Signed version of the KS statistic

[ljosa]

I have implemented a signed version of the KS statistic, with unit tests and documentation. Could you please merge into scipy:master?

Thanks,
Vebjorn

[josef-pkt]

I think adding "signed" for the two-sided test will be misleading. The two-sided test shouldnt really be interpreted as a one sided test. It should be possible to add one-sided options similar to kstest, but I dont know what the distribution of the test statistic is or whether it is available in scipy.

both R and matlab http://www.mathworks.com/help/toolbox/stats/kstest2.html have the one-sided option

A trac ticket to keep track of this would be useful

[ljosa]

@josef-pkt, I added it because I needed it to reimplement a method for cytological profiling (Perlman et al., Science 2004, doi:10.1126/science.1100709).

[rgommers]

For the record, the method from that paper is described in the supporting online material. The one relevant sentence is:

We make repeated use in our analysis of a standard non-parametric method for comparing cdf’s, 
the Kolmogorov-Smirnov (KS) statistic (S2, 3) (Fig. S1). The function KS(f,g) computes f - g at 
the point where |f - g| reaches its maximum. Note that KS(f,g)= - KS(g,f)."

It seems they just made this up. The K-S test computes the distance between distribution functions, or a goodness-of-fit statistic. The test result should simply always be positive.

I think this can be closed. One-sided test would be useful, but that's unrelated to this patch.

[scopatz]

This builds and tests on my system.

[pv]

Ok, closing this. Reason: the signed statistic appears not to be a standard part of the K-S test (for instance R doesn't have it), and can be confused with the one-sided test (which has different critical values). However, the one-sided test could be added: http://projects.scipy.org/scipy/ticket/1771