# What test should I run to show if there is a correlation between two binary variables?

I have two variable religion and healthy. The answers are coded as yes or no. I want to see if health is related to religion.

There is a number of correlation measures for binary data including $\phi$ coefficient and Cohen's $\kappa$ among the commonly used ones. Alexander et al. (1985) after conducting a simulation study concluded that $\phi$ and $\kappa$ are not the most efficient ones with the odds ratio based coefficient by Chambers being the best in their study. Below you can see a table summarizing different measures provided in this paper. Modern methods as tetrachoric correlation are implemented in different software, like R's psych library.
As @Glen_b noticed, you seem mention testing the difference about those two binary variables. If it is so, you may be rather interested in methods such as $\chi^2$ test, binomial test, or logistic regression (cf. here) and odds ratios, for learning more about those methods see here and here.