A binary star is a close pair of stars orbiting around their common centre of mass. It is of interest to astronomers whether the planes of binary star orbits have a common alignment. Observations are often limited by an ambiguity: the direction of the orbital pole (the directed normal to the orbital plane) cannot be distinguished from its reflection in the plane of the sky. Tests of uniformity are presented here that are modifications of Sobolev tests on the sphere. These tests allow also for possible selection effects, in which binary stars may be more or less likely to be detected depending on the inclinations of their orbits as seen from the Earth. Modified Rayleigh and Giné tests are applied to data from a standard catalogue of orbits of visual binary stars. Despite the wide scattering of orbital poles, there is consistent evidence of a lack of uniformity, and some evidence of a common alignment of orbits of binaries that are more than 20 parsecs from the Sun.