A permutation test for comparing rotational symmetry in three-dimensional rotation data sets

Although there have been fairly recent advances regarding inference for three-dimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3-D rotations. In this paper, nonparametric inference is used to test if F 1=F 2, where F i is the degree of rotational symmetry of distribution i, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics.