I can't disagree with the discussion about comparing means, but in my mind
that's not where the K-S test is useful. The D value is sensitive to
differences in the shape of two distributions, regardless of their means. We
have used it in situations in which we think we are seeing a difference in the
shape of the distributions, for example one distribution may have a suggestion
of two populations but they are not resolved. The D value is essentially the
magnitude of the maximum difference in the integral of the two normalized
distributions. An additional parameter that can be derived is the location
(i.e. channel) at which that maximum difference occurs. This gives you an
idea not only about how different the two distributions are, but where the
difference is (mostly) located.
Ken Ault
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