e(3), 236\u0026ndash;245. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.bandc.2005.07.002\u003c/span\u003e\u003cspan address=\"10.1016/j.bandc.2005.07.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDroit-Volet, S., Bigand, E., Ramos, D., \u0026amp; Bueno, J. L. (2010). Time flies with music whatever its emotional valence. \u003cem\u003eActa Psychol (Amst)\u003c/em\u003e, \u003cem\u003e135\u003c/em\u003e(2), 226\u0026ndash;232. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.actpsy.2010.07.003\u003c/span\u003e\u003cspan address=\"10.1016/j.actpsy.2010.07.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDroit-Volet, S., Brunot, S., \u0026amp; Niedenthal, P. M. (2004). Perception of the duration of emotional events. \u003cem\u003eCognition \u0026amp; Emotion\u003c/em\u003e, \u003cem\u003e18\u003c/em\u003e(6), 849\u0026ndash;858. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/02699930341000194\u003c/span\u003e\u003cspan address=\"10.1080/02699930341000194\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDuan, J., Yang, Z., Zhang, F., Zhou, Y., \u0026amp; Yin, J. (2021). Aggressive behaviors in highly sadistic and highly impulsive individuals. \u003cem\u003ePersonality and Individual Differences\u003c/em\u003e, \u003cem\u003e178\u003c/em\u003e, 110875. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.paid.2021.110875\u003c/span\u003e\u003cspan address=\"10.1016/j.paid.2021.110875\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEvans, G. W., \u0026amp; Wener, R. E. (2007). Crowding and personal space invasion on the train: Please don\u0026rsquo;t make me sit in the middle. \u003cem\u003eJournal of Environmental Psychology\u003c/em\u003e, \u003cem\u003e27\u003c/em\u003e(1), 90\u0026ndash;94. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jenvp.2006.10.002\u003c/span\u003e\u003cspan address=\"10.1016/j.jenvp.2006.10.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFraisse, P. (1984). Perception and estimation of time. \u003cem\u003eAnnual Review of Psychology\u003c/em\u003e, \u003cem\u003e35\u003c/em\u003e, 1\u0026ndash;36.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFujimoto, M. (2016). A fundamental study on the interaction of people with their surrounding space and sense of time in a rest. \u003cem\u003eJournal of Home Economics of Japan\u003c/em\u003e, \u003cem\u003e67\u003c/em\u003e(7), 382\u0026ndash;396. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.11428/jhej.67.382\u003c/span\u003e\u003cspan address=\"10.11428/jhej.67.382\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGable, P. A., Neal, L. B., \u0026amp; Poole, B. D. (2016). Sadness speeds and disgust drags: Influence of motivational direction on time perception in negative affect. \u003cem\u003eMotivation Science\u003c/em\u003e, \u003cem\u003e2\u003c/em\u003e(4), 238\u0026ndash;255. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1037/mot0000044\u003c/span\u003e\u003cspan address=\"10.1037/mot0000044\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGable, P. A., \u0026amp; Poole, B. D. (2012). Time flies when you\u0026rsquo;re having approach-motivated fun: Effects of motivational intensity on time perception. \u003cem\u003ePsychological Science\u003c/em\u003e, \u003cem\u003e23\u003c/em\u003e(8), 879\u0026ndash;886. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/0956797611435817\u003c/span\u003e\u003cspan address=\"10.1177/0956797611435817\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGable, P. A., Wilhelm, A. L., \u0026amp; Poole, B. D. (2022). How Does Emotion Influence Time Perception? A Review of Evidence Linking Emotional Motivation and Time Processing. \u003cem\u003eFrontiers in Psychology\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e, 848154. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/fpsyg.2022.848154\u003c/span\u003e\u003cspan address=\"10.3389/fpsyg.2022.848154\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGarver, M. S., \u0026amp; Williams, Z. (2019). Utilizing relative weight analysis in customer satisfaction research. \u003cem\u003eInternational Journal of Market Research\u003c/em\u003e, \u003cem\u003e62\u003c/em\u003e(2), 158\u0026ndash;175. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/1470785319859794\u003c/span\u003e\u003cspan address=\"10.1177/1470785319859794\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGellersen, H. M., Trelle, A. N., Henson, R. N., \u0026amp; Simons, J. S. (2021). Executive function and high ambiguity perceptual discrimination contribute to individual differences in mnemonic discrimination in older adults. \u003cem\u003eCognition\u003c/em\u003e, \u003cem\u003e209\u003c/em\u003e, 104556. