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If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?
  • a)
    0.7
  • b)
    0.65
  • c)
    0.75
  • d)
    0.8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the sum of squares of difference of ranks, given by two judges A an...
Rank Correlation Coefficient:

The rank correlation coefficient measures the degree of agreement between two sets of rankings. It determines whether there is a relationship between the rankings assigned by two judges or evaluators. The coefficient can vary between -1 and 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

Given Information:

- Judges A and B have ranked 8 students.
- The sum of squares of the difference of ranks is 21.

Calculation:

Step 1: Calculate the maximum possible sum of squares of the difference of ranks.
- The maximum possible sum can be calculated using the formula: n(n^2 - 1)/6, where n is the number of observations.
- In this case, n = 8, so the maximum possible sum is (8 * (8^2 - 1)) / 6 = 140.

Step 2: Calculate the rank correlation coefficient using the formula:
- Rank correlation coefficient = 1 - (6 * sum of squares of the difference of ranks) / (n * (n^2 - 1))
- Substituting the given values, the rank correlation coefficient = 1 - (6 * 21) / (8 * (8^2 - 1))
- Simplifying further, the rank correlation coefficient = 1 - 126 / 448
- The rank correlation coefficient = 1 - 0.28125
- The rank correlation coefficient = 0.71875

Conclusion:

The value of the rank correlation coefficient is approximately 0.719. Since none of the given options match this value exactly, the closest option is 0.75 (option C). Therefore, the correct answer is option C, 0.75.
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If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?a)0.7b)0.65c)0.75d)0.8Correct answer is option 'C'. Can you explain this answer?
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