The alignment of transverse vectors on the sky, such as the polarization directions of electromagnetic radiation from astronomical sources, can be an interesting property of the sources themselves or of the intervening medium between source and detector. For many regions of the Milky Way the alignment of the polarization directions of starlight is evident. However evident visually, it is useful to have a numerical alignment function that can be used to judge the significance of the correlations. The test described here evaluates the tendency for aligned directions to focus on points in the sky, as well as correlations in their avoidance of points in the sky. The formulas needed to conduct the test are derived and two illustrative examples are provided. In one sample from the Milky Way, the polarization directions from starlight are seen to converge far from the sample and, for another sample, a set of quasars with polarized radio emissions, the convergence occurs close to the sample.