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cognition.2020.104556\u003c/span\u003e\u003cspan address=\"10.1016/j.cognition.2020.104556\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGil, S., \u0026amp; Droit-Volet, S. (2012). Emotional time distortions: The fundamental role of arousal. \u003cem\u003eCognition And Emotion\u003c/em\u003e, \u003cem\u003e26\u003c/em\u003e(5), 847\u0026ndash;862. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/02699931.2011.625401\u003c/span\u003e\u003cspan address=\"10.1080/02699931.2011.625401\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGray, A. (2001). \u003cem\u003eDefinitions of crowding and the effects of crowding on health: A literature review\u003c/em\u003e. Ministry of Social Policy.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGreenhouse, S. W., \u0026amp; Geisser, S. (1959). On methods in the analysis of profile data. \u003cem\u003ePsychometrika\u003c/em\u003e, \u003cem\u003e24\u003c/em\u003e(2), 95\u0026ndash;112. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/BF02289823\u003c/span\u003e\u003cspan address=\"10.1007/BF02289823\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHaywood, L., Koning, M., \u0026amp; Monchambert, G. (2017). Crowding in public transport: Who cares and why? \u003cem\u003eTransportation Research Part A: Policy and Practice\u003c/em\u003e, \u003cem\u003e100\u003c/em\u003e, 215\u0026ndash;227. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.tra.2017.04.022\u003c/span\u003e\u003cspan address=\"10.1016/j.tra.2017.04.022\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHellstr\u0026ouml;m, \u0026Aring;., \u0026amp; Rammsayer, T. H. (2004). Effects of time-order, interstimulus interval, and feedback in duration discrimination of noise bursts in the 50- and 1000-ms ranges. \u003cem\u003eActa Psychologica\u003c/em\u003e, \u003cem\u003e116\u003c/em\u003e(1), 1\u0026ndash;20. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.actpsy.2003.11.003\u003c/span\u003e\u003cspan address=\"10.1016/j.actpsy.2003.11.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJonides, J., Schumacher, E. H., Smith, E. E., Koeppe, R. A., Awh, E., Reuter-Lorenz, P. A., Marshuetz, C., \u0026amp; Willis, C. R. (1998). The role of parietal cortex in verbal working memory. \u003cem\u003eJournal of Neuroscience\u003c/em\u003e, \u003cem\u003e18\u003c/em\u003e(13), 5026\u0026ndash;5034.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKoenigs, M., Barbey, A. K., Postle, B. R., \u0026amp; Grafman, J. (2009). Superior Parietal Cortex Is Critical for the Manipulation of Information in Working Memory. \u003cem\u003eJournal of Neuroscience\u003c/em\u003e, \u003cem\u003e29\u003c/em\u003e(47), 14980\u0026ndash;14986. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1523/JNEUROSCI.3706-09.2009\u003c/span\u003e\u003cspan address=\"10.1523/JNEUROSCI.3706-09.2009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKuznetsova, A., Brockhoff, P. B., \u0026amp; Christensen, R. H. B. (2017). lmerTest Package: Tests in Linear Mixed Effects Models. \u003cem\u003eJournal of Statistical Software\u003c/em\u003e, \u003cem\u003e82\u003c/em\u003e, 1\u0026ndash;26. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.18637/jss.v082.i13\u003c/span\u003e\u003cspan address=\"10.18637/jss.v082.i13\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLau, W. W. F., \u0026amp; Yuen, A. H. K. (2016). The relative importance of paternal and maternal parenting as predictors of adolescents\u0026rsquo; home Internet use and usage. \u003cem\u003eComputers \u0026amp; Education\u003c/em\u003e, \u003cem\u003e102\u003c/em\u003e, 224\u0026ndash;233. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compedu.2016.09.002\u003c/span\u003e\u003cspan address=\"10.1016/j.compedu.2016.09.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLawrence, C., \u0026amp; Andrews, K. (2004). The influence of perceived prison crowding on male inmates\u0026rsquo; perception of aggressive events. \u003cem\u003eAggressive Behavior\u003c/em\u003e, \u003cem\u003e30\u003c/em\u003e(4), 273\u0026ndash;283. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/ab.20024\u003c/span\u003e\u003cspan address=\"10.1002/ab.20024\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLevine, T. R., \u0026amp; Hullett, C. R. