Rank correlation coefficient
Posted in Maths,The Spearman's rank correlation coefficient, denoted by rs is a method of calculating the correleation coefficient for a set of bivariate data by ranking that data.
The formula for the rank correlation coefficient is:
Where d is the difference in ranks and n is the amount of pairs of data.
Example
Two student's marks on 5 tests are compared, their results are given as follows:
| Test | A | B | C | D |
|---|---|---|---|---|
| Student A | 40 | 45 | 42 | 49 |
| Student B | 38 | 33 | 40 | 32 |
First step is to rank the data, in this case give a rank 1 to the highest value and rank 4 to the lowest value:
| Test | A | B | C | D |
|---|---|---|---|---|
| Student A | 4 | 2 | 3 | 1 |
| Student B | 2 | 3 | 1 | 4 |
Now calculate the difference in ranks for each pair of data and calculate the squared difference too:
| Test | A | B | C | D |
|---|---|---|---|---|
| Student A | 4 | 2 | 3 | 1 |
| Student B | 2 | 3 | 1 | 4 |
| d | 2 | -1 | 2 | -3 |
| d2 | 4 | 1 | 4 | 9 |
Calculate the sum of the differences squared:
Plug the values into the formula: