correlations between ordinal, dichotomous variables

[Musarrat Nahid]

Hello,
I'm asked to do correlations between 2 variables, both of which are ranked and dichotomous; I feel logistic regression with Odds Ratio might be a suitable option. Does anyone have any other ideas? I mean, are there any other methods that can produce correlation coefficients for the aforementioned scenario? Thanks very much!
Sincerely
MN

[Joseph Coveney]

The odds ratio is an index of association between two binary variables, but you can also compute the tetrachoric correlation coefficient, which some of your audience might prefer.

help tetrachoric

[Nick Cox]

If you have two binary variables (say coded zero and one), the Pearson correlation is defined so long as both variables have some zeros and some ones. I doubt, however, that many statistical people would think that it is a good way forward. There is no information available from the correlation that isn't in the two-way table of frequencies, indeed much less. So a real question is about what you are being asked. Bluntly put, do the people asking know more statistics than you do or less?

By the way, if a variable is binary (dichotomous) then I guess calling it ordinal too does no harm but it seems unnecessary. Naturally, an ordinal variable with three or more levels is not binary, for all that it might be represented by two or more indicator variables.

[Musarrat Nahid]

Hi Mr. Cox and Coveney,
Thank you very much to you both!
Sincerely
MN