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.

翻译：两次抽样测试是统计方面的一个基本问题,许多著名的双类抽样测试设计为完全非参数性测试。这些现有方法在位置和规模变化方面效果良好,但在面临更多异国型替代品类别时不那么有力,这些测试的拒绝可能难以解释。在这里,我们提出一个新的单一非参数性双类测试,即AUGUST,目的是改进这些方面。AUGUST对分布不平等的测试,直到使用二进制扩展的对称统计来预先确定的解决办法。AUGUST统计数据完全没有分布,并且有完全不易理解的零星分布,允许快速的P价值计算。在经验研究中,我们显示AUGUST拥有与每种情况下最佳现有方法相似的力量,以及在某些情况下更大的权力。我们说明了AGUST对NBA射击数据的清晰解释性。