I have hunted peer-reviewed journals, statistics forums, and google for guidance on whether using chi square is problematic when group sizes are unequal. I know this is a problem with parametric statistics because of the underlying assumptions but I can find no evidence that it is a problem for non-parametric statistics like chi square test of independence, however, I can find no statement that says it is NOT a problem. I do understand that chi square is sensitive to large sample sizes, but how does this play out when one group is very large and one group is about 250?

If there is a problem with using chi square to detect group differences (dichotomous variable) in birth outcomes (dichotomous variable), what are alternatives to examining group differences? I appreciate your help in advance.