The coefficient of cyclic variation: A novel statistic to measure the magnitude of cyclic variation

Abstract

Background: Periodic or cyclic data of known periodicity are frequently encountered in epidemiological and biomedical research: for instance, seasonality provides a useful experiment of nature while diurnal rhythms play an important role in endocrine secretion. There is, however, little consensus on how to analysis these data and less still on how to measure association or effect size for the often complex patterns seen. Results: A simple statistic, readily derived from Fourier regression models, provides a readily-understood measure cyclic variation in a wide variety of situations. Conclusion: The coefficient of cyclic variation or similar statistics derived from the variance of a Fourier series could provide a universal means of summarising the magnitude of periodic variation.