Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $\rho$ .
Is there any analytic function for sampling error of correlation coefficient if I have finite sample from the population?
I've tried to use Fisher z-transformation, with sampling variance estimation of $1/N$ but it gives inappropriate (lower than actual) estimation of variance. As my simulations show, sampling error of Phi coefficient is a function of population correlation coefficient, frequencies of both binary variables and of course sample size.
Thanks in advance!