Supplementary Material:
Replicability and Reliability of the Background and Target Velocity Effects in Smooth Pursuit
Eye Movements
Rebekka Schröder1, Philine Margarete Baumert1 and Ulrich Ettinger1*
1 Department of Psychology, University of Bonn, Bonn, Germany
* Corresponding author:
Ulrich Ettinger, Department of Psychology, University of Bonn, Kaiser-Karl-Ring 9, 53111 Bonn, Germany,
Email: ulrich.ettinger@uni-bonn.de, Phone: +49 228 734208
Supplementary Table 1: Reliability results for velocity gain
Condition Reliability
type
Pearson correlation Intraclass correlation
r p CI
lower CI
upper ICC p CI
lower CI upper 0.2 Hz, no
background retest short 0.51 .001 0.24 0.7 0.5 < .001 0.23 0.69 retest long 0.61 < .001 0.38 0.77 0.61 < .001 0.39 0.77 split-half T1 0.57 < .001 0.33 0.74 0.56 < .001 0.32 0.74 split-half T2 0.66 < .001 0.45 0.8 0.66 < .001 0.45 0.8 0.4 Hz, no
background retest short 0.67 < .001 0.46 0.8 0.65 < .001 0.44 0.79 retest long 0.61 < .001 0.38 0.77 0.61 < .001 0.39 0.77 split-half T1 0.65 < .001 0.44 0.8 0.64 < .001 0.42 0.79 split-half T2 0.78 < .001 0.63 0.88 0.76 < .001 0.58 0.87 0.6 Hz, no
background retest short 0.76 < .001 0.6 0.87 0.73 < .001 0.54 0.85 retest long 0.79 < .001 0.65 0.88 0.78 < .001 0.62 0.87 split-half T1 0.79 < .001 0.65 0.88 0.78 < .001 0.63 0.87 split-half T2 0.92 < .001 0.86 0.96 0.92 < .001 0.86 0.96 0.2 Hz, background retest short 0.82 < .001 0.7 0.9 0.83 < .001 0.7 0.9 retest long 0.87 < .001 0.78 0.93 0.87 < .001 0.77 0.92 split-half T1 0.61 < .001 0.39 0.77 0.58 < .001 0.35 0.75 split-half T2 0.9 < .001 0.83 0.95 0.9 < .001 0.82 0.95 0.4 Hz, background retest short 0.82 < .001 0.69 0.9 0.81 < .001 0.69 0.89 retest long 0.9 < .001 0.82 0.94 0.89 < .001 0.82 0.94 split-half T1 0.86 < .001 0.76 0.92 0.86 < .001 0.76 0.92 split-half T2 0.92 < .001 0.86 0.96 0.92 < .001 0.86 0.95 0.6 Hz, background retest short 0.92 < .001 0.86 0.96 0.89 < .001 0.69 0.95 retest long 0.94 < .001 0.9 0.97 0.9 .001 0.51 0.97 split-half T1 0.83 < .001 0.71 0.91 0.83 < .001 0.72 0.91 split-half T2 0.91 < .001 0.84 0.95 0.9 < .001 0.83 0.95 Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split- half reliability (separately for T1 and T2). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for velocity gain at three different target velocities in the presence and absence of a stationary background.
Supplementary Table 2: Reliability results for the background effect
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper 0.2 Hz retest short 0.80 < .001 0.65 0.89 0.80 < .001 0.65 0.89
retest long 0.86 < .001 0.75 0.92 0.85 < .001 0.74 0.91 split-half T1 0.62 < .001 0.39 0.77 0.59 < .001 0.35 0.75 split-half T2 0.83 < .001 0.71 0.91 0.83 < .001 0.70 0.90 0.4 Hz retest short 0.76 < .001 0.60 0.86 0.75 < .001 0.58 0.85 retest long 0.76 < .001 0.60 0.86 0.76 < .001 0.61 0.86 split-half T1 0.71 < .001 0.52 0.83 0.71 < .001 0.52 0.83 split-half T2 0.80 < .001 0.66 0.89 0.80 < .001 0.67 0.89 0.6 Hz retest short 0.60 < .001 0.37 0.76 0.60 < .001 0.37 0.76 retest long 0.78 < .001 0.63 0.88 0.75 < .001 0.53 0.86 split-half T1 0.67 < .001 0.47 0.81 0.66 < .001 0.46 0.80 split-half T2 0.71 < .001 0.52 0.83 0.71 < .001 0.53 0.83 Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split- half reliability (separately for T1 and T2) of the background effect (no background condition minus background condition). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for velocity gain at three different target velocities.
Supplementary Table 3: Reliability results for the target velocity effect
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper background retest short 0.79 < .001 0.64 0.88 0.74 < .001 0.45 0.87
retest long 0.84 < .001 0.72 0.91 0.76 .001 0.33 0.90 split-half
T1 0.52 < .001 0.27 0.71 0.51 < .001 0.26 0.70
split-half
T2 0.71 < .001 0.53 0.84 0.71 < .001 0.53 0.83
no
background retest short 0.63 < .001 0.40 0.78 0.57 < .001 0.29 0.75 retest long 0.72 < .001 0.54 0.84 0.69 < .001 0.47 0.83 split-half
T1 0.65 < .001 0.44 0.80 0.64 < .001 0.43 0.79
split-half
T2 0.85 < .001 0.75 0.92 0.86 < .001 0.75 0.92
Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split- half reliability (separately for T1 and T2) of the target velocity effect (0.2 Hz condition minus 0.6 Hz condition).
Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for velocity gain in the presence and absence of a stationary background.
Supplementary Figure 1: Results of the reliability analyses for pursuit gain (Pearson correlations)
Legend: Reliabilities for pursuit gain (Panel A) for the six background and target velocity conditions, pursuit gain background effect (Panel B; no background condition minus background condition) and pursuit gain target velocity effect (Panel C; 0.2 Hz condition minus 0.6 Hz condition). r = Pearson correlation. Error bars represent the upper and lower limit of the 95% confidence interval.
Supplementary Figure 2: Effects of target velocity, background, block and time on pursuit gain
Legend: Effects of target velocity, background, block and time on pursuit gain for T1 (left) and T2 (right) in blocks A (upper panels) and B (lower panels). Data are presented as mean ± standard errors.
Supplementary Table 4: Number of outliers in pursuit gain
Condition Number of
outliers Target
velocity Background Time Block
0.2 Hz yes T1 A 1
0.2 Hz yes T1 B 0
0.2 Hz yes T1 A+B 1
0.2 Hz yes T2 A 2
0.2 Hz yes T2 B 0
0.2 Hz yes T2 A+B 1
0.2 Hz no T1 A 2
0.2 Hz no T1 B 1
0.2 Hz no T1 A+B 1
0.2 Hz no T2 A 2
0.2 Hz no T2 B 2
0.2 Hz no T2 A+B 2
0.4 Hz yes T1 A 0
0.4 Hz yes T1 B 0
0.4 Hz yes T1 A+B 0
0.4 Hz yes T2 A 1
0.4 Hz yes T2 B 0
0.4 Hz yes T2 A+B 0
0.4 Hz no T1 A 2
0.4 Hz no T1 B 1
0.4 Hz no T1 A+B 1
0.4 Hz no T2 A 1
0.4 Hz no T2 B 2
0.4 Hz no T2 A+B 1
0.6 Hz yes T1 A 0
0.6 Hz yes T1 B 0
0.6 Hz yes T1 A+B 0
0.6 Hz yes T2 A 0
0.6 Hz yes T2 B 0
0.6 Hz yes T2 A+B 0
0.6 Hz no T1 A 1
0.6 Hz no T1 B 1
0.6 Hz no T1 A+B 1
0.6 Hz no T2 A 1
0.6 Hz no T2 B 1
0.6 Hz no T2 A+B 1
Legend: Number of pursuit gain outliers in each task condition that were excluded for reliability analyses.
Additional analyses
The analyses reported in the manuscript were also carried out for two additional outcome measures, i.e. catch- up saccade rate and root mean square error (RMSE). Saccades were identified using velocity (≥22°/s), acceleration (≥3800°/s2) and amplitude (≥1°) criteria. Saccades were defined as catch-up saccades if they improved eye position error, started behind the target and landed behind the target or if they started behind the target and landed ahead of the target while reducing position error by at least 50%. RMSE was calculated by first determining the sum of the squared angular distance between eye and target location at each point in the pursuit record. The square root of this sum divided by the number of points of measurement was obtained as the final global measure. Blinks were excluded.
Catch-up saccades
Supplementary Tables 5 and 6 show descriptive statistics of catch-up saccade rate in the different task conditions and for the background and target velocity effects.
A four-way ANOVA on catch-up saccade rate with the within-subjects factors background (present, absent), target velocity (0.2 Hz, 0.4 Hz, 0.6 Hz), time (T1, T2) and block (A, B) revealed main effects of target velocity (F(2, 88) = 299.67, p < .001, 𝜂p2 = .872, 𝜖 = .66) and time (F(1, 44) = 5.96, p = .019, 𝜂p2 = .119). Catch-up saccade rate was higher at higher velocities and at T2.
