Global–local processing and the Ebbinghaus illusion: Group and individual differences in young and older adults

Abstract

The Ebbinghaus illusion is a size illusion, in which a central circle appears larger or smaller depending on the size of surrounding circles. This illusion is widely used to study group-level differences in attentional processing, with the proposal that a local-processing bias reduces susceptibility to the Ebbinghaus illusion. One hundred and forty-five participants (87 young; 58 older) were included in the analyses. Participants completed the Navon hierarchical-figures task, to measure the global–local processing bias, and the Ebbinghaus illusion task, to measure susceptibility to the illusion. First, we investigated whether a strong local-processing bias reduced susceptibility to the Ebbinghaus illusion. Our findings did not support this proposal. At the group level, older participants demonstrated worse performance for global processing compared to young participants, but there were no age-group differences in susceptibility to the illusion. At the individual level, the young and older participants with the stronger local-processing bias were the participants with greater susceptibility to the illusion. Second, we investigated whether longer inspection times during the Ebbinghaus illusion task reduced susceptibility to the illusion. Our findings did support this proposal. At the group level, there were no age-group differences in either inspection time or susceptibility to the Ebbinghaus illusion. At the individual level, we replicated previous findings—the participants with the longer inspection times were the participants with the least susceptibility to the illusion. We discuss alternative cognitive mechanisms that may account for the Ebbinghaus illusion and their relevance to age-related changes and individual differences in visual attention.

Keywords

Ebbinghaus illusion global–local processing ageing group and individual differences young and older adults

Introduction

Our perception of reality is derived from what we see, but what we perceive does not always accurately represent the physical reality of the external environment. Visual illusions are one of these examples where perception diverges from physical reality (Gregory, 2009). Perception of visual illusions can occur at various stages of processing (Coren & Girgus, 1978); for example, at the sensory processing stage, where light input is distorted by optical structures or optical–neural interactions, or at the cognitive processing stage, where interpretation of incoming information can be influenced by visual attentional mechanisms and cognitive strategies. Visual illusions can serve as powerful tools for understanding the visual system.

The Ebbinghaus illusion (also known as the Titchener illusion) is a classic visual illusion that distorts size perception. In this illusion, a central circle is perceived to be larger compared to its physical size when surrounded by smaller contextual circles, or smaller compared to its physical size when surrounded by larger contextual circles (Ebbinghaus, 1902; Titchener, 1901). The Ebbinghaus illusion is proposed to be influenced by visual attentional mechanisms, such as global–local processing (e.g., Happé, 1996). Global–local processing involves directing attention globally (i.e., to the overall visual scene) or locally (i.e., to the finer details within the visual scene). Individual differences in preference for global processing versus local processing have been observed, leading to the identification of two processing styles: (1) a global-processing bias, in which individuals attend globally; and (2) a local-processing bias, in which individuals attend locally (see Happé, 1999; Happé & Frith, 2006).

Happé (1996) was the first to propose that a local-processing bias may reduce susceptibility to the Ebbinghaus illusion. In this study, children on the autistic spectrum—who are believed to show a local-processing bias due to weak central coherence (Shah & Frith, 1983, 1993)—were reported to demonstrate reduced susceptibility to the Ebbinghaus illusion compared to neurotypically developing children. These findings of reduced susceptibility to the Ebbinghaus illusion led to the development of the visual attentional integration theory. According to this theory, in neurotypical individuals, the Ebbinghaus illusion arises when the central circle and the contextual circles are integrated and processed as a global configuration. Individuals with a local-processing bias will have reduced susceptibility to the Ebbinghaus illusion because of a weakening in the strength of this visual attentional integration, leading to processing of the central circle separately from the contextual circles.

Ebbinghaus Illusion as a Measure of Group-Level Differences in the Global–Local Processing Bias

The Ebbinghaus illusion has been used extensively to measure group-level differences in global–local processing, with differences in susceptibility to the Ebbinghaus illusion interpreted as differences in a bias for either global processing or local processing. One of the earliest of these studies was conducted by Phillips et al. (2004), who developed a computerised paradigm for the Ebbinghaus illusion and used this paradigm to measure sex differences in the global–local processing bias. In their classic Ebbinghaus illusion setup, stimuli were positioned side-by-side, with one central circle surrounded by smaller contextual circles, and the other central circle surrounded by larger contextual circles (see Figure 1A). A forced-choice response was used, in which participants were asked to decide whether the larger central circle was on the left or on the right of the presentation. Phillips et al. reported that male participants were more accurate at this task compared to female participants. These results were interpreted to mean that males demonstrated a stronger local-processing bias compared to females, consequently resulting in their reduced susceptibility to the Ebbinghaus illusion. Phillips et al. suggested that their findings regarding sex differences in susceptibility to the Ebbinghaus illusion were in line with previous studies (e.g., Baron-Cohen et al., 2003; see Voyer et al., 1995, for a systematic review) that had used different experiment paradigms to indicate a local-processing bias in males compared to females. Phillips et al. concluded that the Ebbinghaus illusion paradigm can serve as a specific and sensitive measure to investigate group-level differences in the global–local processing bias.

Figure 1.

Examples of stimuli for the Ebbinghaus illusion task and the hierarchical-figures task.

Following the study by Phillips et al. (2004), numerous studies have investigated Happé's (1996) visual attentional integration theory by using the Ebbinghaus illusion to measure group-level differences in the global–local processing bias across cultural, political, and clinical contexts. Group-level differences in the global–local processing bias have been demonstrated between: Eastern and Western cultures (e.g., Doherty et al., 2008; Imada et al., 2013; Köster et al., 2018; Mok & Morris, 2012; Schulze et al., 2022); remote and urban cultures (e.g., Caparos et al., 2012; Caparos & Boissin, 2024; Davidoff et al., 2008; de Fockert et al., 2007; Mavridis et al., 2020); left-oriented and right-oriented political groups (e.g., Caparos et al., 2015); gamers and nongamers (e.g., Kütük et al., 2023); and clinical and nonclinical groups (e.g., Horton & Silverstein, 2011; Joseph et al., 2013; Mittal et al., 2015; Silverstein et al., 2013). The Ebbinghaus illusion has also been used to investigate the developmental trajectory of the global-local processing bias in children (e.g., Doherty et al., 2010).

What remains relatively underexplored is the investigation of group-level differences of the bias in young adults and older adults. To the best of our knowledge, only five studies (Coren & Porac, 1978; Eisner & Schaie, 1971; Grzeczkowski et al., 2017; Mazuz et al., 2024; Wapner et al., 1960; see Table 1 for methodological differences in these studies) have examined the Ebbinghaus illusion in older adults. Of these studies, only Wapner et al. and Mazuz et al. directly investigated age-group differences (between young adults and older adults) in susceptibility to the Ebbinghaus illusion. And, both Wapner et al. and Mazuz et al. reported reduced susceptibility to the Ebbinghaus illusion in older adults compared to young adults. Although these studies did not interpret their findings in terms of group-level differences in the global–local processing bias, the finding of an age-group difference in susceptibility to the Ebbinghaus illusion is in line with studies using various other experiment paradigms to demonstrate that older adults have a local-processing bias (see Insch et al., 2012; Lux et al., 2008; Oken et al., 1999; Slavin et al., 2002; also see Chen et al., 2024).

Table 1.

Methodological differences in studies of the Ebbinghaus illusion with young and older adults.

