# Pre-saccadic Attention (and not Arousal) modulates the Size-Eccentricity Effect

Jad Laaboudi, Anne Hillairet de Boisferon, Céline Paeye

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Jad Laaboudi, Anne Hillairet de Boisferon, Céline Paeye. Pre-saccadic Attention (and not Arousal) modulates the Size-Eccentricity Effect. Scientific Reports, 2025, 15 (1), pp.30622. 10.1038/s41598-025-13968-3. hal-05297979

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OPEN **Pre-saccadic Attention (and not Arousal) modulates the Size-Eccentricity Effect**

Jad Laaboudi<fnref n="1" />, Anne Hillairet de Boisferon<fnref n="1" />,² & Céline Paeye<fnref n="1" />✉

Peripherally located objects are often perceived to be smaller than centrally located objects. This perceptual phenomenon, known as the Size-Eccentricity Effect (SEE), is mainly due to the structural properties of the visual system and is further modulated by covert attention. In this study, we evaluated whether pre-saccadic attention could also compensate for this effect. Participants performed a judgment task where they compared a test disk of varying size, briefly presented in peripheral vision, to a reference disk appearing 450 ms later in foveal vision. When no saccade was made towards the location of the test disk, the SEE was observed. However, when participants initiated saccades about 200 ms after the test disk extinction, points of subjective equality were close to objective equality. The second experiment aimed at excluding an explanation involving non-specific arousal mechanisms, also known to enhance visual perception. Participants executed a keypress or an antisaccade instead of a saccade. The SEE disappeared only in the saccade condition, confirming the crucial role of pre-saccadic attention shifts in this SEE compensation. Therefore, pre-saccadic attention improves not only the processing of orientation, contrast and spatial frequency (as previously demonstrated), but also the processing of peripheral object size.

**Keywords** Size-eccentricity effect, Attention, Action-perception, Saccade, Arousal

As Baldwin et al. (2016)<fnref n="1" /> noted, painters are among the few human beings aware of the apparent size distortion of visual objects seen in peripheral vision. Indeed, several psychophysical studies have confirmed that peripheral stimuli are often judged as being significantly smaller when compared to stimuli presented in central vision<fnref n="1" />⁻³. This perceptual phenomenon, called the *Size-Eccentricity Effect* (SEE), can be explained by several anatomical properties of the visual system. First, cone photoreceptor (responsible for color vision and visual acuity) density peaks in the fovea, a ~1.5 mm wide depression in the inner central surface of the retina, and decreases sharply with eccentricity. Second, the density of ganglion cells is higher in the fovea than in the periphery⁴. In the former, a smaller number of photoreceptors is connected to one ganglion cell. Third, the size of the receptive fields increases with eccentricity, whereas their density drops. The resulting decrease in cortical representation of the fovea with increasing eccentricity is found in almost all structures of the visual cortex⁵⁻⁷.

However, the encoding of objects in peripheral vision has been shown to be more dynamic than if it were explained by the aforementioned structural properties of the visual system alone (for review, see⁸. Losses in peripheral vision can also arise out of – or be compensated by – attentional mechanisms. Visual attention is a central process that enables us to selectively process some aspects of information while ignoring others, by focusing on a certain location or aspect of a visual scene (for review, see⁹.

Indeed, it has been shown that *covert attention* (a form of attention directed to a specific location without eye movement) can modulate the SEE<fnref n="1" />⁻¹². In these experiments, the perceived size of peripheral objects significantly increased when preceded by visual cues at the same location. More specifically, the effect of covert attention on object size perception was reported to depend on the size of the attentional focus. When attention is drawn to the peripheral object location by large cues, the SEE is still observed. In contrast, small cues presented at this location increase the perceived size of these objects¹³,¹⁴, or even reverse the SEE¹⁵, compared to central or irrelevant cues.

Based on these observations, Kirsch et al. (2021)¹³ proposed that attentional effects can explain action-
related influences on size perception. In two different hitting tasks, Kirsch et al.¹³,¹⁶ observed an increase in
perceived target size with an increase in planned movement distance. According to the authors, large-amplitude
movements, which are associated with weaker hitting performance and are therefore experienced as more

<footnote n="1">¹Université Paris Cité, Vision Action Cognition, Boulogne-Billancourt F-92100, France. ²Université de Strasbourg, LPC UR 4440, Strasbourg F-67000, France. ✉email: celine.paeye@u-paris.fr</footnote>
difficult to produce, would require more effort to reach the target. This heightened effort would lead to a more focused mode of attention, which would be in turn responsible for the increase in apparent target size.

Crucial to this reasoning is the assumption that manipulating movement distance in a hitting task is equivalent to manipulating the spread of the attentional focus, a point that the authors did not directly test. However, demonstrating this premise is important. Indeed, other studies<sup>17-19</sup> have shown that the perceived size of target objects is scaled according to the observer's action ability. These authors reported that unsuccessful actions were associated with a *decrease* in the perceived size of target objects, regardless of their eccentricity and other attentional factors. Therefore, further research is required to better understand the role of attention in movement-based perceptual effects.

It is also possible that movement amplitude per se influences the perception of peripheral object size, as suggested by Pressigout et al. (2020)<sup>20</sup>. In their experiment, participants were asked to make ocular saccades (rapid eye movements that quickly align the fovea with the objects of interest). A decrease in saccade amplitude induced by a double-step paradigm<sup>21,22</sup> was associated with a decrease in perceived object size (whereas natural variations in saccade amplitude had no effect on size perception). However, these findings were challenged by Bosco et al. (2020)<sup>23</sup> who reported that the change in size perception was not related to saccadic adaptation. Therefore, the mechanisms underlying the effect of action on peripheral object size perception remain to be fully elucidated.

The latter line of research is particularly interesting as saccadic eye movements are closely linked to attention. This second kind of attention, called pre-saccadic attention, is known to enhance the processing of visual features, including orientation, spatial frequency and contrast sensitivity, at the location of a saccade target, before the eyes move<sup>24-30</sup>. It is possible that such attention also enhances size perception, which is currently unknown.

