In a Fancy-dress competition, two judges accorded the following ranks to eight participants:

Judge X 8 7 6 3 2 1 5 4

Judge Y 7 5 4 1 3 2 6 8

Calculate coefficient of rank correlation.

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Solution

R_X R_Y D = R_X – R_Y D²

8
7
6
3
2
1
5
4 7
5
4
1
3
2
6
8 1
2
2
2
–1
–1
–1
–4 1
4
4
4
1
1
1
16

$\sum_{} D^{2} = 32$

N = 8
$r_{k} = 1 - \frac{6 \sum_{} D^{2}}{N^{3} - N} or, r_{k} = 1 - \frac{6 \times 32}{512 - 8} = \frac{504 - 192}{504} = 0.619 Hence, r_{k} = 0.619$

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R_X	R_Y	D = R_X – R_Y	D²
8 7 6 3 2 1 5 4	7 5 4 1 3 2 6 8	1 2 2 2 –1 –1 –1 –4	1 4 4 4 1 1 1 16
			$\sum_{} D^{2} = 32$

In a Fancy-dress competition, two judges accorded the following ranks to eight participants: Judge X 8 7 6 3 2 1 5 4 Judge Y 7 5 4 1 3 2 6 8 Calculate coefficient of rank correlation.

RX RY D = RX – RY D2 8 7 6 3 2 1 5 4 7 5 4 1 3 2 6 8 1 2 2 2 –1 –1 –1 –4 1 4 4 4 1 1 1 16 ∑D2=32 N = 8 rk= 1-6∑D2N3 -Nor, rk=1-6×32512-8=504-192504=0.619Hence, rk=0.619

In a Fancy-dress competition, two judges accorded the following ranks to eight participants:

Judge X 8 7 6 3 2 1 5 4

Judge Y 7 5 4 1 3 2 6 8

Calculate coefficient of rank correlation.

R_X R_Y D = R_X – R_Y D²

8
7
6
3
2
1
5
4 7
5
4
1
3
2
6
8 1
2
2
2
–1
–1
–1
–4 1
4
4
4
1
1
1
16

$\sum_{} D^{2} = 32$

N = 8
$r_{k} = 1 - \frac{6 \sum_{} D^{2}}{N^{3} - N} or, r_{k} = 1 - \frac{6 \times 32}{512 - 8} = \frac{504 - 192}{504} = 0.619 Hence, r_{k} = 0.619$