Testing the relation between 2 Categorical Data (Gender and 5-leveled consumption) and Visualizing it in R

Question

In my dataset, there are 3 data that I would like to check for relations, which are

$ famsup   : Factor w/ 2 levels "no","yes": 1 2 1 2 2 2 1 2 2 2 ... 
$ schoolsup: Factor w/ 2 levels "0","1": 2 1 2 1 1 1 1 2 1 1 ... 
$ Walc     : Factor w/ 5 levels "1","2","3","4",..: 1 1 3 1 2 2 1 1 1 1 ...

Here, famsup is the families' economic support on students, schoolsup is the schools' economic support on students and walc is the alcohol consumption ratio leveled from very low to very high.

What hypothesis test do I use to check for relations between alcohol consumption and each type of support (or both types at once)? Also, can I visualize this on a graph, if so, which one?

Answer 1

What makes the most sense here is to treat Walc as an ordinal variable.

The classic association test for an ordinal variable and a dichotomous variable is the Cochran-Armitage test. There is an extended version of this test if there are more than two groups in the nominal variable.

In reality, a Wilcoxon-Mann-Whitney test or Kruskal-Wallis test that accounts for ties in ranks will work as well.

There are several measures of the degree of association for an ordinal variable and a nominal variable: Freeman's theta, epsilon-squared (the kind appropriate as an effect size for a Kruskal-Wallis test). If the there are only two groups in the nominal variable, there are several others that can be used: Varga and Delaney's A, Cliff's delta, Kendall's tau-b, and there is an r that used an effect size statistic for a Wilcoxon-Mann-Whitney test.

One way to visual the association between an ordinal variable and a nominal variable is a spine plot. Here, Breakfast is the ordinal variable and Travel is the nominal variable: http://rcompanion.org/handbook/images/image217.png .