On a test statistic for the Kuramoto order parameter of synchronization: An illustration for group synchronization during rocking chairs

We discuss a quantitative approach to detect phase synchronization in noisy experimental multivariate data. To this end, we derive a test statistic based on the Kuramoto order parameter. We derive criteria for rejecting the null hypothesis of zero phase synchronization at given significance levels. We apply the test statistic to a recently conducted study on group behavior that used a rocking chair paradigm. In this context, we quantify the emergence of phase synchronization within small groups of participants.