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For reasons I won't go into, I want to test for group differences between an entire sample A ($n=65$) and a subsample B ($n=45$). All of the variables I want use for mean comparisons are continuous.

Is there an appropriate test for this?

This doesn't seem to meet the sample independence condition for the t-test or Mann-Whitney U. Is it better to just test for group differences using a t-test between B (n=45) and !B (n=20)?

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  • $\begingroup$ Logically if the mean (or other location measure) of $A$ differs from $A+B$ then it differs from $B$, and vice versa. The same applies to a more general U test, even one comparing $P(A<B)$ to 0.5. Rejection of one form of hypothesis implies rejection of the other. If you did form something like a t-test for comparing dependent samples like that, you'd end up with something that was in effect doing the $A$ vs $B$ comparison anyway. $\endgroup$
    – Glen_b
    Sep 27, 2013 at 0:12

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Your last thought is the right one. Test between two sub-samples, not between a sample and a sub-sample. In this, a t-test might be appropriate, if it's other assumptions are met.

The only way I can think of to test between a sample and a subsample would be simulation, but that would wind up equivalent to testing between two sub-samples.

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