Theory question 106
StatisticsThe table shows the scores obtained by a group of artistes in Vocal (X) and Instrumental (Y) music competion.
Vocal (X): 63, 69, 72, 59, 82, 91, 95, 68
Instrumental (Y): 58, 61, 67, 51, 53, 79, 92, 57
Calculate the Spearman's rank correlation coefficient between the scores.
Show the model answer
Model answer
Ranks (highest = 1): X: 7, 5, 4, 8, 3, 2, 1, 6; Y: 5, 4, 3, 8, 7, 2, 1, 6.
d = 2, 1, 1, 0, −4, 0, 0, 0; Σd² = 22.
ρ = 1 − 6Σd²/(n(n² − 1)) = 1 − 132/504 ≈ 0.738.
Explanation
Rank each set separately, then use the differences in rank.