I would like to know which test can be used in this situation:
Suppose we have essentially a categorical variable, like gender. The observations for gender are divided by some other variable, e.g. "is employed" vs "not employed". I would like to find a test which compares the "distributions" of gender and determines if there is a significant difference between the two.
So H0: There is no difference between the two groups. H1: there is a difference.
Normally, I would use chi-square test to determine if the single cells are different, but here I am interested if there is a difference overall.
Note: a special case might be a situation where the categorical variable was originally a numeric variable but was transformed into a categoric variable, e.g. income -> income_groups.