	Study^a	ParticipantsN/Age		Participant inclusion criteria (before screening for outliers)	Stimulus presentation	Response task	Inclusion of inspection time	Stimulus presentation duration	ITI/fixation	No. of trials	Dependent variable(s)
	Study^a	Young	Older		Stimulus presentation	Response task	Inclusion of inspection time	Stimulus presentation duration	ITI/fixation	No. of trials	Dependent variable(s)
1	Wapner et al. (1960)	N = 20/ 20–29 years	N = 20/ 65–80 years	×	Two experiment trial stimuli side-by-side, each arranged in a circular configuration.	Judged whether central circle on right was larger, equal, or smaller than central circle on left.	×	NR	NR	34	Point of subjective equality.
2	Eisner and Schaie (1971)	N = 135/ 55–75 years		×	Two experiment trial stimuli side-by-side, each arranged in a circular configuration.	Judged whether central circle on right was larger, equal, or smaller than central circle on left.	×	NR	NR	34	Point of subjective equality.
3	Coren and Porac (1978)	N = 688/ 5–75 years		×	One experiment trial stimulus, arranged in a circular configuration: “overestimated” condition (with smaller contextual circles) or “underestimated” condition (with larger contextual circles).	Judged size of central circle, by selecting circle which appeared to be equal in size from graded series of circles.	×	NR	NR	NR	Size difference between central circle and circle selected.
4	Grzeczkowski et al. (2017)	N = 144/ 6–81 years (Md = 22)		×	Two experiment trial stimuli side-by-side, each arranged in a circular configuration.	Adjusted size of adjustable central circle on right to size of reference central circle on left.	×	No time restriction	NA	2	Size difference between reference central circle and circle adjusted.
5	Mazuz et al. (2024)	N = 80/ 20–39 years	N = 80/ 61–85 years	×	Two experiment trial stimuli side-by-side, each arranged in a circular configuration.	Decided which of two central circles looked larger.	✓	1,000 ms	1,000 ms fixation	141	Constant error; Just noticeable difference.
6	Present study	N = 87/ 18–30 years (M = 21.49)	N = 58/ 57–88 years (M = 71.72)	Normal/corrected-to-normal vision. No history of self-reported neurological impairments. MoCA: No evidence of cognitive impairment for older participants. 80% accuracy on catch trials.	Two experiment trial stimuli or two catch trial stimuli side-by-side, each arranged in a square configuration.	Decided which of two central circles looked larger.	✓	Until response: maximum 5,000 ms	200 ms ITI	96 (80 experiment trials, 16 catch trials)	Point of subjective equality.

Note. The studies are listed in chronological order (publication year).

NR = not reported; NA = not applicable; Md = median; M = mean; MoCA = Montreal Cognitive Assessment; ITI = intertrial interval.

In Studies 1, 5, and 6, group-level differences in young and older adults’ susceptibility to the Ebbinghaus illusion were investigated. In Studies 2, 3, and 4, older adults were included as participants, but their performance was not directly compared to the performance of young participants.

Ebbinghaus Illusion as a Measure of Individual-Level Differences in Global–Local Processing

While Happé's (1999) visual attentional integration theory has been widely applied for measuring group-level differences in the global–local processing bias, a critical gap exists in the literature concerning whether this theory can account for individual-level differences in the bias. What also remains to be investigated is whether measuring the global–local processing bias using an experiment paradigm other than the Ebbinghaus illusion (e.g., a hierarchical-figures paradigm) will provide support for the finding that individuals with the stronger local-processing bias (as compared with individuals with a stronger global-processing bias) are less susceptible to the Ebbinghaus illusion. Navon's (1977) hierarchical-figures paradigm is another widely used experiment paradigm for measuring the global–local processing bias. In this paradigm, a hierarchical figure comprises a large stimulus (i.e., the global-level stimulus) constructed from smaller stimuli (i.e., the local-level stimuli) (see Figure 1B). To the best of our knowledge, only two studies (Caparos et al., 2012, 2015) have employed the hierarchical-figures paradigm and the Ebbinghaus illusion paradigm together to examine group-level differences in the global–local processing bias, and only Caparos et al. (2012) extended this investigation to include statistical analyses of individual-level differences.

Caparos et al. (2012) examined the global–local processing bias¹ across four cultural groups: Japanese, British, traditional Himba (i.e., seminomadic Namibians), and urbanised Himba. For the hierarchical-figures paradigm, the group-level findings revealed that traditional Himba participants demonstrated the strongest local-processing bias (followed by urbanised Himba and British participants), and that Japanese participants demonstrated the strongest global-processing bias. For the Ebbinghaus illusion paradigm, the group-level findings revealed that traditional Himba participants were the least susceptible to the Ebbinghaus illusion (followed by urbanised Himba and British participants), and that Japanese participants were the most susceptible to the Ebbinghaus illusion. These group-level findings were consistent with Happé's (1996) visual attentional integration theory—the participant groups with a local-processing bias (e.g., traditional Himba participants) were less susceptible to the Ebbinghaus illusion, and the participant groups with a global-processing bias (e.g., Japanese participants) were more susceptible to the Ebbinghaus illusion. Importantly, the individual-level correlations revealed that performance on the hierarchical-figures paradigm was not significantly correlated with performance on the Ebbinghaus illusion paradigm, which suggests that the individuals with the stronger local-processing bias were not necessarily the individuals who were less susceptible to the Ebbinghaus illusion.

These individual-level findings reported by Caparos et al. (2012) have been used to challenge the validity of Happé's (1996) visual attentional integration theory. While Happé's original research focused on group-level differences, some researchers (e.g., Bressan & Kramer, 2021) have suggested that the theory should be capable of being extended to individual-level differences. Bressan and Kramer argued that the inconsistencies between the group-level and individual-level findings in the Caparos et al. study indicate that the previously reported group-level differences in susceptibility to the Ebbinghaus illusion may have been driven by factors other than the global–local processing bias. One such factor is response effort. Participants may expend greater effort when making size judgments, by taking a longer time to inspect the Ebbinghaus illusion. In their study, Bressan and Kramer found that the individuals who spent a longer time inspecting the Ebbinghaus illusion were the individuals who were less susceptible to the Ebbinghaus illusion. They pointed out that inspection time has not been controlled for or even considered to be important in most previous studies that have used the Ebbinghaus illusion paradigm to examine group-level differences in the global–local processing bias, including in the study by Caparos et al. (2012). They conjectured that the traditional Himba participants may have spent a longer time inspecting the Ebbinghaus illusion compared to the other groups of participants, resulting in the observed reduction in susceptibility to the Ebbinghaus illusion among traditional Himba participants.²

Present Study

In the present study, we used Phillips et al.'s (2004) Ebbinghaus illusion paradigm to measure susceptibility to the Ebbinghaus illusion, and Navon's (1977) hierarchical-figures paradigm to measure the global–local processing bias. For the hierarchical-figures paradigm, we used a divided-attention task in which participants were instructed to attend simultaneously to the global level and to the local level of the hierarchical figure, and to respond to a target. The target could appear either at the global level or at the local level. This setup allowed participants to allocate greater attention to their preferred processing level, thus reflecting their predisposed global–local processing bias.

Our first research question concerned the relationship between the global–local processing bias (as measured by the hierarchical-figures paradigm) and susceptibility to the Ebbinghaus illusion at the group level, between young participants and older participants. Previous studies using the hierarchical-figures paradigm (see Insch et al., 2012; Lux et al., 2008; Oken et al., 1999; Slavin et al., 2002; also see Chen et al., 2024) have reported that older adults demonstrate a local-processing bias compared to young adults. Our aim was to replicate these findings of an age-related local-processing bias, and to investigate whether this local-processing bias on the hierarchical-figures paradigm was associated with reduced susceptibility to the Ebbinghaus illusion in older participants compared to young participants.

