# How to Describe Interaction Between Variables

Say I have two demographic variables, job$$\in{j_1, j_2}$$ and lives$$\_$$alone$$\in$${YES, NO}. I also have N books $$B_1$$, $$\ldots$$, $$B_N$$, each labelled with a genre that I know in advance, out of {fiction,non-fiction}.

In an experiment, I ask representatives of each instance of job, and each instance of lives$$\_$$alone, to label the books (off course, they do not know the true labels). That is, I have 4 treatment groups: job=$$j_1$$ and lives$$\_$$alone=YES, job=$$j_1$$ and lives$$\_$$alone=NO, job=$$j_2$$ and lives$$\_$$alone=YES, job=$$j_2$$ and lives$$\_$$alone=NO. So, in the end, each book has 4 labels, one coming from each treatment group.

At this point, I can compute metrics such as accuracy, precision, recall, etc., to get an idea about which group is best at correctly labelling the books. I could also do statistical tests to see if the difference in e.g. accuracy between two groups is significant.

However, where I am stuck is figuring out if there is any interaction between the two variables, job and lives$$\_$$alone. How do I begin to make a statement about how the two variables interact?

Thank you!

An interaction means that the effect of one variable depends on the level of the other. You can examine whether the difference between live_alone = YES and live_alone = NO differs between those with job=$$j_1$$ and those with job=$$j_2$$. If there is a difference between these differences, then you have an interaction. Of course, you need to statistically test for the presence of an interaction, which regression or ANOVA can do.