  As the catalogue of gravitational-wave transients grows, several entries
appear "exceptional" within the population. Tipping the scales with a total
mass of $\approx 150 M_\odot$, GW190521 likely contained black holes in the
pair-instability mass gap. The event GW190814, meanwhile, is unusual for its
extreme mass ratio and the mass of its secondary component. A growing
model-building industry has emerged to provide explanations for such
exceptional events, and Bayesian model selection is frequently used to
determine the most informative model. However, Bayesian methods can only take
us so far. They provide no answer to the question: does our model provide an
adequate explanation for the data? If none of the models we are testing provide
an adequate explanation, then it is not enough to simply rank our existing
models - we need new ones. In this paper, we introduce a method to answer this
question with a frequentist $p$-value. We apply the method to different models
that have been suggested to explain GW190521: hierarchical mergers in active
galactic nuclei and globular clusters. We show that some (but not all) of these
models provide adequate explanations for exceptionally massive events like
GW190521.