Our second research question concerned the relationship between the global–local processing bias (as measured by the hierarchical-figures paradigm) and susceptibility to the Ebbinghaus illusion at the individual level for young participants and older participants. Our aim was to investigate whether the individuals with a stronger local-processing bias on the hierarchical-figures paradigm would be the individuals with less susceptibility to the Ebbinghaus illusion.

Our third research question concerned the relationship between susceptibility to the Ebbinghaus illusion and inspection time of the illusion at both the group and individual level for young participants and older participants. Building on the study by Bressan and Kramer (2021), we investigated whether a longer inspection time of the Ebbinghaus illusion would be associated with reduced susceptibility to the Ebbinghaus illusion.

Methods

Participants

A total of 158 participants were recruited for this study, and 145 participants (87 young participants, 58 older participants) were included in the final statistical analyses. All participants self-reported being of 100% European ancestry. Young participants were students from the Australian National University and the University of Oxford. Older participants were recruited from the University of the Third Age and the broader community in Canberra. Participants were excluded from statistical analyses if they did not meet the following six inclusion criteria:

Normal or corrected-to-normal vision, as indicated by in-laboratory testing with a Snellen chart (Snellen, 1868).

No history of self-reported neurological impairments.

No evidence of cognitive impairment as assessed by the Montreal Cognitive Assessment (Nasreddine, 1996), with a score of 24 or greater indicating intact cognitive functioning (see Pugh et al., 2018; Thomann et al., 2020). Including older adults with mild cognitive impairment in the study may have increased the likelihood of observing reduced susceptibility to the Ebbinghaus illusion in the older participant group, as indicated by some researchers (e.g., Álvarez-San Millán et al., 2022) who found that older adults with mild cognitive impairment demonstrated a stronger local-processing bias compared to cognitively healthy older adults.³

Overall accuracy of 80% or greater on the target-absent trials for the hierarchical-figures task. No response was required on these trials, as no target was presented (see Apparatus, Stimuli, and Procedure). A response to a target-absent trial could have indicated that the participant either did not discriminate targets from distractors or responded quickly but with low accuracy.

Overall accuracy of 80% or greater on the catch trials for the Ebbinghaus illusion task. The stimulus design of the catch trials accentuated the perceptual size difference between the two central circles, so that the physically larger central circle was perceived as notably larger than the physically smaller central circle (see Figure 1A, right panel). An incorrect response to a catch trial indicated that the participant either did not understand the task instructions or did not comply with the instruction to choose the visually larger central circle

The point of subjective equality (PSE) score for the Ebbinghaus illusion task (computed to measure susceptibility to the Ebbinghaus illusion, see Statistical Analysis Plan) did not exceed three standard deviations away from the mean for each of the two age groups.

No exclusions were required for criteria 1, 2, or 3. Two older participants were excluded for criterion 4, six young participants and three older participants were excluded for criterion 5, and one young participant and one older participant were excluded for criterion 6. See Table 2 for the young and older participants’ demographic information. Power analyses using G*Power (version 3.1) indicated that a minimum of 63 young participants and 43 older participants was required to detect a significant group-level difference in an independent samples t-test (d = 0.50; power = 80%; α = .05; sample size ratio = 1.50). All participants provided written consent prior to participation in the study and received monetary compensation (or course credit for eligible young participants). The study was approved by the Human Research Ethics Committee at the Australian National University (Protocol: 2013/605 and Protocol: 2019/795) and the University of Oxford (Protocol: 2010/87). A subset of the participants in the present study was previously reported in Chen et al. (2024).

Table 2.

Demographic information for young and older participants included in the statistical analyses.

Demographic information	Young participants	Older participants
N	87	58
Female (n, %)	47, 54.02%	38, 65.52%
Male (n, %)	40, 45.98%	20, 34.48%
Age
Mean	21.49	71.72
SD	3.01	7.32
Range	18–30	57–88
Highest level of education (n, %)
Secondary	—	4, 6.90%
College	62, 71.26%	7, 12.07%
Undergraduate	11, 12.64%	29, 50.00%
Masters	10, 11.49%	7, 12.07%
Doctoral	4, 4.60%	7, 12.07%
Other	—	4, 6.90%
Experimenter (n, %)^a
1	47, 54.02%	—
2	16, 18.39%	25, 43.10%
3	24, 27.59%	33, 56.90%

Data collection was conducted across two locations by three experimenters. Experimenter 1 recruited young participants studying at the University of Oxford. Experimenters 2 and 3 recruited young participants studying at the Australian National University and older participants from the local Canberra community.

Apparatus, Stimuli, and Procedure

Participants were tested individually in a distraction-free room. The hierarchical-figures task was conducted first, followed by the Ebbinghaus illusion task. Both tasks were presented on a desktop monitor. A forehead-and-chin rest was used to maintain a constant eye-to-screen viewing distance for each participant. Reaction time (RT) and accuracy were recorded using a response pad for the hierarchical-figures task and a computer keyboard for the Ebbinghaus illusion task. See Table 3 for apparatus details.

Table 3.

Apparatus and experiment design for the hierarchical-figures task.

Apparatus and experiment design	Experimenter 1	Experimenter 2	Experimenter 3
Apparatus
Display size	17 inches	18 inches	27 inches
Resolution	1,024 × 768	1,280 × 1,024	2,560 × 1,440
Frequency (Hz)	75	85.26	60
Viewing distance (cm)	50	50	57
Hierarchical-figures task
Programming software	E-Prime 2.0	E-Prime 2.0	Inquisit 6.2.1
Response pad	Chronos PST-100430	Chronos PST-100430	Cedrus RB-844
Stimuli
Targets	H, T	S, T	S, T
Distractors	D, E, U, V	D, C, K, L, U, V	D, C, K, L, U, V
Global-target stimulus^a	H-E, H-D, T-V, T-U	S-K, S-V, T-C, T-U	S-K, S-V, T-C, T-U
Local-target stimulus^a	V-H, U-H, E-T, D-T	K-S, V-S, C-T, U-T	K-S, V-S, C-T, U-T
Target-absent stimulus^a	D-E, D-V, E-V, E-U, U-D, U-V, V-E, V-D	D-K, D-V, K-D, V-D, L-C, L-U, U-l, C-l	D-K, D-V, K-D, V-D, L-C, L-U, U-l, C-l
Presentation duration
Fixation cross (ms)	1,000	500	500
Hierarchical figure (ms)	150	150	150
Poststimulus mask (ms)	1500	1,000	1,000
Intertrial interval (ms)	—	1,000	1,000
No. of trials
Global-target figure	64	48	32
Local-target figure	64	48	32
Target-absent figure	128	96	64

Each pairing indicates the stimuli for one hierarchical figure, where the first letter indicates the global stimulus and the second letter indicates the local stimulus (e.g., H-E = a global “H” stimulus made up of local “E” stimuli).

Hierarchical-Figures Task

The hierarchical figures—large letters (size = 2.30° × 3.08°–3.90°) composed of seven to 14 small local letters (size = 0.40° × 0.50°)—were presented in black against a white background. There were two types of letters: targets (i.e., H, S, T) and distractors (i.e., D, C, E, K, L, U, V). See Table 3 for the full details of the letter stimuli. Within each hierarchical figure, a target was either presented (target-present hierarchical figure) or not presented (target-absent hierarchical figure). There were two types of target-present hierarchical figures: global-target figures (one target appeared at the global level and one distractor appeared at the local level) and local-target figures (one target appeared at the local level and one distractor appeared at the global level). The target-absent figures were made up of two different distractors (one distractor appeared at the global level and one distractor appeared at the local level). See Figure 1B for examples of the hierarchical figures, including global-target, local-target, and target-absent figures.

