  The standard cosmological model predicts statistically isotropic cosmic
microwave background (CMB) fluctuations. However, several summary statistics of
CMB isotropy have anomalous values, including: the low level of large-angle
temperature correlations, $S_{1/2}$; the excess power in odd versus even
low-$\ell$ multipoles, $R^{TT}$; the (low) variance of large-scale temperature
anisotropies in the ecliptic north, but not the south, $\sigma^2_{16}$; and the
alignment and planarity of the quadrupole and octopole of temperature,
$S_{QO}$. Individually, their low $p$-values are weak evidence for violation of
statistical isotropy. The correlations of the tail values of these statistics
have not to this point been studied. We show that the joint probability of all
four of these happening by chance in $\Lambda$CDM is likely
$\leq3\times10^{-8}$. This constitutes more than $5\sigma$ evidence for
violation of statistical isotropy.
