Independence hypothesis test

A hypothesis test formally tests whether 2 categorical variables are independent.

When both variables are random, the hypothesis of interest is whether the variables are independent.

The null hypothesis states that the variables are independent, against the alternative hypothesis that the variables are not independent. That is, in terms of the contingency table, the null hypothesis states the event "an observation is in row i" is independent of the event "that same observation is in column j," for all i and j, against the alternative hypothesis that is the negation of the null hypothesis.

When the test p-value is small, you can reject the null hypothesis and conclude that the variables are not independent.