Introduction

Our own actions influence perception profoundly (Rolfs & Schweitzer, 2022). For example, we can barely tickle ourselves, whereas the same tactile stimulation produced by someone else or by an object can be pretty ticklish (Blakemore et al., 1998; Weiskrantz et al., 1971). In the domain of time judgement, Haggard and colleagues reported an illusion of temporal attraction between an action and a slightly delayed sensory event, known as temporal binding (or intentional binding). Temporal binding is comprised of action binding (i.e. the action being reported as occurring later) and outcome binding (i.e. the sensory event being reported as occurring earlier), with outcome binding having a much bigger effect size (Haggard et al., 2002; Wolpe et al., 2013). Over the two past decades, the temporal binding effect has attracted cross-disciplinary attention with regards to its cognitive/neural mechanisms and the potential applications especially with its widespread use as an implicit measure of sense of agency (Antusch et al., 2021; Buehner & Humphreys, 2009; Dogge et al., 2012; Haggard, 2017; Kirsch et al., 2019; Legaspi & Toyoizumi, 2019; Moore & Obhi, 2012).

However, the impact of visuospatial attention has been heavily overlooked when considering the measurement of time judgement with the widely used Libet clock method (Libet et al., 1983; Wundt, 1874). In the standard testing procedure (e.g. Haggard et al., 2002), an event was presented (e.g. a keypress or a sound) while participants watched a clock face with a rapid rotating clock hand. Participants should indicate the event time by reporting where the clock hand was positioned at the event onset. This essentially transforms a timing task to a spatial localisation task. It is well-know that attention plays an important role in spatial localisation (Fortenbaugh & Robertson, 2011; Tse et al., 2011; Visser & Enns, 2001; Zhou et al., 2017). When the location of an object is ambiguous, participants tend to localise the object to the place where attention is directed to (Adam et al., 2008; Binda et al., 2009; Kirsch, 2015). This is particularly relevant to the temporal binding measured with Libet clock method, as the fast rotating clock hand makes the location report a challenging task (Haggard & Cole, 2007).

Outcome binding is usually obtained by comparing an Action Sound (AS) condition and a Sound Only (SO) condition. In both conditions, participants report where the clock hand pointed to at the time of sound play. The reported time is earlier in the AS condition than in the SO condition (Figure 1a). Suppose that the clock hand is positioned at 12 o’clock when a sound is played (Figure 1a). In the SO condition, the sound is controlled by the computer. Since the onset time of the sound is not known in advance, attention may accumulate towards the clock rim only after the sound is played. Therefore, the amount of attention resource is low at the clock hand location before the sound play but high after. In the AS condition, the sound is triggered by an action, which is executed when the clock hand is at around 10 o’clock position (given a sound delay of 250 ms and a revolution period of the clock hand for 1800 ms as employed in the current study). Previous research has provided ample evidence that action modulates the distribution of attention according to the action goal (Deubel & Schneider, 1996; Rolfs et al., 2011; Tipper et al., 1998). For example, when reaching towards a target, visual attention was shown to be drawn towards the target before the onset of the reaching action (Baldauf & Deubel, 2010; Deubel et al., 1998; Eimer et al., 2006; Rolfs et al., 2013). The keypress in the Libet clock method can be successfully performed rather easily without considering the information of a target. However, the timing report task requires the identification of the clock hand position around the time of the keypress. Conceivably, the task goal (i.e. reporting the clock hand position) may be associated with an attention shift towards the clock rim similar to the attention shift to a target in a target reaching task. This attention shift should result in a high amount of attention resource to the clock hand location before the sound onset in the AS condition (Figure 1a). The predicted attention difference between AS and SO conditions bears a striking resemblance to the timing report difference between the two conditions. Due to the tight link between attention and spatial localisation as noted earlier, an earlier attention activation in the AS condition compared to the SO condition can lead to an earlier reported clock hand position (i.e. outcome binding).

Figure 1

The attention hypothesis may also be extended to action binding (Figure 1b). Action binding is obtained by comparing an AS condition and an Action Only (AO) condition. The reported keypress time is later in the AS condition than in the AO condition. The only difference between the two conditions is that no sound is played after a keypress in the AO condition. The sound in the AS condition may have the effect as an extra source for attention attraction, resulting in a higher amount of attention resource at the clock hand location after the keypress in the AS condition than in the AO condition, which can lead to a later reported keypress time in the AS condition (i.e. action binding).

In a series of 4 experiments, we demonstrated distinct patterns of attention modulation in temporal binding induced by action and sensory stimulation using the Libet clock method. Furthermore, computational modelling work using the attention measure alone can reproduce the temporal binding effect, providing strong supporting evidence to the attention hypothesis of temporal binding.

