  The energy test method is a multi-dimensional test of whether two samples are
consistent with arising from the same underlying population, through the
calculation of a single test statistic (called the $T$-value). The method has
recently been used in particle physics to search for differences between
samples that arise from CP violation. The generalised extreme value function
has previously been used to describe the distribution of $T$-values under the
null hypothesis that the two samples are drawn from the same underlying
population. We show that, in a simple test case, the distribution is not
sufficiently well described by the generalised extreme value function. We
present a new method, where the distribution of $T$-values under the null
hypothesis when comparing two large samples can be found by scaling the
distribution found when comparing small samples drawn from the same population.
This method can then be used to quickly calculate the $p$-values associated
with the results of the test.
