  The complexity underlying real-world systems implies that standard
statistical hypothesis testing methods may not be adequate for these peculiar
applications. Specifically, we show that the likelihood-ratio test's
null-distribution needs to be modified to accommodate the complexity found in
multi-edge network data. When working with independent observations, the
p-values of likelihood-ratio tests are approximated using a $\chi^2$
distribution. However, such an approximation should not be used when dealing
with multi-edge network data. This type of data is characterized by multiple
correlations and competitions that make the standard approximation unsuitable.
We provide a solution to the problem by providing a better approximation of the
likelihood-ratio test null-distribution through a Beta distribution. Finally,
we empirically show that even for a small multi-edge network, the standard
$\chi^2$ approximation provides erroneous results, while the proposed Beta
approximation yields the correct p-value estimation.
