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.
|
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 = \(1 - \frac{6 \sum d^{2}}{n(n^{2} - 1)}\)
= \(1 - \frac{6(10)}{5(5^{2} - 1)}\)
= \(1 - \frac{60}{120}\)
= \(0.5\)
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