Determining dependences between directional quantities and position on a sphere

Two astronomically useful statistical tests to detect dependences of a circular quantity on a spherical one are presented: a nonparametric test and one, developed by Jupp and Mardia, which is based on multivariate statistics. A preliminary investigation of some of the statistical properties of the nonparametric test is undertaken. These tests are applied to a set of radio data to show that neither the integrated polarization vector nor the alignment of the source axes show any dependence on the source's position in the sky. This applies to a global sample, as well as to subsets in redshift, rotation measure, resolution of the radio map, etc.