Overview(rank correlation)
A group of n individuals may be arranged in order to merit with respect to some characteristics. The same group would give different orders for different characteristics. Considering the orders corresponding to two characteristics A and B, the correction between these n pairs of rank is called the rank correlation in the characteristics A and B for that group of individuals.
formula
Let 
Assuming nor two individuals are equal in https://bcfma.com/admission/ either classification, each individual takes the values 1, 2, 3, and hence their arithmetic means are, each
Suppose that
Then
Here X and Y are deviations from the mean.
Which is called the rank correlation or Spearman’s rank correlation coefficient and we denote it by Rho
Solved examples
Example: Compute Spearman’s rank correlation coefficient r for the following data:
| Person | A | B | C | D | E | F | G | H | I | J |
| Rank Statistics | 9 | 10 | 6 | 5 | 7 | 2 | 4 | 8 | 1 | 3 |
| Rank in income | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Solution:
| Person | Rank Statistics | Rank in income | d= R1 – R2 |  |
| A | 9 | 1 | 8 | 64 |
| B | 10 | 2 | 8 | 64 |
| C | 6 | 3 | 3 | 9 |
| D | 5 | 4 | 1 | 1 |
| E | 7 | 5 | 2 | 4 |
| F | 2 | 6 | -4 | 16 |
| G | 4 | 7 | -3 | 9 |
| H | 8 | 8 | 0 | 0 |
| I | 1 | 9 | -8 | 64 |
| J | 3 | 10 | -7 | 49 |
Example. Three judges A,B,C give the following ranks. Find which pair of judges has common approach
A 1 6 5 10 3 2 4 9 7 8
B 3 5 8 4 7 10 2 1 6 9
C 6 4 9 8 1 2 3 10 5 7
Solution
Here n = ten, so that we get the following table,
| A (=x) | Ranks byB(=y) | C (=z) | d1 = x-y | d2 = y – z | d3 = z-x |  |  |  |
| 1 | 3 | 6 | -2 | -3 | 5 | 4 | 9 | 25 |
| 6 | 5 | 4 | 1 | 1 | -2 | 1 | 1 | 4 |
| 5 | 8 | 9 | -3 | -1 | 4 | 9 | 1 | 16 |
| 10 | 4 | 8 | 6 | -4 | -2 | 36 | 16 | 4 |
| 3 | 7 | 1 | -4 | 6 | -2 | 16 | 36 | 4 |
| 2 | 10 | 2 | -8 | 8 | 0 | 64 | 64 | 0 |
| 4 | 2 | 3 | 2 | -1 | -1 | 4 | 1 | 1 |
| 9 | 1 | 10 | 8 | -9 | 1 | 64 | 81 | 1 |
| 7 | 6 | 5 | 1 | 1 | -2 | 1 | 1 | 4 |
| 8 | 9 | 7 | -1 | 2 | -1 | 1 | 4 | 1 |
| Total | 0 | 0 | 0 | 200 | 214 | 60 |
.
Since 
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