Results

An attention distribution shift in outcome binding

Participants reported the sound onset time using the Libet clock method (Figure 2). During the experiment, they were asked to fixate the centre of the visual presentation, but no eye-tracking was employed to ensure the compliance with the instruction. A clear outcome binding effect was confirmed in Experiment 1 (t(17) = 9.78, p < 0.001, dz = 2.30, one-tailed paired-sample t-test, BF₊₀ = 1.21e6; Figure 3a). The reported time was earlier when the sound was triggered by participants through a keypress (AS condition; M = –79.31 ms, 95% CI = [-102.93 –55.68] ms) than when the sound was controlled by computer (SO condition; M = 34.17 ms, 95% CI = [12.73 55.60] ms). Crucially, the pattern of visuospatial attention distribution around the onset of the sound (i.e. the event being judged), operationalised as the probe detection rate, was drastically different between the two conditions (Figure 3b). In the SO condition, the detection rate was low before the sound play (referring to both the clock hand locations and the time before the sound play), but high after. In the AS condition, the detection rate was high at the time of keypress, gradually increased, and peaked just before the sound play. After the sound play, the detection rate underwent a sharp decrease. The attention distribution difference was confirmed with a significant interaction effect in a two-way (condition: AS vs. SO; probe location: –50°, –30°, –10°, 10°, 30°, and 50°) within-participants ANOVA comparing the detection rate (F(5,85) = 12.44, p < 0.001, η ² = 0.42, BF_incl = 1.87e8). The ANOVA also revealed significant main effects of probe location (F(5,85) = 11.04, p = 0.001, η ² = 0.39, BF = 1.15e4) and condition (F(1,17) = 8.17, p = 0.011, η ² = 0.32, BF = 3.63).

Figure 2

Figure 3

The above findings were replicated in Experiment 2 with a new group of 20 participants. Experiment 2 was the same as Experiment 1 except that a strict eye movements control was applied. During the testing, the eye fixation of participants never exceeded the central area of the clock face (ensured via an eye tracking device). Again, a clear outcome binding effect was confirmed (t(13) = 6.15, p < 0.001 dz = 1.64, one-tailed paired-sample t-test, BF₊₀ = 1.45e3; Figure 3c). The reported time was earlier in the AS condition (M = –46.61 ms, 95% CI = [-85.29 –7.93] ms) than in the SO condition (M = 47.86 ms, 95% CI = [22.15 73.57] ms). The pattern of visual detection performance was almost identical to that found in Experiment 1 where there was no eye movements control. In the SO condition, attention was low before the sound play, but high after. In the AS condition, attention was high at the time of keypress, gradually increased to its peak just before the sound play, and started to decrease after the sound play (Figure 3d). This demonstrates the robustness of the attention modulation induced by action in the AS condition and by the sound in the SO condition. The two-way (condition: AS vs. SO; probe location: –50°, –30°, –10°, 10°, 30°, and 50°) within-participants ANOVA comparing the detection rate confirmed a significant interaction effect (F(5,65) = 4.18, p = 0.013, η_p² = 0.24, BF_incl = 32.91). The ANOVA also revealed a significant main effect of probe location (F(5,65) = 8.21, p < 0.001, η ²= 0.39, BF = 2.99e3) and a non-significant main effect of condition (F(1,13) = 0.01, p = 0.941, η_p² < 0.01, BF_incl = 0.26).

The attention distribution shift is functionally relevant to outcome binding

Experiments 1 and 2 demonstrated the existence of an attention effect in outcome binding. Experiment 3 sought to demonstrate a functional relevance of the attention effect in outcome binding. To this end, the SO condition was replaced with a VS condition, in which a vibrotactile stimulation was applied to the finger 250 ms before the sound play (no keypress). The vibrotactile stimulation had the same timing as the keypress in the AS condition. It should have a similar effect on attention to the keypress in the AS condition, as it is a signal predictive of the sound onset and the timing report task. If this is the case, the binding pattern should vanish when comparing VS and AS conditions.

Another 40 participants were recruited for Experiment 3. Experiment 3 was similar to Experiment 2, but a VS condition replaced the SO condition. Since the crucial evidence here is a null effect (i.e. no statistical difference between VS and AS conditions, or at least the difference between VS and AS conditions is much smaller than the difference between SO and AS conditions in Experiments 1&2), the sample size was doubled compared to Experiments 1&2. Indeed, no binding was found between VS and AS conditions (t(38) = 1.04, p = 0.305, dz = 0.17, two-tailed paired-sample t-test, BF₁₀ = 0.29; AS condition: M = –65.19 ms, 95% CI = [-87.80 –42.59] ms; VS condition: M = –40.96 ms, 95% CI = [-87.41 5.49] ms; Figure 3e). The size of binding in Experiment 3 (as calculated in Experiments 1&2) was smaller than in Experiments 1&2 (t(69) = –2.99, p = 0.002, ds = –0.71, one-tailed unpaired t-test, BF_-0 = 19.56). The pattern of attention distribution also appeared similar between VS and AS conditions. In both conditions, attention was high before the sound play, but low after (Figure 3f). The two-way (condition: AS vs. VS; probe location: –50°, –30°, –10°, 10°, 30°, and 50°) within-participants ANOVA comparing the detection rate only revealed a significant main effect of probe location (F(5,190) = 28.31, p < 0.001, η ² = 0.43, BF = 7.17e17). The interaction effect (F(5,190) = 1.74, p = 0.137, η ² = 0.04, BF_incl = 0.23) and the main effect of condition (F(1,38) = 1.34, p = 0.254, η ²= 0.03, BF_incl = 0.41) were not significant.