Participants were familiarised with the hierarchical figures to be used in the task before completing two practice blocks. Feedback about accuracy was provided in the practice blocks to ensure participants’ understanding of and compliance with the task instructions. In the experiment block, each trial began with a central fixation cross, followed by a hierarchical figure presented unilaterally either to the left visual field (LVF) or to the right visual field (RVF), and then two poststimulus masks were presented bilaterally. All trials were presented in a randomised order, with the hierarchical figure randomly presented either to the LVF or to the RVF in equal proportions. The medial edges of the hierarchical figures were positioned 0.50° to the left or to the right of the central fixation cross. Participants were instructed to focus on the central fixation cross and to respond to the target as quickly and as accurately as possible, by pressing a button on the response pad (with their right index finger) when they saw a target appear at either the global level or the local level. Participants were also instructed not to respond if a target did not appear at either the global level or the local level. Feedback about accuracy was not provided in the experiment block. See Table 3 for details of the hierarchical-figures task design.

The Ebbinghaus Illusion Task

The Ebbinghaus illusion task used in the present study was developed by Phillips et al. (2004). The Ebbinghaus illusion task comprised 96 trials, including 80 experiment trials and 16 catch trials. The stimuli consisted of two separate 3 × 3 arrays of nine solid black circles against a white background. The stimuli in each experiment trial featured two central circles, each of which was surrounded by eight contextual circles. One of the two central circles had a fixed diameter of 100 pixels (one pixel subtended 0.034° for Experimenter 1, 0.028° for Experimenter 2, and 0.023° for Experimenter 3), while the other central circle was either larger in size (with five possible larger diameters = 102, 106, 110, 114, 118 pixels) or smaller in size (with five possible smaller diameters = 82, 86, 90, 94, 98 pixels). An additional feature of the experiment trial stimuli was that the larger of the two central circles was surrounded by larger contextual circles (diameter = 125 pixels), and the smaller of the two central circles was surrounded by smaller contextual circles (diameter = 50 pixels). These features of the experimental trial stimuli yielded 10 possible percentage size differences between the central circle surrounded by the larger contextual circles and the central circle surrounded by the smaller contextual circles (i.e., $(\frac{Size of central circle with larger contextual circles}{Size of central circle with smaller contextual circles}) \times 100 %$ ): 102.00% (102 pixels/100 pixels), 102.04% (100 pixels/98 pixels), 106.00% (106 pixels/100 pixels), 106.38% (100 pixels/94 pixels), 110.00% (110 pixels/100 pixels), 111.11% (100 pixels/90 pixels), 114.00% (114 pixels/100 pixels), 116.28% (100 pixels/86 pixels), 118.00% (118 pixels/100 pixels), and 121.95% (100 pixels/82 pixels). This configuration of the experiment trial stimuli reduced the perceived size difference between the two central circles. Specifically, the larger of the two central circles appeared smaller than its physical size because it was surrounded by contextual circles larger than itself, whereas the smaller of the two central circles appeared larger than its physical size because it was surrounded by contextual circles smaller than itself.

The catch trial stimuli also featured two central circles (surrounded by eight contextual circles). One of the two central circles had a fixed diameter of 100 pixels, while the other central circle was either 2 pixels larger (diameter = 102 pixels) or 2 pixels smaller (diameter = 98 pixels). In contrast to the experiment trial stimuli, for the catch trial stimuli, the larger of the two central circles was surrounded by smaller contextual circles (diameter = 50 pixels), and the smaller of the two central circles was surrounded by larger contextual circles (diameter = 125 pixels). This configuration of the catch trial stimuli accentuated the perceived size difference between the two central circles. Specifically, the larger of the two central circles appeared larger than its physical size because it was surrounded by contextual circles smaller than itself, whereas the smaller of the two central circles appeared smaller than its physical size because it was surrounded by contextual circles larger than itself. See Figure 1A for examples of the Ebbinghaus illusion stimuli for experiment trials and catch trials.

Participants were familiarised with one example of the Ebbinghaus illusion stimulus printed on hardcopy, before beginning the Ebbinghaus illusion task on the computer. There was no computerised practice block. Each trial began with the Ebbinghaus illusion stimuli presented on the screen for up to 5,000 ms or until a response was made, followed by a 200 ms intertrial interval. All trials were presented in a randomised order across participants. Participants were instructed to ignore the contextual circles, and to decide which of the two central circles looked larger. They were informed that the two central circles would never be the same size, and if they were not sure which of the two central circles looked larger, they should take a guess. Participants were instructed to respond as quickly and as accurately as possible, and to press the left arrow key (with their right index finger) to indicate the left central circle looked larger or to press the right arrow key (with their right middle finger) to indicate the right central circle looked larger. Feedback about accuracy was not provided in the Ebbinghaus illusion task.

Statistical Analysis Plan

Our first research question concerned the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion at the group level. This first question was addressed with two group-level analyses: the first to examine whether there was a local-processing bias in the hierarchical-figures task in older participants compared to young participants (see Part 1 below); the second to examine age-group differences in susceptibility to the Ebbinghaus illusion (see Part 2 below). Our second research question concerned the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion at the individual level. This second question was addressed with an individual-level analysis between the global–local processing bias in the hierarchical-figures task and susceptibility to the Ebbinghaus illusion (see Part 3 below). Our third research question concerned the relationship between susceptibility to the Ebbinghaus illusion and inspection time of the illusion at both the group level and the individual level. This third question was addressed with a group-level analysis (see Part 2 below) and with an individual-level analysis (see Part 3 below) for susceptibility to the Ebbinghaus illusion and inspection time of the illusion. The statistical analyses comprised three parts.

Part 1, “Group-level age-related differences for the global–local processing bias in the hierarchical-figures task,” was a group-level analysis that examined whether there was a local-processing bias in older participants compared to young participants. This bias would be indicated by performance differences between young participants and older participants for the local-target figures compared to the global-target figures in the hierarchical-figures task (see Insch et al., 2012; Lux et al., 2008; Oken et al., 1999; Slavin et al., 2002; also see Chen et al., 2024). Linear mixed-effects models were performed. See Table 4 for details of the setup of the linear mixed-effects model in Part 1.

Table 4.

Setup of the linear mixed-effects models for the group-level analyses of the hierarchical-figures task and the Ebbinghaus illusion task.

Setup	Part 1. Hierarchical-figures task	Part 2. Ebbinghaus illusion task
Dependent variable(s)	Reaction time (ms): for each correct trial in the hierarchical-figures task for each participant	Point of subjective equality (PSE): threshold of percentage size difference at which participants perceived the central circle surrounded by larger contextual circles and the central circle surrounded by smaller contextual circles to be of the same sizeInspection time (ms): average inspection time of all correct and incorrect responses for the experiment trials (not including catch trials)
Independent variable(s)	Age group (young, older)Level (global, local)Visual field (LVF, RVF)	Age group (young, older)
Random intercept(s)	Experimenter Participant	Experimenter
Random slopes^a	Level (global, local) Visual field (LVF, RVF)	NA

Note. Age group (young, older), level (global, local), and visual field (LVF, RVF) were deviation coded to obtain an ANOVA-style interpretation of the main effects.

LVF = left visual field; RVF = right visual field; NA = not applicable; ANOVA = analysis of variance.

For Part 1, the two within-subjects predictors—level (global, local) and visual field (LVF, RVF)— were entered into random slopes to capture dependencies in the repeated-measures design (Barr, 2013).

