Answer
It compares the ranks of both variables by subtracting the rank of the first variable from the rank of the second variable. If the variables are positively associated, the ranks will be close to each other and the square of the differences will be small resulting in a small summation of the squares of the differences. And, according to the formula on page 772, we will find a test statistic, $r_s$, close to 1. If the variables are negatively associated, the ranks will not be close to each other and the square of the differences will be large resulting in a large summation of the squares of the differences. And, according to the formula on page 772, we will find a test statistic, $r_s$, close to -1.
Work Step by Step
Given above.