In addition, we found a significant two-way interaction between background and target velocity
(F(2, 88) = 3.67, p = .038, 𝜂p2 = .077, 𝜖 = .81). Post-hoc Bonferroni-corrected t-tests revealed that catch-up saccade rate was higher in the background condition compared to the no background condition only at the intermediate target velocity (0.2 Hz: background vs. no background t(44) = 1.86, p = 0.07, n.s. at the Bonferroni-corrected alpha-level, dav = .24; 0.4 Hz: background vs. no background t(44) = 2.72, p = 0.01, dav = .28; 0.6 Hz: background vs. no background t(44) = -.52, p = 0.6, n.s. at the Bonferroni-corrected alpha-level, dav = -.05).
We also found a significant two-way interaction between background and time (F(1, 44) = 4.08, p = .050, 𝜂p2 = .085). Post-hoc Bonferroni-corrected t-tests revealed that catch-up saccade rate increased from T1 to T2 only in the background condition but not in the no background condition (background: T1 vs. T2 t(44) = -3.18, p = 0.003, dav = -.12; no background: T1 vs. T2 t(44) = -1.05, p = 0.3, n.s. at the Bonferroni-corrected alpha-level, dav = -.04).
Moreover, there was a three-way interaction between background, time and block (F(1, 44) = 4.43, p = .041, 𝜂p2 = .091). Catch-up saccade rate increased from T1 to T2 in all conditions except for the no background condition in block A (background, block A: T1 vs. T2 t(44) = -2.52, p = 0.02, n.s. at the Bonferroni-corrected alpha-level, dav = -.14; background, block B: T1 vs. T2 t(44) = -2.24, p = 0.03, n.s. at the Bonferroni-corrected alpha-level, dav = -.11; no background, block A: T1 vs. T2 t(44) = .52, p = 0.61, n.s. at the Bonferroni-corrected alpha-level, dav = .03; no background, block B: T1 vs. T2 t(44) = -2.11, p = 0.04, n.s. at the Bonferroni-corrected alpha-level, dav = -.11). However, this pattern of results did not survive Bonferroni-correction.
There were no main effects of background and block and there were no further interactions (all p > .05).
Supplementary Figures 3 and 4 depict the task and time effects.
Supplementary Tables 7, 8 and 9 and Figures 5 and 6 summarize the results of the reliability analyses of catch-up saccade rate for the direct performance outcome and the background and target velocity effects.
Supplementary Table 10 shows how many participants had to be excluded for catch-up saccade analyses for each of the task conditions.
Supplementary Table 5: Descriptive statistics of catch-up saccade rate (N/s)
Target
velocity Time Block Background No background
M SD M SD
0.2 Hz T1 A 0.13 0.14 0.11 0.11
B 0.15 0.14 0.12 0.16
A+B 0.14 0.13 0.12 0.12
T2 A 0.19 0.19 0.13 0.19
B 0.16 0.17 0.12 0.16
A+B 0.17 0.15 0.12 0.16
0.4 Hz T1 A 0.67 0.43 0.62 0.33
B 0.64 0.34 0.55 0.25
A+B 0.65 0.34 0.58 0.26
T2 A 0.78 0.38 0.64 0.38
B 0.77 0.37 0.65 0.36
A+B 0.78 0.34 0.65 0.34
0.6 Hz T1 A 1.29 0.66 1.37 0.59
B 1.26 0.58 1.30 0.51
A+B 1.28 0.56 1.34 0.49
T2 A 1.39 0.48 1.28 0.53
B 1.31 0.50 1.41 0.46
T2 A+B 1.35 0.45 1.34 0.46
Legend: Descriptive statistics (M mean and SD standard deviation) of catch-up saccade rate (N/s) of the background and no background conditions at three different target velocities of two sessions (T1, T2) one week apart, separately for blocks A and B and a joint version of the blocks (A+B) in a sample of N = 44 participants.
Supplementary Table 6: Descriptive statistics of the background and target velocity effects on catch-up saccade rate
Time Block Background effect Target velocity effect
0.2 Hz 0.4 Hz 0.6 Hz Background No background
M SD M SD M SD M SD M SD
T1 A -0.02 0.14 -0.05 0.39 0.08 0.50 -1.16 0.68 -1.26 0.59
T1 B -0.03 0.19 -0.09 0.32 0.04 0.49 -1.11 0.58 -1.18 0.48
T1 A+B -0.02 0.15 -0.07 0.27 0.06 0.41 -1.14 0.57 -1.22 0.48
T2 A -0.06 0.16 -0.14 0.39 -0.11 0.43 -1.20 0.52 -1.15 0.53
T2 B -0.04 0.17 -0.12 0.35 0.10 0.50 -1.14 0.50 -1.28 0.46
T2 A+B -0.05 0.15 -0.13 0.31 -0.01 0.39 -1.17 0.47 -1.22 0.45
Legend: Descriptive statistics (M mean and SD standard deviation) of catch-up saccade rate (N/s) background effect (no background condition minus background condition) at three different target velocities and velocity gain target velocity effect (0.2 Hz condition minus 0.6 Hz condition) of the two background conditions of two sessions (T1, T2) one week apart, separately for blocks A and B and a joint version of the blocks (A+B) in a sample of N = 44 participants.
