-1
$\begingroup$

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.

$\endgroup$
3
$\begingroup$

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.

enter image description here

Since a number of different measures exist, you should probably start with doing a review of their pros and cons for your particular purpose.

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.


Alexander, R. A., Alliger, G. M., Carson, K. P., & Barrett, G. V. (1985). The empirical performance of measures of association in the 2× 2 table. Educational and psychological measurement, 45(1), 79-87.

David Kirk (1973) On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient. Psychometrika, 38, 259-268.

$\endgroup$
  • 2
    $\begingroup$ +1 Since the question seems to be about testing rather than measuring (see the title), it might be worth mentioning testing. $\endgroup$ – Glen_b -Reinstate Monica Nov 30 '15 at 10:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.