Correlation

CORRELATION &
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

0.9825

42.8

373.74

17.594

r

=

r

=

(ΣX)( ΣY)
Σ XY - ------------N
-------------------------------------------------------(ΣX)2
(ΣY)2
ΣX2 - ------ΣY2 - ------N
N
17.594 - (1.91)(42.8) / 5
-----------------------------------------------------------0.9825 – (1.91) 2 /5

373.74 – (42.8) 2 /5

Regression
• Regression and correlation are closely related. At the most basic level, they both involve relationship between two variables, and they both utilize the same set of basic data: paired scores taken from the same or matched subjects.
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