Supplementary Figure 3: Effects of target velocity, background, block and time on catch-up saccade rate
Legend: Effects of target velocity, background, block and time on catch-up saccade rate (N/s) for T1 (left) and T2 (right) in blocks A (upper panels) and B (lower panels). Data are presented as mean ± standard errors.
Supplementary Figure 4: Interactive effects of target velocity, background, time and block on catch-up saccade rate
Legend: Two-way interaction of target velocity and background (Panel A), two-way interaction of background and time (Panel B), three-way interaction of time, block (A left, B right) and background (Panel C) on catch-up saccade rate (N/s). All depicted interactions are significant at α = .05. Data are presented as mean ± standard errors.
Supplementary Table 7: Reliability results for catch-up saccade rate (N/s)
Condition Reliability
type
Pearson correlation Intraclass correlation
r p CI
lower CI
upper ICC p CI
lower CI upper 0.2 Hz,
no background
retest short 0.41 .007 0.12 0.63 0.41 .003 0.12 0.64 retest long 0.55 < .001 0.31 0.73 0.55 < .001 0.31 0.73 split-half T1 0.30 .054 0.00 0.55 0.30 .027 -0.01 0.55 split-half T2 0.46 .002 0.18 0.67 0.44 .002 0.16 0.66 0.4 Hz,
no background
retest short 0.45 .002 0.17 0.66 0.45 .001 0.18 0.66 retest long 0.61 < .001 0.39 0.77 0.58 < .001 0.36 0.75 split-half T1 0.59 < .001 0.35 0.75 0.56 < .001 0.32 0.73 split-half T2 0.64 < .001 0.42 0.78 0.64 < .001 0.42 0.78 0.6 Hz,
no background
retest short 0.64 < .001 0.43 0.79 0.63 < .001 0.42 0.78 retest long 0.72 < .001 0.54 0.83 0.72 < .001 0.54 0.84 split-half T1 0.59 < .001 0.35 0.75 0.58 < .001 0.35 0.74 split-half T2 0.70 < .001 0.52 0.83 0.68 < .001 0.48 0.81 0.2 Hz,
background
retest short 0.40 .008 0.11 0.63 0.35 .007 0.07 0.58 retest long 0.43 .004 0.15 0.64 0.39 .003 0.11 0.61 split-half T1 0.32 .032 0.03 0.57 0.31 .017 0.02 0.55 split-half T2 0.35 .020 0.06 0.59 0.36 .009 0.06 0.59 0.4 Hz,
background
retest short 0.65 < .001 0.44 0.79 0.62 < .001 0.40 0.78 retest long 0.77 < .001 0.62 0.87 0.73 < .001 0.47 0.86 split-half T1 0.53 < .001 0.29 0.72 0.52 < .001 0.27 0.71 split-half T2 0.65 < .001 0.44 0.79 0.66 < .001 0.45 0.80 0.6 Hz,
background
retest short 0.66 < .001 0.46 0.80 0.63 < .001 0.41 0.78 retest long 0.78 < .001 0.64 0.88 0.76 < .001 0.61 0.86 split-half T1 0.66 < .001 0.46 0.80 0.66 < .001 0.46 0.80 split-half T2 0.68 < .001 0.48 0.81 0.68 < .001 0.48 0.81 Legend. Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split-half reliability (separately for T1 and T2). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for catch-up saccade rate at three different target velocities in the presence and absence of a stationary background.
