  Two-sample testing is a fundamental problem in statistics, and many famous
two-sample tests are designed to be fully non-parametric. These existing
methods perform well with location and scale shifts but are less robust when
faced with more exotic classes of alternatives, and rejections from these tests
can be difficult to interpret. Here, we propose a new univariate non-parametric
two-sample test, AUGUST, designed to improve on these aspects. AUGUST tests for
inequality in distribution up to a predetermined resolution using symmetry
statistics from binary expansion. The AUGUST statistic is exactly
distribution-free and has a well-understood asymptotic distribution, permitting
fast p-value computation. In empirical studies, we show that AUGUST has power
comparable to that of the best existing methods in every context, as well as
greater power in some circumstances. We illustrate the clear interpretability
of AUGUST on NBA shooting data.
