Formula

1. `r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

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Examples
1. Calculate Spearman's Rank Correlation Coefficient from the following Rank

X	3	5	8	4	7	10	2	1	6	9
Y	6	4	9	8	1	2	3	10	5	7

Solution:

`Rx`	`Ry`	`d=Rx-Ry`	`d^2`
3	6	-3	9
5	4	1	1
8	9	-1	1
4	8	-4	16
7	1	6	36
10	2	8	64
2	3	-1	1
1	10	-9	81
6	5	1	1
9	7	2	4
---	---	---	---
--	--	--	214

`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

`=1 - (6 * 214)/(10 * (10^2 - 1))`

`=1 - (6 * 214)/(10 * (100 - 1))`

`=1 - 1284/990`

`=1 - 1.297`

`=-0.297`

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2. Calculate Spearman's Rank Correlation Coefficient from the following Rank

X	1	7	2	9	12	8	6	3	13	15	14	10	11	4	5
Y	2	9	1	7	15	8	5	3	13	14	11	10	12	6	4

Solution:

`Rx`	`Ry`	`d=Rx-Ry`	`d^2`
1	2	-1	1
7	9	-2	4
2	1	1	1
9	7	2	4
12	15	-3	9
8	8	0	0
6	5	1	1
3	3	0	0
13	13	0	0
15	14	1	1
14	11	3	9
10	10	0	0
11	12	-1	1
4	6	-2	4
5	4	1	1
---	---	---	---
--	--	--	36

`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

`=1 - (6 * 36)/(15 * (15^2 - 1))`

`=1 - (6 * 36)/(15 * (225 - 1))`

`=1 - 216/3360`

`=1 - 0.0643`

`=0.9357`

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