We collected data of 30 participants at the University of Würzburg and reimbursed them with monetary compensation or partial course credit. The sample size grants a power of 1-β > .99 to detect the effect of tone certainty on action binding in Wolpe et al. (2013). Three participants were excluded (for reasons, see the Data preprocessing section). The remaining sample reported a mean age of 31.9 (±12.7) years, six self-identified as male and 21 as female, and one participant reported being left-handed.
Apparatus and stimuli
The experiment was programmed with Matlab Version 2016a and the Psychtoolbox plugin. Following the classic temporal binding paradigm, we assessed the subjective timing of actions and following auditory effects. That is, in operant blocks participants performed actions and thereby generated auditory effects, whereas they performed key-presses without auditory effects and encountered isolated auditory stimuli in baseline blocks. Temporal binding should be evident in later estimates of the key-press in operant blocks as compared to baseline blocks (action binding) and in earlier estimates of the auditory stimulus in operant blocks as compared to baseline blocks (effect binding).
Actions were performed with the left index finger either via key-press on a keyboard (certain action) or on a force sensor fixed on the table (uncertain action). The keyboard was a standard computer keyboard and thus came with clearly defined onsets and offsets for each key-press (3.5-mm travel distance to bottom out key). Presses on the force sensor were accepted if pressure remained within a predefined force range for 50 ms. Participants were asked not to lift their finger between presses. How to perform a successful action via force sensor was explained and briefly trained before the experiment. Effect sounds were played via headphones and were either a 200-ms, 600-Hz beep (certain tone) or 827 ms of white noise that slowly rose and fell (uncertain tone; see Fig. 1A).
During every block, participants saw a Libet clock with ticks at every quarter hour on which they were instructed to estimate the timing of either actions or auditory events. The clock hand began to rotate at the beginning of the trial (taking a full turn every 2 s) and continued to do so for 1.2–1.5 s after the event in question had occurred. Then it stopped moving and jumped to a random position on the clock. Participants were then asked to judge the timing of one element of the trial by moving the clock hand with the arrow keys on the keyboard to the position it had been in at the time of the event, using their right hand. The Libet clock and all written instructions were presented on a 24-in. monitor with a refresh rate of 60 Hz.
We implemented two kinds of actions and two kinds of effects that differed in how precisely their timing could be perceived (see Fig. 1A). As is standard in temporal binding experiments, both actions and both effects were once probed in isolation to generate a baseline measure of temporal judgments. Additionally, these actions and effects were combined in three operant conditions (see Fig. 1B).
The “certain action – certain effect” (c-c) condition served as a control condition by replicating typical setups in the literature. Here, a key-press on the keyboard triggered a 200-ms beep tone with a constant delay of 500 ms. In the “uncertain action – certain effect” (u-c) condition, a force sensor press triggered a 200-ms beep tone at a constant delay of 500 ms, whereas in the “certain action – uncertain effect” (c-u) condition, a key-press on the keyboard triggered 827 ms of white noise with a slow rise and fall. The white noise began to rise after a 173-ms delay. All three operant conditions were either presented as action blocks, that is, participants only had to judge the timing of the action in this block, or as effect blocks, in which they only had to judge the timing of the effect. In effect baseline blocks, tones were presented at a random interval of 2–3 s after trial start. In all other blocks, participants were asked to wait at least 1 s before performing their action. Overall, the experiment had ten block types: four baseline blocks, three operant action blocks, and three operant effect blocks. Each block was once presented in a practice phase, which was not entered into data analysis. During the main experiment, every block was presented three times with 15 trials each in an unconstrained randomized order.
We excluded trials in which participants did not wait for at least a full turn before initiating their actions (4.4%), did not move the Libet clock hand during judgment (2.2% of all trials), and trials in which the temporal judgments deviated more than 2.5 standard deviations (SDs) of the participant’s cell mean (2.1%). Additionally, three participants were excluded: one consistently failed to move the clock hand, one had too many errors (failure to respect the inter-trial interval), and one had too high a variance in their judgments (2.5 SDs above the mean of the full sample). These participant exclusions were not preregistered, but we deemed them preferable to avoid a biased assessment of the results. A re-analysis of the whole sample, including these participants, is available in Appendix A. Furthermore, we computed the estimation error for each block type (judged time – actual time). If the judgment was in the clock half after the actual timing, we assumed a shift forward in time, and if it was in the clock half before the actual timing, we assumed a shift backward in time.Footnote 2
As a manipulation check, we computed the variance of the estimation errors in baseline blocks, which is assumed to be the inverse of the respective events’ certainty. Baseline blocks of uncertain actions as well as baseline blocks of uncertain effects should thus come with higher variances than certain baseline blocks (see Fig. 2A and Table 1). Indeed, one-tailed paired t-tests showed higher variances in uncertain than in certain baseline blocks for actions, t(26) = 4.67, p < .001, d = 0.90, whereas the differences of variance for effects conformed to our hypothesis numerically, but did not reach significance, t(26) = 1.70, p = .051, d = 0.33.
