Spearman’s Rank Correlation Coefficient

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. X44725717169217
Y16882016151220258
Solution: Step 1. Ho: X=Y

4. Step 5. Computation of r.
X Y Rank XRank 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