Quantifying rhythmicity in perceptual reports

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.