  Polarizations of electromagnetic waves from distant galaxies are known to be
correlated with the source orientations. These quantities have been used to
search for signals of cosmological birefringence. We review and classify
transformation properties of the polarization and source orientation
observables. The classifications give a firm foundation to certain practices
which have sprung up informally in the literature. Transformations under parity
play a central role, showing that parity violation in emission or in the
subsequent propagation is an observable phenomenon. We also discuss statistical
measures, correlations and distributions which transform properly and which can
be used for systematic data analysis.