Part 2, “Group-level age-related differences for susceptibility to the Ebbinghaus illusion and for inspection time of the Ebbinghaus illusion,” was a group-level analysis that examined age-group differences (between young and older participants) in susceptibility to the Ebbinghaus illusion. Susceptibility to the Ebbinghaus illusion was measured by the PSE and the duration of time spent inspecting the Ebbinghaus illusion (hereafter referred to as “inspection time”). The PSE was calculated as the threshold of percentage size difference at which participants perceived the central circle surrounded by the larger contextual circles and the central circle surrounded by the smaller contextual circles to be of the same size (see Caparos et al., 2012). Higher PSE scores indicated greater susceptibility to the Ebbinghaus illusion, whereas lower PSE scores indicated less susceptibility to the Ebbinghaus illusion. Linear mixed-effects models were performed, with additional Welch's two-sample t-tests. See Table 4 for details of the setup of the linear mixed-effects models in Part 2.

Part 3, “Individual-level correlations for the global–local processing bias, susceptibility to the Ebbinghaus illusion and inspection time of the Ebbinghaus illusion,” was an individual-level analysis that examined individual-level differences in the relationship between the global–local processing bias, susceptibility to the Ebbinghaus illusion and inspection time of the illusion. The global–local index was computed as a measure of the within-individual global–local processing bias in the hierarchical-figures task. This index was calculated as the difference in average RT (ms) between the correct responses to global-target figures compared to local-target figures for each participant. Higher scores on the global–local index indicated a higher degree of within-individual local-processing bias, whereas lower scores on the global–local index indicated a higher degree of within-individual global-processing bias. Pearson correlations were conducted for each of the following three pairs of variables: global–local index, PSE, and inspection time. Additional Pearson partial correlations, controlling for inspection time, were conducted for the analyses between the global–local index and PSE. Pearson correlations and Pearson partial correlations were conducted for: (1) age groups combined (i.e., young participants and older participants); (2) young participants only; and (3) older participants only. See Table 5 for details of the setup of the correlations. To estimate the internal consistency of the variables, Spearman–Brown-corrected reliability was computed for the global–local index, PSE, and inspection time.

Table 5.

Setup of the individual-level correlations for the global–local processing bias in the hierarchical-figures task, susceptibility to the Ebbinghaus illusion, and inspection time of the Ebbinghaus illusion.

Analysis	Type of correlation		Outliers excluded
Analysis	Pearson correlation	Pearson partial correlation (controls for inspection time)	Outliers excluded
1. Global–local index and PSE	✓	✓	Young = 4, Older = 4
2. Inspection time and PSE	✓	×	Young = 5, Older = 4
3. Global–local index and inspection time	✓	×	Young = 5, Older = 5

Note. PSE = point of subjective equality; ✓ = conducted; × = not conducted.

All statistical analyses were performed in R Studio (version 2024.09.1 + 394). The PSE values were computed using the “glm” function from the “stats” package. The response variable was the binary data for each trial, indicating whether the central circle surrounded by the larger contextual circles was selected (i.e., selected, not selected). The predictor variable was the percentage size difference between the central circle surrounded by the larger contextual circles and the central circle surrounded by the smaller contextual circles for each trial. The data was fitted with the psychometric function of $p = ϕ ((k - d) / σ)$ , where p is the probability of choosing the central circle surrounded by the larger contextual circles, which equals to 50% at the PSE; $ϕ (z)$ is the inverse cumulative distribution function for a standard normal distribution; k is the required threshold for deciding that the central circle surrounded by the larger contextual circles is the larger central circle; and d is the percentage size difference between the central circle surrounded by the larger contextual circles and the central circle surrounded by the smaller contextual circles, calculated as $(\frac{Size of central circle with larger contextual circles}{Size of central circle with smaller contextual circles}) \times 100 %$ ; and $σ$ is the standard deviation of the normally distributed noise (see Caparos et al., 2012).⁴ The linear mixed-effects models were performed using the “lmer” function from the “lme4” package. Type-III analyses of variance tables with Wald chi-square tests were obtained using the “Anova” function from the “car” package. Post hoc pairwise comparisons with Tukey-corrected p values were conducted using the “emmeans” function from the “emmeans” package. Effect size d_{mixed-effects} for post hoc pairwise comparisons was computed using the “eff_size” function from the “emmeans” package. The Welch's two-sample t-tests were performed using the “t.test” function from the “stats” package. Cohen's d for Welch's two-sample t-tests was calculated by dividing the mean difference by the pooled standard deviation. The Pearson correlations were performed using the “cor” function from the “stats” package. The Pearson partial correlations were performed using the “pcor.test” function from the “ppcor” package. The confidence intervals for Pearson partial correlations were computed using online codes available on Stack Overflow (Barradas, 2020). Spearman–Brown-corrected reliability was computed with 5,000 random splits using the “splithalf” function from the “splithalf” package. For the individual-level analyses between three pairs of variables (global–local index, PSE, inspection time), a separate linear regression model was fitted to screen for outliers for each of the two age groups, resulting in a total of six regression models. For each of the six regression models, outliers were identified using four diagnostic plots (standardised residuals plot, Q–Q plot, scale-location plot and Cook's distance plot) generated by the “plot” function in R. See Table 5 for details of outlier exclusions.

Results

Part 1. Group-Level Age-Related Differences for the Global–Local Processing Bias in the Hierarchical-Figures Task

There were significant main effects for level (χ²(1) = 70.63, p < .001) and age group (χ²(1) = 23.77, p < .001), and significant interactions for Level × Age Group (χ²(1) = 125.11, p < .001) and Level × Visual Field (χ²(1) = 89.72, p < .001). There was no significant main effect for visual field (p = .35), and no significant interactions for Visual Field × Age Group (p = .54) or Level × Visual Field × Age Group (p = .80).

Post hoc pairwise comparisons for the significant Level × Age Group interaction indicated that: (1) young participants demonstrated no RT differences in detecting global targets and local targets, whereas older participants were faster in detecting local targets compared to global targets; and (2) young participants were faster in detecting global targets compared to older participants, whereas there were no RT differences between young participants and older participants in detecting local targets.

Post hoc pairwise comparisons for the significant Level × Visual Field interaction indicated that: (1) global targets were detected faster in the LVF compared to the RVF, and local targets were detected faster in the RVF compared to the LVF; and (2) there were no RT differences in detecting global targets and local targets in the LVF whereas, in the RVF, local targets were detected faster compared to global targets. See Table 6 for the statistics of the age-related differences for the global–local processing bias, and Figure 2 for the estimated marginal means.

Figure 2.

Group-level age-related differences for the global–local processing bias in the hierarchical-figures task: estimated marginal means for the Level × Age Group interaction and the Level × Visual Field interaction.

Table 6.

Group-level age-related differences for the global–local processing bias in the hierarchical-figures task: post hoc pairwise comparisons for the Level × Age Group interaction and the Level × Visual Field interaction.

Comparison	MD	95% CI	SE	z	p	d _{mixed-effects}
Level × Age Group interaction
Young: global–local	−15.27	[−32.68, 2.14]	6.78	−2.25	.11	0.11
Older: global–local	107.55	[85.35, 129.74]	8.64	12.45	<.001***	0.74
Global: young–older	133.48	[95.09, 171.86]	14.94	8.93	<.001***	0.92
Local: young–older	−10.66	[−53.18, 31.86]	16.55	0.64	.92	0.07
Level × Visual Field interaction
LVF: global–local	15.47	[−1.10, 32.03]	6.45	2.40	.08	0.11
RVF: global–local	76.81	[60.63, 93.00]	6.30	12.20	<.001***	0.53
Global: LVF–RVF	−27.75	[−38.37, −17.13]	4.13	−6.71	<.001***	0.19
Local: LVF–RVF	33.60	[21.15, 46.05]	4.85	6.93	<.001***	0.23

Note. LVF = left visual field; RVF = right visual field; MD = mean difference (ms); CI = confidence intervals; SE = standard errors.

