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Question
A random sample of recent repair jobs was selected and estimated cost, actual cost were recorded.
| Estimated cost | 30 | 45 | 80 | 25 | 50 | 97 | 47 | 40 |
| Actual cost | 27 | 48 | 73 | 29 | 63 | 87 | 39 | 45 |
Calculate the value of spearman’s correlation.
Solution
| Estimated cost (X) | Actual cost (Y) | RX | RY | d = RX − RY | d2 |
| 30 | 27 | 2 | 1 | 1 | 1 |
| 45 | 48 | 4 | 5 | − 1 | 1 |
| 80 | 73 | 7 | 7 | 0 | 0 |
| 25 | 29 | 1 | 2 | − 1 | 1 |
| 50 | 63 | 6 | 6 | 0 | 0 |
| 97 | 87 | 8 | 8 | 0 | 0 |
| 47 | 39 | 5 | 3 | 2 | 4 |
| 40 | 45 | 3 | 4 | − 1 | 1 |
| ∑d2 = 8 |
Spearman’s Rank correlation coefficient
ρ = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6(8))/(8(8^2 - 1))`
= `1 - 6/63`
= 1 − 0.095
ρ = 0.905
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