A similar attention mechanism in action binding

Attention might influence action binding because the action and the sound in the AS (action sound) condition both can be salient cues for attention orientation, especially in the case of action time judgement. Whereas in the AO (action only) condition, no sound was played after the action. Therefore, it is conceivable that the attention resource right after the sound play should be higher in the AS condition than in the AO condition (Figure 1b). Experiment 4 tested the idea of attention involvement in action binding by measuring action binding and attention distribution in the same experiment as similarly done with outcome binding (Figure 4a). The action binding effect was confirmed (t(22) = 3.45, p = 0.001, dz = 0.72, one-tailed paired-sample t-test, BF₊₀ = 34.64; Figure 4b). The reported keypress time was later in the AS condition (M = 102.28 ms, 95% CI = [86.06 118.50] ms) than in the SO condition (M = 78.37 ms, 95% CI = [58.91 97.83] ms). The general pattern of attention distribution looks different to that found in the outcome binding task. In both AS and AO conditions, attention was high right after the keypress and then underwent a sharp drop (Figure 4c). This is probably due to the fact that the task here was to report the keypress time rather than the sound time. Therefore, attention dropped quickly after the keypress execution. As predicted, there was a significant difference in the attention distribution between the two conditions, which was was confirmed by a significantly interaction effect in the two-way (condition: AS vs. AO; probe location: –50°, –40°, –30°, –20°, –10°, 0°, 10°, 20°, 30°, 40° and 50°) within-participants ANOVA comparing the detection rate (F(10,220) = 2.93, p = 0.026, η ²= 0.12, BF_incl = 18.06). After the sound play, the amount of attention resource was numerically higher in the AS condition than in the AO condition. The main effect of probe location was unsurprisingly significant (F(10, 220) = 79.56, p < 0.001, η_p² = 0.78, BF_incl = 1.13e64), and the main effect of condition was not significant (F(1,22) = 1.66, p = 0.210, η ² = 0.07, BF = 0.25).

Figure 4

Computational modelling of temporal binding using the attention measure

If attention is critically involved in temporal binding as measured in the current study, it should be theoretically possible to predict temporal binding using the attention measure alone. The attention hypothesis posits that attention is directly related to the timing report. The spatial location receiving more attention should contribute more towards the result of the spatial localisation of the clock hand (i.e. timing report). Each location of attention measure corresponded to a potential value of the timing report (e.g. the location where the clock hand pointed to at the time of sound play corresponds to 0 ms in the sound time report task and 250 ms in the keypress time report task). A model was built to predict the individual timing report in each condition through integrating all the measured locations weighted by the attention measure (Figure 5a; see also Equations 1-3 in the methods section).

Figure 5

The modelled timing report significantly correlated with the actual timing report in each single condition. In the AS condition of outcome binding (Experiments 1-3), a significant positive correlation was found between the modelled timing report of the sound and the actual timing report of the sound (r(65) = 0.55, p < 0.001, one-tailed Spearman correlation, 4 outliers removed, BF₊₀ = 4.32e3, Figure 5b; without removing outliers: r(69) = 0.51, p < 0.001, one-tailed Spearman correlation, BF₊₀ = 2.05e3). The same correlation was also found in the SO condition (here the SO condition from Experiments 1&2 and the VS condition from Experiment 3 were combined) (r(65) = 0.36, p = 0.001, one-tailed Spearman correlation, 4 outliers removed, BF₊₀ = 19.16, Figure 5c; without removing outliers: r(69) = 0.26, p = 0.014, one-tailed Spearman correlation, BF₊₀ = 2.83). For the timing report of the keypress (Experiment 4), a significant correlation was found between the modelled timing report and the actual timing report in both AS condition (r(21) = 0.43, p = 0.021, one-tailed Spearman correlation, BF₊₀ = 4.78, Figure 5e; no outlier detected) and AO condition (r(20) = 0.72, p < 0.001, one-tailed Spearman correlation, 1 outlier removed, BF₊₀ = 240.40, Figure 5f; without removing outliers: r(21) = 0.74, p < 0.001, one-tailed Spearman correlation, BF₊₀ = 391.20). The modelled temporal binding effect based on attention was obtained by taking the difference of the modelled timing reports in single conditions. For outcome binding (Experiments 1-3), a significant correlation was found between the modelled effect and the actual effect (r(69) = 0.43, p < 0.001, one-tailed Spearman correlation, no outliers found, BF₊₀ = 199.22, Figure 5d). For action binding (Experiment 4), a similar correlation was found (r(20) = 0.60, p = 0.002, one-tailed Spearman correlation, 1 outlier removed, BF₊₀ = 16.28, Figure 5g; without removing outliers: r(21) = 0.60, p = 0.001, one-tailed Spearman correlation, BF₊₀ = 17.87).

