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I need to compare the distribution (unknown) of a set of data to the distribution of another one (unknown). In particular, I want to check for equality of the two distributions.

What are some statistical tests for this?

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Essentially the same question as stats.stackexchange.com/questions/18408/… –  jbowman Jun 18 '12 at 17:31
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1 Answer 1

A huge subject! The standard all-purpose test is Kolmogorov-Smirnov.

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There is chi-square also. Most nonparametric tests compare the empirical cdfs. For examp[le the Kolmogorov-Smirnov test looks at the maximum difference of the two ecdfs. –  Michael Chernick Jun 18 '12 at 20:53
    
@André Nicolas I was going to use Kolmogorov-Smirnov, but then I read this: "# Perhaps the most serious limitation is that the distribution must be fully specified. That is, if location, scale, and shape parameters are estimated from the data, the critical region of the K-S test is no longer valid. It typically must be determined by simulation." itl.nist.gov/div898/handbook/eda/section3/eda35g.htm This is a problem for me, right? –  Ricky Robinson Jun 19 '12 at 9:46
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Depends on what you want to determine. If you are interested in determining whether the distributions have the same mean, and don't care about the rest, then K-S is not best. K-S is very good for determining whether two samples in essence come from the same population. –  André Nicolas Jun 19 '12 at 12:49
    
No, I need a non-parametric test. I don't know the distribution of either data set and I want to compare one with the other. What are good solutions for this? Mann whitney u test, for instance? –  Ricky Robinson Jun 27 '12 at 11:50
    
From your description, it is K-S that seems to fit your description best. If you are interested mainly in comparing locations, then Mann-Whitney is the standard non-parametric test. –  André Nicolas Jun 27 '12 at 13:07
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