Spearman’s rank correlation
This is a non-parametric method of finding the correlation between two random variables. The
calculation is carried out under the following assumptions:
1.
2.
The pairs of observations are at least at the order scale of measurement.
The observations have been sampled from a bivariate population of continuous random
variables.
The distribution needs not be of any specific form.
3.
Merits
1.
2.
Not much needs to be known about the population.
This method is very useful in a wide variety of applications.
Drawbacks
1.
Unlike the Pearson’s correlation coefficient, this method does not take into account the values
of the observations.
This method is not very appropriate with too many ties.
2.
Example
The following table represents the marks, out of 100, obtained by 8 students (A to H) in both
English and French. Calculate the Spearman’s rank correlation coefficient between the two subjects and
interpret your result.
Students
English
French
A
60
68
B
50
51
C
60
82
D
67
77
E
53
68
F
78
89
G
54
68
H
75
77
A
60
68
4.5
3
1.5
2.25
B
50
51
1
1
0
0
C
60
82
4.5
7
–2.5
6.25
D
67
77
6
5.5
1.5
0.25
E
53
68
2
3
–1
1
F
78
89
8
8
0
0
G
54
68
3
3
0
0
H
75
77
7
5.5
2.5
6.25
Solution
Students
English (X)
French (Y)
Rank (X)
Rank (Y)
Difference, d
d2
r =1−
6
∑d
2
n( n 2 − 1)
= 0.82