Lastly, the size of the modelled temporal binding effect was checked for each experiment. In Experiment 1, the modelled outcome binding effect (M = 75.97 ms) was statistically significant (t(17) = 3.98, p < 0.001, dz = 0.94, one-tailed paired-sample t-test, BF₊₀ = 77.53; Figure 5h), but showed a marginally significant reduction compared to the actual outcome binding effect (M = 113.47 ms; t(17) = –2.01, p = 0.061, dz = 0.47, two-tailed paired-sample t-test, BF₁₀ = 1.24). The same is true for Experiment 2. In Experiment 2, the modelled outcome binding effect (M = 41.23 ms) was statistically significant (t(13) = 3.22, p = 0.003, dz = 0.86, one-tailed paired-sample t-test, BF₊₀ = 15.74; Figure 5i), but significantly smaller than the actual outcome binding effect (M = 94.46 ms; t(13) = –3.61, p = 0.003, dz = –0.96, two-tailed paired-sample t-test, BF₁₀ = 14.61). In Experiment 3, the actual outcome binding was not statistically significant due to the attention matching manipulation. The modelled outcome binding was also not significant (M = –14.94 ms, t(38) = 1.61, p = 0.116, dz = 0.26, two-tailed paired-sample t-test, BF₁₀ = 0.56; Figure 5j). Furthermore, there was no significant difference between the modelled effect and the actual effect (t(38) = –1.72, p = 0.093, dz = –0.28, two-tailed paired-sample t-test, BF₁₀ = 0.66). Importantly, like the actual outcome binding effect showed earlier, the modelled outcome binding in Experiment 3 was significantly smaller than the modelled outcome binding in Experiments 1&2 (t(69) = –5.00, p < 0.001, ds = –1.19, one-tailed unpaired t-test, BF_-0 = 7.44e3). In Experiment 4, the modelled action binding effect (M = 10.83 ms) was statistically significant (t(22) = 2.16, p = 0.021, dz = 0.45, one-tailed paired-sample t-test, BF₊₀ = 2.97; Figure 5k), and significantly smaller than the actual action binding effect (M = 23.91 ms; t(22) = –2.17, p = 0.041, dz = –0.45, two-tailed paired-sample t-test, BF₁₀ = 1.53).

Discussion

The current study investigated the visuospatial attention distribution in the temporal binding effect measured with the classic Libet clock method. In 4 complementary experiments, it was demonstrated that the visuospatial attention had a direct link to the event timing report, with the reported time corresponding to the location on the clock where attention was paid to. Action and sensory input both can activate the attention concentration to the clock, resulting in a dynamic attention distribution pattern around the event which required a timing report. Critically, the difference in the attention distribution pattern activated by action and sensory input contributes massively to the temporal binding effect. Temporal binding consists of two effects in opposite directions, i.e. a shift of outcome time towards the past in outcome binding, and a shift of action time towards the future in action binding. The attention account provides at least a partial explanation for both outcome binding and action binding in terms of an attention bias.

It seems thus an immediate question is what temporal binding really means. The canonical view of temporal binding is that it reflects an illusion in timing judgement (Haggard et al., 2002; Tanaka et al., 2019; Wen & Imamizu, 2022). That is, an action appears to occur later when it is followed by a sensory outcome than when not (action binding), and a sensory input seems to occur earlier when it follows an action than when not (outcome binding). In contrast, the data from the current study illustrate the fact that when the event timing judgement is measured with the Libet clock method, there are differences in the contrasting conditions with regards to how the timing judgement is read out from the measurement tool (i.e. the Libet clock). Therefore, the bias in the way of reading measurements poses a challenge to a clear understanding of the variable being measured (i.e. timing judgement). It is unlikely that a changed timing judgement leads to a changed attention distribution, at least in outcome binding. In the outcome binding test, the attention activation following the keypress in the AS condition was before the sound onset, i.e. before the event that requires timing judgement (Figure 3b,d). Since timing judgement is a constructive process which integrates available information from both before and after the event of interest (Cao et al., 2020; Haggard et al., 2002; Klaffehn et al., 2021; Moore & Haggard, 2008; Takahata et al., 2012), there is a theoretical possibility that a common process before the action triggers both a change in attention and a change in timing judgement. One candidate for this common process may be the prediction of the action outcome. However, this idea needs further evidence.

Directly built on the attention hypothesis of temporal binding, the computational modelling can reproduce the temporal binding effect using the attention measure alone. This further strengthens the core claim of the current study, i.e. temporal binding is at least severely confounded by attention when measured with the Libet clock method. However, the modelled temporal binding effect is smaller than the measured effect (Figure 5i,k). This seems to indicate that there is a genuine timing judgement component in temporal binding on top of attention. However, the impact of attention may not have been fully captured in the current study. First, attention was only measured in a limited spatial area (100 degrees starting with the clock hand position at the keypress time). In fact, attention outside this area may also contribute to the timing report. The spatial attention to the locations where the clock hand pointed to at the action preparation stage especially may have a strong influence on the timing report. Due to the unpredictability of the exact action time, measuring the attention before action execution is an experimental challenge. Second, attention may be measured at multiple time points for a given spatial location. We only measured one time point for each spatial location, i.e. the time point when the clock hand was pointing to the specified location. Attention at this time point may have higher relevance to the task compared to other time points, though. This might explain why the size of modelled temporal binding does no match the size of measured temporal binding, i.e. there may be missing attention points that contribute to the timing report. Importantly, strong and reliable predictive power of attention on the timing report in all single conditions and on temporal binding can be demonstrated (Figure 5b-g). Experiment 3 actually provided causal evidence that attention drives the outcome binding effect, as outcome binding was not statistically significant when the attention difference was experimentally controlled for between contrasting conditions (with doubled sample size). Previous research also showed that temporal binding declined when the temporal predictability of action and effect was controlled for (Kirsch et al., 2019).