Supplementary Table 8: Reliability results for the background effect on catch-up saccade rate (N/s)
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper
0.2 Hz retest short 0.27 .089 -0.04 0.53 0.25 .045 -0.04 0.51
retest long 0.43 .004 0.15 0.65 0.42 .002 0.15 0.64
split-half T1 0.15 .351 -0.16 0.43 0.14 .182 -0.17 0.43
split-half T2 0.31 .048 0.00 0.56 0.31 .022 0.01 0.56
0.4 Hz retest short 0.39 .008 0.11 0.62 0.38 .004 0.11 0.60
retest long 0.40 .006 0.12 0.62 0.39 .003 0.12 0.61
split-half T1 0.18 .228 -0.12 0.45 0.18 .115 -0.12 0.45
split-half T2 0.37 .014 0.08 0.60 0.37 .007 0.08 0.60
0.6 Hz retest short 0.29 .052 0.00 0.54 0.27 .027 0.00 0.51
retest long 0.52 < .001 0.26 0.70 0.51 < .001 0.26 0.70
split-half T1 0.40 .007 0.12 0.62 0.40 .003 0.12 0.62
split-half T2 0.38 .009 0.10 0.61 0.35 .006 0.08 0.58
Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split- half reliability (separately for T1 and T2) of the background effect (no background condition minus background condition). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for catch-up saccade rate (N/s) at three different target velocities.
Supplementary Table 9: Reliability results for the target velocity effect on catch-up saccade rate (N/s)
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper background retest short 0.69 < .001 0.49 0.82 0.67 < .001 0.47 0.81
retest long 0.78 < .001 0.63 0.87 0.77 < .001 0.62 0.87 split-half T1 0.65 < .001 0.44 0.79 0.65 < .001 0.44 0.79 split-half T2 0.76 < .001 0.59 0.86 0.75 < .001 0.58 0.86 no
background
retest short 0.64 < .001 0.42 0.79 0.63 < .001 0.41 0.78 retest long 0.71 < .001 0.52 0.83 0.71 < .001 0.53 0.83 split-half T1 0.65 < .001 0.44 0.80 0.63 < .001 0.42 0.78 split-half T2 0.70 < .001 0.50 0.83 0.69 < .001 0.49 0.82 Legend: Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split-half reliability (separately for T1 and T2) of the target velocity effect (0.2 Hz condition minus 0.6 Hz condition). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for catch-up saccade rate in the presence and absence of a stationary background.
Supplementary Figure 5: Results of the reliability analyses (intraclass correlations) for catch-up saccade rate
Legend: Reliabilities for catch-up saccade rate (Panel A) for the six background and target velocity conditions, catch-up saccade rate background effect (Panel B; no background condition minus background condition) and catch-up saccade rate target velocity effect (Panel C; 0.2 Hz condition minus 0.6 Hz condition). ICC = intraclass correlation. Error bars represent the upper and lower limit of the 95% confidence interval.
Supplementary Figure 6: Results of the reliability analyses (Pearson correlations) for catch-up saccade rate
Legend: Reliabilities for catch-up saccade rate (Panel A) for the six background and target velocity conditions, catch-up saccade rate background effect (Panel B; no background condition minus background condition) and catch-up saccade rate target velocity effect (Panel C; 0.2 Hz condition minus 0.6 Hz condition). r = Pearson correlation. Error bars represent the upper and lower limit of the 95% confidence interval.
Supplementary Table 10: Number of outliers in each condition of catch-up saccade rate
Condition Number of
outliers Target
velocity Background Time Block
0.2 Hz yes T1 A 1
0.2 Hz yes T1 B 1
0.2 Hz yes T1 A+B 1
0.2 Hz yes T2 A 2
0.2 Hz yes T2 B 1
0.2 Hz yes T2 A+B 1
0.2 Hz no T1 A 1
0.2 Hz no T1 B 2
0.2 Hz no T1 A+B 1
0.2 Hz no T2 A 3
0.2 Hz no T2 B 1
0.2 Hz no T2 A+B 1
0.4 Hz yes T1 A 0
0.4 Hz yes T1 B 0
0.4 Hz yes T1 A+B 0
0.4 Hz yes T2 A 0
0.4 Hz yes T2 B 0
0.4 Hz yes T2 A+B 0
0.4 Hz no T1 A 0
0.4 Hz no T1 B 0
0.4 Hz no T1 A+B 0
0.4 Hz no T2 A 1
0.4 Hz no T2 B 0
0.4 Hz no T2 A+B 0
0.6 Hz yes T1 A 0
0.6 Hz yes T1 B 0
0.6 Hz yes T1 A+B 0
0.6 Hz yes T2 A 0
0.6 Hz yes T2 B 0
0.6 Hz yes T2 A+B 0
0.6 Hz no T1 A 0
0.6 Hz no T1 B 0
0.6 Hz no T1 A+B 0
0.6 Hz no T2 A 0
0.6 Hz no T2 B 0
0.6 Hz no T2 C 0
Legend: Number of catch-up saccade rate (N/s) outliers in each task condition that were excluded for reliability analyses.
RMSE
Supplementary Tables 11 and 12 show descriptive statistics of RMSE in the different task conditions and for the background and target velocity effects.
