  Radiation traversing the observable universe provides powerful ways to probe
anisotropy of electromagnetic propagation. A controversial recent study claimed
a signal of dipole character. Here we test a new and independent data set of
361 points under the null proposal of {\it statistical independence} of linear
polarization alignments relative to galaxy axes, versus angular positions. The
null hypothesis is tested via maximum likelihood analysis of best fits among
numerous independent types of factored distributions. We also examine
single-number correlations which are parameter free, invariant under coordinate
transformations, and distributed very robustly. The statistics are shown
explicitly not to depend on the uneven distribution of sources on the sky.
  We find that the null proposal is not supported at the level of less than 5%
to less than 0.1% by several independent statistics. The signal of correlation
violates parity, that is, symmetry under spatial inversion, and requires a
statistic which transforms properly. The data indicate an axis of correlation,
on the basis of likelihood determined to be $[{\rm R.A.}=(0^{\rm h},9^{\rm m})
\pm (1^{\rm h},0^{\rm m})$, ${\rm Decl.} = -1^o\pm 15^o]$.
