In each of the previous exercises, we assessed whether there was an association between a quantitative variable (math scores) and a BINARY categorical variable (school). The categorical variable is considered binary because there are only two available options, either MS or GP. However, sometimes we are interested in an association between a quantitative variable and non-binary categorical variable. Non-binary categorical variables have more than two categories.

When looking at an association between a quantitative variable and a non-binary categorical variable, we must examine all pair-wise differences. For example, suppose we want to know whether or not an association exists between math scores (G3) and (Mjob), a categorical variable representing the mother’s job. This variable has five possible categories: at_home, health, services, teacher, or other. There are actually 10 different comparisons that we can make. For example, we can compare scores for students whose mothers work at_home or in health; at_home or other; at home or `services; etc.. The easiest way to quickly visualize these comparisons is with side-by-side box plots:

sns.boxplot(data = df, x = 'Mjob', y = 'G3')
plt.show()

Visually, we need to compare each box to every other box. While most of these boxes overlap with each other, there are some pairs for which there are some apparent differences. For example, scores appear to be higher among students with mothers working in health than among students with mothers working at home or in an “other” job. If there are ANY pairwise differences, we can say that the variables are associated; however, it is more useful to specifically report which groups are different.