A four-way ANOVA on RMSE with the within-subjects factors background (present, absent), target velocity (0.2 Hz, 0.4 Hz, 0.6 Hz), time (T1, T2) and block (A, B) revealed main effects of background (F(1, 44) = 23.81, p < .001, 𝜂p2 = .351), target velocity (F(2, 88) = 51.31, p < .001, 𝜂p2 = .538, 𝜖 = .71), time (F(1, 44) = 6.81, p = .012, 𝜂p2 = .134) and block (F(1, 44) = 5.41, p = .025, 𝜂p2 = .110). RMSE was higher in the presence of a stationary background, at higher velocities, at T1 and in block A.
In addition, we found a significant two-way interaction between background and target velocity
(F(2, 88) = 11.17, p < .001, 𝜂p2 = .202). Post-hoc Bonferroni-corrected t-tests revealed that differences between the two background conditions were significant only at the higher target velocities but not at 0.2 Hz (0.2 Hz:
background vs. no background t(44) = 1.32, p = 0.2, n.s. at the Bonferroni-corrected alpha-level, dav = .11; 0.4 Hz:
background vs. no background t(44) = 4.03, p < .001, dav = .38; 0.6 Hz: background vs. no background t(44) = 6.21, p < .001, dav = .44).
We also found a significant two-way interaction between target velocity and time (F(2, 88) = 10.35, p < .001, 𝜂p2 = .190, 𝜖 = .72). Post-hoc Bonferroni-corrected t-tests revealed that RMSE decreased from T1 to T2 only at the higher target velocities but not at 0.2 Hz (0.2 Hz: T1 vs. T2 t(44) = .08, p = 0.94, n.s. at the Bonferroni- corrected alpha-level, dav = .01; 0.4 Hz: T1 vs. T2 t(44) = 2.13, p = 0.04, n.s. at the Bonferroni-corrected alpha- level, dav = .18; 0.6 Hz: T1 vs. T2 t(44) = 4.59, p < .001, dav = .38).
Moreover, there was a two-way interaction between background and time (F(1, 44) = 7.86, p = .008, 𝜂p2 = .151) suggesting that RMSE decreased from T1 to T2 only in the background condition but not in the no background condition (background: T1 vs. T2 t(44) = 3.73, p < .001, dav = .27; no background: T1 vs. T2 t(44) = 1.20, p = 0.24, n.s. at the Bonferroni-corrected alpha-level, dav = .11).
There were no further interactions (all p > .05).
Supplementary Figures 7 and 8 depict the task and time effects. Supplementary Tables 13, 14 and 15 and Supplementary Figures 9 and 10 summarize the results of the reliability analyses of RMSE for the direct performance outcome and the background and target velocity effects. Supplementary Table 16 shows how many participants had to be excluded for RMSE analyses for each of the task conditions.
Supplementary Table 11: Descriptive statistics of RMSE Target
velocity Time Block Background No
background
M SD M SD
0.2 Hz T1 A 1.57 0.87 1.31 0.73
B 1.41 0.64 1.27 0.59
A+B 1.52 0.70 1.33 0.59
T2 A 1.38 0.69 1.47 0.81
B 1.35 0.75 1.34 0.85
A+B 1.39 0.68 1.44 0.77
0.4 Hz T1 A 1.86 0.97 1.43 0.86
B 1.72 0.98 1.44 0.72
A+B 1.83 0.91 1.46 0.73
T2 A 1.62 0.77 1.38 0.66
B 1.58 0.93 1.27 0.66
A+B 1.62 0.82 1.35 0.62
0.6 Hz T1 A 2.42 1.01 1.96 0.93
B 2.29 1.22 1.79 0.81
A+B 2.40 1.03 1.91 0.80
T2 A 1.94 0.82 1.67 0.86
B 1.91 0.81 1.53 0.63
A+B 1.94 0.78 1.62 0.71
Legend: Descriptive statistics (M mean and SD standard deviation) of RMSE of the background and no background conditions at three different target velocities of two sessions (T1, T2) one week apart, separately for blocks A and B and a joint version of the blocks (A+B) in a sample of N = 44 participants.
