Calculate Spearman's rank correlation coefficient for the following ranks given by three judges in a music contest. Indicate which pair of judges has the nearest approaches to music.
Calculate Spearman's rank correlation coefficient for the following ranks given by three judges in a music contest. Indicate which pair of judges has the nearest approaches to music.
$$\begin{array}{c|cccccccccc} \text{1}^{\text{st}}\text{ Judge} & 2 & 1 & 4 & 6 & 5 & 8 & 9 & 10 & 7 & 3 \ \text{2}^{\text{nd}}\text{ Judge} & 4 & 3 & 2 & 5 & 1 & 6 & 8 & 9 & 10 & 7 \ \text{3}^{\text{rd}}\text{ Judge} & 5 & 8 & 4 & 7 & 10 & 2 & 1 & 6 & 9 & 3 \ \end{array}$$
[5]
$n = 10$ competitors. Competitor 1st Judge ($R1$) 2nd Judge ($R2$) 3rd Judge ($R3$) :---::---::---::---: 1 2 4 5 2 1 3 8 3 4 2 4 4 6 5 7 5 5 1 10 6 8 6 2 7 9 8 1 8 10 9 6 9 7 10 9 10 3 7 3 Formula: $$rs = 1 - \frac{6\sum d^2}{n(n^2 - 1)}, \quad n(n^2-1) = 10 \times 99 = 990$$ Comp $R1$ $R2$ $R3$ ...