Re: Kolmogorov-Smirnov 2-sample test

*To*: mathgroup at smc.vnet.net*Subject*: [mg111083] Re: Kolmogorov-Smirnov 2-sample test*From*: Ray Koopman <koopman at sfu.ca>*Date*: Tue, 20 Jul 2010 03:40:57 -0400 (EDT)*References*: <i20q8i$kje$1@smc.vnet.net>

On Jul 18, 11:10 pm, Aaron Bramson <aaronbram... at gmail.com> wrote: > Hello Everybody, > > I would like to perform a 2-sample k-s test. I've seen some posts on the > archive about the one-sample goodness-of-fit version of the > Kolgomorov-Smirnov test, but I'm interested in the 2-sample version. > > Here's a description of the method: > http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Two-sample_Kolmogorov.E2.80.93Smirnov_test > > I think all the necessary components are available; e.g. > Accumulate[BinCounts[_list_]] to get the ecdf of both datasets, abs, max of > a list, etc. But the data management is a bit above my current skill > level. Also, since all other software packages seem to include this test > capability, I would be really surprised if there > wasn't a package somewhere that included it by now, but I've searched a lot > and can't find it. Can anybody help me locate this this? > > Alternatively, would anybody like to work with me to build this in case it > can't be found? > > Thanks in Advance, > Aaron This is based on code by Thomas Waterhouse, taken from https://stat.ethz.ch/pipermail/r-devel/2009-July/054106.html The arguments y1 and y2 are lists of data. It returns {x,p}, where x is the usual K-S test statistic n1*n2*Max|cdf1-cdf2|, and p is the corresponding p-value, conditional on the distribution of ties in the pooled data. ks2[y1_,y2_] := Block[{n1 = Length@y1, n2 = Length@y2, pool = Sort@Join[y1,y2], x,n,u}, {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]]} ]