For the main analysis, we contrasted the judgment error in operant blocks with the judgment error in baseline blocks with paired t-tests (one-tailed) to test for the existence of temporal binding. There was significant action and effect binding for all conditions, as shown in Table 1.
Action and effect binding were computed for each type of operant block by subtracting the respective baseline judgment error. Bigger action binding is thus shown by more positive values, whereas effect binding is shown by more negative values. The binding values were entered into a repeated-measures analysis of variance (ANOVA) with the factor certainty-relation (c-u vs. c-c vs. u-c) separately for action judgments and effect judgments. Sphericity could not be assumed for either, and reported p-values are based on Greenhouse-Geisser corrected degrees of freedom. Differences between conditions were tested by planned contrasts (see Fig. 2). The ANOVA for action binding showed a significant impact of certainty-relation, F(2,52) = 4.25, p = .044, ηp2 = 0.14, ε = 0.56. Action binding was strongest when the action was uncertain and the effect certain (u-c), and was significantly smaller when the certainty relation was reversed (Action_u-c vs. Action_c-u), t(26) = 2.18, p = .039, d = 0.42 (two-tailed), but also when only the action certainty increased (Action_u-c vs. Action_c-c), t(26) = 1.98, p = .029, d = 0.38 (one-tailed). The ANOVA for effect binding did not show a significant impact of certainty relation, F(2,52) = 1.01, p = .357, ε = 0.79, and neither did the planned contrasts (all |t|s < 1.13, all ps > .135).
Based on the marked differences in variances, especially in action blocks, we followed up on the above pre-registered analyses and performed a non-parametric confirmation of the main analysis. That is, we compared action and effect binding in c-u and u-c blocks in a two-tailed paired Wilcoxon signed-rank test (action binding: Z = -1.87, p = .061; effect binding: Z = -1.35, p = .178), which did not reach significance.
Nevertheless, the observed pattern of results corroborates the predicted trade-off between action and effect binding, and it may therefore not be appropriate to analyze the two binding scores only in separation. Following this finding, we computed the sum of action and effect binding in all three conditions as a measure of an action-effect binding trade-off (with action binding coming with a positive sign and effect binding coming with a negative sign). If the trade-off account is true, this action-effect sum should be smallest in the “certain action – uncertain effect” (c-u) condition, because the absolute value of action binding is small relative to effect binding, while it should be biggest in the “uncertain action – certain effect” (u-c) condition. On the other hand, if the manipulation influenced action and effect binding in a similar way, as would be predicted by motor or causality accounts, the action-effect sum should not change between conditions. Two-tailed paired t-tests show that the sum of both binding scores was bigger in the u-c than in the c-u condition, t(26) = 2.75, p = .011, d = 0.53 (c-u vs. c-c: t(26) = 1.26, p = .221; c-c vs. u-c: t(26) = 2.23, p = .034, d = 0.43), supporting a trade-off account.
Significant action and effect binding was present in all conditions of Experiment 1. Furthermore, the relationship between action and effect binding strikingly resembled the trade-off predicted by the multisensory approach. A stronger action binding and a descriptively weaker effect binding were observed when the action was comparatively difficult, and the effect rather easy to pinpoint in time (i.e., in the u-c condition) than when the certainty-relation was reversed (i.e., in the c-u condition). Moreover, the results suggest an effect of action certainty on action binding independently from effect certainty, as actions were bound more strongly to the same effect, when they were uncertain as compared to when they were certain.
On the other hand, effect bindings did not differ significantly between conditions, and variances between certain and uncertain effects were not significantly affected by the manipulation either. In addition, participants judged the timing of the uncertain tone very close to its onset, rather than its peak (see Fig. 2 for an illustration of the problem). These observations might indicate an inapt effect manipulation. We thus conducted a second experiment, where we retained our action manipulation, but replaced the effect manipulation with one that was modelled more closely on the manipulation applied in previous work (Wolpe et al., 2013).