In the present study, we aim to clarify the influence of action on peripheral object size perception. We adapted the protocol of Pressigout et al. (2020)<sup>20</sup> to test whether variations in saccade amplitudes, beyond natural variations or changes induced by saccadic adaptation, would affect this type of perception. In each trial of the first experimental condition (called the “Saccade” condition, see Fig. 1a), a brief peripheral disk of varying size was presented to the left of a central fixation cross, at a constant eccentricity. After the disappearance of this peripheral disk, participants made a leftward saccade towards a second cross presented at eccentricities varying across different blocks of trials. This cross disappeared during the saccade and was replaced (in central vision)

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Experimental procedure. Each trial started with the presentation of a fixation cross, followed by a test disk of a varying size, presented at an eccentricity of 14 degrees of visual angle (dva) for 100 ms. Each trial ended with the presentation of the reference disk in foveal vision, which participants had to compare with the test disk. Participants indicated their judgment with a manual response. (a) In the Saccade condition, as soon as the peripheral test disk was replaced by a peripheral cross and the fixation cross extinguished, participants made a saccade towards the peripheral cross. The latter appeared at different eccentricities (4, 9, 14, 18 or 24 dva) from fixation, depending on the block of trials. (b) In the Fixation condition, participants were instructed to maintain their fixation throughout the trial, even when no stimulus was displayed (which was intended to maintain consistency across conditions). (c) In the Keypress condition, participants maintained their fixation. One-hundred ms after the test disk disappeared and was replaced by a peripheral cross, an auditory signal prompted participants to press a button with their finger. (d) The Antisaccade condition was similar to the Saccade condition, except participants made a saccade to the mirror position of the peripheral cross in the opposite hemifield.</figcaption></figure>
by a reference disk, whose size was compared with that of the first disk. Participants also performed a “Fixation” condition (Fig. 1b). The procedure was the same as in the Saccade condition except that participants were instructed to maintain fixation at the location of the initial fixation cross throughout the trial. In this condition, both the second cross and the reference disk were presented in central vision. This Fixation condition provided a baseline for the SEE in the absence of eye movements. In this first experiment, we observed that executing a saccade, irrespective of its amplitude, consistently decreased the SEE magnitude.

Importantly, in a second experiment, we excluded an alternative explanation involving non-specific arousal mechanisms known to enhance visual perception³¹. We replicated the two previous conditions with a separate group of participants who additionally performed a “Keypress” and an “Antisaccade” condition. In the Keypress condition (Fig. 1c) participants responded to an acoustic “go” signal by pressing a key with their dominant hand while maintaining fixation at the initial cross location, after the test disk disappeared. We hypothesized that this simple and stereotypical finger movement would require from participants a level of engagement similar to the Saccade condition, while keeping the allocation of their visuospatial attention similar to that in the Fixation condition (the auditory signal was intended to postpone finger movements, thereby ensuring that attention was focused on the visual objects rather than on the target of the finger movement²⁶,³². In the Antisaccade condition, participants were asked to make a saccade to the mirror position of the second (peripheral) cross in the opposite hemifield (Fig. 1d). Therefore, participants executed the same movement as in the Saccade condition, while pre-saccadic attention was manipulated. Indeed, previous research by Klapetek et al. (2016)³³ suggests that attention is divided before antisaccades, allocated in parallel to the visual triggering cue and the antisaccade goal. We predicted that if arousal was responsible for the SEE attenuation, the perceived size of the peripheral disk would be similar in the Saccade, Keypress and Antisaccade conditions. In contrast, if the allocation of pre-saccadic attention explained the increase in perceived object size, the SEE should be as strong in the Keypress condition as in the Fixation condition, intermediate in the Antisaccade condition (where pre-saccadic attention was divided), and weakest in the Saccade condition. Our results were consistent with the latter predictions, confirming that the SEE compensation associated with saccades can be attributed to a shift of pre-saccadic attention.

## Results

To estimate the SEEs obtained when participants prepared a saccade to a target appearing near or at the location of the peripheral test object, pressed a key, or maintained fixation, we computed psychometric function parameters. Figure 2 shows these functions, fitting the proportion of trials per ratio (test disk diameter/reference disk diameter) in which the post-saccadic reference disk was judged smaller than the pre-saccadic test disk, for two participants in Experiment 1. The two parameters of interest are the Points of Subjective Equality (PSEs) and the Just Noticeable Differences (JNDs). The PSE, which corresponds to the size of the pre-saccadic test disk judged to be equal to the reference disk in 50% of the trials, provides an indication of possible bias. Here, a PSE above zero indicates the presence of a SEE (i.e., the peripheral object size appears smaller than the reference size). The JND, related to the function steepness, serves as an indicator of participants’ discrimination sensitivity (i.e., the ability to detect differences between object sizes). This index was calculated as half of the difference between

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Examples of individual psychometric functions in Experiment 1, for the Fixation and the different Saccade conditions (according to target eccentricities): (a) for a participant with some of the best fit qualities (all RMSEs < 0.051, all adjusted R² values > 0.99, all *p*-values from Chi² tests > 0.925); (b) for a participant with some of the lowest fit qualities (RMSEs range: 0.04 to 0.20, range of adjusted R² values: 0.66 to 0.99, *p*-values from Chi² tests = 1, 0.309, < 0.001, 0.986, < 0.001 and 0.999 for the Fixation condition and for the Saccade conditions at target eccentricities of 4, 9, 14, 18, and 24 dva, respectively). Y-axis: Proportion of “smaller” responses (to the question: “Is the second disk larger or smaller than the first one?”). X-axis: Ratios of the test disk's diameter (variable) to the reference disk's diameter. Error bars indicate 95% bootstrap confidence intervals.</figcaption></figure>
the thresholds at 25% and 75% of perception levels. A lower JND indicates greater precision in discriminating object size.

## Experiment 1

### Eye movement data

First, we examined the characteristics (amplitude and latency) of the saccades recorded in the different target eccentricity conditions (see Table 1). Naturally, there was an effect of target eccentricity (Linear Mixed Model - LMM: $F(4,60)=14.547, p<.001$, marginal $R^2=0.997$) on mean saccade amplitudes. Additionally, we verified that saccade precision (i.e., the variance of amplitudes) remained constant across the Saccade conditions, suggesting no differences in the difficulty level of the oculomotor tasks. A Mauchly's test of sphericity indicated no significant differences between these variances ($W=0.61, p=.679$).

LMM also revealed an eccentricity effect ($F(4,60)=4.80, p=.002$, marginal $R^2=0.13$) on saccade latencies. For the 24 degrees of visual angle (dva) eccentricity condition, saccades exhibited significantly longer latencies ($M=239$ ms, $SD=109$ ms) compared to all other conditions (Latency range = 167 to 185 ms; Tukey's HSD, all $p_s < 0.029$,) except for the 18-dva condition ($p=.061$, anecdotal evidence for H0: $BF_{01}=2.50$).

