Distinguishing between periodicity and consistency over trials: Reply to Re, Tosato, Fries, and Landau

Oscillations in the brain may lead to oscillations in behavior. How can we test for oscillations in behavior, while ensuring that we do not mistake aperiodic temporal structure for rhythms? In their response article, Re and colleagues attempt to restore the shuffling-in-time method as a viable statistical test of rhythmic structure in brief behavioral time-series. They begin by reiterating the central message of my study: "rejecting the null hypothesis of no temporal structure does not unequivocally demonstrate the presence of periodic structure". Because shuffling-in-time tests the null hypothesis of no temporal structure, and prior studies relied on shuffling-in-time, this statement is an agreement that prior studies did not provide evidence for rhythms in behavior. Instead of updating their interpretation of those studies, however, Re and colleagues maintain that prior studies using shuffling-in-time do in fact provide evidence for rhythms in behavior. In doing so, they lose sight of the distinction between periodic and aperiodic temporal structure. Here I clarify several points of confusion in their article. Shuffling-in-time cannot identify oscillations in a time-series because it cannot distinguish between oscillations and aperiodic temporal structure.