  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 $O(N\log(N))$ time with $O(N)$ memory. Using the package's
functions, I perform several simulation studies showing the power improvements.
