Testing for departure from uniformity and estimating mean direction for circular data

Abstract

Although circular data are common in biological studies, the analysis of such data is often more rudimentary than it need be. One of the most common hypotheses tested is whether the data suggest that samples are clustered around a certain specified direction, rather than being uniformly spread across all possible directions. Here, I use data from a recent publication on the compass directions of epiphytes and mistletoes on tree trunks. This is used to demonstrate how with relatively little extra work researchers can improve the rigour of testing such hypotheses, and this improved rigour can lead to biological insights missed by simpler analyses. Specifically, I highlight that a much broader range of null hypotheses can be tested than current practice, and that a range of methods are available for estimating a confidence interval for mean direction. I offer advice on appropriate selection for both tests and parameter estimation methods, and highlight the need to correct for the fact that sample estimates are biased estimates of population parameters for circular data.