An investigation of hypothesis testing procedures for circular and spherical mean vectors

Numerous testing procedures for directional data have been proposed over the years and a natural question that springs is which to use and when. The aim of this paper is to answer this question, via a large scale Monte Carlo simulation study that covers circular and spherical data for the two mean directions problem. The results evidently signify that tests assuming equal concentration parameters should be avoided as they tend to inflate the test size, while the heterogeneous test that does not make this assumption is to be preferred, but unfortunately only with large sample sizes. Permutation calibration does not improve the performance of any testing procedure, whereas bootstrap does. Specifically, bootstrap calibrated tests exhibited superior performance; they attain the type I error in the vast majority of the case scenarios examined and possess nearly indistinguishable empirical power levels. Finally, examples with real data illustrate the performance of the bootstrap calibrated tests.