Which test of statistical significance for 2 variables (categorical data), but with more than 2 categories on one of the variables?

Question

So I'm working on a project, one aspect of which looks at the effect of nationality (my independent variable) on the tendency to quit a job (my dependent variable) and I can't figure out which test to use.

I know if it was two categorical variables each with only two categories (e.g., the effect of sex on tendency to quit) I could use a chi-square test. And I think I'm right in saying if I was working with one categorical variable with more than 2 categories and one scale variable (e.g., the effect of nationality on IQ) I could use simple ANOVA, but my knowledge of stats isn't advanced enough to know what to do in these circumstances.

Can anyone help?

Answer 1

The chi-square test works just fine with more than two categories--in fact it works for arbitrary two-dimensional contingency tables. For instance Wikipedia gives the general formula for the statistic and you can find examples of doing this in R, etc. Just be sure you meet the frequency assumptions, which can be difficult if you have too many categories compared to your sample size.