### JNDs

We verified that the amplitude of the required saccades did not systematically influence discrimination sensitivity, suggesting no differences in the difficulty level of the perceptual tasks. Analyses do not support any effect of Condition (Fixation vs. Saccade conditions, see Table 1) on JNDs for the size judgment task ($F(5,75)=2.25, p=.058$, marginal $R^2=0.08$, $BF_{01}=2.78$; JNDs range: 0.09 to 0.13).

### PSEs

Figure 3a shows boxplots for PSEs for each condition. Mean PSEs were first submitted to one-sample t-tests against the 1 value, representing the point of objective equality. Analyses confirmed a SEE for the Fixation condition ($M=1.14, SD=0.06, t(15)=9.96, p<.001$, Cohen's $d=2.49$), and a SEE for Saccade conditions with variations in its magnitude depending on the specific eccentricity conditions (Mean PSE range: 1.03 to 1.08). Whereas participants consistently perceived the peripheral object as smaller than the object presented in central vision in the 4-dva ($t(15)=3.39, p=.004$, Cohen's $d=0.85$), 9-dva ($t(15)=4.52, p<.001$, Cohen's $d=1.13$), and 18-dva ($t(15)=3.09, p=.007$, Cohen's $d=0.77$) eccentricity conditions, when targets were presented at 14-dva ($t(15)=2.05, p=.058$, Cohen's $d=0.51$), and 24-dva ($t(15)=1.91, p=.075$, Cohen's $d=0.48$) eccentricities, it was no longer possible to discern the SEE (Bayesian one-sample t-tests only revealed anecdotal evidence in support of H1, with $BF_{01}=0.75$ and $BF_{01}=0.91$, respectively).

To further evaluate the influence of executing a saccade on the perception of peripheral object size, and its dependence or not on the saccade amplitude, we conducted LMM analyses on Percent Changes in PSE relative to the Fixation condition with Saccade eccentricity conditions as fixed effects (Fig. 3b). LMM analyses showed that there were no significant variations in PSE Percent Change based on the eccentricity of the peripheral target, i.e., saccade amplitude ($F(4,60)=1.28, p=.29$, marginal $R^2=0.042$, with substantial evidence for H0: $BF_{01}=6.67$). Importantly, one-sample t-tests against the null value (which indicates no change in PSE compared to the Fixation condition) revealed significant changes in PSE for all eccentricity conditions (all $p_s < 0.001$, Cohen's $d_s=0.99$ to 1.59). This shows a similar decrease of the SEE when a saccade was made, irrespectively of its amplitude (Percent Change range: -5.2% to -9.2%).

Additionally, we examined the potential influence of natural variations in saccade amplitude (independent of eccentricity manipulation) on the SEE. We computed two PSEs per participant: one for small saccades (< median amplitude) and one for large saccades (> median amplitude). When the Fixation condition was excluded from the analysis, LMM (with Saccade eccentricity conditions and Type of amplitude as fixed effects) revealed a significant effect of Saccade conditions ($F(4,135)=2.99, p=.021$, marginal $R^2=0.049$), reflecting the potential absence of a SEE in one of the conditions. Crucially, the Type of amplitude did not affect the SEE ($F(1,135)=0.02, p=.898$, marginal $R^2=0.0003$, with substantial evidence for H0: $BF_{01}=5.89$) and the interaction did not reach significance ($F(4,135)=0.04, p=.997$, marginal $R^2=0.0002$, with strong evidence for H0: $BF_{01}=18.8$). This indicates that natural variations in saccade precision did not affect the estimation of the peripheral disk size.

<table><caption>**Table 1.** Mean number of valid trials, mean number of repeated trials, mean saccade amplitudes, mean of median latencies and mean JNDs (± SD) for the different conditions according to the eccentricity of targets: fixation, 4, 9, 14, 18, and 24 degrees of visual angle (dva).</caption><thead><tr><th>Saccade target eccentricity</th><th>Mean number of valid trials (± SD)</th><th>Mean number of repeated trials (± SD)</th><th>Mean saccade amplitudes in dva (± SD)</th><th>Mean of median latencies in ms (± SD)</th><th>Mean JNDs (± SD)</th></tr></thead><tbody><tr><td>Fixation</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.09 (0.04)</td></tr><tr><td>4 dva</td><td>182.7 (5.64)</td><td>22.44 (18.69)</td><td>3.57 (0.27)</td><td>177 (27)</td><td>0.13 (0.05)</td></tr><tr><td>9 dva</td><td>182.1 (4.99)</td><td>27.19 (17.35)</td><td>8.67 (0.39)</td><td>181 (65)</td><td>0.12 (0.05)</td></tr><tr><td>14 dva</td><td>180.4 (8.14)</td><td>19.31 (17.16)</td><td>13.75 (0.36)</td><td>167 (38)</td><td>0.10 (0.03)</td></tr><tr><td>18 dva</td><td>182.7 (4.20)</td><td>53.69 (46.58)</td><td>17.48 (0.37)</td><td>185 (54)</td><td>0.11 (0.05)</td></tr><tr><td>24 dva</td><td>180.1 (4.20)</td><td>136.9 (90.67)</td><td>22.87 (0.30)</td><td>239 (109)</td><td>0.13 (0.08)</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Main results of Experiment 1. (a) Boxplots of PSEs in each experimental condition. The horizontal dotted line represents the point of objective equality. A PSE above 1 indicates a SEE. (b) Boxplots of percent changes in PSE compared to the Fixation condition, in each experimental condition. The horizontal dotted line represents no change in PSE. A negative percent change in PSE indicates SEE compensation.</figcaption></figure>

<table><caption>**Table 2.** Mean number of valid trials, mean number of repeated trials, mean saccade amplitudes, mean of median latencies and mean JNDs (± SD) for the different experimental conditions (Fixation, saccade, keypress, and Antisaccade).</caption><thead><tr><th>Condition</th><th>Mean number of valid trials (± SD)</th><th>Mean number of repeated trials (± SD)</th><th>Mean saccade amplitudes in dva (± SD)</th><th>Mean of median latencies in ms (± SD)</th><th>Mean JNDs (± SD)</th></tr></thead><tbody><tr><td>Fixation</td><td>165.2 (18.70)</td><td>—</td><td>—</td><td>—</td><td>0.11 (0.04)</td></tr><tr><td>Saccade (14 dva)</td><td>176.4 (5.35)</td><td>9.75 (10.47)</td><td>13.28 (0.47)</td><td>196 (96)</td><td>0.13 (0.04)</td></tr><tr><td>Keypress</td><td>170.4 (14.26)</td><td>—</td><td>—</td><td>1311 (452)</td><td>0.11 (0.04)</td></tr><tr><td>Antisaccade</td><td>180.6 (2.37)</td><td>24.25 (11.03)</td><td>13.51 (0.59)</td><td>144 (35)</td><td>0.11 (0.04)</td></tr></tbody></table>

