In addition to tetrachoric correlation coefficient, I have read about:
The Phi Correlation Coefficient, which is designed to measure the
degree of relation for two variables which are binary (each has only
two values --- also called dichotomous).
To compute you first convert your two binary variable into 1's and 0's,
and then follow the procedure for Pearson correlation.
(http://forrest.psych.unc.edu/research/vista-frames/others.html)
From what I recall, if the proportions coded 1.0 and 0 are close in the
40-60% range, phi performs ok.
The use of the tetrachoric implies assumption of underlying
(unassessed) normal distribution. I don't know if there are cases
where the phi would outperform the tetrachoric (or on what standards
one would evaluate performance) if the tetrachoic assumptions were
wrong, but I would be interested in knowing...
