The low level of correlation observed in the CMB sky at large angular
  scales and the low quadrupole variance
  The angular two-point correlation function of the temperature of the cosmic
microwave background (CMB), as inferred from nearly all-sky maps, is very close
to zero on large angular scales. A statistic invented to quantify this feature,
$S_{1/2}$, has a value sufficiently low that only about 7 in 1000 simulations
generated assuming the standard cosmological model have lower values; i.e., it
has a $p$-value of 0.007. As such, it is one of several unusual features of the
CMB sky on large scales, including the low value of the observed CMB
quadrupole, whose importance is unclear: are they multiple and independent
clues about physics beyond the cosmological standard model, or an expected
consequence of our ability to find signals in Gaussian noise? We find they are
not independent: using only simulations with quadrupole values near the
observed one, the $S_{1/2}$ $p$-value increases from 0.007 to 0.08. We also
find strong evidence that corrections for a "look-elsewhere effect" are large.
To do so, we use a one-dimensional generalization of the $S_{1/2}$ statistic,
and select along the one dimension for the statistic that is most extreme.
Subjecting our simulations to this process increases the $p$-value from 0.007
to 0.03; a result similar to that found in Planck XVI (2016). We argue that
this optimization process along the one dimension provides an $underestimate$
of the look-elsewhere effect correction for the historical human process of
selecting the $S_{1/2}$ statistic from a very high-dimensional space of
alternative statistics $after$ having examined the data.
