Fig 1.
Simulated white-noise and pink-noise time series and associated time-series analyses: The autocorrelation function and the power spectrum.
Both the simulated white-noise (top left panel) and pink-noise (bottom left panel) time series contain 1000 events of varying amplitude levels. The autocorrelation reflects the correlation of a time series with itself at different lags. For example, a lag-0 autocorrelation reflects the correlation of each value in the time series with itself. In that case, the correlation will always be r = 1. The lag-1 autocorrelation reflects the correlation of each time-series value with the very next time-series value; the lag-100 autocorrelation is the correlation of each time-series value with the value 100 events into the future. In the current figure, the autocorrelation spans lag 1 to lag 100. Another method of time-series analysis is spectral analysis: The power spectrum (right panels) decomposes a signal into component sinusoidal frequencies and assigns a power value scaled to the magnitude of each frequency’s contribution to the time series. For white noise, by definition, each observation in the time series is independent of every other event in the time series, and across all autocorrelation lags the correlations hover around a value of zero (top middle panel). For the white-noise power spectrum, each frequency in the spectrum contributes similar levels of power to the signal; as reflected by the slope of the frequency-power regression equation, there is essentially no change in power as a function of frequency (top right panel). In contrast, for the pink-noise time series one may observe low-frequency wavelike oscillations that reduce in magnitude as frequency increases (bottom left panel). That gives rise to elevated autocorrelations (bottom middle panel) and an inversely proportional reduction in power as a function of frequency: The slope of the frequency-power regression equation is essentially −1 (bottom left panel).
Fig 2.
Schematic depiction of visual information displayed in the visual feedback and no-visual feedback conditions.
As shown in the left panels, all conditions contained an initial period, over movements 1 to 100, where the targets, a target marker (+) (marking the currently active target), and a mouse-driven cursor (+) were displayed on the video monitor. In addition, the computer sounded an error “beep” (not referenced in the figure) whenever a movement terminated outside the target boundaries. Then, from movements 101 to 500, in the visual feedback condition the targets and cursor remained visible (top right panel), but in the no-visual feedback condition only the targets remained visible (bottom right panel). (Furthermore, during movements 101 to 500, the error “beep” was disabled in all conditions.) Note that the elements in the current illustration have not been drawn to scale; the actual targets appeared as white rectangular outlines superimposed on a black video-screen background; both the target markers and cursor were identical white crosshairs.
Fig 3.
Representative movement amplitude time series from the four experimental conditions.
The time series for ID-2 no-visual feedback (top left panel), ID-5 no-visual feedback (top right panel), ID-2 visual feedback (bottom left panel), and ID-5 visual feedback (bottom right panel) were taken from Participant 29, 17, 30, and 5, respectively. As with all data submitted to spectral analysis in the study, each panel in the figure contains a linearly detrended (and demeaned) movement amplitude time series from the last 300 consecutive movements in each condition (see ‘‘Spectral analysis of movement amplitude time series”). As one means of highlighting across-condition changes in movement amplitude time-series structure—namely, the contribution of low-frequency wavelike oscillations—sixth-order polynomial regression equations were fit to each time series.
Fig 4.
Changes in the group-mean movement amplitude as a function of the index of difficulty (ID) and visual feedback condition.
The height of each bar represents the group-mean movement amplitude based on an across-participant average at each ID and visual feedback condition. The error bar extending above each group-mean bar represents 1 SEM. The upper and lower horizontal-dotted lines mark the movement amplitude requirements under ID 2 (15.88 mm) and ID 5 (127 mm), respectively.
Fig 5.
Changes in the group-mean movement time as a function of the index of difficulty (ID) and visual feedback condition.
The height of each bar represents the group-mean movement time based on an across-participant average at each ID and visual feedback condition. The error bar extending above each group-mean bar represents 1 SEM.
Fig 6.
Changes in the group-mean power spectrum across index of difficulty (ID) and visual feedback conditions.
Each data point within each spectrum represents the across-participant average of log10 power within a given log10 frequency bin. The negative of the slope (−b) of the linear regression equation—y = bx + a—fit to each group-mean power spectrum was equivalent to the exponent (β) of a power function—y = 1/xβ—that is, if b = −1, then β = 1. β was the primary index of movement amplitude time-series structure. The amount of spectral power within each frequency bin represents the magnitude (size) of the time-series oscillations or variability within that frequency bin. In turn, the elevation of each spectrum represents the amount of overall movement amplitude variability across the range of frequencies.
Fig 7.
Changes in the group-mean β as a function of the index of difficulty (ID) and visual feedback condition.
β is the exponent of a power function—y = 1/xβ. A β value was calculated for each participant’s power spectrum at each ID level and visual feedback condition. Then, each group-mean β value was calculated by averaging across the individual-participant βs at a given ID and visual feedback condition. The error bar extending above each group-mean bar represents 1 SEM.