The degrees of freedom are equal to (R-1)(C-1) where R is the number of rows and C is the number of columns. In this example, R = 2 and C = 2, so df = (2-1)(2-1) = 1. A chi square table can be used to determine that for df = 1, a chi square of 22.01 has a probability value less than 0.0001.

In a table with two rows and two columns, the chi square test of independence is equivalent to a test of the difference between two sample proportions. In this example, the question is whether the proportion graduating from high school differs as a function of condition. Whenever the degrees of freedom equal one (as they do when R = 2 and C = 2), chi square is equal to z². Note that the test of the difference between proportions for these data results in a z of 4.69 which, when squared, equals 22.01.