Conceivably, such control allows the attention deployment to operate in a similar manner in different conditions. Therefore, it is still an open question about the cognitive underpinnings of temporal binding at the moment.

The present study also has important implications to the clock method in mental chronometry. Wundt probably was the first to use the clock with a fast rotating hand for the scientific study of mental chronometry (Wundt, 1874). The method is now also known as the Libet clock method, as Libet popularised this method in his famous study on free will (Libet et al., 1983). It is known that the timing report results from this method are quite variable among individuals and strongly depend on the method details such as the speed of the clock hand (Ivanof et al., 2022; Miller et al., 2010; Pockett & Miller, 2007; Sanford, 1974; Seifried et al., 2010; Wundt, 1874; Yabe & Goodale, 2015). However, the results are quite often used to draw conclusions about the temporal properties of mental processing. In fact, all these results have involved attention to spatial locations on a clock-like device in order to produce a timing report. The current study suggests that any difference between conditions in the timing report from this method may be in fact due to (or at least confounded by) differences in spatial attention. We should therefore investigate when and how such differences in spatial attention might arise in detail in order to better understand the results produced by this method.

Some limitations of the current study need to be born in mind. First, as mentioned before, a full picture of the spatiotemporal visual attention distribution is still waiting to be revealed in the timing report task with the Libet clock method. In the current study, attention was only measured at a limited time points and locations. A full picture of the attention distribution pattern could help achieve a complete understanding of the impact of attention on the timing report in the Libet clock method (Hon, 2022; Schwarz & Weller, 2023). In addition, a within-participants design paired with an attention intervention paradigm could help determine the impact of attention on temporal binding at the individual level. Second, the Libet clock method may not be the optimal tool for resolving the issue of a timing judgement component in temporal binding. Even if attention could fully account for the temporal binding measured with the Libet clock, it could also mean that the timing judgement component could not be easily measured in this way (Stetson et al., 2006). The temporal attraction between an action and the action outcome may exist like a Gestalt. However, the Gestalt is lost when measuring its constituting elements (i.e. reporting time of the action and the outcome separately).

Indeed, temporal binding has also been demonstrated using paradigms in which visual attention does not seem to be critically involved, including but not limited to the interval estimation paradigm (Engbert et al., 2007; Humphreys & Buehner, 2009) and the auditory timer paradigm (Martinez et al., 2018; Muth et al., 2021). Of course, whether attention in other modalities or other cognitive processes could explain the temporal binding effect reported there is an intriguing question for further investigations.

To sum up, the current study provided novel and important insights into the understanding of temporal binding and time judgement in general measured with the Libet clock method.

Attention is critically involved in temporal binding, at least when the measurement process involves attention. It is important to discount the contribution of attention in a clock-like method study before drawing conclusions about the temporal properties in cognition.

Materials and Methods

Experiment 1

Participants

20 participants (11 females; mean age = 21.2, SD = 1.8) were recruited from a local participant pool. Assuming an effect size of 0.89 (note that this is the effect size of outcome binding and action binding combined as reported in a meta-analysis, see Tanaka et al. (2019). Since outcome binding has larger effect size than action binding, the real effect size of outcome binding should be larger than this), 18 participants (2 excluded in the formal data analysis, see below) should lead to a statistical power of 0.98 (alpha = 0.05; one-tailed) (Faul et al., 2007). All participants have normal or corrected-to-normal vision. Written informed consent was obtained prior to experiment, and participants were debriefed and received monetary payment after the experiment. The experiment was conducted in accordance with the Declaration of Helsinki (2013) and was approved by the Ethics Committee of Department of Psychology and Behavioural Sciences, Zhejiang University (ethics application number: [2022]003).

Stimuli, Task and Procedure

The experiment consisted of three parts: threshold testing, AS condition, and SO condition, in this order.

In the threshold testing session, the luminance threshold of the visual probe used in AS and SO conditions was obtained using a 2-down-1-up staircase procedure (Levitt, 1971).

