Obtain Spearman rank correlation coefficient from the following data.

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written 7.8 years ago by

teamques10 ★ 70k

• modified 3.9 years ago

x	32	55	49	60	43	37	43	49	10	20
y	40	30	70	20	30	50	72	60	45	25

Subject: Applied Mathematics 4

Topic: Correlation & Regression

Difficulty: Medium

engineering mathematics

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1 Answer

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written 7.6 years ago by

teamques10 ★ 70k

x	y	R$_1$	R$_2$	d = R$_1$ - R$_2$	d$^2$
32	40	3	5	-2	4
55	30	9	3.5	5.5	30.25
49	70	7.5	9	-1.5	2.25
60	20	10	1	9	81
43	30	5.5	3.5	2	4
37	50	4	7	-3	9
43	72	5.5	10	-4.5	20.25
49	60	7.5	8	-0.5	0.25
10	45	1	6	-5	25
20	25	2	2	0	0
					176

$ r_{xy} = 1 - \frac{6}{n(n^2-1)}[\sum d^2 + \frac{1}{12}m_1(m_1^2 - 1) + \frac{1}{12}m_2(m_2^2 - 1) + \frac{1}{12}m_3(m_3^2 - 1)] $

Where,

m$_1$ = 2: 43 is repeated twice

m$_2$ = 2: 49 is repeated twice

m$_3$ = 3: 30 is repeated twice

$ r_{xy} = 1 - [\frac{6}{10(100-1)} (176 + \frac{1}{12}(2)(4-1) + \frac{1}{12}(2)(4-1) + \frac{1}{12}(2)(4-1))] \\ = 1 - [\frac{6}{990}(176 + \frac{1}{2} + \frac{1}{2} + \frac{1}{2})] \\ = 1 - [\frac{6}{990}(176 + 1.5)] = -0.07575 \sim -0.08 $

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