# Comparing sample correlation coefficient with population correlation coefficient

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.

• You were asking for a technique to compare sample correlation to population correlation. I'm not sure if this questions really fits your described situation: It may be that I am missing something, but it seems to me that you are rather trying to compare correlations across different populations, one ($C_i$ for i in 1...m) being a a subset of your full population P. Apr 25, 2019 at 9:40