Experiment stimuli were presented on a grey background (RGB value: [128 128 128]; used throughout the experiment). The staircase procedure for obtaining the luminance threshold was run in two parallel lines, with one line having the luminance intensity starting at 128 (RGB value: [128 128 128]; intensity increase line) and the other starting at 200 (RGB value: [200 200 200]; intensity decrease line). Each trial picked a random line until 15 reversals was obtained for each line. In each trial, participants watched a clock face (diameter: 2.7 degrees of visual angle, dva) with a rapid clockwise rotating hand (1800 ms per revolution). The clock hand started rotating from a random angle, and participants were asked to make a keypress (‘k’ on a standard QWERTY keyboard with the right index finger) no earlier than 1 second from the trial start. A trial would be aborted with a visual warning signal and repeated if it was made before 1 second. After the keypress, a visual probe (a disk with a diameter of 0.1 dva) and a sound (1000 Hz tone, 50 ms long, 5 ms rise/fall envelop, comfortable volume level) were both presented with a delay of 250 ms. The visual probe was presented for 30 ms outside the clock rim (distance to the clock centre: 1.5 dva) but aligned to the position of the clock hand at the onset of the visual probe. After the visual probe presentation, the clock hand continued rotating for a random period between 750 and 1250 ms. Participants were then asked if a visual probe was detected.

In the AS condition, a visual detection task was employed together with the outcome binding measurement using the Libet clock method (Libet et al., 1983). Participants were asked to report the time of a sound play (timing report trials) or to report if a visual probe was detected (a visual probe was presented in visual probe trials to assess the distribution of attention; no visual probe was presented in catch trials, for assessing the false alarm rate). In each trial, the clock hand started rotating from a random angle (Figure 2a). Participants were asked to make a keypress (‘k’ on a standard QWERTY keyboard with the right index finger) at their own decision. However, they were told that no strategies should be used to plan the keypress time (e.g. making a keypress when the clock hand was at 3 o’clock position) and that the keypress should not be made within 1 second from the start of the trial. If a keypress was made within 1 second from the start of the trial, a visual warning signal was displayed, and the trial was repeated. After the keypress, a sound was played via the headphones (1000 Hz tone, 50 ms long, 5 ms rise/fall envelop, comfortable volume level) with a 250 ms delay. After the sound, the clock hand continued rotating for a random period between 750 and 1250 ms. In visual probe trials, the threshold titrated visual probe was presented for 30 ms right outside the clock rim (distance to the clock centre: 1.5 dva) close to the top of the clock hand. The location where the clock hand pointed to at the time of sound play was defined as 0° (time 0).

Accordingly, the clock hand would point to 10° 50 ms after the sound play, and –10° 50 ms before the sound play, given its rotation speed of 1800 ms per revolution. Visual probes were presented at 6 possible locations (corresponding to 6 time points): –50° (–250 ms; this is when the keypress was made in the AS condition), –30° (–150 ms), –10° (–50 ms), 10° (50 ms), 30° (150 ms), and 50° (250 ms) (Figure 2b). In catch trials and timing report trials, no visual probe was presented. At the end of the trial, participants should indicate if a visual probe was detected in both visual probe trials and catch trials. In timing report trials, the clock hand always stopped at the 12 o’clock position after the random period succeeding the sound. This is to ensure that the stop position of the clock hand does not introduce any bias in the judgement. Participants should move the clock hand to its position at the time of the sound, using the left hand (pressing ‘a’ and ‘s’ to move the clock hand counter-clockwise by 10° and 1°, respectively; pressing ‘d’ and ‘f’ to move the clock hand clockwise by 1° and 10°, respectively). There were 50 catch trials, 50 timing report trials, and 180 visual probe trials (30 trials for each visual probe location/timing). Trials were presented in a random order.

Intermixing all trial types provides the advantage of simultaneous measure of timing report and attention distribution. The validity of the testing paradigm can be directly assessed through checking the existence of the classic outcome binding effect. Since there were more trials asking for visual probe detection than trials asking for timing report, the participants were told in the beginning of the experiment that they should perform the task as if the timing report were required in each trial, with the aim of ensuring a good quality in the timing report. 5 trials of practice were given before the formal testing.

The SO condition was identical to the AS condition except that the sound play was controlled by computer (i.e. no keypress was required to trigger the sound). The timing information of the keypress and the stimulus presentation from the AS condition was recorded for its full replication in the SO condition. For this reason, the SO condition always followed the AS condition.

The stimuli were presented on a liquid crystal display screen (refresh rate: 100 Hz; 24 inch screen size). Stimulus generation and presentation was controlled by Psychtoolbox-3 (Kleiner et al., 2007) using Matlab (The MathWorks Inc., USA). The sound was presented using a pair of headphones (Beyerdynamic DT 770 pro, 32 OHM, Germany). The experiment was performed in a well-lit, soundproof testing booth.

Experiment 2

A new group of 20 participants were recruited for Experiment 2 (10 females; mean age = 22.1, SD = 2.7). Assuming an effect size of 0.89, 14 participants (6 excluded in the formal data analysis, see below) should lead to a statistical power of 0.93 (alpha = 0.05; one-tailed) (Faul et al., 2007). Experiment 2 was the same as Experiment 1 except that a strict eye movement control was employed. In Experiment 1, participants were asked to fixate the centre of the clock face but no measures were taken to enforce this requirement. In Experiment 2, the movements of the right eye were monitored at 1000 Hz with an eye tracking device (Eyelink Portable Duo, SR Research Ltd, Canada). In all the three parts of testing (threshold testing, AS condition, and SO condition), participants fixated the centre of the clock face. If the right eye was out of a square area of 2.0 dva centring on the clock face at any time from the start of a trial to the point when the clock hand stopped rotating, the trial would be aborted with a visual warning signal and repeated after.

