Testing for Circular Reflective Symmetry about a Known Median Axis

Circular data arise in many contexts, a particularly rich source being animal orientation experiments. Often, in the analysis of such data, a fundamental question of scientific interest is whether the underlying distribution is reflectively symmetric about some specific axis. In this paper, the situation in which the axis of interest is known to be a median axis is considered and a simple, asymptotically distribution- free test for circular reflective symmetry against skew alternatives is developed. The results from a simulation study lead to a testing strategy incorporating the new test and the circular analogue of the modified runs test of Modarres & Gastwirth (1996). The application of the testing strategy is illustrated using circular data arising from two animal orientation experiments.