  We introduce several coordinate invariant statistical procedures in order to
test for local alignment of polarizations. A large scale alignment of optical
polarizations from distant QSOs has recently been observed by \huts and
collaborators. The new statistical procedures are based on comparing
polarizations at different angular coordinates by making a parallel transport.
The results of these statistical procedures continue to support the existence
of the large scale alignment effect in the QSO optical polarization data. The
alignment is found to be much more pronounced in the data sample with low
degrees of polarization $p\le 2$%. This suggests that the alignment may be
attributed to some propagation effect. The distance scale over which the
alignment effect is dominant is found to be of order 1 Gpc. We also find that a
very large scale alignment is present in the large redshift, $z\ge 1$, data
sample. Infact the data sample with $z\ge 1$ appears to be aligned over the
entire celestial sphere. We discuss possible physical effects, such as
extinction and pseudoscalar-photon mixing, which may be responsible for the
observations.
