Five finalists in a beauty pageant were ranked by two judges X and Y as shown in the table :
| Judges | Anne | Linda | Susan | Rose | Erica |
| X | 1 | 4 | 3 | 5 | 2 |
| Y | 3 | 2 | 4 | 5 | 1 |
Calculate the Spearman’s rank correlation coefficient.
Explanation
|
Rank X (R_{X}) |
Rank Y (R_{Y}) |
(d = R_{X} – R_{Y}) | (d^{2}) |
| 1 | 3 | -2 | 4 |
| 4 | 2 | 2 | 4 |
| 3 | 4 | -1 | 1 |
| 5 | 5 | 0 | 0 |
| 2 | 1 | 1 | 1 |
| (sum) | 10 |
Spearman’s rank correlation coefficient = (1 – frac{6 sum d^{2}}{n(n^{2} – 1)})
= (1 – frac{6(10)}{5(5^{2} – 1)})
= (1 – frac{60}{120})
= (0.5)