Formula
|
1. `r = 1 - (6 * sum d^2)/(n(n^2 - 1))`
|
Examples
1. Calculate Spearman's Rank Correlation Coefficient from the following Data
| X | 35 | 40 | 42 | 43 | 40 | 53 | 54 | 49 | 41 | 55 |
| Y | 102 | 101 | 97 | 98 | 38 | 101 | 97 | 92 | 95 | 95 |
Solution:
| `x` | `y` | `Rx` | `Ry` | `d=Rx-Ry` | `d^2` |
| 35 | 102 | 10 | 1 | 9 | 81 |
| 40 | 101 | 8.5 | 2.5 | 6 | 36 |
| 42 | 97 | 6 | 5.5 | 0.5 | 0.25 |
| 43 | 98 | 5 | 4 | 1 | 1 |
| 40 | 38 | 8.5 | 10 | -1.5 | 2.25 |
| 53 | 101 | 3 | 2.5 | 0.5 | 0.25 |
| 54 | 97 | 2 | 5.5 | -3.5 | 12.25 |
| 49 | 92 | 4 | 9 | -5 | 25 |
| 41 | 95 | 7 | 7.5 | -0.5 | 0.25 |
| 55 | 95 | 1 | 7.5 | -6.5 | 42.25 |
| --- | --- | --- | --- | --- | --- |
| -- | -- | -- | -- | -- | 200.5 |
`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`
`=1 - (6 * 200.5)/(10 * (10^2 - 1))`
`=1 - (6 * 200.5)/(10 * (100 - 1))`
`=1 - 1203/990`
`=1 - 1.22`
`=-0.22`
2. Calculate Spearman's Rank Correlation Coefficient from the following Data
| X | 42 | 43 | 40 | 53 | 54 | 49 | 41 | 55 |
| Y | 97 | 98 | 38 | 101 | 97 | 92 | 95 | 95 |
Solution:
| `x` | `y` | `Rx` | `Ry` | `d=Rx-Ry` | `d^2` |
| 42 | 97 | 6 | 3.5 | 2.5 | 6.25 |
| 43 | 98 | 5 | 2 | 3 | 9 |
| 40 | 38 | 8 | 8 | 0 | 0 |
| 53 | 101 | 3 | 1 | 2 | 4 |
| 54 | 97 | 2 | 3.5 | -1.5 | 2.25 |
| 49 | 92 | 4 | 7 | -3 | 9 |
| 41 | 95 | 7 | 5.5 | 1.5 | 2.25 |
| 55 | 95 | 1 | 5.5 | -4.5 | 20.25 |
| --- | --- | --- | --- | --- | --- |
| -- | -- | -- | -- | -- | 53 |
`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`
`=1 - (6 * 53)/(8 * (8^2 - 1))`
`=1 - (6 * 53)/(8 * (64 - 1))`
`=1 - 318/504`
`=1 - 0.631`
`=0.369`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
