Robust circular cluster-based statistics for respiration-brain coupling

The rapidly developing research field of brain-body neuroscience faces methodological challenges, as analysts continue to develop new analysis strategies for robust statistics in the absence of established best practices. This quest for robust statistics is further complicated by the (naturally) circular data involved in the study of phase-locked effects, e.g. in respiration-brain coupling. Circularity of respiratory data particularly affects the problem of multiple comparisons in phase-related inferential statistics. In this tutorial, we propose a robust pipeline for respiration-related analyses based on a circular extension of cluster-based permutation testing we developed. We highlight and offer guidance on critical parameters in the analysis, systematically compare various approaches being used in the field today, and provide open-access software code for flexible use and future development of our proposed pipeline.