Re: Kolmogorov-Smirnov 2-sample test

*To*: mathgroup at smc.vnet.net*Subject*: [mg111284] Re: Kolmogorov-Smirnov 2-sample test*From*: Ray Koopman <koopman at sfu.ca>*Date*: Mon, 26 Jul 2010 06:37:47 -0400 (EDT)

ks2a[y1_,y2_] := Block[{n1 = Length@y1, n2 = Length@y2, pool = Sort@Join[y1,y2], x,n,u}, If[Equal@@pool, {0,1.}, {x = Max@Abs[n2*Tr@UnitStep[y1-#]-n1*Tr@UnitStep[y2-#]&/@Rest@Union@pool], n = n1+n2; u = Table[0,{n2+1}]; Do[ Which[ i+j == 0, u[[j+1]] = 1, i+j < n && pool[[i+j]] < pool[[i+j+1]] && Abs[n2*i-n1*j] >= x, u[[j+1]] = 0, i == 0, u[[j+1]] = u[[j]], j > 0, u[[j+1]] += u[[j]]], {i,0,n1},{j,0,n2}]; N[1 - Last@u/Multinomial[n1,n2]]}] ] ks2a[{1,1,1},{1,1,1,1}] {0,1.} ----- Aaron Bramson <aaronbramson at gmail.com> wrote: > Hello everybody and thank you, > > This has been very helpful, and now the two-sided K-S test for Mathematica > is online for everybody to enjoy. > > I have implemented the new code from Andy and from Ray on my data set and > the code from Ray works out better for me...though I don't have the skill to > decipher what that "ugly" code is doing, I've verified several results so > I'm using those exact p-values. I'm going to build a table of the p-values > from these tests (which is made into plot over time with the test being > performed on the individual-trial data streams of two cohorts at each time > step). > > I have one last question, or maybe it's a request.. In Ray's code if I put > in two data sets wherein all the points are at the same value (e.g. all > zero) the result is not a K-stat of 0, and a p-value of 1, but rather > {-\[Infinity], 0.}. That doesn't seem like the right answer (and in any > case not the answer that I expect or can use) so this input combination > doesn't work with how the technique calculates the stats. So I'd like to > request a small change to the code Ray provided so that if the inputs are > all identical the output is {0,1} instead of {-\[Infinity], 0.}. I could do > this post-facto with a replacement rule, but it would probably be better and > faster to do this in the original calculation. But with THAT code I don't > know where to make the appropriate changes. > > Again, thanks everybody for your help. > > Best, > Aaron > > p.s. I may end up using the Kuiper test and I might therefore have a similar > question about implementing that in Mathematica very soon.