Rajarshi Guha wrote: > Hi, > I'm working on a problem in which I'd like to determine whether two > sets of data come from the same distribution. It seems that the > Kolmogorv Smirnov test will give me the information I need. > > However I'd like to go further than just accept or reject the H0 for > the test. Is there any way (using this test or someother test) to > determine > *how* similar the distributions of two sets are? > > Am I correct in thinking that a P value for the KS test would > provide this information?
The P value would mix up two ideas: (a) how close two "underlying population" distributions are (b) the ability of the sample size(s) you have to allow you to distinguish the populations. In principle, the KS test value itself provides a direct estimate of how close the distributions are (although you might need to de-rescale-it to provide a direct measure of distance) , but you might want to add also an estimate of the standard-deviation of your estimate. > I looked up Conovers book on non parametric > statistics for the algorithm of the KS test. However it does not > mention any way of calculating a P for the test. Is it possible? You could try looking in "Biometrika Tables for Statisticians" Vol 2. > > Are there any other tests that would be able to tell me how similar > the distributions of two sets of observations are There are other measures of how close distributions are: the Cramer-Wold and Anderson-Darling tests are based on different underlying distance measures than Kolmogorov-Smirnov, but may not be so easily applied in a two-sample context. David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
