Two panel of judges, X and Y, rank 8 brands of cooking oil as follows :
| Cooking oil type | A | B | C | D | E | F | G | H |
| X | 8 | 5 | 1 | 7 | 2 | 6 | 3 | 4 |
| Y | 6 | 3 | 4 | 8 | 5 | 7 | 1 | 2 |
Calculate the Spearmann’s rank correlation coefficient.
Explanation
| \(R_{X}\) | \(R_{Y}\) | \(D = R_{X} - R_{Y}\) | \(D^{2}\) |
| 8 | 6 | 2 | 4 |
| 5 | 3 | 2 | 4 |
| 1 | 4 | -3 | 9 |
| 7 | 8 | -1 | 1 |
| 2 | 5 | -3 | 9 |
| 6 | 7 | -1 | 1 |
| 3 | 1 | 2 | 4 |
| 4 | 2 | 2 | 4 |
| Total | 36 |
Spearmann's rank correlation coefficient = \(1 - \frac{6\sum D^{2}}{N(N^{2} - 1)}\)
= \(1 - \frac{6(36)}{8(64 - 1)}\)
= \(1 - \frac{216}{504}\)
= \(1 - 0.4286\)
= \(0.5714\)
\(\approxeq 0.57\).