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Two-sample testing is a fundamental problem in statistics, and many famoustwo-sample tests are designed to be fully non-parametric. These existingmethods perform well with location and scale shifts but are less robust whenfaced with more exotic classes of alternatives, and rejections from these testscan be difficult to interpret. Here, we propose a new univariate non-parametrictwo-sample test, AUGUST, designed to improve on these aspects. AUGUST tests forinequality in distribution up to a predetermined resolution using symmetrystatistics from binary expansion. The AUGUST statistic is exactlydistribution-free and has a well-understood asymptotic distribution, permittingfast p-value computation. In empirical studies, we show that AUGUST has powercomparable to that of the best existing methods in every context, as well asgreater power in some circumstances. We illustrate the clear interpretabilityof AUGUST on NBA shooting data.

The AUGUST Two-Sample Test: Powerful, Interpretable, and Fast