Thirty-six participants (age M = 24.8 years, SD = 4.3 years) volunteered in exchange for €7–10, depending on their performance on the tasks. Participants were recruited from the payed participant pool of the University of Groningen. The study was approved by the Psychology Ethical Committee of the University of Groningen (17129-SP-NE), and participants signed a form giving their informed consent.
Materials and procedure
Participants performed a timing task and a distance-estimation task, of which the order was counterbalanced between participants. In each task, participants tried to earn as many points as possible (each point was worth 0.69 eurocent). The accumulation of points and money was shown to the participants during the course of the experiment.
Stimuli were presented on a 12-inch touch-screen monitor (SCHURTER Electronics) using OpenSesame (Mathot, Schreij, & Theeuwes, 2012), and responses were made with the left or right rear buttons of a gamepad (Microsoft Sidewinder), depending on the participants’ preferred hand. Since the viewing distance was not precisely controlled, the descriptions of stimuli contain only estimations of visual angle. All code needed to run this experiment is publicly available (https://osf.io/f68wm/).
Participants performed an interval reproduction task, in which they had to reproduce a single interval of 750 ms. First, five passive learning trials were presented, in order to become familiar with the target interval. In each trial, participants were first shown a white intertrial fixation circle with a 3-mm diameter (0.46 ° visual angle) for a random duration between 1,000 ms and 2,000 ms. Next, a yellow circle with an 18-mm diameter (visual angle of 2.6° visual angle) was on the screen for 750 ms, then disappeared for random duration between 1,000 ms and 2,000 ms. Subsequently, during the experimental trials, participants were asked to reproduce the previously learned interval. The trial procedure was similar to the learning trials; the reproduction interval was initiated by the appearance of the yellow circle, and the participant marked the offset with a gamepad button press. Feedback on whether the produced interval was too long, too short, or within the 30% margins of 750 ms was presented for 1,000 ms. An example of the trial procedure is shown in Fig. 2a.
Equally spread over five experimental blocks, 250 intervals were produced, preceded by a practice block of 50 trials. In the experimental blocks, participants earned 5 points for responding within the 30% margin. In Block 2 and Block 4, points would be deducted if the response was too early. Before each block started, the payoff scheme was presented on the screen. The payoff scheme is shown in Table 1. The total number of points and money collected was shown together with each trial’s feedback.
Distance estimation task
Participants did a distance estimation task on the same touch-screen monitor as used for the timing task. Each trial started with a “start circle” presented at a random location below the right diagonal for right-handed participants and below the left diagonal for left-handed participants. After touching the start circle, an arrow appeared originating from the start circle, pointing to an invisible target that was always 55 mm (7.9° visual angle) away from the center of the start circle at a random angle (see Fig. 2b). The participant then tried to touch the invisible target to earn points. Feedback was presented on whether the tap was a hit, too close, or too far away relative to the start circle. Also, the accumulation of money was shown during the feedback screen, followed by a 1,000-ms to 2,000-ms intertrial period. In order to learn the distance, participants were shown a visible target once at the typical distance from the start circle during the instructions at the beginning of each block.
Participants performed the distance estimation 250 times, equally spread over five experimental blocks, preceded by 50 practice trials. The procedure regarding points and feedback was identical to the timing task: Participants earned 5 points for touching the target, but points would be deducted in Blocks 2 and 4 if their response was too close to the start circle (see Table 1).
Response times and distance estimations that deviated more than three median absolute deviations from the median, pooled over all trials per participant, were excluded from the analysis (2.7% of the timing trials, 2.1% of the distance estimation trials).
Three hierarchical linear mixed-effects models (LMMs) were performed using the lme4 package (Version 1.1-14; Bates, Mächler, Bolker, & Walker, 2014) in R (Version 3.6.0; R Core Team, 2018). Separate models for timing and distance estimation were estimated to test the effect of punishment level and the precision of the timer on adjustment of mean response. Adjustment was calculated as the difference between mean responses of the blocks with punishment and Block 1 and were used as dependent continuous variables (in seconds for the timing task and mm for the distance estimation task). Punishment level was added as a categorical fixed factor, in which the 5-punishment condition was the reference group and standard deviations per participant and block was added as a continuous fixed factor. To assess the relationship between the performance in the two different tasks a model was estimated with timing optimality (i.e., the difference between the actual adjustment and the optimal adjustment) as continuous dependent variable, distance optimality as continuous fixed factor, and punishment level as categorical fixed factor.
For each LMM we started with an intercept-only model, including participant as a random factor. We then sequentially added the relevant fixed factors. To test whether a fixed factor improved the model, we calculated Bayes factors using the lmBF function from the BayesFactor (Version 0.9.12-4.2; Morey & Rouder, 2018) package for R. The default priors of the BayesFactor package as described in Rouder and Morey (2012) were used. We will denote the evidence for the alternative hypothesis (H1; i.e., the model including the fixed factor) over the null hypothesis (H0; i.e., the model excluding the fixed factor) as BF10. Fixed factors that yielded a model with a BF over 3 were included in the models (Wagenmakers, 2007).