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MANOVA, Rayleigh test, Directional data, Orientation, Periodicity
Abstract:
Background: A broad range of scientifc studies involve taking measurements on a circular, rather than linear, scale
(often variables related to times or orientations). For linear measures there is a well-established statistical toolkit based
on linear modelling to explore the associations between this focal variable and potentially several explanatory factors
and covariates. In contrast, statistical testing of circular data is much simpler, often involving either testing whether
variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two
levels is supported.
Methods: We use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular
data in comparison to commonly used statistical tests.
Results: Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as
powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally
ofering extension to multi-factorial modelling that these conventional circular statistical tests do not.
Conclusions: The herein presented MANOVA approach ofers a substantial broadening of the scientifc questions
that can be addressed statistically using circular data.
