Spearmans Rank

Normally, if you try to see whether or not there is a correlation in a set of data, you would see if there appears to be a trend. However, that is not the most reliable of methods.

Spearmans Rank is reliable method of calculation to determine whether or not there is a correlation in a set of data. It also gives a represenation of the strength of the corelation as well as the significance.

Spearman developed a formual of calculation as follows:
 rho = 1- {frac {6 sum d_i^2}{n(n^2 - 1)}}.
rho = 1- {frac {6 sum d_i^2}{n(n^2 - 1)}}.


d = the difference between the ranks of the x and y values
n = the number of pairs of values in the sequence

There is also a correlation scale determining what type of correlation there is and its strength.

A value closer to -1 means there is a strong negative correlation, whereas a value closer to 1 means that there is a strong positive correlation. If the value is closer to 0, it indicates that there is no apparent correlation.


e.g.


IQ, Xi
Hours of TV per week, Yi
rank xi
rank yi
di
i
86
0
1
1
0
0
97
20
2
6
−4
16
99
28
3
8
−5
25
100
27
4
7
−3
9
101
50
5
10
−5
25
103
29
6
9
−3
9
106
7
7
3
4
16
110
17
8
5
3
9
112
6
9
2
7
49
113
12
10
4
6
36

With found i, we can add them to find
sum d_i^2 = 194
sum d_i^2 = 194
. The value of n is 10. So these values can now be substituted back into the equation,
 rho = 1- {frac {6times194}{10(10^2 - 1)}}
rho = 1- {frac {6times194}{10(10^2 - 1)}}

Which evaluates to ρ = −0.175757575

This low value shows that the correlation between IQ and hours spent watching TV is very low. However, whenever there seems to be a correlation, it does not imply causation; it is only probable.

By Muhammed