Experiment 3

A new group of 40 participants were recruited for Experiment 3 (24 females; mean age = 21.9, SD = 2.4). Since the critical evidence in Experiment 3 is a significantly decreased outcome binding effect (to the point even no outcome binding could be found), the sample size was doubled compared to Experiments 1 and 2. This also led to a balanced sample size between Experiment 3 and the combination of Experiments 1 and 2, making an unpaired t-test between the two statistically appropriate. Assuming an effect size of 0.89, 39 participants (1 excluded in the formal data analysis, see below) should lead to a statistical power of > 0.99 (alpha = 0.05; one-tailed) (Faul et al., 2007). Experiment 3 has the following 3 changes as compared to Experiment 2. First, the SO condition was replaced by a Vibration Sound condition (VS). In the VS condition, the right index finger (the keypressing finger) received a mild and short vibrotactile stimulation (two impulses in 10 ms) from a miniature electromagnetic solenoid-type stimulator (Dancer Design, UK) 250 ms before the sound play. The onset of the vibrotactile stimulation aligned with the keypress time in the AS condition. The order of AS and VS conditions was counterbalanced across participants. For participants starting with the VS condition, the onset time of the vibrotactile stimulation was sampled from a normal distribution with the mean and standard deviation taking from the participants starting with the AS condition. Second, the total number of trials in each condition reduced to 170 (20 catch trials, 30 timing report trials, and 120 visual probe trials with 20 trials for each of the 6 visual probe locations). Third, the visual fixation area was a circle centred on the clock centre (diameter was the same as the side length of the square in Experiment 2, i.e. 2.0 dva).

Experiment 4

A new group of 30 participants were recruited for the test of attention in action binding (16 females; mean age = 21.2, SD = 1.9). Two previous studies from our own group using a similar set-up reported an effect size of 0.79 (n = 52) (Cao et al., 2021) and 0.62 (n = 42) (Cao et al., 2020). Assuming an effect size of 0.70 here, 23 participants (7 excluded in the formal data analysis, see below) lead to a statistical power of 0.95 (alpha = 0.05; one-tailed) (Faul et al., 2007).

Action binding and attention were measured in the same experiment using a similar set-up as in the outcome binding. In the action sound (AS) condition, participants made a voluntary keypress, which was followed by a 250 ms delayed sound. In timing report trials, the keypress time was reported as the clock hand position at the time of keypress. In visual probe trials, participants should report if a visual probe was detected during the testing. Visual probes were presented at 11 possible locations (corresponding to 11 time points): –50° (0 ms; this is when the keypress was made), –40° (50 ms), –30° (100 ms), –20° (150 ms), –10° (200 ms), 0° (250 ms; this is when the sound was played), 10° (300 ms), 20° (350 ms), 30° (400 ms), 40° (450 ms), and 50° (500 ms) (Figure 4a). Here the keypress time was defined as time 0 as the event of interest in action binding is the keypress. The location definition followed the routine set in the outcome binding experiments. In the action only (AO) condition, the keypress was not followed by an auditory outcome. Everything else was the same as the AS condition. There were 480 trials in each condition (100 catch trials, 50 timing report trials, and 330 visual probe trials with 30 trials for each of the 11 visual probe locations). The order of trials was randomised.

The order of the AS and the AO condition was counterbalanced across participants as there is a clear impact of the testing order on the size of action binding (Cao et al., 2021). The threshold of the visual probe was obtained prior to the action binding measure using a 2-down-1-up staircase procedure (Levitt, 1971). No eye movements control was applied.

Data analysis

The same data analysis procedure was applied to the 4 experiments.

The false alarm rate in the catch trials (calculated as the ratio of trials reporting a visual probe was detected) was used for participant exclusion. Four participants were excluded due to extremely high false alarm rate (1 from Experiment 1: 0.63; 1 from Experiment 2: 0.98; 2 from Experiment 4: 0.69 and 0.89). For the remaining participants, the average false alarm rate was 0.04 (SD = 0.07) in Experiment 1, 0.02 (SD = 0.01) in Experiment 2, 0.06 (SD = 0.08) in Experiment 3, and 0.04 (SD = 0.03) in Experiment 4.

For the timing report trials, the reported time in each trial was calculated as the difference between the reported position of the clock hand and the actual position of the clock hand. This difference in spatial location was converted to a temporal judgement error, based on the clock hand rotation speed of 1800 ms per revolution. The standard deviation and the median of the reported time in each condition (50 trials in each condition for Experiments 1, 2, and 4; 30 trials in each condition for Experiment 3) was used for subject exclusion. Individuals with extreme values of either the standard deviation or the median of reported time were excluded using the median absolute deviation from median (MAD–median) rule: let p be the individual value and P be the individual values from the whole sample. If |p − median(P)| ×0.6745 > 3 × MAD–median, this value is an outlier (Leys et al., 2013). This procedure further excluded 1 participant from Experiments 1, 5 participants from Experiment 2, 1 participant from Experiment 3, and 5 participants from Experiment 4. The remaining participants were included in the formal analysis (18 in Experiments 1, 14 in Experiment 2, 39 in Experiment 3, 23 in Experiment 4).

