  Ever since WMAP announced its first results, different analyses have shown
that there is weak evidence for several large-scale anomalies in the CMB data.
While the evidence for each anomaly appears to be weak, the fact that there are
multiple seemingly unrelated anomalies makes it difficult to account for them
via a single statistical fluke. So, one is led to considering a combination of
these anomalies. But, if we "hand-pick" the anomalies (test statistics) to
consider, we are making an \textit{a posteriori} choice. In this article, we
propose two statistics that do not suffer from this problem. The statistics are
linear and quadratic combinations of the $a_{\ell m}$'s with random
co-efficients, and they test the null hypothesis that the $a_{\ell m}$'s are
independent, normally-distributed, zero-mean random variables with an
$m$-independent variance. The motivation for such statistics is generality;
equivalently, it is a non \textit{a posteriori} choice. But, a very useful
by-product of considering such statistics is this: Because most physical models
that lead to large-scale anomalies result in coupling multiple $\ell$ and $m$
modes, the "coherence" of this coupling should get enhanced if a combination of
different modes is considered. Using fiducial data, we demonstrate that the
method works and discuss how it can be used with actual CMB data to make quite
general statements about how incompatible the data are with the null
hypothesis.
