# A New ECDF Two-Sample Test Statistic

arXiv: https://arxiv.org/abs/2007.01360 · HTML: https://mlsanity.com/paper/2007.01360/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Scope Compliance Uncertainty Estimate](https://mlsanity.com/paper/2312.10801/) (2023)

## Abstract (arXiv)

Empirical cumulative distribution functions (ECDFs) have been used to test the hypothesis that two samples come from the same distribution since the seminal contribution by Kolmogorov and Smirnov. This paper describes a statistic which is usable under the same conditions as Kolmogorov-Smirnov, but provides more power than other extant tests in that vein. I demonstrate a valid (conservative) procedure for producing finite-sample p-values. I outline the close relationship between this statistic and its two main predecessors. I also provide a public R package (CRAN: twosamples [2018]) implementing the testing procedure in O(Nlog(N)) time with O(N) memory. Using the package's functions, I perform several simulation studies showing the power improvements.