I assume “a no-difference hypothesis” is just the null hypothesis that both groups are drawn from exactly the same distribution – the null for something like a KS test.

]]>What exactly do you mean by “no difference”?

]]>Thanks. Very interesting.

]]>Indeed, the two sample problem can be viewed as an instance of the independence problem. However, sometimes there are subtleties (e.g. handling of ties) that require specific changes for the two sample case. Furthermore, sometimes more efficient algorithms can be used for the two sample case. In fact, we are working on a more efficient version of our independence test for the two sample problem and if you contact us directly we can supply you with a preliminary version of the R package. Similarly, in the energy package you can find an implementation of dcov for the two sample problem.

Regarding other methods, Larry Wasserman in his blog had an excellent post on the two sample problem at http://normaldeviate.wordpress.com/2012/07/14/modern-two-sample-tests/

I want to use an independence test to reject a no-difference hypothesis in a 2-sample test (by testing the independence of a group A/B indicator variable with the group A/B sample vectors).

Which one of these tests would be most suited for this specific task?

]]>http://dependence2013.wikischolars.columbia.edu/Nonparametric+measures+of+dependence+workshop

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