Quantifying rhythmicity in perceptual reports

Abstract

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.

Investigating the role of task relevance during rhythmic sampling of spatial locations

“…We analysed rhythmicity of performance across the cue-to-target interval using stLSS analysis. The stLSS analysis, in combination with a Max-Based correction for multiple comparisons, offers a sensitive and specific analysis for this type of behavioural data 34 . We showed that endogenous attentional orienting operates on a theta-rhythmic pattern, but that its manifestation at the cued location depends on the validity of the cue.…”

“…Data analysis and visualisation was conducted in Python (version 3.8) and documented using Jupyter Notebooks. The single-trial least squares spectrum (stLSS) analysis is conducted using code from Tosato et al 34 , translated from MATLAB into Python. Jupyter Notebooks containing code, explanations of each analysis step and additional plots can be found at https://github.com/olofvanderwerf/rhythmic-attention .…”

“…For each visual field and condition, we applied the Single-Trial Least Square Spectrum (stLSS) analysis method, the most sensitive and specific method for such data as proposed by Tosato et al 34 (see also 29 , 37 for implementations of this method). This method calculates a Generalised Linear Model (GLM) per frequency of interest, predicting, for each trial, the RT (dependent variable) given the trial’s cue-to-target interval (independent variable).…”

“…We applied the same analysis steps (see above) and ended up with a surrogate distribution of 1000 power spectra, to which we could compare the observed power spectrum. We used the Max-Based correction for multiple comparisons 34 , 38 which works as follows: we determined the maximum power for each permutation to obtain a distribution of maximum values. Next, we compared the observed power spectrum to this distribution to obtain the p-value for each frequency.…”

Aperiodic processes explaining rhythms in behavior: A matter of false detection or definition?

“…the probability of hits/misses as a function of time in each trial. The conventional method for significance testing of frequencies in the estimated ATC involves shuffling hits/misses in time, and creating a surrogate distribution of white noise time series to test against (for a primer, see Tosato et al (2022)). If only a few frequencies reach significance, then this is often taken as evidence for rhythmicity (e.g., (Landau and Fries, 2012;Fiebelkorn et al, 2013)).…”