Non-parametric procedures for the determination of phase markers of circadian rhythms

The accurate determination of phase markers is an essential procedure in the analysis of the temporal organization of circadian rhythms. The method of cosinor analysis, a parametric procedure, has been often used to determine the time at which the peak of a rhythm (the "acrophase") occurs. To avoid several difficulties associated with the use of parametric procedures, two non-parametric procedures are described in this paper. One of them is based on the onset times of dichotomous (and, by derivation, of fully numerical) variables. The other one is based on the acrophase of data previously smoothed by the method of moving averages. These two procedures are very easy to conduct, do not make assumptions about the distribution of the data (except that there is indeed a daily or circadian rhythm), and do not require stationary rhythms. They constitute a powerful alternative to the use of cosinor analysis.