The multivariate analysis of variance as a powerful approach for circular data

Abstract

A broad range of scientific studies involve taking measurements on a circular rather than linear scale (often 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. However, most statistical testing of circular statistics 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. Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as effective as the most-commonly used tests in these simple situations, while additionally it offers extension to multi-factorial modelling that these conventional tests do not. This, in combination with recent developments in Bayesian approaches, offers a substantial broadening of the scientific questions that can be addressed statistically with circular data.

Distinctive Effects of D1 and D2 Receptor Agonists on Cortico-Basal Ganglia Oscillations in a Rodent Model of L-DOPA-Induced Dyskinesia

“…Comparisons of instantaneous phase differences were done with a MANOVA approach based on trigonometric functions of the circular data [46] using RStudio with factors treatment and structure. In addition, a one sample test for the mean angle was applied (circ_mtest in MATLAB Circ-Stat toolbox [43]).…”