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Question
An examination of 11 applicants for a accountant post was taken by a finance company. The marks obtained by the applicants in the reasoning and aptitude tests are given below.
| Applicant | A | B | C | D | E | F | G | H | I | J | K |
| Reasoning test | 20 | 50 | 28 | 25 | 70 | 90 | 76 | 45 | 30 | 19 | 26 |
| Aptitude test | 30 | 60 | 50 | 40 | 85 | 90 | 56 | 82 | 42 | 31 | 49 |
Calculate Spearman’s rank correlation coefficient from the data given above.
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Solution
| X | Y | RX | RY | d = RX − RY | d2 |
| 20 | 30 | 10 | 11 | − 1 | 1 |
| 50 | 60 | 4 | 4 | 0 | 0 |
| 28 | 50 | 7 | 6 | 1 | 1 |
| 25 | 40 | 9 | 9 | 0 | 0 |
| 70 | 85 | 3 | 2 | 1 | 1 |
| 90 | 90 | 1 | 1 | 0 | 0 |
| 76 | 56 | 2 | 5 | − 3 | 9 |
| 45 | 82 | 5 | 3 | 2 | 4 |
| 30 | 42 | 6 | 8 | − 2 | 4 |
| 19 | 31 | 11 | 10 | 1 | 1 |
| 26 | 49 | 8 | 7 | 1 | 1 |
| ∑d2 = 22 |
N = 11, Σd2 = 22
Rank correlation (ρ) = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6 xx 22)/(11(121 - 1))`
= `1 - 12/120`
= 1 − 0.1
= 0.9
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