Supplementary Materials 3

Supplementary Materials 3

This sectionSupplementary Material 3 describes an experiment designed to challenge the SRC account. We refer to this as Experiment 1. The key results are summarized in the main manuscript.

Experiment 1 Mmethod

Forty-eight participants (ageds 18– to 41 years, 10 Mmale, 4four left -handed) were involved. Participants sat 57 cm from a 60 -Hz CRT monitor, with the head stabilized in a chin rest. They had normal or corrected -to -normal vision. All experiments had local ethics committee approval and were conducted in accordance with the Declaration of Helsinki (revised 2008). All experiments were programmed using Python and the open source PsychoPy libraries(Peirce, 2007).

In the position trials, a blue vertical line moved leftwards or rightwards along a 20° track, then disappeared. In the number trials, a large ‘10.00’ appeared in the centre of the screen, and counted down towards 0 in decrements of 0.2. The counter disappeared before completion (see Fig.ureS3.1). In both kinds of trial, participants pressed when they judged the hidden process to be complete.

In both tasks, speed be expressed in ‘percent per second’, and were matched in this way (Makin & Bertamini, 2014; Makin & Chauhan, 2014). For example, consider trials where speed was ‘20% per second’— - This means that 20% percent of the process would be completed in one second: That is, 20% of the track (4°) or 20% of the number line (2.00 units).

There were 5 five blocks of trials. The order of these blocks was crucial to the experimental design. There was a practice block, then 4 experimental blocks, which came in two pairs: [false feedback block > adapted probe block] or [accurate feedback block > normal probe block]. The order of these blocks was counterbalanced across subjects (see Table S3.1)

Figure 1Fig. S3.1- Experiment 1 Mmethod

Practice blocks

The practice block contained both position and number trials. Speed was randomly chosen from a range between 10% and 40%/s, and occlusion onset varied between 20% and 80%. Participants received accurate feedback on every trial after they had responded. This gave CTE/occlusion duration as a percentage, and a verbal sign as to whether response was too early or too late. For example, if the participant pressed at 500 ms on a 1,000 -ms occlusion trial, the screen would say ‘’50.0% of actual hidden duration you were TOO EARLY’ and the text was green. However, if they pressed at 1,500 ms on a 1,000 -ms occlusion trial, the feedback screen would read ‘150.0% of actual hidden duration. You were Too Late’ and the text was red. If CTE was within +/- 20% of occlusion duration, the verbal sign read ‘Close, Well Done’, and a ‘rewarding’ three-tone audio cue sounded.

False feedback blocks

The false feedback block only had one kind of task. For half the participants, this was a position task, for the other half it was a number task (see Table S3.1). There were 10 trials with 1-s, 2.5-s or 4-second occlusions, and 30 fillers with randomized parameters. There were thus 60 trials in total, presented in a different random sequence for each participant. As in the practice block, feedback was given on every trial after participants pressed the button. However, crucially, the accuracy of this feedback continuously reduced throughout the block. On the first two trials, feedback was correct. However, after each increment of two trials, another 2% was added to the real feedback score, so participants kept being told they were pressing later than they really were. By the end of the false feedback block, feedback as 30% too late. The effect was that participants were trained to press early to counter the erroneous feedback.

It is likely that this chronological grading of feedback error magnitude was important. Pilot work with the same range of feedback in a random order did not find the same effect on subsequent probe performance.

Accurate feedback blocks

Accurate feedback blocks were exactly like the false feedback blocks, except feedback was correct on every trial.

Probe blocks

In the probe blocks, there were both position and number trials. The temporal parameters of the position and number trials were matched. In both tasks the stimulus moved at 20%/s occlusion began at 20%, 50%, or 80% of the way through the dynamic presentation, giving the 4-s, 2.5-s, and 1 -s occlusions. There were 10 repeats of each condition, giving 60 experiment trials. There were an additional 30 filler trials, where parameters were chosen at random. Trials were presented in a different randomized sequence for every participant. There was no feedback in the probe blocks.

The design of the Experiment 1 is shown in Table S3.1. The important comparison is between CTEs on the probe trials following the false feedback block (adapted probe block), with probe trials following the accurate feedback block (normal probe block). The false feedback blocks trained participants to press too early in just one type of PM task (either position or number). The important question is whether feedback alters CTEs in same type of trials only (position > position; number > number), or whether feedback generalizes (position > number; number > position).

Table S3.1 Design of Experiment 1. Participants completed five blocks, which were arranged in one of four ways. Analysis averaged over Orders 1 and 2

Table 1-Design of Experiment 1. Participants completed five blocks, which were arranged in one of four ways. Analysis averaged over orders 1 and 2.

Analysis

Results were analysed with repeated- measures ANOVA. The Greenhouse –Geisser correction factor was used when the assumption of Sphericity was violated (p0.05, according to Mauchly’s test of Ssphericity). The corrected degrees of freedom are shown.

Results

VE vs.versus CTE slopes

Before looking at the effects of feedback, it is worth testing whether VE vs.versus CTE slopes were similar in the position and number tasks, as found by Makin and Chauhan (2014). Mean CTE and VE were measured in all conditions of the probe blocks, collapsing over all between-subjects factors. Results are shown in Fig.ureS3.2. VE vs.versus CTE slopes are very similar in the position and number tasks,(t (47) = 1.474, p = 0.147). This null result is consistent with the CRC predictions.

