# Corelation between two dichotomous variables

I have a data from a research with responses (yes/no) about three questions (A,B,C) and I would to see if the variables are correlated.

First of all i compared the proportion of agreement(yes-yes, no-no) of them. The results was:

A-B= 78%

A-C=59%

B-C is out of my objective.

So I run a Pearson Correlation test, and the results was:

A-B=0,17 (p-value = 0,03)

A-C=0,11 (p-value=0,15)

Which test should I do to verify the correlation between these variables? Chi-square test? Why the correlation between A and C is bigger then A and B when the proportion of agreement between A and B is bigger?

• Correlation is not appropriate for categorical variables. What exactly is your objective? Also have a look at en.wikipedia.org/wiki/Phi_coefficient – user2974951 Jan 18 '19 at 12:42
• My objective is to measure the "association/correlation" between A-C, A-B.. We are analyzing answers about food consumption. I've already saw Phi coefficient before, but the text says that " (...) a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient." Is it correct? – Oalvinegro Jan 18 '19 at 15:29
• Yes, Pearson and Phi will be equal for binary categorical variables (a 2x2 table), so you could use Pearson in this case. Also, in regards to your question, A-B have higher correlation than A-C. – user2974951 Jan 21 '19 at 12:47
• The correlations are inverted. A-C=0,17 and A-B=0,11. So, that is the problem. Considering that the proportion of agreement to A-B is 78% and the Pearson correlation coefficient is 0,17, Pearson is a good measure to this case? – Oalvinegro Jan 23 '19 at 12:10
• Maybe if you could share your data and upload it here we would be able to better help you. Are your sample sizes equal across all groups? Do you have missing values? – user2974951 Jan 24 '19 at 13:14