Spearman's Rank Correlation Coefficient - Example

Example

In this example, we will use the raw data in the table below to 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

First, we must find the value of the term . To do so we use the following steps, reflected in the table below.

  1. Sort the data by the first column . Create a new column and assign it the ranked values 1,2,3,...n.
  2. Next, sort the data by the second column . Create a fourth column and similarly assign it the ranked values 1,2,3,...n.
  3. Create a fifth column to hold the differences between the two rank columns ( and ).
  4. Create one final column to hold the value of column squared.
IQ, Hours of TV per week, rank rank
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, we can add them to find . The value of n is 10. So these values can now be substituted back into the equation,

which evaluates to ρ = −0.175757575... with a P-value = 0.6864058 (using the t distribution)

This low value shows that the correlation between IQ and hours spent watching TV is very low. In the case of ties in the original values, this formula should not be used. Instead, the Pearson correlation coefficient should be calculated on the ranks (where ties are given ranks, as described above).

Read more about this topic:  Spearman's Rank Correlation Coefficient

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