Covariant symmetry classifications for observables of cosmological birefringence

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.