  Testing the global earthquake catalogue for indications of non-Poissonian
attributes has been an area of intense research, especially since the 2011
Tohoku earthquake. The usual approach is to test statistically for the
hypothesis that the global earthquake catalogue is well explained by a
Poissonian process. In this paper we analyse one aspect of this problem which
has been disregarded by the literature: the power of such tests to detect
non-Poissonian features if they existed; that is, the probability of type II
statistical errors. We argue that the low frequency of large events and the
brevity of our earthquake catalogues reduces the power of the statistical tests
so that an unequivocal answer for this question is not granted. We do this by
providing a counter example of a stochastic process that is clustered by
construction and by analysing the resulting distribution of p-values given by
the current tests.
