Five finalists in a beauty pageant were ranked by two judges X and Y as shown in the table : Judges Anne Linda Susan Rose Erica X 1 4 3 5 2 Y 3 2 4 5 1 Calc...
Question 1 Report
Five finalists in a beauty pageant were ranked by two judges X and Y as shown in the table :
| Judges | Anne | Linda | Susan | Rose | Erica |
| X | 1 | 4 | 3 | 5 | 2 |
| Y | 3 | 2 | 4 | 5 | 1 |
Calculate the Spearman's rank correlation coefficient.
Answer Details
Spearman's rank correlation coefficient is \(r_s=1-\dfrac{6\sum d^2}{n(n^2-1)}\), where \(d\) is the difference between paired ranks and \(n\) is the number of individuals. Here \(n=5\).
| Finalist | Judge X | Judge Y | \(d=X-Y\) | \(d^2\) |
|---|---|---|---|---|
| Anne | 1 | 3 | -2 | 4 |
| Linda | 4 | 2 | 2 | 4 |
| Susan | 3 | 4 | -1 | 1 |
| Rose | 5 | 5 | 0 | 0 |
| Erica | 2 | 1 | 1 | 1 |
| \(\sum d^2\) | 10 | |||
\[r_s=1-\frac{6\times 10}{5(5^2-1)}=1-\frac{60}{5\times 24}=1-\frac{60}{120}=1-0.5=0.5\]
The Spearman's rank correlation coefficient is 0.5, indicating a moderate positive agreement between the two judges.
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