Supplementary Table 12: Descriptive statistics of the background and target velocity effects on RMSE
Time Block Background effect Target velocity effect
0.2 Hz 0.4 Hz 0.6 Hz Background No background
M SD M SD M SD M SD M SD
T1 A -0.26 0.60 -0.43 0.84 -0.46 0.68 -0.85 0.82 -0.65 0.91 T1 B -0.14 0.61 -0.28 0.90 -0.50 0.84 -0.87 0.98 -0.52 0.72 T1 A+B -0.19 0.47 -0.36 0.75 -0.49 0.54 -0.87 0.76 -0.58 0.73
T2 A 0.09 0.68 -0.24 0.52 -0.28 0.70 -0.56 0.65 -0.19 0.81
T2 B -0.01 0.57 -0.31 0.67 -0.38 0.55 -0.56 0.69 -0.19 0.67 T2 A+B 0.05 0.53 -0.27 0.51 -0.32 0.52 -0.55 0.55 -0.18 0.69 Legend: Descriptive statistics (M mean and SD standard deviation) of RMSE background effect (no background condition minus background condition) at three different target velocities and velocity gain target velocity effect (0.2 Hz condition minus 0.6 Hz condition) of the two background conditions of two sessions (T1, T2) one week apart, separately for blocks A and B and a joint version of the blocks (A+B) in a sample of N = 44 participants.
Supplementary Figure 7: Effects of target velocity, background, block and time on RMSE
Legend: Effects of target velocity, background, block and time on RMSE for T1 (left) and T2 (right) in blocks A (upper panels) and B (lower panels). Data are presented as mean ± standard errors.
Supplementary Figure 8: Interactive effects of target velocity, background, time and block on RMSE
Legend: Two-way interaction of target velocity and background (Panel A), two-way interaction of target velocity and time (Panel B), two-way interaction of time and background (Panel C) on RMSE. All depicted interactions are significant at α = .05. Data are presented as mean ± standard errors.
Supplementary Table 13: Reliability results for RMSE
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper 0.2 Hz, no
background
retest short 0.50 < .001 0.24 0.69 0.49 < .001 0.24 0.68
retest long 0.45 .002 0.18 0.66 0.44 .001 0.17 0.64
split-half T1 0.43 .003 0.16 0.65 0.42 .002 0.14 0.63
split-half T2 0.64 < .001 0.42 0.79 0.60 < .001 0.37 0.76 0.4 Hz, no
background
retest short 0.56 < .001 0.32 0.74 0.57 < .001 0.32 0.74 retest long 0.57 < .001 0.33 0.74 0.57 < .001 0.34 0.74 split-half T1 0.58 < .001 0.34 0.75 0.58 < .001 0.34 0.75 split-half T2 0.72 < .001 0.55 0.84 0.72 < .001 0.54 0.84 0.6 Hz, no
background
retest short 0.42 .005 0.14 0.64 0.30 .018 0.02 0.54
retest long 0.57 < .001 0.32 0.74 0.48 .001 0.18 0.69 split-half T1 0.53 < .001 0.28 0.72 0.51 < .001 0.26 0.70 split-half T2 0.61 < .001 0.38 0.77 0.61 < .001 0.38 0.77 0.2 Hz,
background
retest short 0.57 < .001 0.33 0.74 0.55 < .001 0.31 0.72 retest long 0.60 < .001 0.37 0.76 0.59 < .001 0.37 0.75 split-half T1 0.62 < .001 0.40 0.77 0.59 < .001 0.36 0.75 split-half T2 0.69 < .001 0.49 0.82 0.69 < .001 0.50 0.82 0.4 Hz,
background
retest short 0.73 < .001 0.56 0.84 0.69 < .001 0.49 0.82 retest long 0.82 < .001 0.69 0.90 0.79 < .001 0.63 0.89 split-half T1 0.65 < .001 0.44 0.79 0.65 < .001 0.44 0.79 split-half T2 0.87 < .001 0.77 0.93 0.85 < .001 0.75 0.92 0.6 Hz,
background
retest short 0.75 < .001 0.59 0.86 0.66 .001 0.27 0.83 retest long 0.83 < .001 0.71 0.90 0.72 .002 0.29 0.87 split-half T1 0.60 < .001 0.38 0.76 0.60 < .001 0.37 0.75 split-half T2 0.85 < .001 0.75 0.92 0.86 < .001 0.75 0.92 Legend: Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split-half reliability (separately for T1 and T2). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for RMSE at three different target velocities in the presence and absence of a stationary background.
