The rank correlation coefficient of a debating contest involving 10 participants was calculated as 0.6. However, it was later discovered that the difference in the ranks of some participants was read as 8 instead of 3. Find the correct correlation coefficient:
A)0.933
B)0.652
C)0.854
D)0.751

Question

Quizplus · Accepted Answer

The correct rank correlation coefficient can be recalculated by adjusting the sum of the squares of the differences in ranks (d^2) used in Spearman's rank correlation coefficient formula. The error in reading the difference in ranks as 8 instead of 3 affects the calculation of d^2. The incorrect d^2 would have included (8^2 = 64), and the correct d^2 should include (3^2 = 9). The difference between the incorrect and correct d^2 values is 64 - 9 = 55. This difference needs to be subtracted from the initially calculated sum of d^2 to correct the error. The corrected rank correlation coefficient, after adjusting for this error, is found to be significantly higher, reflecting a stronger positive correlation between the ranks of participants.

The Rank Correlation Coefficient of a Debating Contest Involving 10