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. \u003cem\u003eHuman Communication Research\u003c/em\u003e, \u003cem\u003e28\u003c/em\u003e(4), 612\u0026ndash;625. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1468-2958.2002.tb00828.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1468-2958.2002.tb00828.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLewis, P. A., \u0026amp; Miall, R. C. (2003a). Brain activation patterns during measurement of sub- and supra-second intervals. \u003cem\u003eNeuropsychologia\u003c/em\u003e, \u003cem\u003e41\u003c/em\u003e(12), 1583\u0026ndash;1592.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLewis, P. A., \u0026amp; Miall, R. C. (2003b). Distinct systems for automatic and cognitively controlled time measurement: Evidence from neuroimaging. \u003cem\u003eCurrent Opinion in Neurobiology\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(2), 250\u0026ndash;255. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0959-4388(03)00036-9\u003c/span\u003e\u003cspan address=\"10.1016/S0959-4388(03)00036-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLewis, P. A., \u0026amp; Miall, R. C. (2006). Remembering the time: A continuous clock. \u003cem\u003eTrends in Cognitive Sciences\u003c/em\u003e, \u003cem\u003e10\u003c/em\u003e(9), 401\u0026ndash;406.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLin, J. Y. J., Jenelius, E., Cebecauer, M., Rubensson, I., \u0026amp; Chen, C. (2023). The equity of public transport crowding exposure. \u003cem\u003eJournal of Transport Geography\u003c/em\u003e, \u003cem\u003e110\u003c/em\u003e, 103631. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jtrangeo.2023.103631\u003c/span\u003e\u003cspan address=\"10.1016/j.jtrangeo.2023.103631\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu, J., \u0026amp; Li, H. (2020). How individuals perceive time in an anxious state: The mediating effect of attentional bias. \u003cem\u003eEmotion\u003c/em\u003e, \u003cem\u003e20\u003c/em\u003e(5), 761\u0026ndash;772. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1037/emo0000586\u003c/span\u003e\u003cspan address=\"10.1037/emo0000586\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu, Y., Zhang, D., Ma, J., Li, D., Yin, H., \u0026amp; Luo, Y. (2013). The attention modulation on timing: An event-related potential study. \u003cem\u003ePLOS ONE\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e(6), e66190. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0066190\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0066190\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLuo, W., \u0026amp; Azen, R. (2013). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. \u003cem\u003eJournal of Educational and Behavioral Statistics\u003c/em\u003e, \u003cem\u003e38\u003c/em\u003e(1), 3\u0026ndash;31. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3102/1076998612458319\u003c/span\u003e\u003cspan address=\"10.3102/1076998612458319\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMacar, F., Grondin, S., \u0026amp; Casini, L. (1994). Controlled attention sharing influences time estimation. \u003cem\u003eMemory \u0026amp; Cognition\u003c/em\u003e, \u003cem\u003e22\u003c/em\u003e(6), 673\u0026ndash;686.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaeng, A., \u0026amp; Tanner, R. J. (2013). Construing in a crowd: The effects of social crowding on mental construal. \u003cem\u003eJournal of Experimental Social Psychology\u003c/em\u003e, \u003cem\u003e49\u003c/em\u003e(6), 1084\u0026ndash;1088. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jesp.2013.07.010\u003c/span\u003e\u003cspan address=\"10.1016/j.jesp.2013.07.010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaeng, A., Tanner, R. J., \u0026amp; Soman, D. (2013). Conservative When Crowded: Social Crowding and Consumer Choice. \u003cem\u003eJournal of Marketing Research\u003c/em\u003e, \u003cem\u003e50\u003c/em\u003e(6), 739\u0026ndash;752. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1509/jmr.12.0118\u003c/span\u003e\u003cspan address=\"10.1509/jmr.12.0118\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNieuwenhuijsen, K., \u0026amp; de Waal, F. B. M. (1982). Effects of spatial crowding on social behavior in a chimpanzee colony. \u003cem\u003eZoo Biology\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e(1), 5\u0026ndash;28. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/zoo.1430010103\u003c/span\u003e\u003cspan address=\"10.1002/zoo.1430010103\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eO\u0026rsquo;Brien, E. H., Anastasio, P. A., \u0026amp; Bushman, B. J. (2011). Time Crawls When You\u0026rsquo;re Not Having Fun: Feeling Entitled Makes Dull Tasks Drag On. \u003cem\u003ePersonality and Social Psychology Bulletin\u003c/em\u003e, \u003cem\u003e37\u003c/em\u003e(10), 1287\u0026ndash;1296. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/0146167211408922\u003c/span\u003e\u003cspan address=\"10.1177/0146167211408922\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOliveri, M., Vicario, C. M., Salerno, S., Koch, G., Turriziani, P., Mangano, R., Chillemi, G., \u0026amp; Caltagirone, C. (2008). Perceiving numbers alters time perception. \u003cem\u003eNeuroscience Letters\u003c/em\u003e, \u003cem\u003e438\u003c/em\u003e(3), 308\u0026ndash;311.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR Core Team (2022). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.R-project.org/\u003c/span\u003e\u003cspan address=\"https://www.R-project.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRammsayer, T. (2006). Effects of pharmacologically induced changes in NMDA receptor activity on human timing and sensorimotor performance. \u003cem\u003eBrain Research\u003c/em\u003e, \u003cem\u003e1073\u003c/em\u003e, 407\u0026ndash;416.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRammsayer, T., \u0026amp; Ulrich, R. (2011). Elaborative rehearsal of nontemporal information interferes with temporal processing of durations in the range of seconds but not milliseconds. \u003cem\u003eActa Psychologica\u003c/em\u003e, \u003cem\u003e137\u003c/em\u003e(1), 127\u0026ndash;133. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.actpsy.2011.03.010\u003c/span\u003e\u003cspan address=\"10.1016/j.actpsy.2011.03.010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRaudenbush, S. W., \u0026amp; Bryk, A. S. (2002). \u003cem\u003eHierarchical linear models: Applications and data analysis methods\u003c/em\u003e (2nd ed.). Sage.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evan Rompay, T. J. L., Galetzka, M., Pruyn, A. T. H., \u0026amp; Garcia, J. M. (2008). Human and spatial dimensions of retail density: Revisiting the role of perceived control. \u003cem\u003ePsychology \u0026amp; Marketing\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e(4), 319\u0026ndash;335. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/mar.20211\u003c/span\u003e\u003cspan address=\"10.1002/mar.20211\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSackett, A. M., Meyvis, T., Nelson, L. D., Converse, B. A., \u0026amp; Sackett, A. L. (2010). You\u0026rsquo;re having fun when time flies: The hedonic consequences of subjective time progression. \u003cem\u003ePsychological Science\u003c/em\u003e, \u003cem\u003e21\u003c/em\u003e(1), 111\u0026ndash;117.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSadeghi, S., Daziano, R., Yoon, S. Y., \u0026amp; Anderson, A. K. (2023a). Affective experience in a virtual crowd regulates perceived travel time. \u003cem\u003eVirtual Reality\u003c/em\u003e, \u003cem\u003e27\u003c/em\u003e(2), 1051\u0026ndash;1061. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10055-022-00713-8\u003c/span\u003e\u003cspan address=\"10.1007/s10055-022-00713-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSadeghi, S., Daziano, R., Yoon, S. Y., \u0026amp; Anderson, A. K. (2023b). Crowding and Perceived Travel Time in Public Transit: Virtual Reality Compared With Stated Choice Surveys. \u003cem\u003eTransportation Research Record\u003c/em\u003e, \u003cem\u003e2677\u003c/em\u003e(5), 296\u0026ndash;307. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/03611981221130346\u003c/span\u003e\u003cspan address=\"10.1177/03611981221130346\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchmidt, D. E., \u0026amp; Keating, J. P. (1979). Human crowding and personal control: An integration of the research. \u003cem\u003ePsychological Bulletin\u003c/em\u003e, \u003cem\u003e86\u003c/em\u003e(4), 680\u0026ndash;700.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShimokawa, K., \u0026amp; Sugimori, E. (2019). Using Virtual Reality to Study Subjective Time in Crowded Versus Uncrowded Environments. \u003cem\u003ePerceptual and Motor Skills\u003c/em\u003e, \u003cem\u003e126\u003c/em\u003e(5), 737\u0026ndash;752. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/0031512519857869\u003c/span\u003e\u003cspan address=\"10.1177/0031512519857869\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSimonet, D. V., Miller, K. E., Luu, S., Askew, K. L., Narayan, A., Cunningham, S., Pena, C., Attar, A., Fonseca, R., \u0026amp; Kobezak, H. M. (2019). Who is empowered? Relative importance of dispositional and situational sources to psychological empowerment. \u003cem\u003eEuropean Journal of Work and Organizational Psychology\u003c/em\u003e, \u003cem\u003e28\u003c/em\u003e(4), 536\u0026ndash;554. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/1359432X.2019.1624532\u003c/span\u003e\u003cspan address=\"10.1080/1359432X.2019.1624532\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStokols, D. (1972). On the distinction between density and crowding: Some implications for future research. \u003cem\u003ePsychological Review\u003c/em\u003e, \u003cem\u003e79\u003c/em\u003e(3), 275\u0026ndash;277. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1037/h0032706\u003c/span\u003e\u003cspan address=\"10.1037/h0032706\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTamm, M., Uusberg, A., Allik, J., \u0026amp; Kreegipuu, K. (2014). Emotional modulation of attention affects time perception: Evidence from event-related potentials. \u003cem\u003eActa Psychologica\u003c/em\u003e, \u003cem\u003e149\u003c/em\u003e, 148\u0026ndash;156. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.actpsy.2014.02.008\u003c/span\u003e\u003cspan address=\"10.1016/j.actpsy.2014.02.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTonietto, G. N., VanEpps, E. M., Malkoc, S. A., \u0026amp; Maglio, S. J. (2022). Time Will Fly During Future Fun (But Drag Until Then). \u003cem\u003eJournal of Consumer Psychology\u003c/em\u003e, \u003cem\u003e32\u003c/em\u003e(3), 475\u0026ndash;483. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/jcpy.1247\u003c/span\u003e\u003cspan address=\"10.1002/jcpy.1247\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUnited Nations. (2019). \u003cem\u003eWorld Urbanization Prospects: The 2018 Revision (ST/ESA/SER.A/420)\u003c/em\u003e. United Nations, Department of Economic and Social Affairs.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVallet, W., Laflamme, V., \u0026amp; Grondin, S. (2019). An EEG investigation of the mechanisms involved in the perception of time when expecting emotional stimuli. \u003cem\u003eBiological Psychology\u003c/em\u003e, \u003cem\u003e148\u003c/em\u003e, 107777. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.biopsycho.2019.107777\u003c/span\u003e\u003cspan address=\"10.1016/j.biopsycho.2019.107777\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVaske, J. J., \u0026amp; Shelby, L. B. (2008). Crowding as a Descriptive Indicator and an Evaluative Standard: Results from 30 Years of Research. \u003cem\u003eLeisure Sciences\u003c/em\u003e, \u003cem\u003e30\u003c/em\u003e(2), 111\u0026ndash;126. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/01490400701881341\u003c/span\u003e\u003cspan address=\"10.1080/01490400701881341\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWalsh, V. (2003a). A theory of magnitude: Common cortical metrics of time, space and quantity. \u003cem\u003eTrends in Cognitive Sciences\u003c/em\u003e, \u003cem\u003e7\u003c/em\u003e(11), 483\u0026ndash;488. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.tics.2003.09.002\u003c/span\u003e\u003cspan address=\"10.1016/j.tics.2003.09.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWalsh, V. (2003b). Time: The back-door of perception. \u003cem\u003eTrends in Cognitive Sciences\u003c/em\u003e, \u003cem\u003e7\u003c/em\u003e(8), 335\u0026ndash;338.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWardman, M., \u0026amp; Whelan, G. (2011). Twenty Years of Rail Crowding Valuation Studies: Evidence and Lessons from British Experience. \u003cem\u003eTransport Reviews\u003c/em\u003e, \u003cem\u003e31\u003c/em\u003e(3), 379\u0026ndash;398. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/01441647.2010.519127\u003c/span\u003e\u003cspan address=\"10.1080/01441647.2010.519127\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWiener, M., Kliot, D., Turkeltaub, P. E., Hamilton, R. H., Wolk, D. A., \u0026amp; Coslett, H. B. (2012). Parietal influence on temporal encoding indexed by simultaneous transcranial magnetic stimulation and electroencephalography. \u003cem\u003eJournal of Neuroscience\u003c/em\u003e, \u003cem\u003e32\u003c/em\u003e(35), 12258\u0026ndash;12267. