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Question
A random sample of recent repair jobs was selected and estimated cost and actual cost were recorded.
| Estimated cost | 300 | 450 | 800 | 250 | 500 | 975 | 475 | 400 |
| Actual cost | 273 | 486 | 734 | 297 | 631 | 872 | 396 | 457 |
Calculate the value of spearman’s correlation coefficient.
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Solution
| X | Y | RX | RY | d = RX − RY | d2 |
| 300 | 273 | 7 | 8 | − 1 | 1 |
| 450 | 486 | 5 | 4 | 1 | 1 |
| 800 | 734 | 2 | 2 | 0 | 0 |
| 250 | 297 | 8 | 7 | 1 | 1 |
| 500 | 631 | 3 | 3 | 0 | 0 |
| 975 | 872 | 1 | 1 | 0 | 0 |
| 475 | 396 | 4 | 6 | − 2 | 4 |
| 400 | 457 | 6 | 5 | 1 | 1 |
| ∑d2 = 8 |
N = 8, Σd2 = 8
Rank correlation (ρ) = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6 xx 8)/(8(64 - 1))`
= `1 - 6/63`
= 0.905
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