***p < .001.

Part 2. Group-Level Age-Related Differences for Susceptibility to the Ebbinghaus Illusion and for Inspection Time of the Ebbinghaus Illusion

Both the linear mixed-effects models and the Welch's two-sample t-tests indicated that there were no group-level differences between young participants and older participants in either: (1) susceptibility to the Ebbinghaus illusion; or (2) inspection time of the Ebbinghaus illusion. See Table 7 for the statistics of the age-related differences for susceptibility to the Ebbinghaus illusion and inspection time of the Ebbinghaus illusion, and Figure 3 for the estimated marginal means.

Figure 3.

Group-level age-related differences for susceptibility to the Ebbinghaus illusion and for inspection time of the Ebbinghaus illusion: estimated marginal means for young participants and older participants.

Table 7.

Group-level age-related differences for susceptibility to the Ebbinghaus illusion and for inspection time of the Ebbinghaus illusion: results for the linear mixed-effects models and Welch's two-sample t-tests.

Analysis comparing two age groups	MD_{young–older}, 95% CI	t	df	p	d_{mixed-effects}/d
Susceptibility to the Ebbinghaus illusion (PSE)
Linear mixed-effects model	0.85, [−1.19, 2.88]	1.18	113.79	.41	0.17
Welch's two-sample t-test	0.85, [−1.19, 2.88]	0.46	130.98	.65	0.08
Inspection time (ms)
Linear mixed-effects model	−26.00, [−229.26, 177.26]	−0.27	13.95	.79	0.06
Welch's two-sample t-test	−26.00, [−229.26, 177.26]	−0.36	139.05	.72	0.06

Note. MD = mean difference (ms); CI = confidence intervals.

Part 3. Individual-Level Correlations for the Global–Local Processing Bias, Susceptibility to the Ebbinghaus Illusion, and Inspection Time of the Ebbinghaus Illusion

Individual-level correlations were conducted between three pairs of variables: global–local index and PSE, inspection time and PSE, and global–local index and inspection time. For each pair of variables, three analyses were conducted—for the two age groups combined, for young participants only, and for older participants only.

For the relationship between the global–local index and PSE, there were significant positive Pearson correlations and significant positive Pearson partial correlations (after controlling for inspection time) for the analyses of: the two age groups combined; the young participants only; and the older participants only. These findings indicated that the participants with the higher degree of within-individual local-processing bias were the participants who were more susceptible to the Ebbinghaus illusion.

For the relationship between inspection time and PSE, there were significant negative Pearson correlations for the analyses of: the two age groups combined; the young participants only; and the older participants only. These findings indicated that the participants who spent a longer time inspecting the Ebbinghaus illusion were the participants who were less susceptible to the Ebbinghaus illusion.

For the relationship between the global–local index and inspection time, there were no significant Pearson correlations for the analyses of: the two age groups combined; the young participants only; or the older participants only. These findings indicated that the amount of time participants spent inspecting the Ebbinghaus illusion was not related to their within-individual global–local processing bias. See Table 8 for the statistics of the individual-level correlations for the global–local processing bias, susceptibility to the Ebbinghaus illusion and inspection time of the Ebbinghaus illusion, Table 9 for the Spearman–Brown-corrected reliability for each variable in the individual-level correlations, and Figure 4 for illustrations of the individual-level correlations.

Figure 4.

Individual-level correlations between the global–local processing bias and susceptibility to the Ebbinghaus illusion, and between inspection time of the illusion and susceptibility to the Ebbinghaus illusion.

Table 8.

Individual-level correlations for the global–local processing bias, susceptibility to the Ebbinghaus illusion and inspection time of the Ebbinghaus illusion.

Analysis	All participants				Young participants				Older participants
Analysis	r/r_partial, 95% CI	t	df	p	r/r_partial, 95% CI	t	df	p	r/r_partial, 95% CI	t	df	p
Global–local index and PSE
Pearson correlation	.26, [.09, .41]	3.09	135	.002**	.25, [.04, .44]	2.34	81	.02*	.36, [.10, .57]	2.77	52	.008**
Pearson partial correlation	.26, [.10, .41]	3.18	135	.002**	.28, [.07, .47]	2.62	81	.01*	.34, [.07, .55]	2.54	52	.01*
Inspection time and PSE
Pearson correlation	−.46, [−.58, −.32]	−6.03	134	<.001***	−.46, [−.62, −.27]	−4.64	80	<.001***	−.48, [−.66, −.24]	−3.92	52	<.001***
Global–local index and inspection time
Pearson correlation	−.002, [−.19, .15]	−0.28	133	.78	.07, [−.15, .28]	0.65	80	.52	−.24, [−.48, .03]	−1.78	51	.08

Note. PSE = point of subjective equality; CI = confidence intervals.

*p < .05, **p < .01, ***p < .001.

Table 9.

Spearman–Brown-corrected reliability estimates for the global–local processing bias, susceptibility to the Ebbinghaus illusion and inspection time of the Ebbinghaus illusion.

Analysis		All participants	Young participants	Older participants
1	Global–local index/PSE	.88, [.84, .91]	.71, [.60, .80]	.82, [.74, .89]
1	Global–local index/PSE	.87, [.84, .90]	.87, [.83, .91]	.87, [.81, .91]
2	Inspection time/PSE	.97, [.96, .98]	.97, [.96, .98]	.96, [.93, .97]
2	Inspection time/PSE	.86, [.83, .89]	.86, [.81, .90]	.87, [.82, .92]
3	Inspection time/global–local index	.96, [.95, .97]	.97, [.96, .98]	.95, [.93, .97]
3	Inspection time/global–local index	.88, [.85, .91]	.70, [.59, .79]	.82, [.73, .89]

Note. Numbers in square brackets represent 95% confidence intervals. There were 137 participants (83 young participants, 54 older participants) in Analyses 1, 136 participants (82 young participants, 54 older participants) in Analyses 2, and 135 participants (82 young participants, 53 older participants) in Analyses 3.

PSE = point of subjective equality.

Discussion

Susceptibility to the Ebbinghaus illusion has been proposed to be modulated by the relative bias for global processing versus local processing, such that a bias for local processing reduces susceptibility to the Ebbinghaus illusion, whereas a bias for global processing increases susceptibility to the Ebbinghaus illusion (Happé, 1996). While in previous research, the Ebbinghaus illusion has been used extensively to measure and interpret group-level differences in the global–local processing bias (e.g., Doherty et al., 2008; Phillips et al., 2004), questions remained regarding whether the Ebbinghaus illusion can account for individual-level differences in the global–local processing bias. In the present study, we examined systematically the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion at both the group level (i.e., young adults versus older adults) and at the individual level. Navon's (1977) hierarchical-figures task was used to measure the global–local processing bias, and the Ebbinghaus illusion task was used to measure susceptibility to the illusion.

Our findings provide three key insights for age-related changes and the role of individual differences in the perception of the Ebbinghaus illusion. First, at the group level, older participants (as compared to young participants) demonstrated worse performance for global processing in the hierarchical-figures task, but there were no differences in susceptibility to the Ebbinghaus illusion between the two age groups. Second, at the individual level, the participants with the stronger within-individual local-processing bias were the participants who demonstrated greater susceptibility to the Ebbinghaus illusion. Third, also at the individual level, the participants with longer inspection times of the Ebbinghaus illusion were the participants who demonstrated reduced susceptibility to the illusion.

