Let's say we have k binomial variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check if there is a correlation between these variables, so the null hypothesis assumes that they are all independent (no correlation).
Is there a formula to calculate the minimum sample size n required to identify a "significant" correlation (p <= alpha) between these variables?
That is, how are n, k, f and alpha linked to each other mathematically?
Are any other parameters involved in the formula, e.g., beta, $R^2$, etc.?
I have a feeling that this relates to power and/or sample size calculations for multiple logistic regression, but I'm really not sure. Could the Wald test or likelihood-ratio test be used here?