The table shows the scores obtained by a group of artistes in Vocal (X) and the instrument (Y) musical competition.
| Vocal (X) | 63 | 69 | 72 | 59 | 82 | 91 | 95 | 68 |
| Instrument (Y) | 58 | 61 | 67 | 51 | 53 | 79 | 92 | 57 |
Calculate the spearman’s rank correlation coefficient between the scores.
Explanation
p = \(1 - \frac{6Σ(d_i)^2}{n(n^2-1}\)
p = Spearman's rank correlation coefficient
di = difference between the two ranks of each observation
n = number of observation
| X | R\(_x\) | Y | R\(_y\) | D\(_I\)(R\(_x\) - R\(_y\)) |
D\(_i\)\(^2\) |
| 63 | 2 | 58 | 4 | -2 | 4 |
| 69 | 4 | 61 | 5 | -1 | 1 |
| 72 | 5 | 67 | 6 | -1 | 1 |
| 59 | 1 | 51 | 1 | 0 | 0 |
| 82 | 6 | 53 | 2 | 4 | 16 |
| 91 | 7 | 79 | 7 | 0 | 0 |
| 95 | 8 | 92 | 8 | 0 | 0 |
| 68 | 3 | 57 | 3 | 0 | 0 |
P = \(1 - \frac{6(4+1+1+0+16+0+0+0)}{8(8^2-1)}\)
p = \(1 - \frac{6(22)}{8(63)}\)
p = \(1 - \frac{132}{504}\)
p = \(1 - \frac{11}{42}\)
p = \(\frac{11}{42}\) or 0.7381