A chi-square test （also called Pearson’s chi-squared test) is used to assess two types of comparison: tests of goodness of fit and tests of independence (here).
The test of independence is applied when you have two categorical variables from a single population. It is used to determine whether there is a significant association between the two variables.
Suppose that Variable A has r levels, and Variable B has c levels. The null hypothesis states that knowing the level of Variable A does not help you predict the level of Variable B. That is, the variables are independent.
H0: Variable A and Variable B are independent. Ha: Variable A and Variable B are not independent.
The alternative hypothesis is that knowing the level of Variable A can help you predict the level of Variable B (not independent).
Expected cell count rule: Adequate expected cell counts needed. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero expected count. When the expected cell counts less than 5, using Fisher’s exact test instead.