Rank Correlation when each individual gets exactly opposite rank by two judges

When two judges assign ranks to a group of individuals, it is possible that the ranks assigned by one judge may be exactly opposite to the ranks assigned by the other judge. In such cases, the rank correlation between the two sets of ranks can be calculated using the following formula:

Spearman's Rank Correlation Coefficient = 1 - (6 x sum of squared differences between ranks)/(n x (n^2 -1))

where n is the number of individuals and the sum of squared differences between ranks is calculated as the sum of the squared differences between the first set of ranks and the second set of ranks.

Explanation

The Spearman's Rank Correlation Coefficient measures the degree of association between two sets of ranks. A value of +1 indicates a perfect positive correlation, where the ranks in both sets are identical. A value of -1 indicates a perfect negative correlation, where the ranks in one set are exactly opposite to the ranks in the other set. A value of 0 indicates no correlation between the two sets of ranks.

In the case where each individual gets exactly opposite rank by two judges, the sum of squared differences between ranks will be maximum, as every rank will be different in the two sets. Therefore, the numerator of the formula will be 6 times the sum of the squared differences between the ranks. The denominator of the formula will also be a maximum, as it depends on the number of individuals and the number of ranks. Therefore, the value of the Spearman's Rank Correlation Coefficient will be -1, indicating a perfect negative correlation between the two sets of ranks.

Conclusion

When each individual gets exactly opposite rank by two judges, the rank correlation between the two sets of ranks can be calculated using the Spearman's Rank Correlation Coefficient formula. The value of the coefficient will be -1, indicating a perfect negative correlation between the two sets of ranks.

It is negative of one i.e.-1.