Theory question 113
StatisticsThe essays of 10 candidates were ranked by three examiners as shown in the table.
Candidate: 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 II; (ii) Examiners I and III (iii) Examiners II and III. (b) Using the results in 13(a), state which two examiners agree most.
Show the model answer
ρ = 1 − 6Σd²/(n(n² − 1)), n = 10, so n(n² − 1) = 990.
(a)(i) I and II: Σd² = 144, ρ = 1 − 864/990 ≈ 0.13.
(ii) I and III: Σd² = 90, ρ = 1 − 540/990 ≈ 0.45.
(iii) II and III: Σd² = 78, ρ = 1 − 468/990 ≈ 0.53.
(b) Examiners II and III agree most (largest coefficient).
The bigger the coefficient, the closer the agreement.