Abstract
The neural and perceptual effects of attention were traditionally assumed to be sustained over time, but recent work suggests that covert attention rhythmically switches between objects at 3-8 Hz. Here I use simulations to demonstrate that the analysis approaches commonly used to test for rhythmic oscillations generate false positives in the presence of aperiodic temporal structure. I then propose two alternative analyses that are better able to discriminate between periodic and aperiodic structure in time series. Finally, I apply these alternative analyses to published datasets and find no evidence for behavioural rhythms in attentional switching after accounting for aperiodic temporal structure. The techniques presented here will help clarify the periodic and aperiodic dynamics of perception and of cognition more broadly.