Dear Professor Mean, Can the Chi-square test be used for anything besides categorical data?
The Chi-square test exists in many different forms. It is useful for testing whether a categorical variable conforms to a set of hypothesized probabilities. It can also test whether two categorical variables are independent. Both of these tests involve comparing expected counts to observed counts.
There is also a Chi-square test for examining whether a sample variance is equal to a hypothesized value. For this test, you look at the ratio of the sample variance to the hypothesized variance.
Finally many nonparametric tests rely on the Chi-square distribution as an approximation when you don't have exact tables available.
You can find an earlier version of this page on my original website.