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.
