Testing the Alignment Tendency of Some Polarized Radio Sources

Measuring the alignment of polarized radio sources requires comparing vectors at different locations on the sky, i.e. on a sphere. A test of alignment is derived herein. While both large scale and coordinate independent, the test avoids the mathematical subtleties involved when comparing vectors at different locations on a curved surface. Applied to 5442 sources drawn from a published catalog, the analysis finds a level of alignment that would be matched by only 7% to 14% of data sets with the same sources but with random polarization directions. The locations of the sources involved and the directions that the vectors favor and the regions avoided are described as well.