Global–Local Processing Bias and Susceptibility to the Ebbinghaus Illusion at the Group Level

In response to our first research question, concerning the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion at the group level, we found (see Results, Part 1) that older participants (as compared to young participants) demonstrated worse performance for global processing in the hierarchical-figures task, but that these age-group differences in global processing were not associated with reduced susceptibility to the Ebbinghaus illusion. Our group-level findings for the hierarchical-figures task are consistent with two previously reported findings that indicate differences in the global–local processing bias between young adults and older adults. When comparing within each age group, older adults were faster at local processing compared to global processing (i.e., a within-group local-processing bias in older adults), whereas young adults did not demonstrate performance differences between global processing and local processing (Chen et al., 2024; Insch et al., 2012; Lux et al., 2008; Oken et al., 1999). When comparing between age groups, older adults were slower at global processing compared to young adults, whereas there were no age-group differences in local processing (Chen et al., 2024). Our findings, along with previous findings by Chen et al., indicate that age-group differences in the global–local processing bias are driven by the older adults’ performance, which was worse for global processing than for local processing.

Our group-level findings for the Ebbinghaus illusion task (see Results, Part 2) indicate that there were no differences in susceptibility to the illusion between young participants and older participants. These findings are not consistent with previously reported findings; for example, Wapner et al. (1960) and Mazuz et al. (2024) reported reduced susceptibility to the Ebbinghaus illusion in older adults compared to young adults. However, consideration needs to be given to the fact that there are methodological differences that may account for these inconsistent findings. First, both Wapner et al. and Mazuz et al. adopted a circular configuration for the contextual circles in the Ebbinghaus illusion stimuli; in the present study, we adopted a square configuration for the contextual circles. Second, neither Wapner et al. nor Mazuz et al. accounted for the potential effects of mild cognitive impairment on overall task performance in older adults (e.g., Álvarez-San Millán et al., 2022); in the present study, we screened for cognitive functioning in older participants using the Montreal Cognitive Assessment (Nasreddine, 1996).

Overall, our group-level findings indicate that, while older adults demonstrate worse performance for global processing compared to young adults, participants in the two age groups did not differ in their susceptibility to the Ebbinghaus illusion. These group-level findings do not provide support for Happé's (1996) visual attentional integration theory, which posits that group-level differences in the global–local processing bias can account for susceptibility to the Ebbinghaus illusion.

Concerns have been raised previously about the practice of using the Ebbinghaus illusion to measure group-level differences in the global–local processing bias. Several studies (Manning et al., 2017; Ropar & Mitchell, 1999, 2001) have failed to replicate Happé's (1996) original findings of reduced susceptibility to the Ebbinghaus illusion in children on the autistic spectrum compared to neurotypically developing children. These researchers found no differences in susceptibility to the Ebbinghaus illusion between the two groups, despite the proposal that children on the autistic spectrum would demonstrate a local-processing bias due to weak central coherence (Shah & Frith, 1983, 1993). Several methodological differences may account for these inconsistent group-level findings for susceptibility to the Ebbinghaus illusion in children on the autistic spectrum. In the study by Happé, the Ebbinghaus illusion stimuli were presented for one trial on a hard copy, and the viewing distance was not controlled. However, in the studies that failed to replicate Happé's (1996) original findings, there were multiple trials with the Ebbinghaus illusion stimuli (see Manning et al.: 80 trials in Experiment 1; Ropar and Mitchell (1999): 10 trials in Experiment 1; Ropar and Mitchell (2001): six trials), and these trials were presented with a fixed viewing distance from the computer screen. These previous findings, combined with the group-level findings in the present study, suggest that the relationship between susceptibility to the Ebbinghaus illusion and the global–local processing bias at the group level may be more nuanced than initially proposed.

Global–Local Processing Bias and Susceptibility to the Ebbinghaus Illusion at the Individual Level

In response to our second research question, concerning the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion at the individual level, we found (see Results, Part 3) that the young participants and older participants with the stronger within-individual local-processing bias (i.e., faster detection of the local level compared to the global level) in the hierarchical-figures task were the participants who demonstrated greater susceptibility to the Ebbinghaus illusion. These findings were unexpected as they do not provide support for Happé's (1996) visual attentional integration theory, which predicts that a stronger local-processing bias will lead to reduced susceptibility to the Ebbinghaus illusion.

To the best of our knowledge, only Caparos et al. (2012) have examined individual-level differences in the global–local processing bias using both the hierarchical-figures task and the Ebbinghaus illusion. While their findings also do not provide support for Happé's (1996) visual attentional integration theory, they found no significant correlation between the within-individual global–local processing bias and susceptibility to the illusion. The inconsistent individual-level findings between the present study and those of Caparos et al. may stem from several methodological differences in the hierarchical-figures task. First, the present study employed a divided-attention task, where one hierarchical figure was presented per trial, and participants attended simultaneously to the global level and local level of the hierarchical figure. In contrast, Caparos et al. employed a similarity-matching task, where three hierarchical figures were presented per trial, and participants chose which of two hierarchical figures was most like the third hierarchical figure (see Note 1). Second, the present study used RT as the measure for the global-local processing bias, whereas Caparos et al. used percentage (of choosing one out of the two hierarchical figures). Given the limited research examining individual-level differences in the global–local processing bias and susceptibility to the Ebbinghaus illusion, future research is warranted to examine systematically the methodological differences in how this hierarchical-figures task influences the individual-level relationship.

Susceptibility to the Ebbinghaus Illusion and Inspection Time of the Illusion at the Group Level and at the Individual Level

In response to our third research question, concerning susceptibility to the Ebbinghaus illusion and inspection time, we found that although the young and older age groups did not differ in their inspection time of the Ebbinghaus illusion, individual participants (both young and older) with the longer inspection times of the Ebbinghaus illusion were the participants who demonstrated reduced susceptibility to the illusion. Our group-level findings (see Results, Part 2) indicated there were no differences between the two age groups for either susceptibility to the Ebbinghaus illusion or inspection time of the illusion. Our individual-level findings (see Results, Part 3) indicated that the young and older participants who spent a longer time inspecting the Ebbinghaus illusion were the participants who were less susceptible to the Ebbinghaus illusion. These findings for young participants are consistent with the studies by Bressan and Kramer (2013, 2021), who reported that young adults with longer inspection times were less susceptible to the Ebbinghaus illusion. Our study is the first to extend these individual-level findings to older adults, demonstrating that longer inspection times are associated with reduced susceptibility to the Ebbinghaus illusion for both young and older age groups. Additionally, we demonstrated that the amount of time individual participants (both young and older participants) spent inspecting the Ebbinghaus illusion was not related to their global–local processing bias as demonstrated in the hierarchical-figures task.

Bressan and Kramer (2013) have proposed that shorter inspection times induce a global-processing bias during the Ebbinghaus illusion task, while longer inspection times induce a local-processing bias. Therefore, shorter inspection times can facilitate rapid size judgments, but they can also increase susceptibility to the illusion. Whereas longer inspection times enable detailed size judgments, which can reduce susceptibility to the illusion. Intriguingly, this proposal implies that the global–local processing bias can be modulated by the stimulus inspection time adopted in different experiment paradigms. An individual may demonstrate a stronger local-processing bias in an experiment that allows for longer stimulus inspection time, whereas the same individual may demonstrate a stronger global-processing bias in another experiment that has a shorter stimulus inspection time. In the present study, we examined the relationship between the global–local processing bias and susceptibility to the Ebbinghaus illusion using two different experiment paradigms. To measure the global–local processing bias, we employed Navon's (1977) hierarchical-figures task, which had a constant stimulus inspection time of 150 ms. To measure susceptibility to the Ebbinghaus illusion, we employed the Ebbinghaus illusion task, in which stimulus inspection time could vary across trials as stimuli were presented on the screen until a response was made. When participants take a longer time to inspect the Ebbinghaus illusion stimuli, they may demonstrate a stronger within-individual local-processing bias in the Ebbinghaus illusion task compared to their global–local processing performance in the hierarchical-figures task. Conversely, when participants take a shorter time to inspect the Ebbinghaus illusion stimuli, they may demonstrate a stronger within-individual global-processing bias in the Ebbinghaus illusion task compared to their global–local processing performance in the hierarchical-figures task. Therefore, the global–local processing bias as measured by Navon's hierarchical-figures task in the present study may not represent participants’ global–local processing bias during the Ebbinghaus illusion task.

