  The classical two-sample test of Kolmogorov-Smirnov (KS) is widely used to
test whether empirical samples come from the same distribution. Even though
most statistical packages provide an implementation, carrying out the test in
big data settings can be challenging because it requires a full sort of the
data. The popular Apache Spark system for big data processing provides a
1-sample KS test, but not the 2-sample version. Moreover, recent Spark versions
provide the approxQuantile method for querying $\epsilon$-approximate
quantiles. We build on approxQuantile to propose a variation of the classical
Kolmogorov-Smirnov two-sample test that constructs approximate cumulative
distribution functions (CDF) from $\epsilon$-approximate quantiles. We derive
error bounds of the approximate CDF and show how to use this information to
carry out KS tests. Psuedocode for the approach requires 15 executable lines. A
Python implementation appears in the appendix.
