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Solution
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Solution provided by AtoZmath.com
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Spearman's Rank Correlation Coefficient (RHO) calculator
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1. Ten participants in a contest are ranked by two judges as follows
| X |
1 |
6 |
5 |
10 |
3 |
2 |
4 |
9 |
7 |
8 |
| Y |
6 |
4 |
9 |
8 |
1 |
2 |
3 |
10 |
5 |
7 |
Calculate the Spearman's Rank Correlation Coefficient.
2. The values of the same 15 student in two subject A and B are given below
the two numbers within the brackets denoting the ranks of the same student in A and B respectively.
(1,10), (2,7), (3,2), (4,6), (5,4), (6,8), (7,3), (8,1), (9,11),(10,15), (11,9), (12, 5), (13, 14), (14,12), (15, 13). Find the rank correlation coefficient.
3. Ten competitors in a musical test were ranked by the three judges A, B andC in the following order:
| judge A |
1 |
6 |
5 |
10 |
3 |
2 |
4 |
9 |
7 |
8 |
| judge B |
3 |
5 |
8 |
4 |
7 |
10 |
2 |
1 |
6 |
9 |
| judge C |
6 |
4 |
9 |
8 |
1 |
2 |
3 |
10 |
5 |
7 |
Using rank correlation method. Discuss which pair of judges has the nearest approach to common liking in music.
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Example1. Calculate Spearman's Rank Correlation Coefficient from the following Data
| X | 35 | 40 | 42 | 43 | 40 | 53 | 54 | 49 | 41 | 55 | | Y | 102 | 101 | 97 | 98 | 38 | 101 | 97 | 92 | 95 | 95 |
Solution:| `x` | `y` | `Rx` | `Ry` | `d=Rx-Ry` | `d^2` | | 35 | 102 | 10 | 1 | 9 | 81 | | 40 | 101 | 8.5 | 2.5 | 6 | 36 | | 42 | 97 | 6 | 5.5 | 0.5 | 0.25 | | 43 | 98 | 5 | 4 | 1 | 1 | | 40 | 38 | 8.5 | 10 | -1.5 | 2.25 | | 53 | 101 | 3 | 2.5 | 0.5 | 0.25 | | 54 | 97 | 2 | 5.5 | -3.5 | 12.25 | | 49 | 92 | 4 | 9 | -5 | 25 | | 41 | 95 | 7 | 7.5 | -0.5 | 0.25 | | 55 | 95 | 1 | 7.5 | -6.5 | 42.25 | | --- | --- | --- | --- | --- | --- | | -- | -- | -- | -- | -- | 200.5 |
`r = 1 - (6 * sum d^2)/(n(n^2 - 1))` `=1 - (6 * 200.5)/(10 * (10^2 - 1))` `=1 - (6 * 200.5)/(10 * (100 - 1))` `=1 - 1203/990` `=1 - 1.22` `=-0.22`
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