Samples of directional or axial measurements arise in geophysical, biological and econometric contexts. We represent the rotational difference between two mean directions (or two mean axes) as a direction (or axis). We then construct nonparametric simultaneous confidence sets for all pair-wise rotational differences among the mean directions or mean axes of $s$ samples. By specialization, this methodology yields nonparametric simultaneous tests for pairwise equality of directional means or axes.
"Nonparametric comparison of mean directions or mean axes." Ann. Statist. 26 (2) 472 - 493, April 1998. https://doi.org/10.1214/aos/1028144845