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1523/JNEUROSCI.2511-12.2012\u003c/span\u003e\u003cspan address=\"10.1523/JNEUROSCI.2511-12.2012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXuan, B., Chen, X. C., He, S., \u0026amp; Zhang, D. R. (2009). Numerical magnitude modulates temporal comparison: An ERP study. \u003cem\u003eBrain Research\u003c/em\u003e, \u003cem\u003e1269\u003c/em\u003e, 135\u0026ndash;142.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXuan, B., Zhang, D., He, S., \u0026amp; Chen, X. (2007). Larger stimuli are judged to last longer. \u003cem\u003eJournal Of Visualization\u003c/em\u003e, \u003cem\u003e7\u003c/em\u003e(10), 1\u0026ndash;5. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1167/7.10.2\u003c/span\u003e\u003cspan address=\"10.1167/7.10.2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYin, H. Z., Bai, Y. L., Liu, S. G., \u0026amp; Li, D. (2021). The influence of motivation direction and intensity on time perception in positive and negative emotions. \u003cem\u003eJournal of Psychological Science\u003c/em\u003e, \u003cem\u003e44\u003c/em\u003e(6), 1313\u0026ndash;1321.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYin, H. Z., Cui, X. B., Bai, Y. L., Cao, G., Zhang, L., Ou, Y. H., Li, D., \u0026amp; Liu, J. P. (2021). The Effects of Angry Expressions and Fearful Expressions on Duration Perception: An ERP Study. \u003cem\u003eFrontiers in Psychology\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3389/fpsyg.2021.570497\u003c/span\u003e\u003cspan address=\"10.3389/fpsyg.2021.570497\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.frontiersin.org/articles/\u003c/span\u003e\u003cspan address=\"https://www.frontiersin.org/articles/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYin, H. Z., Zhang, L., Liu, P. Y., \u0026amp; Li, D. (2023). How the dimension of negative emotional motivation influences time perception: The mediating role of attention control and attention bias. Acta Psychologica Sinica, 55(12), 1917. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3724/SP.J.1041.2023.01917\u003c/span\u003e\u003cspan address=\"10.3724/SP.J.1041.2023.01917\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZakay, D., \u0026amp; Block, R. A. (1997). Temporal Cognition. \u003cem\u003eCurrent Directions in Psychological Science\u003c/em\u003e, \u003cem\u003e6\u003c/em\u003e(1), 12\u0026ndash;16.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"time perception, crowding, automatic timing, cognitively controlled timing, withdrawal motivation, cross-dimension interference","lastPublishedDoi":"10.21203/rs.3.rs-4008302/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4008302/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCrowding has been found to slow down subjective time. This study aimed to investigate the modulation of crowding on time perception after excluding valence and arousal. In the pre-experiment, three types of crowding pictures (non-crowding, crowded objects, and crowded people) were screened, and the valence and arousal of the pictures were controlled. No significant difference in valence and arousal was found among the three types of pictures. Participants conducted a temporal bisection task with different types of pictures on sub-second (Experiment 1) and supra-second (Experiment 2) timescales. The results showed that crowding modulated time perception on the supra-second timescale rather than the sub-second. Linear mixing models and dominance analysis both confirmed that crowding, but not valence and arousal, can effectively predict subjective time on supra-second timescales. The results suggest that, excluding valence and arousal, crowding can modulate cognitively controlled timing on supra-second timescales. Both withdrawal motivation and cross-dimensional interference have been implicated in the modulation of crowding on time and need to be disentangled in future work.\u003c/p\u003e","manuscriptTitle":"Crowding modulates time perception while controlling for valence and arousal","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-07 19:29:58","doi":"10.21203/rs.3.rs-4008302/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9983b016-0fbd-42fb-b21d-73141f662620","owner":[],"postedDate":"March 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-03-27T13:45:33+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-07 19:29:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4008302","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4008302","identity":"rs-4008302","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}