Bressan and Kramer's (2013) proposal provides a plausible explanation for our group-level findings regarding susceptibility to the Ebbinghaus illusion and inspection time of the illusion. In the present study, the young and older participants did not differ either in their susceptibility to the Ebbinghaus illusion nor in their average inspection time of the illusion, even though their inspection time could vary across trials, because the stimuli were presented on the screen until a response was made. These findings can be interpreted to mean that the two age groups did not differ in susceptibility to the Ebbinghaus illusion—at the group level, they did not differ in their relative bias for global processing versus local processing during the Ebbinghaus illusion task. However, Bressan and Kramer's proposal does not explain the findings of Mazuz et al. (2024), in which the older participants demonstrated reduced susceptibility to the Ebbinghaus illusion compared to young participants. In Mazuz et al.'s study, the Ebbinghaus illusion stimuli were presented for a fixed duration on each trial, therefore there could be no differences demonstrated by the participants in regard to the length of inspection time of the illusion. The inconsistent findings between the present study and Mazuz et al. highlight the need for future research to compare systematically the presentation time of the Ebbinghaus illusion, a comparison between fixed stimulus duration (e.g., Bressan & Kramer, 2021; Mazuz et al., 2024) and unlimited stimulus duration (e.g., Phillips et al., 2004) in young and older adults.

Theoretical Considerations

Happé's (1996) visual attentional integration theory proposes that the Ebbinghaus illusion arises when the central circle and the contextual circles are integrated and processed globally, as a whole configuration. But there are ongoing debates concerning the mechanism underlying the Ebbinghaus illusion. In addition to the visual attentional integration theory, there are two major theories that provide alternative explanations for the Ebbinghaus illusion: the constancy scaling theory and the contouring interaction theory. Supporters of the constancy scaling theory argue that the Ebbinghaus illusion arises from misinterpreting contextual circles as depth cues, with larger contextual circles perceived as closer and smaller contextual circles perceived as farther away (Day, 1972; Gregory, 1963). Ropar and Mitchell (2001) suggested that both depth perception and global–local processing mechanisms may contribute to the perception of the Ebbinghaus illusion, thus making it difficult to isolate the specific effects of the global–local processing bias when using the illusion as a measure.

Recent studies favour the contouring interaction theory, which proposes that the Ebbinghaus illusion arises from retinal–neural interaction occurring at a lower level, before the involvement of visual attention or cognition (e.g., Eriksson, 1970; Jaeger & Klahs, 2015; Rose & Bressan, 2002; Sherman & Chouinard, 2016; Takao et al., 2019; Todorović & Jovanović, 2018). This theory suggests that the neural representation of the Ebbinghaus illusion is modulated by the relative retinal distance between the contours of the central circle and the contextual circles. A plausible implication of the contouring interaction theory is that susceptibility to the Ebbinghaus illusion should remain constant across individuals and groups who have healthy retinal and neural structures, given the proposal that the illusion arises at a lower level. Our group-level findings were consistent with this implication—there were no differences in susceptibility to the Ebbinghaus illusion between our young participants and older participants, all of whom had normal or corrected-to-normal vision and no history of self-reported neurological impairments. However, this interpretation warrants careful consideration, as ageing is associated with various changes in retinal structures (see Bonnel et al., 2003, for a review), and the specific retinal–neural mechanisms underlying the Ebbinghaus illusion remain unclear. Additionally, the contouring interaction theory cannot fully account for our individual-level findings, which indicate that susceptibility to the Ebbinghaus illusion can be modulated by the duration of time spent inspecting the illusion. Future research is warranted to investigate the influence of age-related retinal changes and inspection time on the perception of the Ebbinghaus illusion at the stage of retinal–neural interactions.

Kirsch and Kunde (2021) have suggested a more nuanced account of the Ebbinghaus illusion, which is that susceptibility to the Ebbinghaus illusion is modulated by a combination of factors. In particular, Kirsch and Kunde reported two perceptual factors that independently modulate susceptibility to the Ebbinghaus illusion: spatial extent (i.e., the size of the overall Ebbinghaus illusion configuration) and spatial frequency (i.e., the size of the contextual circles). Their findings indicated that susceptibility to the Ebbinghaus illusion is unlikely to be fully explained by a single mechanism, such as the global–local processing bias, the constancy scaling theory, or the contouring interaction theory. Instead, it is influenced by multiple factors. This underlines the need for caution when using the Ebbinghaus illusion to interpret group-level or individual-level differences in a single mechanism, such as the global–local processing bias. Future research is warranted to manipulate these different factors systematically, and to clarify their independent effects on the perception of the Ebbinghaus illusion.

Conclusion

Our study was the first to examine both the age-group differences and the individual-level differences in young and older adults’ perception of the Ebbinghaus illusion. Our results for the group-level differences between young adults and older adults indicate that healthy ageing does not affect susceptibility to the Ebbinghaus illusion, but that healthy ageing does affect the global–local processing bias when measured with the hierarchical-figures task. The older adults’ performance was worse for global processing than for local processing—local processing remained intact in older participants, and it did not differ from that of young adults. Our results for the individual-level differences within young adults and older adults indicate that, regardless of age group, an individual's relative attentional processing bias (global-processing bias versus local-processing bias) plays an important role in the perception of the Ebbinghaus illusion. The individuals with the stronger local-processing bias on the hierarchical-figures task were the individuals who were more susceptible to the Ebbinghaus illusion. Overall, our results reveal there is a nuanced relationship between the visual attentional mechanisms of global–local processing and susceptibility to the Ebbinghaus illusion. Contrary to Happé's proposal, a bias for local processing is not associated with reduced susceptibility to the Ebbinghaus illusion at either the group level or the individual level. Our results also highlight valid concerns that have been made regarding using the Ebbinghaus illusion as the sole measure for examining differences in the global–local processing bias, and suggest that future studies should employ multiple experiment paradigms when examining these differences. Further research is warranted to investigate the theoretical underpinnings of the Ebbinghaus illusion and its broader implications for visual attention across the life span.

Footnotes

Acknowledgments

We would like to thank Dr Hayley Darke and Dr Simone Ray for their contributions to the data collection process of this study. We are grateful to Professor William Phillips and Professor Martin Doherty for generously providing the Ebbinghaus illusion computer program.

ORCID iDs

Haiwen Chen

Anne M. Aimola Davies

Ethical Approval and Informed Consent Statements

The study was approved by the Human Research Ethics Committee at the Australian National University (Protocol: 2013/605 and 2019/795) and the University of Oxford (Protocol: 2010/87). All participants provided written consent prior to participation in the study.

Author Contribution(s)

Haiwen Chen: Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Visualization; Writing – original draft; Writing – review & editing.

Anne M. Aimola Davies: Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing – original draft; Writing – review & editing.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data from this study cannot be made publicly available, as the informed consent for our study specifies that de-identified participant data will only be accessible to the researchers on this project. The R code for statistical analyses will be made available at the Open Science Framework on publication: https://osf.io/wyubx, This study was not preregistered.

Notes

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