I have two binary variables and want to test their association. From what I’ve read I need to use the chi-squared ($χ^2$) test. The measure of their association is then described through the Phi coefficient ($φ$).
My question is, can I compare the phi coefficient to a regular Pearson correlation coefficient $r$ (among continuous variables)? Are these two comparable?
For example if two binary variables $b_1$ and $b_2$ have a $φ=0.6$ between them and two continuous variables $c_1$ and $c_2$ have a $r=0.5$. Can I say that the association between $b_1$ and $b_2$ is stronger than between $c_1$ and $c_2$?