# Correlation

**Topics:**Regression analysis, Spearman's rank correlation coefficient, Linear regression

**Pages:**16 (454 words)

**Published:**December 5, 2014

LINEAR REGRESSION

Prof. Jemabel Gonzaga-Sidayen

Spearman rank order correlation

coefficient rho (rs)

• Spearman rho is really a linear correlation

coefficient applied to data that meet the

requirements of ordinal scaling

• Formula:

rs = 1 - 6 Σ D i 2

N3 - N

– Di = difference between the ith pair of ranks

– R(Xi) = rank of the ith X score

– R(Yi) = rank of the ith Y score

– N = number of pairs of ranks

Try this

Subject

Proportion of

Similar

Attitudes (X)

Attraction

(Y)

Rank of Xi

Rank of Yi

Di

Di 2

1

0.30

8.9

5

7

-2

4

2

0.44

9.3

7

8

-1

1

3

0.67

9.6

11

10

1

1

4

0.00

6.2

1

1

0

0

5

0.50

8.8

8

6

2

4

6

0.15

8.1

3

5

-2

4

7

0.58

9.5

9

9

0

0

8

0.32

7.1

6

2

4

16

9

0.72

11.0

12

13

-1

1

10

1.00

11.7

15

15

0

0

11

0.87

11.5

14

14

0

0

12

0.09

7.3

2

3

-1

1

13

0.82

10.0

13

11.5

1.5

2.25

14

0.64

10.0

10

11.5

-1.5

2.25

15

0.24

7.5

4

4

0

0

Solution

ΣDi 2 = 36.5

rs = 1 - 6 (36.5)

= 1 = 0.93

153 - 15

219_

3360

Pearson r correlation

r

=

(ΣX)( ΣY)

Σ XY - ------------N

---------------------------------------------------(ΣX) 2

(ΣY)2

ΣX 2 - ------ΣY2 - ------N

N

Subject

Proportion of

Similar

Attitudes (X)

X2

Attraction

(Y)

Y2

XY

1

0.30

0.09

8.9

79.21

2.67

2

0.44

0.1936

9.3

86.49

4.092

3

0.67

0.4489

9.6

92.16

6.432

4

0.00

0.00

6.2

38.44

0.00

5

0.50

0.25

8.8

77.44

4.4

Σ

1.91

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