This document discusses Spearman's rank correlation coefficient, a non-parametric measure of statistical dependence between two variables. It does not assume a normal distribution like other correlation coefficients. The Spearman coefficient is calculated by ranking the values of each variable separately and then calculating the difference between their ranks, summing the squared differences, and dividing by the number of samples. The document provides an example calculation of the Spearman coefficient between two variables and its interpretation.

1. 
Non parametric method:
Less power but more robust.
 Does not assume normal distribution.


Also varies between -1 and 1

2. 
The usual way of writing Spearman Rank
Coefficient is:
Where:
d: differences between the ranks of the two variables
n: number of samples

3. X
4
4
7
25
21
7
Y
16
8
8
20 16 15 12 20 25
8
Solution: Step 1. Ho:
7
17 16
X=Y
9

4. Step 5. Computation of r.
X
Y
Rank X
Rank Y
D
D²
4
16
9.5
4.5
5
25
4
8
9.5
9
-0.5
0.25
7
8
7
9
-2
4
25
20
1
2.5
-1.5
2.25
7
16
7
4.5
2.5
6.25
17
15
3
6
-3
9
16
12
4
7
-3
9
9
20
5
2.5
2.5
6.25
21
25
2
1
1
1
7
8
7
9
-2
4

5. Step 6. Decision: Accept Ho since r = 0.594 is
less than 0.602.
Interpretation: The values of X and Y are not
related.

6. 1. Calculate the correlation between the IQ of a
person with the number of hours spent in front of TV
per week.
IQ
Hours of TV per
week
106
7
86
0
100
27
101
50
99
28
103
29
97
20
113
12
112
6
110
17

7. 1. Calculate the correlation between the IQ of a
person with the number of hours spent in front of TV
per week.
IQ
Hours of TV per
week
106
7
86
0
100
27
101
50
99
28
103
29
97
20
113
12
112
6
110
17