Fig 1.
Illustration of the process for generating a simulated DFA α value for a single subject.
A random number (green line) is drawn from a normal distribution with mean 0 and SD = 0.09 which represents expected inter-individual variability. Then two random numbers are drawn from the distribution centered on the individual deviation value (red dotted line) and SD = 0.16. This distribution simulates the expected variability of DFA α from trial to trial when using time series consisting of 100 data points (the SD of this distribution is smaller for longer time series). In this case, two trials are illustrated but we used 1, 2, 4, 6, and 8 trials in the full simulation. The experimental error is added to the trial values. in the final step of the simulation. The overall group value, μ, is then added to the average of the two resulting values to obtain the simulated DFA α value for a single individual. In the between-subjects version of the Monte Carlo simulations, two groups are simulated by drawing randomly from two independent normal distributions. In the within-subjects version, random numbers were drawn from a bivariate normal distribution ensuring correlation of 0.89 (see Method section).
Fig 2.
(A-B) These panels depict the expected power for between- and within-subject designs using 100 strides and an expected group difference of 0.1, corresponding to a medium effect size. (C-D) depict the same information for 200 strides per trial.
Fig 3.
Comparison of power predictions (solid lines) with the experimentally observed power (dotted lines) for different trial lengths.
(A) 100, (B) 150, and (C) 200 strides. Colored lines indicate the number of trials used per subject: 1 (blue), 2 (orange), 4 (yellow), and 6 trials (purple).
Fig 4.
DFA α differences between the synchronization conditions as a function of trial length in experimental data.
(A) Between-subject mean DFA α in the self-paced (blue lines) and persistent metronome (orange lines) conditions. (B) Standard deviation of DFA α in the same conditions. The solid blue line is the predicted between-subject variability from the simulation.