Assume there is a population, P, of size N. Each member of the population has three variables associated with it, a nominal variable C (with m unique categories), and two continuous variables X and Y.
The Pearson correlation of X and Y for the entire population P was determined to be r(P).
I would like to determine, for each category C, whether the Pearson r of the the members of each individual caterogy, -- P(C1), P(C2), ..., P(Cm) -- differs from the population's Pearson r.
In other words,
- H0(C1): r(P(C1)) = r(P),
- H1(C1): r(P(C1)) <> r(P).
and so on for C2, C3, ..., Cm.
(Note that I am not talking about the difference in means, but strictly the difference in the correlations.)
I am aware of this question here, but I wonder if I can use the same technique for comparing a sample to its population.