Differences between the group-level and participant-level AR-surrogate analyses.

A) Brookshire’s (2022) group-level AR-surrogate analysis. The participant-level behavioural time-courses are averaged and the group-average time-course is fit with an AR(1) model and used to generate a large number of surrogate time-courses. The real data and the surrogates are pre-processed in the same manner then Fourier transformed. The surrogate spectra are used to produce a null distribution of amplitude values at each frequency against which to compare the amplitude values of the real data. Typical corrections for multiple comparisons are applied (not shown here). B) For the participant-level AR-surrogate analysis, each of the participant-level time-courses are fit with an AR(1) model which is used to generate a large number of surrogate time-courses. The time-courses are pre-processed and Fourier transformed, then the average of the surrogate spectra is subtracted from the amplitude spectrum of the real data to produce a periodic spectrum. The periodic spectra for each participant are then analysed with typical statistical approaches (e.g., t-tests). Typical corrections for multiple comparisons are applied (not shown here). Panel A adapted from Brookshire (2022) under Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0/.

Example data simulation.

The behavioural responses were simulated by creating a probability time-course (example shown in C) that was the sum of an aperiodic component (example shown in A) and an oscillatory component (example shown in B). After producing the probability time-course, the behavioural response time-course (D) was produced by comparing one random number for each simulated trial to the probability value at the relevant time-point for that trial. Values above the probability threshold were considered ’hits’. This example reflects the process for one participant in one simulated experiment with a behavioural depth modulation of 10%.

Example results for a 10 Hz behavioural oscillation.

This simulation involved 500 experiments per depth modulation, each with 10 simulated participants. Sensitivity to detect the behavioural oscillation was above 0.95 for all depth modulations of 15% and above.

Comparison of participant-level and group-level AR-surrogate method.

A) The results of simulated experiments (500 per cell) analysed with the participant-level AR-surrogate method. Results only shown for the target frequency (10 Hz). B) The same data analysed with the group-level AR-surrogate method.

Proportion of false positives.

A) Proportion of simulated experiments producing false positives when the behavioural oscillation was absent (Depth Modulation of 0%). For this analysis, a significant oscillation at any frequency was deemed a false positive. B) Proportion of simulated experiments producing significant behavioural oscillations at any frequency other than the simulated oscillation frequency.

Effect of trial numbers.

A) The sensitivity of the participant-level AR surrogate analysis increases with more trials-per-time-point and with increasing depth modulation. The sensitivity for a sample size of 10 participants is shown here. B) False positives demonstrated in the oscillation-absent condition (depth modulation 0%). False positives are above 5% when fewer than 4 trials per cell are employed.

Sensitivity to oscillations of different frequencies.

A) Target frequency by depth modulation. Example shown here is for experiments with 10 simulated participants. Sensitivity is further increased at all higher participant numbers. B) Target frequency by number of participants. Example shown here is for the weakest depth modulation tested, 5%. For depth modulations of 10% or more, sensitivity was above 0.9 for all frequencies for participant numbers >20.

False positives across frequency.

A) In the noise-only condition, false positives are produced outside the recommended 3-20Hz range. B) This is due to the AR(1) process not capturing the full variability of the data. The blue line shows the average amplitude spectrum produced from 500 simulated experiments of 10 participants each with no oscillation present. The red line shows the average amplitude spectrum from 1000 surrogate time-courses generated from the AR(1) processes fitted to each simulated participants’ time-course. The surrogate spectrum underestimates amplitudes at the lowest and highest frequencies, and overestimates amplitudes in the mid-frequency range.