# correlation between categorical variables

I remember that Pearson correlation works for continuous variables and also if one is continuous and the other a dummy. For the latter, it does not provide a correlation but provides a portion. What is the best approach, when we have 2 dummy variables. Would you suggest to calculate correlation for them or what is a good way to look at the relationship between 2 dichotomous variables. Ex: gender and religious status.

You're looking for estimates of association for contingency tables. You've got a few options. Here's a great summary of two of the most popular measures, the phi coefficient and Cramer's V: http://www.people.vcu.edu/~pdattalo/702SuppRead/MeasAssoc/NominalAssoc.html

Both measure the strength of the association between categorical variables. The chi coefficient only works for 2x2 tables (like the example you give: "2 dichotomous variables. Ex: gender and religious status"), but Cramer's V works for larger tables as well. For a 2x2 table, phi and V will be equal.

Phi is a chi-square based measure of association. The chi-square coefficient depends on the strength of the relationship and sample size. Phi eliminates sample size by dividing chi-square by n, the sample size, and taking the square root.

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Cramer's V is the most popular of the chi-square-based measures of nominal association because it gives good norming from 0 to 1 regardless of table size, when row marginals equal column marginals. V equals the square root of chi-square divided by sample size, n, times m, which is the smaller of (rows - 1) or (columns - 1): V = SQRT(X2/nm).

Another measure similar to Cramer's V is Cohen's w, explained on this page: http://stats.idre.ucla.edu/other/mult-pkg/faq/general/effect-size-power/faqhow-is-effect-size-used-in-power-analysis/

Effect size w is the square root of the standardized chi-square statistic.

• upvoted as the correct answer but think it's important to make the distinction here that association means it is not correlation. Nominal variables will not provide covariance of direction. Apr 30 '17 at 1:18