On a 3x2, like in this example, I could perform an additional follow up chi-squared to test differences between only two groups I'm interested in (e.g. between vaccinated a year before and just before the epidemic groups).
But if I had an additional column, making it a 3x3 table, even an additional chi-sqared wouldn't suffice to see where all the significant differences are (in which columns).
I've come upon the option to use standardized residuals, but they seem to need a different interpretation than using follow-up chi-squared test. With a follow up chi-squared, I would interpret by saying that, yes, the selected groups differ on how many diseased people there are. But when using standardized residuals I can't make a sweeping statement about groups, because the std. residuals only pertain to cells. That confuses me. E.g. in the 3x2 example, for the unvaccinated group, the std. residuals for the unvaccinated group would be z = 6,8 for the diseased and z = -2,3 for non-diseased. So one is significant at α = 0.01, but the other is not, even though they are just two sides of the same coin (one being 115 people short because they're in the other group). How do I interpret these standardized residuals?
What if I want to compare two cells one to another in a 3x3 or larger table? Can I do that with std. residuals, or are they only useful while looking at a single cell? Or maybe I can perform a follow up chi-squared on only the cells I'm interested in?
One more question, if I were to add a third variable, would it make sense to merge existing two variables into one (so it would have 6 groups: 1) unvaccinated diseased, 2) unvaccinated non-diseased...)? That way I could still perform a chi-squared on data with 3 variables. Or would I have to use loglinear analysis?