Then, we verified whether SEE compensation was influenced by saccade latency. Indeed, previous studies demonstrated that the timing of stimulus presentation relative to saccade onset is crucial for the influence of saccade on visual perception<sup>24,30,34–36</sup>. Saccades were categorized into long and short latencies for each participant based on their median latency. LMM analyses with Saccade conditions and Type of latency (short vs. long) as fixed effects showed no significant effect of the Type of latency on PSE values ($M_{long}$ = 1.06, $SD_{long}$ = 0.05; $M_{short}$ = 1.05, $SD_{short}$ = 0.06; $F(1,135) = 1.67, p = .20$, marginal $R^2$ = 0.007, with anecdotal evidence for H0: $BF_{01}$ = 2.75), nor interaction between the Type of latency and Saccade eccentricity conditions ($F(4,135) = 0.11, p = .98$, marginal $R^2$ = 0.001, with strong evidence for H0: $BF_{01}$ = 17.3).

## Experiment 2

### Movement data

Mean saccade amplitudes and movement latencies are presented in Table 2. The amplitudes observed in the Saccade condition ($M = 13.28$ dva, $SD = 0.49$ dva) were similar to those observed in the Antisaccade condition ($M = 13.51$ dva, $SD = 0.61$ dva, paired t-test = 1.10, $p = .288$, anecdotal evidence for H0: $BF_{01}$ = 2.33). To verify that saccade precision did not differ between the Saccade and Antisaccade conditions, we computed 95% bootstrapped confidence intervals for amplitude variances. The interval computed for the Saccade condition ($\sigma_{sacc}$ = 0.24, 95% CI = [0.09–0.40]) encompassed the variance observed in the Antisaccade condition ($\sigma_{antisacc}$ = 0.37, 95% CI = [0.20–0.50]), and vice versa, indicating no difference between variances.

LMM revealed an effect of Movement conditions ($F(2,30) = 167.8, p < .001$, marginal $R^2$ = 0.86) on latencies. As expected, latencies for the Keypress condition ($M = 1312$ ms, $SD = 452$ ms) were longer compared to Saccade ($M = 196$ ms, $SD = 99$ ms; Tukey's *HSD*, $p < .001$) and Antisaccade conditions ($M = 144$ ms, $SD = 35$ ms; $p < .001$). For the eye movement conditions (Saccade and Antisaccade), latencies were comparable ($p = .22, BF_{01}$ = 12.05).
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Main results of Experiment 2. (a) Boxplots of PSEs in each experimental condition. The horizontal dotted line represents the point of objective equality. A PSE above 1 indicates a SEE. (b) Boxplots of percent changes in PSE compared to the Fixation condition, in each experimental condition. The horizontal dotted line represents no change in PSE. A negative percent change in PSE indicates SEE compensation. * *p*-corrected < 0.05 for planned *t*-tests comparisons.</figcaption></figure>

### JNDs

JNDs for the size judgment task did not differ across conditions (Table 2) indicating that producing a finger movement (Keypress), a saccade (Saccade or Antisaccade) or no movement (Fixation), had comparable effects on the precision of participants’ judgments (LMM: $F(3,45) = 2.16, p = .11$, marginal $R^2 = 0.05$, with substantial evidence for H0: $BF_{01} = 3.79$; JNDs range: 0.11 to 0.13).

### PSEs

Figure 4a shows boxplots for PSEs for each condition. Mean PSEs were submitted to one-sample *t*-tests against the 1 value. As for Experiment 1, analyses confirmed a SEE for the Fixation condition ($M = 1.11, SD = 0.11, t(15) = 4.25, p = .001$, Cohen's *d* = 1.06). A SEE was also observed when participants had to perform a keypress task ($M = 1.11, SD = 0.12, t(15) = 3.63, p = .002$, Cohen's *d* = 0.91) or when they were required to divide their attention across the two visual hemifields (Antisaccade condition, $M = 1.07, SD = 0.09, t(15) = 3.14, p = .007$, Cohen's *d* = 0.78). Importantly, when participants performed a saccade at the exact same location the test disk was presented (Saccade condition), the SEE was no longer present ($M = 1.02, SD = 0.08, t(15) = 0.90, p = .39$, but evidence for H0 is, however, anecdotal: $BF_{01} = 2.76$).

To test our hypothesis that the SEE would manifest with similar intensity in the Keypress condition as in the Fixation condition, would be moderately pronounced in the Antisaccade condition, and least apparent in the Saccade condition, we conducted two additional sets of analyses on mean PSE Percent Changes (Fig. 4b).

First, one-sample *t*-tests against the null value (i.e., no change in PSE compared to the Fixation condition) confirmed significant changes in PSE for the Antisaccade ($t(15) = -2.92, p = .011$, Cohen's *d* = 0.73) and Saccade conditions ($t(15) = -5.07, p < .001$, Cohen's *d* = 1.27), but not for the Keypress condition ($t(15) = -0.18, p = .86$, Cohen's *d* = 0.05, substantial evidence for H0: $BF_{01} = 3.86$). Second, the LMM analysis indicated a significant influence of the condition on the percent change in PSE ($F(2,30) = 8.16, p = .001$, marginal $R^2 = 0.23$). Planned comparisons, with Bonferroni corrections, further revealed significantly larger changes in PSE for the Saccade condition ($M = -8.1\%, SD = 6.4$) in comparison to the Antisaccade condition ($M = -3.4\%, SD = 4.7, t(15) = -2.66, p\*-corrected = 0.036$, Cohen's *d* = 0.66) and for the Saccade condition in comparison to the Keypress condition ($M = 0.3\%, SD = 6.6, t(15) = -3.21, p\*-corrected = 0.012$, Cohen's *d* = 0.80).