Individual outcome binding effect was calculated as the difference in the median reported sound time between SO and AS conditions (SO – AS; Experiments 1 and 2) or the difference between VS and AS (VS – AS; Experiment 3). Individual action binding effect as calculated as the difference in the median reported keypress time between AS and AO conditions (AS – AO). Group level outcome binding effect was evaluated with a one-tailed paired-sample t-test comparing the reported sound time between SO and AS conditions for Experiments 1 and 2 (assuming an outcome binding effect), and a two-tailed paired-sample t-test comparing VS and AS conditions for Experiment 3 (assuming the outcome binding effect would be smaller than in Experiments 1 and 2, but not sure to what extent or if the effect could be reversed).

Group level action binding effect was evaluated with a one-tailed paired-sample t-test comparing the reported keypress time between AO and AS conditions (assuming an action binding effect).

The comparison of the outcome binding effect between Experiment 3 and Experiments 1&2 was made with one-tailed unpaired t-tests (assuming a smaller effect in Experiment 3). Since no significant difference in outcome binding was found between Experiment 1 and Experiment 2 (t(30) = 1.01, p = 0.322, ds = 0.36, two-tailed unpaired t-test) and the testing set-up was quite similar, data from Experiments 1&2 were combined for the comparison.

For the visual probe trials (with visual probe presentation), the detection rate was calculated for each probe location as the ratio of trials with the probe detected. This was used as a measure of visual attention. The potential attention distribution difference between conditions was evaluated with a two-way (condition and probe location) within-participants ANOVA.

Computational modelling

For each condition, we performed computational modelling of the timing report results based on the attention distribution pattern of each individual. The rationale is that the reported clock hand position should correspond to the location where attention is directed to. A full cover of the spatiotemporal attention distribution pattern may be necessary for a precise modelling of the reported location. However, the limited (yet highly relevant) attention sampling points in the current study should at least provide a modelling result proportionate to the empirically measured result. That is, the modelled timing report may not be exactly the same as the actual timing report, but should at least be proportionate to the actual value (e.g. 60% of the actual value). The modelling of timing report in the outcome binding experiments (Experiments 1-3) was performed as:

where k is the 6 attention sampling points (i.e. –250, –150, –50, 50, 150, 250 ms; sound play time is 0 ms). D_k is the individual detection rate at time point k. D is all the 6 detection rates, and min(D) is the smallest among the 6 detection rates. The modelling of timing report in the action binding experiment (Experiment 4) was performed as:

where k is the 11 attention sampling points (i.e. 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500 ms; keypress time is 0 ms). A one-tailed Spearman’s rank correlation analysis was performed between the modelled timing report and the actual timing report across participants in each single condition, as a positive correlation was predicted. Modelled temporal binding effects were calculated using the modelled timing report in single conditions (SO – AS or VO – AS for modelled outcome binding; AS – AO for modelled action binding). Since positive values were predicted for modelled outcome binding (Experiment 1, 2) and modelled action binding (Experiment 4), one-tailed paired-sample t-test was used. In Experiment 3, the modelled outcome binding may be positive or negative (two-tailed paired-sample t-test), but was predicted to be smaller than in Experiments 1 and 2 (one-tailed unpaired t-test; data in Experiments 1 and 2 were combined). To compare the size of the modelled temporal binding effect and the actual temporal binding effect, a two-tailed paired-sample t-test was used for each experiment. As already noted, the modelled temporal binding effect was predicted to be at least proportionate to the actual temporal binding effect (one-tailed Spearman’s rank correlation). In all correlation analyses, bivariate outliers in correlation analyses were detected using the box-plot rule (Pernet et al., 2013), and excluded afterwards. However, results without outlier exclusion were also reported for reference.

Bayesian statistics

Along with the traditional frequentist statistics, Bayesian statistical results obtained with JASP (version 0.17.2.1) were reported (JASP Team, 2023). The default prior setting from JASP was used. For the ANOVA, matched models were used to assess the effects. For the correlation analysis, Kendall’s rank correlation was used as Spearman’s rank correlation was not available in JASP.

Compliance and Ethics

We declare no conflict of conflict of interest. We have conformed with the Helsinki Declaration of 1975 (as revised in 2013) concerning Human and Animal Rights.

Open Practices Statement

The original data and Matlab analysis code are freely available from Figshare (doi:10.6084/m9.figshare.23917062).

Acknowledgements

We would like to thank Patrick Haggard for the insightful discussions and helpful comments on an earlier draft, Wilfried Kunde for helpful comments on an earlier draft, and Junyi Dai for statistical consultations. This work was supported by the National Natural Science Foundation of China (grant number: 32271078) and the STI 2030—Major Projects (grant number: 2021ZD0200409).