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Brookshire (2022) claims that previous analyses of periodicity in detection performance after a reset event suffer from extreme false-positive rates. Here we show that this conclusion is based on an incorrect implemention of a null-hypothesis of aperiodicity, and that a correct implementation confirms low false-positive rates. Furthermore, we clarify that the previously used method of shuffling-in-time, and thereby shuffling-in-phase, cleanly implements the null hypothesis of no temporal structure after the reset, and thereby of no phase locking to the reset. Moving from a corresponding phase-locking spectrum to an inference on the periodicity of the underlying process can be accomplished by parameterizing the spectrum. This can separate periodic from non-periodic components, and quantify the strength of periodicity.

Several recent studies investigated the rhythmic nature of cognitive processes that lead to perception and behavioral report. These studies used different methods, and there has not yet been an agreement on a general standard. Here, we present a way to test and quantitatively compare these methods. We simulated behavioral data from a typical experiment and analyzed these data with several methods. We applied the main methods found in the literature, namely sine-wave fitting, the Discrete Fourier Transform (DFT) and the Least Square Spectrum (LSS). DFT and LSS can be applied both on the averaged accuracy time course and on single trials. LSS is mathematically equivalent to DFT in the case of regular, but not irregular sampling - which is more common. LSS additionally offers the possibility to take into account a weighting factor which affects the strength of the rhythm, such as arousal. Statistical inferences were done either on the investigated sample (fixed-effect) or on the population (random-effect) of simulated participants. Multiple comparisons across frequencies were corrected using False-Discovery-Rate, Bonferroni, or the Max-Based approach. To perform a quantitative comparison, we calculated Sensitivity, Specificity and D-prime of the investigated analysis methods and statistical approaches. Within the investigated parameter range, single-trial methods had higher sensitivity and D-prime than the methods based on the averaged-accuracy-time-course. This effect was further increased for a simulated rhythm of higher frequency. If an additional (observable) factor influenced detection performance, adding this factor as weight in the LSS further improved Sensitivity and D-prime. For multiple comparison correction, the Max-Based approach provided the highest Specificity and D-prime, closely followed by the Bonferroni approach. Given a fixed total amount of trials, the random-effect approach had higher D-prime when trials were distributed over a larger number of participants, even though this gave less trials per participant. Finally, we present the idea of using a dampened sinusoidal oscillator instead of a simple sinusoidal function, to further improve the fit to behavioral rhythmicity observed after a reset event.

Several recent studies investigated the rhythmic nature of cognitive processes that lead to perception and behavioral report. These studies used different methods, and there has not yet been an agreement on a general standard. Here, we present a way to test and quantitatively compare these methods. We simulated behavioral data from a typical experiment and analyzed these data with several methods. We applied the main methods found in the literature, namely sine-wave fitting, the discrete Fourier transform (DFT) and the least square spectrum (LSS). DFT and LSS can be applied both on the average accuracy time course and on single trials. LSS is mathematically equivalent to DFT in the case of regular, but not irregular sampling - which is more common. LSS additionally offers the possibility to take into account a weighting factor which affects the strength of the rhythm, such as arousal. Statistical inferences were done either on the investigated sample (fixed-effects) or on the population (random-effects) of simulated participants. Multiple comparisons across frequencies were corrected using False Discovery Rate, Bonferroni, or the Max-Based approach. To perform a quantitative comparison, we calculated sensitivity, specificity and D-prime of the investigated analysis methods and statistical approaches. Within the investigated parameter range, single-trial methods had higher sensitivity and D-prime than the methods based on the average accuracy time course. This effect was further increased for a simulated rhythm of higher frequency. If an additional (observable) factor influenced detection performance, adding this factor as weight in the LSS further improved sensitivity and D-prime. For multiple comparison correction, the Max-Based approach provided the highest specificity and D-prime, closely followed by the Bonferroni approach. Given a fixed total amount of trials, the random-effects approach had higher D-prime when trials were distributed over a larger number of participants, even though this gave less trials per participant. Finally, we present the idea of using a dampened sinusoidal oscillator instead of a simple sinusoidal function, to further improve the fit to behavioral rhythmicity observed after a reset event.

Several studies have probed perceptual performance at different times after a self-paced motor action and found frequency-specific modulations of perceptual performance phase-locked to the action. Such action-related modulation has been reported for various frequencies and modulation strengths. In an attempt to establish a basic effect at the population level, we had a relatively large number of participants (n=50) perform a self-paced button press followed by a detection task at threshold, and we applied both fixed- and random-effects tests. The combined data of all trials and participants surprisingly did not show any significant action-related modulation. However, based on previous studies, we explored the possibility that such modulation depends on the participant’s internal state. Indeed, when we split trials based on performance in neighboring trials, then trials in periods of low performance showed an action-related modulation at ≈17 Hz. When we split trials based on the performance in the preceding trial, we found that trials following a “miss” showed an action-related modulation at ≈17 Hz. Finally, when we split participants based on their false-alarm rate, we found that participants with no false alarms showed an action-related modulation at ≈17 Hz. All these effects were significant in random-effects tests, supporting an inference on the population. Together, these findings indicate that action-related modulations are not always detectable. However, the results suggest that specific internal states such as lower attentional engagement and/or higher decision criterion are characterized by a modulation in the beta-frequency range.