As in Experiment 1, we investigated the potential influence of natural variations in saccade amplitude on PSEs. LMM analyses with Type of amplitude (*<*median amplitude vs. *> median amplitude*) and Saccade conditions (Saccade vs. Antisaccade) confirmed the significant effect of Conditions ($F(1,45) = 16.22, p < 0.001$, marginal $R^2 = 0.085$). The SEE did not depend on natural variations in saccade amplitude: indeed, we found no significant effect of the Type of amplitude on PSE values ($F(1,45) = 0.52, p = .476$, marginal $R^2 = 0.006$, with substantial evidence for H0: $BF_{01} = 3.4$) and no interaction between both factors ($F(1,45) = 0.92, p = .341$, marginal $R^2 = 0.004$, with anecdotal evidence for H0: $BF_{01} = 2.07$).

Finally, to verify whether SEE compensation was influenced by latency to initiate a movement we conducted LMM analyses on mean PSEs with Movement conditions (Saccade, Antisaccade and Keypress) and Type of latency (short vs. long) as fixed effects. Analysis revealed no significant effect of the Type of latency on PSE values ($M_{long} = 1.07, SD_{long} = 0.09$; $M_{short} = 1.06, SD_{short} = 0.09$; $F(1,75) = 1.14, p = .29$, marginal $R^2 = 0.005$, with
substantial evidence for H0: $BF_{01} = 3.35$), nor importantly, interaction between the Type of latency and Movement conditions ($F(2, 75) = 0.37, p = .692$, marginal $R^2 = 0.002$, with substantial evidence for H0: $BF_{01} = 4.92$).

Discussion

The two experiments reported here show that the specific shift of attention accompanying saccade execution is responsible for an increase in the perceived size of a peripheral disk presented before an eye movement. This effect is observed regardless of whether this disk appeared near or at the location of the future saccade target. In other words, pre-saccadic attention shifts are able to compensate for the SEE observed during fixation. Crucially, the SEE was not reduced when participants executed a stereotypical finger movement (Keypress condition) instead of a saccade. This condition was intended to induce a similar level of arousal as in the Saccade condition without affecting visuospatial attention<sup>26,32,37</sup>. Therefore, the SEE compensation induced by saccade execution cannot be ascribed to non-specific arousal mechanisms. Finally, in instances where participants executed antisaccades, which are known to divide attention between the two hemifields<sup>33</sup>, we observed a smaller SEE compensation than in the Saccade condition. This provides a further argument in favor of the crucial role of pre-saccadic attention in the increase of peripheral object size perception.

The results of our first experiment contradict Pressigout et al.'s (2020)<sup>20</sup> claim that saccade amplitude would influence the perception of peripheral object size. These authors suggested that movement magnitude (i.e., spatio-temporal action parameters, like amplitude or velocity) would be a significant contributor to the effect of action on perception. More specifically, they hypothesized that if an action parameter changes in a particular direction, the perception of other magnitudes would change in the same direction. Indeed, Pressigout et al. (2020)<sup>20</sup> observed that a decrease in saccade amplitude, artificially induced by a saccadic adaptation paradigm<sup>21,22</sup>, was associated with an underestimation of peripheral object size. This view extends the ATOM (A Theory Of Magnitudes<sup>38</sup> literature which posits that all *perceptual* dimensions that can be represented along a continuous scale of increasing or decreasing magnitudes ("more" or "less") interact insofar as they are processed by a generalized magnitude system. As a consequence, modifying one perceptual dimension would affect the perception of another dimension in the same direction (i.e., more A-more B). For instance, large stimuli are perceived as lasting longer than small stimuli<sup>39</sup>. Pressigout et al. (2020)<sup>20</sup> proposed that movement magnitude could be one of the dimensions processed by the generalized system. Nevertheless, both the present study and the research conducted by Bosco et al. (2020)<sup>23</sup> contradict this assumption.

According to the action-specific account of perception, objects appear larger as the perceiver's ability to interact with these objects increases<sup>17-19,40</sup>. In our first experiment, saccades generated towards the 24-dva eccentricity target exhibited longer latencies than the saccades made to other targets, and the number of repeated trials in this condition was noticeably higher (see Table 1). This could reflect a higher level of motor task difficulty, or a reduced action ability, which should consequently have led to larger PSEs (i.e., smaller perceived sizes) than in the other Saccade conditions — although saccade precision did not differ between conditions. However, in our study the lack of any effect of saccade amplitude on PSEs does not support the claim that action ability impacts size perception. Our conclusion that action influences peripheral object size perception through attention (pre-saccadic attention in the present study), is therefore closer to that of Kirsch et al. (2021)<sup>13</sup>, although we did not observe an effect of movement amplitude.

Interestingly, reaching movements are another type of goal-directed movements typically preceded by a shift of attention<sup>41-43</sup>. This raises the question of whether a SEE compensation effect would also occur if participants were asked to reach the target instead of making a saccade. On the one hand, if we used a similar protocol (i.e., a single target location, in a blocked design) it is reasonable to assume that we would not observe this compensation. Indeed, Hanning et al. (2018)<sup>37</sup> demonstrated that repeated reaching movements to a fixed target do not induce attentional shifts to that target. Furthermore, Stewart et al. (2019)<sup>44</sup> showed that discriminative sensitivity near or at a manual target location was not higher in the context of a reaching movement than after a shift of covert attention alone, when this shift was induced by a valid cue (as is the case in our study, due to trial repetition). On the other hand, Kirsch et al. (2014; 2021)<sup>13,16</sup> observed that when participants hit a target with a stylus by moving it from various starting positions, their estimation of the target's size varied positively with movement distance. Notably, in their experiments, the target position also remained constant across trials. However, unlike in the aforementioned studies, eye movements were not monitored, even though they could have induced attentional shifts. Another key difference between our protocol and that of Kirsch et al. (2014; 2021)<sup>13,16</sup> is that, in their design, the movement target al.so served as the stimulus to be judged. Given these mixed findings, further dedicated studies should investigate whether SEE compensation can occur in the context of reaching movements, or, perhaps more ecologically, in conditions where reaching is accompanied by eye movements.

