# Quantification of differences between distributions

I am trying to find a method that will allow me to quantitatively differentiate between 2 distributions. The distributions show a peak where there is positive alignment in a certain direction and have a flat shape when there is no alignment or random alignment. Is there a method for doing this?

The Kolmogorov-Smirnov test may be what you're looking for: it's an omnibus test for difference in two distributions. It has less power than more specific tests (e.g. a $t$-test or permutation test for means) for a given setting, but isn't restricted to just testing one individual aspect of the distribution.