I am practicing statistics on the gss dataset. I want to study the relationship between people owning guns in the USA and political inclination. Owning guns or not is a nominal variable while political inclination ranges from extremely liberal to extremely conservative.
After some exploratory data analysis I got suspicious that people that are more liberal seem to own more guns. How can I test this suspicion? I am aware of $\chi^2$ independence tests, and after conducting one on the data I can say that evidence of the pair of variables not being independent is very high, gun ownership rates depend on political inclinations, while this insight its valuable it says nothing about what I want to test.
I have been investigating Kruskal-wallis, but I am not sure if this is what I want.. Any help is appreciated!
EDIT: Is checking that $\mu_a \leq \mu_b \leq \mu_c \leq \mu_c$ the way to prove this relationship? this surely is a trivial statistics question, can anyone look into it?