While our results strongly argue in favor of the role of pre-saccadic attention in peripheral object size perception, they leave open the question of the spatiotemporal course of its deployment. A first possibility is that pre-saccadic attention quickly shifted or was even already allocated to the test disk upon its appearance. Indeed, while pre-saccadic attention is, in most cases<sup>35</sup>, selectively directed to the saccade target 50 to 75 ms before an eye movement, some of these attentional resources can be allocated to other stimuli earlier before the saccade<sup>24,34,35</sup>. This was even more plausible in our study, considering that the disk presentation could be fully predicted from the preceding trials<sup>45</sup>. A recent study by Szinte et al. (2019)<sup>46</sup> further supports this assumption. These authors demonstrated that when observers have memorized the saccade goal about a second before the eye movement, attentional benefits on visual perception extend to peripheral locations situated up to 7.1 dva from this future goal. Interestingly, these benefits became more pronounced as the delay between the (extinguished) saccade target and the onset of the eye movement increased. In our first experiment, participants may have memorized and predicted the position of the future saccade target (the cross) based on preceding trials, i.e., over a longer timescale than the ~1-second delay tested by Szinte et al. (2019)<sup>46</sup>. The good SEE compensation observed when
participants made saccades to targets located at ±10 dva (in the 4 and 24-dva Saccade conditions) from the predicted saccade target location suggests that the spread of attentional resources may have been broader than that measured by Szinte et al. (2019)⁴⁶ — possibly due to better memorization of the saccade target location. The amount of these resources also seems to be larger, as suggested by the consistent PSEs observed across all Saccade eccentricities. However, the unexpected proportion of these resources raises doubts regarding this interpretation.

The second possibility is that participants programmed a sequence of two saccades, first to the peripheral disk and then to the cross, and inhibited the initial eye movement. This assumption is consistent with numerous experiments concluding on the high specificity of pre-saccadic attention shifts based on selective perceptual enhancements at the location of visual objects spanning 1- or 2-dva²⁴,²⁶,²⁷,³⁴,³⁶. This statement is also in line with the study by Godijn and Theeuwes (2003)⁴⁷ which showed that prior to the execution of a saccade sequence, pre-saccadic attention is distributed in parallel to all saccade goals. Nevertheless, this does not explain the similarity in Experiment 1 between the PSEs obtained from the different Saccade conditions. Indeed, in the 14-dva Saccade condition, participants did not need to program two different saccades, and thus their attentional resources were not divided. This should have resulted in a better SEE compensation than in the other Saccade conditions. We solely observed such a significant difference in SEE compensation for the Saccade-Antisaccade comparison (Experiment 2). It is possible that this difference emerged because of the greater distance between the test disk and the saccade goal. Further experiments are necessary to conclusively address the aforementioned hypotheses.

Together with studies on the influence of covert attention on object size perception¹⁰⁻¹⁵, our study suggests that objects generally appear smaller in the visual periphery not only because of the structural properties of the visual system¹⁻³ but also because of a lack of spatial attention. However, it can be assumed from the consistent level of precision in size discrimination (i.e., comparable JNDs) across all conditions that there was no major deficit of attention in the Fixation conditions (where the SEE was the largest). It is possible that the repeated presentations of the test disk at a fully predicted location in the periphery mobilized covert attention *only*, which was not sufficient to fully compensate for the structurally induced SEE. When participants were asked to execute eye movements, the addition of pre-saccadic attentional resources magnified the perceived size of the peripheral disk. This constitutes another instance of a dissociation between pre-saccadic and covert spatial attention (for a review, see²⁹.

At the neural level, SEE compensation has been attributed to the shift of cortical neurons' receptive fields towards the focus of attention¹⁰⁻¹³,¹⁵,⁴⁸. According to this view, some of the receptive fields that are initially outside of an object are shifted towards the center of the attentional focus. As a consequence, a greater number of receptive fields, including more distant ones, are activated by the same object. As these receptive fields retain the labels of their original retinal position, the object is perceptually stretched and would then appear larger. It can be postulated that saccade preparation potentiates this effect. Indeed, it is established that receptive fields shift in the direction of the visual target prior to saccades⁴⁹,⁵⁰. Possibly, in the Saccade conditions, this second source of dynamic receptive field modulation could be added to the one induced by covert attention.

Interestingly, Jurkiewicz et al. (2021)⁵¹ found that patients with optic ataxia, whose superior parietal lobule and intraparietal sulcus were damaged, showed an exaggerated SEE in the contralesional field. In addition, variations in the size, location, and structure of receptive fields in the lateral intraparietal area were induced in monkeys by manipulating the state of attention engagement⁵². These modifications were consistent with the shift of receptive fields towards the attentional focus described above. These studies suggest that these posterior parietal cortex areas play an important role in compensating for the SEE.

Overall, our results provided evidence that pre-saccadic attention not only improves the processing of orientation, contrast and spatial frequency (as previously demonstrated²⁸⁻³⁰, but also improves the processing of peripheral object size. The observed compensation of the SEE could not be ascribed to non-specific arousal mechanisms. Presumably, the shift of receptive fields observed towards the focus of covert attention, likely responsible for the modulation of peripheral object size perception, is potentiated by pre-saccadic attention.

# Methods

## Participants

The sample size was determined a priori based on a previous study by Kirsch et al. (2021)¹³ on the impact of movement on attentional SEE modulation. We found that 15 participants would be sufficient to reliably detect an interaction of the same effect size as the one observed by Kirsch et al. (2021)¹³ in Experiment 1 ($\eta_p^2$ = 0.241). The desired power was set to 1-$\beta$ = 0.95, $\alpha$ to 0.05 and the correlation was factored into the effect size. In anticipation of potential failures to complete the experiment and/or calibration difficulties, we recruited 19 participants per experiment.

Thirty-two participants (Experiment 1: 16 participants, mean age 28.3 years (SD = 9.9), 11 females; Experiment 2: 16 participants, mean age 20.5 years (SD = 2.4), 13 females) finally contributed data in this study. An additional four adults (two per experiment) were tested but excluded because of failure to complete the experiment. Before conducting the analyses, we used the Sn method⁵³ with a criterion of 3⁵⁴, to detect possible PSE and JND outliers in the Fixation and 14-dva Saccade conditions (common to both experiments). One outlier was identified in each experiment and not included in the analyses.

In both experiments, participants were healthy adults (recruited through the online platform of the University Paris Cité). Participants, all naive about the purpose of the study, received compensation of €10 per hour in Experiment 1 or course credit in Experiment 2. They all had normal or corrected-to-normal vision and audition. Experiments were conducted in accordance with the principles of the Declaration of Helsinki and approved by the local ethics committee Comité d'Ethique de la Recherche CER U-Paris Cité (Experiment 1: CER-PD: 2018-62; Experiment 2: IRB 00012023-16). Written informed consent was obtained from all individual participants included in the study.
## Setup

Stimuli were projected on a 598×344 inches screen (1280×720 pixels) by a digital micromirror video projector (PROPixx Full, VPixx Technologies®, 244 Hz). Participants sat in a dimly lit room with their head stabilized by a chin and forehead rest at 140 cm from the screen. Eye movements were recorded with an Eyelink 1000 Plus Desktop Mounted eye tracker sampling at 1000 Hz (SR Research, Ontario, Canada). The experiment was designed and run with a customized program using the Psychophysics and EyeLink toolboxes<sup>55-57</sup> in MATLAB (MathWorks, Natick, MA, USA).

