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प्रश्न
Ranking of 8 trainees at the beginning (X) and at the end (Y), of a certain course are given below :
| Trainees | A | B | C | D | E | F | G | H |
| X | 1 | 2 | 4 | 5 | 6 | 8 | 3 | 7 |
| Y | 2 | 4 | 3 | 7 | 8 | 1 | 5 | 6 |
Calculate Spearman's rank correlation coefficient.
बेरीज
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उत्तर
| 1 | 2 | 3 | 4 | 5 |
| Trainee code | Rank xi | Rank yi | di = xi - yi | `d_"t"^2` |
| A | 1 | 2 | -1 | 1 |
| B | 2 | 4 | -2 | 4 |
| C | 4 | 3 | 1 | 1 |
| D | 5 | 7 | -2 | 4 |
| E | 6 | 8 | -2 | 4 |
| F | 8 | 1 | 7 | 49 |
| G | 3 | 5 | -2 | 4 |
| H | 7 | 6 | 1 | 1 |
| `sum "d"_"i"^2 = 68` |
Given n = 8 , `sum "d"_"i"^2 = 68`
Rank correlation (R) = 1 - `(6 xx sum "d"_"i"^2)/("n"("n"^2 - 1))`
= `1 - (6 xx 68)/(8 xx 63)`
= 1 - 0.8095
= 0.1905
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