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Question
The rank of 10 students of the same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.
| Rank of A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Rank of B | 6 | 7 | 5 | 10 | 3 | 9 | 4 | 1 | 8 | 2 |
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Solution
| RX | RY | d = RX − RY | d2 |
| 1 | 6 | − 5 | 25 |
| 2 | 7 | − 5 | 25 |
| 3 | 5 | − 2 | 4 |
| 4 | 10 | − 6 | 36 |
| 5 | 3 | 2 | 4 |
| 6 | 9 | − 3 | 9 |
| 7 | 4 | 3 | 9 |
| 8 | 1 | 7 | 49 |
| 9 | 8 | 1 | 1 |
| 10 | 2 | 8 | 64 |
| ∑d2 = 226 |
N = 10, Σd2 = 226
Rank correlation (ρ) = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6 xx 226)/(10(100 - 1))`
= `1 - (6 xx 226)/(10 xx 99)`
= − 0.37
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