## Stimuli

Stimuli were black disks displayed on a 7.5 cd/m² luminance gray background. The reference disk had a constant diameter of 1.8 dva. The ratios of the test disk diameter with respect to the reference disk diameter varied from 0.7 to 1.3, with increments of 0.1. Each diameter value was randomly presented 24 times during the session. Two test disks of more extreme diameters (ratios = 0.4 and 1.6) were also inserted eight times each throughout the course of the session. Disks were blurred using a cumulative Gaussian gradient covering 20% of the diameter (Pressigout et al., 2020)<sup>20</sup>. A 0.7×0.7 dva black cross served as a fixation point and possibly as a saccade target. In the keypress task introduced in the second experiment, a sound (440-Hz sinusoidal wave lasting 200 ms) was used to prompt participants to press one key on a 5-button input device (MilliKey-5, LabHackers).

## Experimental design and procedure

Figure 1 shows the experimental design (adapted from<sup>20</sup> used to compare the roles of covert attention (Fixation condition), pre-saccadic attention (Saccade and Antisaccade conditions), and arousal (Keypress condition) in the perception of peripheral disk size. In each experimental condition, participants compared the size of a test disk presented in peripheral vision and a reference disk presented in central vision. The method of Constant Stimuli (184 trials) was used to obtain psychometric function parameters.

### Experiment 1

The goal of this first experiment was twofold: (i) to compare the SEEs that might be observed with and without eye movements and (ii) to determine whether saccade amplitude modulates this effect. This experiment was therefore composed of two different types of trial blocks: one fixation block and five saccade blocks. In the fixation block, participants were instructed to maintain their gaze at the location of the initial fixation cross for the entire trial, and we ensured that they kept fixating within the designated 1.5-dva-radius area surrounding this location. In the saccade blocks, participants were asked to make a saccade to a target appearing after the test disk disappearance, at five different eccentricities (4, 9, 14, 18, or 24 dva, varying between blocks). Participants always started with the 14-dva saccade block (considered as the easiest one) whereas the presentation order of the other blocks was counterbalanced across participants. Before these experimental blocks, participants were familiarized with the size judgment task through the completion of 32 trials (data not analyzed) in which only the two extreme test disk size ratios were presented. The experiment was divided into three sessions, each lasting from 45 min to 1 h, with an average separation of 24 h between sessions.

In the Fixation condition (Fig. 1b), participants were first presented with a fixation cross displayed between 4 dva and 7 dva to the right of the center of the screen. After a random delay (500 to 700 ms), the test disk was displayed for 100 ms at 14 dva to the left of the fixation cross on which participants were instructed to keep fixating. This disk was then followed by a cross appearing in central vision for 200 ms. After a fixed 450-ms delay, the reference disk was displayed for 100 ms at the fixation location. Then, participants had to answer the following question: “Was the second disk smaller or larger than the first one?” by pressing the up (“larger” response) or down (“smaller” response) arrow keys on the keyboard with their dominant hand. Five hundred milliseconds after the response, a new fixation cross signaled the beginning of the next trial. If a saccade was detected during a trial, this trial was aborted and run later during the block.

The Saccade conditions (Fig. 11a) were similar to the Fixation condition, except that participants were asked to execute a saccade towards a peripheral cross that appeared as soon as the test disk and the initial fixation cross disappeared. The saccade target eccentricity remained fixed during a saccade block but varied between blocks (see above). After saccade detection, the target cross disappeared, and following a 400-ms empty screen, the reference disk was presented in central vision for 100 ms, on condition that the saccade landed within 2 dva from the target cross. Participants had then to indicate their size judgment. If a saccade onset was detected before the extinction of the initial fixation cross or after the main saccade, if saccade latency exceeded 1200 ms or if the saccade landed outside a 2-dva region around the target, the trial was aborted and run later during the block.

### Experiment 2

This experiment was designed to replicate the main findings of Experiment 1 and to rule out an alternative explanation in terms of arousal. The experimental design was identical to Experiment 1 with the exception of a single 14-dva saccade condition and the introduction of two additional blocks of trials (the Keypress and Antisaccade conditions). The experiment started with a familiarization block (data not analyzed). Participants then performed the fixation and saccade blocks, in counterbalanced order. They finally achieved the keypress and more demanding antisaccade blocks in this fixed order. The experiment was divided into two sessions (of two conditions each), lasting approximately 45 min and separated by an average of 24 h.

The trial structure of the fixation and saccade blocks was the same as in Experiment 1 (see Fig. 1a and b). In the Keypress condition (Fig. 1c), designed to test a possible effect of arousal, participants were instructed to generate a stereotypical finger movement instead of a saccade. Indeed, recent findings<sup>37</sup> indicate that repeated hand movements directed towards a fixed manual target do not elicit attentional shifts to this target. It is even more likely that a smaller movement, such as a keypress, would have little to no impact on attention allocation
to the peripheral disk. As in the Saccade condition, the test disk was replaced by a peripheral cross, followed by an additional 100-ms fixation period intended to postpone the finger movement. This also ensured that a significant amount of attentional resources could be allocated to the disk during its presentation – just as in the other experimental conditions – rather than to the target of the finger movement<sup>26,32</sup>. Then, a 440-Hz sound was played and participants had then 1200 ms to press a key with the index of their dominant hand. If the key was pressed within 1200 ms and gaze fixation maintained correctly, the reference disk was presented in foveal vision after a 400-ms delay and participants were asked to report their size judgment (with the index of their non-dominant hand). If manual reaction time exceeded 1200 ms or if a saccade occurred, the trial was aborted and run later during the block.

In the Antisaccade condition (Fig. 1d), the procedure was similar to the Saccade condition, except that participants were instructed to execute a saccade to the mirror position of the peripheral cross in the opposite hemifield. If saccade latency exceeded 1200 ms, if saccade amplitude fell outside the 12–18 dva range, or if a second saccade occurred, the trial was aborted and run later during the block.

## Data analyses

### Ocular and manual responses analysis

We recorded saccade latency, saccade amplitude, manual response time (in the Keypress condition) and the frequency of “smaller” responses for each disk size ratio (i.e., the diameter of the test disk divided by the diameter of the reference disk). Saccade latency was defined as the delay (in ms) between saccade target (i.e., the peripheral cross) appearance and movement onset. Amplitude (in dva) corresponded to the distance covered by the eyes to reach the target (or its mirror position in the Antisaccade condition). In off-line analyses, we used the EyeLink parser to identify saccade onset and offset (velocity threshold: 30°/s, acceleration threshold: 8,000°/s²). Manual response time was defined as the elapsed time (in ms) between the sound played after the peripheral disk extinction and the keypress.