Supplementary Table 14: Reliability results for the background effect on RMSE
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper
0.2 Hz retest short -0.03 .866 -0.32 0.27 -0.02 .567 -0.27 0.25
retest long 0.34 .023 0.05 0.57 0.30 .014 0.03 0.54
split-half T1 0.19 .212 -0.11 0.46 0.19 .103 -0.11 0.46 split-half T2 0.26 .097 -0.05 0.52 0.24 .053 -0.05 0.50 0.4 Hz retest short 0.56 < .001 0.32 0.74 0.49 < .001 0.23 0.69 retest long 0.51 < .001 0.25 0.70 0.48 < .001 0.22 0.68
split-half T1 0.42 .005 0.13 0.64 0.41 .003 0.13 0.63
split-half T2 0.46 .001 0.19 0.66 0.45 .001 0.18 0.65
0.6 Hz retest short 0.18 .245 -0.13 0.46 0.18 .128 -0.13 0.45
retest long 0.55 < .001 0.30 0.73 0.52 < .001 0.27 0.71 split-half T1 0.24 .113 -0.06 0.50 0.23 .065 -0.07 0.49
split-half T2 0.36 0.02 0.06 0.60 0.36 .009 0.06 0.60
Legend: Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split-half reliability (separately for T1 and T2) of the background effect (no background condition minus background condition). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for RMSE at three different target velocities.
Supplementary Table 15: Reliability results for the target velocity effect on RMSE
Condition Reliability type
Pearson correlation Intraclass correlation
r p CI
lower
CI
upper ICC p CI
lower
CI upper
background retest short 0.43 .003 0.16 0.65 0.40 .002 0.13 0.61
retest long 0.54 < .001 0.29 0.72 0.46 .001 0.18 0.67
split-half T1 0.34 .022 0.05 0.58 0.34 .011 0.05 0.58
split-half T2 0.29 .049 0.00 0.54 0.30 .024 0.00 0.54
no
background
retest short 0.46 .002 0.18 0.67 0.38 .007 0.08 0.62
retest long 0.23 .137 -0.08 0.50 0.20 .072 -0.07 0.45
split-half T1 0.32 .039 0.02 0.56 0.29 .025 0.00 0.54
split-half T2 0.49 .001 0.22 0.70 0.44 .002 0.15 0.66
Legend: Test-retest reliability of the short (only block A) and long version of the task (blocks A and B combined) and split-half reliability (separately for T1 and T2) of the target velocity effect (0.2 Hz condition minus 0.6 Hz condition). Numbers indicate Pearson correlation and intraclass correlation coefficients, significance value and upper and lower 95% confidence interval limits for RMSE in the presence and absence of a stationary background.
Supplementary Figure 9: Results of the reliability analyses (intraclass correlations) for RMSE
Legend: Reliabilities for RMSE (Panel A) for the six background and target velocity conditions, RMSE background effect (Panel B; no background condition minus background condition) and RMSE target velocity effect (Panel C; 0.2 Hz condition minus 0.6 Hz condition). ICC = intraclass correlation. Error bars represent the upper and lower limit of the 95% confidence interval.
Supplementary Figure 10: Results of the reliability analyses (Pearson correlations) for RMSE
Legend: Reliabilities for RMSE (Panel A) for the six background and target velocity conditions, RMSE background effect (Panel B; no background condition minus background condition) and RMSE target velocity effect (Panel C; 0.2 Hz condition minus 0.6 Hz condition). r = Pearson correlation. Error bars represent the upper and lower limit of the 95% confidence interval.
Supplementary Table 16: Number of outliers in each condition of RMSE
Condition Number
of outliers Target
velocity Background Time Block
0.2 Hz yes T1 A 0
0.2 Hz yes T1 B 0
0.2 Hz yes T1 A+B 0
0.2 Hz yes T2 A 0
0.2 Hz yes T2 B 0
0.2 Hz yes T2 A+B 0
0.2 Hz no T1 A 0
0.2 Hz no T1 B 1
0.2 Hz no T1 A+B 0
0.2 Hz no T2 A 0
0.2 Hz no T2 B 2
0.2 Hz no T2 A+B 0
0.4 Hz yes T1 A 0
0.4 Hz yes T1 B 0
0.4 Hz yes T1 A+B 0
0.4 Hz yes T2 A 0
0.4 Hz yes T2 B 0
0.4 Hz yes T2 A+B 0
0.4 Hz no T1 A 1
0.4 Hz no T1 B 1
0.4 Hz no T1 A+B 1
0.4 Hz no T2 A 0
0.4 Hz no T2 B 0
0.4 Hz no T2 A+B 0
0.6 Hz yes T1 A 0
0.6 Hz yes T1 B 0
0.6 Hz yes T1 A+B 0
0.6 Hz yes T2 A 0
0.6 Hz yes T2 B 0
0.6 Hz yes T2 A+B 0
0.6 Hz no T1 A 0
0.6 Hz no T1 B 1
0.6 Hz no T1 A+B 0
0.6 Hz no T2 A 3
0.6 Hz no T2 B 0
0.6 Hz no T2 C 2
Legend: Number of RMSE outliers in each task condition that were excluded for reliability analyses.
