3. Experiment 2
3.1.1 Task . Nine out of the ten participants that took part in the experiment described in the main text (hereafter referred to as Experiment 1) participated in Experiment 2. The same apparatus was used as in Experiment 1 albeit that the stylus’ position on the graphics tablet was sampled at a frequency of 100 Hz. The participants were requested to repetitively move the hand-held stylus between two targets for 32.5 cycles per trial (i.e., 65 aiming movements) at a tempo initially dictated by a (digital) metronome. Both the amplitude between the targets’ midpoints (again 0.20 m) and the target widths (0.10 m) were held constant. Twelve different movement times were implemented by varying the metronome frequency. For each participant, metronome frequencies were chosen so that their movement times corresponded to those observed under the conditions of Experiment 1. After 15 aiming movements the metronome stopped and the targets disappeared. The participants were instructed to continue moving at the imposed tempo while trying to maintain the amplitude of movement constant.
Whenever a participant’s movement time deviated more than ± 10% from the target movement time more than in half of all the movements the trial was performed anew (cf.
Bongers, Fernandez, &. Bootsma, in press). Each condition was repeated ten times, resulting in a total of 120 trials. The trials were presented in blocks of twelve trials in which each condition occurred once and was randomly presented. After each block a short rest was provided. The experiment was performed in two sessions of five blocks that were held on different days. The participants performed six practice trials (covering the entire range of implemented movement times) in each session preceding the experiment proper.
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3.2 Data Analysis . The kinematical analyses, the vector field reconstruction, and principal component analysis were performed similarly as in Experiment 1 albeit that averages were computed across blocks of trails with adjacent movement frequencies instead of adjacent
ID ’s.
3.3 Results and Discussion . The average movement ( MT ) increased across blocks of ten trials with increasing adjacent movement frequencies from 0.228 s to 1.366 s; the corresponding average effective ID increased monotonously from 4.64 to 5.27 (see Figure 1); its maximum was 6.21.
The durations of the acceleration and deceleration phases of each participant are shown in
Figure 2 as a function of the realized movement time. The duration of both phases significantly increased as a function of movement time (both P
’s < .001). In addition, for both phases post-hoc analysis indicated that generally all pair-wise comparisons were significant except for adjacent pairs at the longer movement times (see Table 1). In contrast to
Experiment 1, no evidence was found that the acceleration phase as a function of (here) movement time involved a discontinuity; the sum of the residuals squared for the double linear regression was not significantly different than for the exponential regression ( P > .05).
As in Experiment 1, the vector field analysis indicated that at short movement times the participants utilized limit cycle dynamics. Contrary to Experiment 1, however, there were no indications for the existence of fixed points around the movement reversal points at any movement time (see Figure 3; compare with Figure 1 in the main text). As movement time increased, a little scatter of adjacent vectors with large angles was found in small areas but only so at the edges of the ‘flat doughnut’.
Thus, we were unable to evoke a control mechanism involving fixed points in the absence of targets. In addition, the effective ID produced appeared to be limited and seems to
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exponentially saturate as the ‘imposed’ movement time increases. Furthermore, no indications for a discontinuous evolution of the acceleration phase as a function of movement time were found. In combination, these results – also with reference to Experiment 1 – strongly suggest that a ‘discrete’ control mechanism requires the presence of environmentally-specified targets, without which a high degree of accuracy cannot be attained.
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Electronic Supplementary Material 3 Table 1: Summary of Post-hoc results for the duration of the acceleration phase (upper right side of the diagonal) and deceleration phase (lower left side of the diagonal) for Experiment 2. Pair-wise significant difference ( P < .05) are indicated by an asterisk (*).
DT
AT
1
1 2 3 4 5 6 7 8 9 10 11 12
* * * * * * * * * * *
2 *
3 * *
* * * * * * * * * *
* * * * * * * * *
4 * * *
5 * * * *
* * * * * * * *
* * * * * *
6 * * * * * * * * * *
7 * * * * * * * * *
8 * * * * * * *
9 * * * * * * * *
10 * * * * * * * *
*
*
*
11 * * * * * * * * *
12 * * * * * * * * * * *
*
*
*
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References
R. M. Bongers, L. Fernandez, R. J. Bootsma, Exp Psychol Hum Percept Perform, in press.
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Electronic Supplementary Material 3 Figure 1
Figure 1. Average effective ID (IDe) as a function of movement time (MT) in Experiment 2.
Vertical bars represent the mean within-participant standard deviations.
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Electronic Supplementary Material 3 Figure 2
Figure 2. Duration of the acceleration (red) and deceleration (blue) phase as a function of movement time. The horizontal axis represents movement time (MT); the vertical axis time
[s]. Each dot represents a single trial.
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Electronic Supplementary Material 3 Figure 3
Figure 3. Reconstructed angle diagrams as a function of movement time (MT) averaged across participants. The horizontal axes represent normalized position (x); the vertical axes normalized velocity (y). MT increases from the upper left panel (MT = 0.228 s)—from left to right and top to bottom—to the lower right panel (MT= 1.366 s). The colour coding (right side of the panel) represents the maximum angle between adjacent vectors (see Method and main text).
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