### Psychometric function fitting

Psychometric functions were obtained from valid trials (trials where blinks or no-response occurred were removed), with a maximum of 184 trials per condition. In Experiment 1, on average there were 182 ± 5 valid trials (see Table 1) and 173 ± 14 valid trials (Table 2) in Experiment 2. Since some trials could be aborted and repeated later within a block (see the procedure description as well as Tables 1 and 2), the total number of presented trials could vary across conditions. In Experiment 1, the Linear Mixed Model on the number of repeated trials revealed an eccentricity effect ($F(4,60)=22.8, p<.001$, marginal $R^2=0.44$). Consequently, a significantly larger number of saccades were performed for the 24-dva eccentricity condition compared to the other conditions (all $p_s < 0.001$, Tukey's HSD post-hoc analyses; *emmeans R* package<sup>58</sup>. In addition, in the 18-dva eccentricity condition, more saccades were performed compared to the 4- and 14-dva conditions ($p=.029$ and $p=.001$, respectively) but not compared to the 9-dva condition ($p=.22$, with substantial evidence for H0: $BF_{01}=3.32$). In Experiment 2, Wilcoxon signed-rank test indicated that a larger number of saccadic eye movements was performed in the Antisaccade condition in comparison to the Saccade condition ($Z=3.38, p<.001$; Shapiro-Wilk normality tests: $W_{Antisac}=0.96, p=.68$; $W_{sac}=0.71, p<.001$).

We plotted the proportion of trials per disk diameter ratio in which the post-saccadic reference disk was judged as smaller than the pre-saccadic test disk. Psychometric functions were parametrically fitted with a logistic function, using the *fminsearch* algorithm in MATLAB. Goodness-of-fit values (*RMSEs*, Adjusted $R^2$s and *p*-values of $Chi^2$ tests) along with all psychometric functions are presented in the Supplementary material. In summary, in Experiment 1, *RMSEs* ranged from 0.02 to 0.20 ($M=0.06$), adjusted $R^2$ values ranged from 0.66 to 1 ($M=0.96$) and 90.6% of the $Chi^2$ tests were non-significant. In Experiment 2, *RMSEs* ranged from 0.01 to 0.16 ($M=0.06$), adjusted $R^2$ values ranged from 0.77 to 1 ($M=0.96$) and 91.7% of the $Chi^2$ tests were non-significant.

Fit parameters were estimated with the maximum likelihood method. The PSE (Point of Subjective Equality, i.e., the size of the pre-saccadic test disk judged to be equal to the reference disk in 50% of the trials) provides information about possible response biases. To estimate the discrimination sensitivity of each participant, we computed JNDs (Just Noticeable Differences) from the psychometric functions. This parameter defines the smallest difference perceived between two stimuli. The JND was calculated as follows: $JND = (x_{.75} - x_{.25})/2$, with $x_{.75}$ and $x_{.25}$ corresponding to the stimulus values at which the probability of a “smaller” response is equal to 75% and 25%, respectively. Percent changes in PSEs were computed for each of the Saccade, Keypress, and Antisaccade conditions with respect to the Fixation condition (considered as the baseline), as follows: $\text{PercentChange} = (\text{PSE}_{\text{Condition}} - \text{PSE}_{\text{Fixation}})/\text{PSE}_{\text{Fixation}} * 100$.

### Statistical analyses

For the main analyses, Linear Mixed Models (LMM; *lme4 R* package<sup>59</sup> were used to examine a potential effect of the different conditions (depending on the Experiment) on Percent changes in PSE and JND estimates and median latencies ($\alpha=0.05$). As random effects, we had intercepts for participants. The normality assumption of residuals was tested using the Shapiro-Wilk normality test ($p>.05$) and visual inspection of normal Q-Q plot. For *F* tests on fixed effects, we used Satterthwaite's approximation (*lmerTest R* package<sup>60</sup>. Marginal $R^2$ values are reported as a measure of the variance explained by fixed factors<sup>61</sup>. In order to corroborate the absence of effects, we also conducted Bayesian LMM using JZS prior (Jeffreys-Zellner-Siow) to compute Bayes Factor (*BayesFactor R* package<sup>62</sup>. Results are expressed as Bayes factors ($BF_{01}$) for each model against the null model. *BF* values in the range of 1–3 and 1/3–1 are considered as “anecdotal evidence”, values in the range of 3–10 and 1/10–1/3 as “substantial evidence”, and those falling in the range of 10–100 and 1/100–1/10 as “strong to very strong evidence” (see<sup>63</sup>. When considerable deviation from normality were observed we transformed our data (JNDs and Median Latencies) using a logarithmic transformation based on the Box-Cox procedure<sup>64</sup>. To compare saccade precision
across target eccentricity conditions, we tested for equality of variances. In Experiment 1, we used Mauchly's test of sphericity, as all distributions were normal (Shapiro-Wilk tests, all $p_s > 0.08$). In Experiment 2, the distribution of (pro)saccade amplitudes was not normal (Shapiro-Wilk test, $p=.027$) and exhibited substantial skewness ($Skewness = 1.05$). Consequently, we computed 95% bootstrapped confidence intervals for amplitude variances.

## Data availability

The datasets generated during and analyzed during the current study are available in the Open Science Framework repository: https://osf.io/u456d/?view_only=2dba1d99221448499ef3d788a58aed35.

Received: 16 April 2024; Accepted: 27 July 2025

Published online: 20 August 2025

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## Acknowledgements

This work was supported by the Grant ANR-18-CE28-0001 from the Agence Nationale de la Recherche to C.P. This article has been published with the support of the Sociétés & Humanités faculty of Université Paris Cité.

## Author contributions

Conceptualization and design: C.P. with input from A.H.B. and J.L.; Experimental software programming: C.P. and J.L.; Data collection: J.L. and A.H.B; Data analysis: A.H.B and J.L. with input from C.P.; Writing: C.P., A.H.B. and J.L.; Manuscript revision: C.P. with input from A.H.B. and J.L.; Supervision and funding acquisition: C.P.

## Competing interests

The authors declare no competing interests.

## Additional information

Correspondence and requests for materials should be addressed to C.P.

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