  The anomalous lack of large angle temperature correlations has been a
surprising feature of the cosmic microwave background (CMB) since first
observed by COBE-DMR and subsequently confirmed and strengthened by the
Wilkinson Microwave Anisotropy Probe. This anomaly may point to the need for
modifications of the standard model of cosmology or may indicate that our
Universe is a rare statistical fluctuation within that model. Further
observations of the temperature auto-correlation function will not elucidate
the issue; sufficiently high precision statistical observations already exist.
Instead, alternative probes are required. In this work we explore the
expectations for forthcoming polarization observations. We define a
prescription to test the hypothesis that the large-angle CMB temperature
perturbations in our Universe represent a rare statistical fluctuation within
the standard cosmological model. These tests are based on the temperature-$Q$
Stokes parameter correlation. Unfortunately these tests cannot be expected to
be definitive. However, we do show that if this $TQ$-correlation is observed to
be sufficiently large over an appropriately chosen angular range, then the
hypothesis can be rejected at a high confidence level. We quantify these
statements and optimize the statistics we have constructed to apply to the
anticipated polarization data. We find that we can construct a statistic that
has a 25 per cent chance of excluding the hypothesis that we live in a rare
realization of LCDM at the 99.9 per cent confidence level.
