The essays of 10 candidates were ranked by three examiners as shown in the table.
| candidates | A | B | C | D | E | F | G | H | I | J |
| Examiner I | 1st | 3rd | 6th | 2nd | 10th | 9th | 7th | 4th | 8th | 5th |
| Examiner II | 2nd | 1st | 3rd | 9th | 7th | 4th | 8th | 10th | 5th | 6th |
| Examiner III | 3rd | 2nd | 1st | 6th | 9th | 8th | 7th | 5th | 4th | 10th |
a) Calculate the Spearman’s rank correlation coefficient of the ranks assigned by:
(i) Examiners I and lI;
(ii) Examiners I and III
(iii) Examiners II and II.
(b) Using the results in (a), state which two examiners agree most.
Explanation
(a)(i)
Rank coefficient = I = \(\frac{6\sum d^2}{n(n^2 - 1)}\)
= 1 - \(\frac{6(141)}{10(10^2 - 1)}\)
= 1 - \(\frac{6(141)}{10 \times 99}\)
= 1 - \(\frac{846}{990}\)
= 1 - 0.85
= 0.15
(ii)
Rank coefficient = 1 - \(\frac{6(78)}{10(10^2 - 1)}\)
= 1 - \(\frac{468}{990}\)
= 1 - 0.472
= 0.53
(iii)
Rank coefficient = 1 - \(\frac{6(78)}{10(10^2 - 1)}\)
= 0.53
(b) Examiner II and III