Interpreting null results is problematic. The conventional p value tells us the probability of obtaining the data if the null hypothesis were true, not the probability of the null hypothesis being true given the data. Fortunately, Bayesian alternatives to null hypothesis significance testing can circumvent this. Given the data, we can assign one p value to the null hypothesis (pH0) and one alterative hypothesis (pH1) (Masson, 2011). This procedure found that the null hypothesis, pH0, has a probability of = 0.701, and consequently, the alternative hypothesis, pH1 = 0.299. We can thus be more confident that these slopes are the same (see Supplementary mMaterials 2for more of this analysis).

Figure 2-Fig. S3.2 VE vs.versus CTE in Experiment 1

Feedback generalization

Results from the group of participants where feedback was given on the position task are shown in the left column of Figure Fig. S3.3, and results from the group where feedback was given on the number taskare shown right column of Fig. S3.Figure 3.

Feedback blocks

Performance on the feedback blocks was altered appropriately. This can be seen in Fig. S3.Figure 3aA for the position task and Fig. S3.Figure 3Bb for the number task. Here, CTE is shown as a proportion of occlusion duration (a metric called pError). pError was calculated for each trial, and then the data was arranged in chronological order. The average pError from bins of 5 five trials was then obtained. pError approached 1 towards the end of the accurate feedback block, and reduced below 1 in the false feedback block, because participants were trained to respond too early. This resulted in a significant Feedback ×X Time interaction,(F (7.90, 363.37) = 7.983, p0.001, partial 2 = 0.148).

Probe blocks

The experience of receiving accurate or false feedback systematically altered CTEs in the subsequent probe blocks. Most importantly, feedback on position trials generalized onto number probe trials, and feedback on the number trials generalized onto position trials. This can be seen most clearly in Fig. S3.Figure 3Cc–d and D (which collapse over occlusion duration). There was a significant overall difference between normal probe blocks (following a block of accurate feedback) and adapted probe blocks (following a block of false feedback),(F (1,47) = 32.952, p0.001, partial 2 = 0.417). This feedback effect was stronger within tasks than across tasks, giving a three-way interaction,[Probe bBlock (normal, adapted) ×X Probe tTask (position, number) ×X Task on feedback block (position, number); F (1, 47) = 10.082, p = 0.003, partial 2 = 0.180]. However, paired t tests show an effect of feedback in all conditions (smallest effect),;t (23) = 2.099, p = 0.047). The green arrows in Fig. S3.Figure 3Cc–d and D illustrate the direction of generalization.

Figure 3-Fig. S3.3 Experiment 1 Results. The Left column shows results from participants who were given feedback on position task; the right column shows results from participants given feedback on the number task. Panels A and Ba–bshow pError in the feedback block. Panels C and Dc–dshow CTE in each task on the subsequent probe block (note the effect of adaption carries over across tasks, green arrows). E-He–hshows CTE as a function of occlusion duration in the normal and adapted blocks.

Figure S3.3 E-He–h show these CTE effects with the additional factor of occlusion duration. The interesting result here is that the CTE difference between normal and adapted probe blocks was larger for longer occlusions. Analysis of CTE vs.versus occlusion duration slopes shows that the relationship was steeper in the normal probe block (0.97) than the adapted probe block (0.92), (F (1, 46) = 7.639, p = 0.008, partial 2 = 0.142). The intercept was also higher in normal probe block (0.14) than the adapted probe block (0.07),(F (1, 46) = 6.060, p = 0.018, partial 2 =0.116).

On the position probe trials, slopes we significantly steeper in the normal (0.95) than in the adapted probe block (0.90), (F (1, 46) = 4.924, p = 0.031, partial 2 = 0.097,) and this did not interact with tTask on feedback block,(F (1, 46) < 1). The intercept was also higher in the normal block (0.33) than in the adapted block (0.24),(F (1, 46) = 4.606, p = 0.037, partial 2 = 0.097), and again there was no interaction with Ttask on feedback block,(F (1, 46) < 1).

In the number probe trials, slopes were also significantly steeper in the normal (1.00) than the adapted block (0.95),(F (1, 46) = 5.525, p = 0.023, partial 2 = 0.107,) this did not interact tTask on feedback block,(F (1, 46) = 1.660, p = 0.204). Here, the intercept did not differ between Nnormal (−-0.06) and adapted blocks (−-0.09),(F (1, 46) = 1.706, p = 0.198), and this did not interaction with task on feedback block,(F (1, 46) < 1).

The observed slope differences are consistent with the claim thatthe common rate controller was ticking faster in the adapted blocks. Motor potentiation would produce intercept effects only. Conversely, slope effects are arguably inconsistent with response bias explanations. However, this is debatable.We should bear in mind the nature of the feedback signal, which was given a percentage. At present, we cannot be sure that the rate controller sped up by the false feedback. This will have to be established with future research.

References

Makin, A. D. J., & Bertamini, M. (2014). Do different types of dynamic extrapolation rely on the same mechanism? Journal of Experimental Psychology: Human Perception and Performance, 40(4), 1566–1579.

Makin, A. D. J., & Chauhan, T. (2014). Memory-guided tracking through physical space and feature space. Journal of Vision, 14(13).

Masson, M. E. J. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing. Behavior Research Methods, 43(3), 679–690.

Peirce, J. W. (2007). PsychoPy: - Psychophysics software in Python. Journal of Neuroscience Methods, 162(1/–2), 8–13.

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