  Anomalies in the large-scale CMB temperature sky measured by WMAP have been
suggested as possible evidence for a violation of statistical isotropy on large
scales. In any physical model for broken isotropy, there are testable
consequences for the CMB polarization field. We develop simulation tools for
predicting the polarization field in models that break statistical isotropy
locally through a modulation field. We study two different models: dipolar
modulation, invoked to explain the asymmetry in power between northern and
southern ecliptic hemispheres, and quadrupolar modulation, posited to explain
the alignments between the quadrupole and octopole. For the dipolar case, we
show that predictions for the correlation between the first 10 multipoles of
the temperature and polarization fields can typically be tested at better than
the 98% CL. For the quadrupolar case, we show that the polarization quadrupole
and octopole should be moderately aligned. Such an alignment is a generic
prediction of explanations which involve the temperature field at recombination
and thus discriminate against explanations involving foregrounds or local
secondary anisotropy. Predicted correlations between temperature and
polarization multipoles out to l = 5 provide tests at the ~ 99% CL or stronger
for quadrupolar models that make the temperature alignment more than a few
percent likely. As predictions of anomaly models, polarization statistics move
beyond the a posteriori inferences that currently dominate the field.
