Spearman's Rank Correlation Coefficient
Spearman's rank correlation coefficient is a method used to measure the
strength and direction of the relationship between two variables. It is more
suitable in cases where the data is not normally distributed, unlike Pearson's
coefficient of correlation. In this blog, we will focus on Spearman's rank
correlation and how to calculate it.
Ranking Strategy
To calculate Spearman's rank correlation, first, we need to rank the data. We
can assign ranks to data by giving the highest number the lowest rank or the
lowest number the highest rank. The highest number should always be given
the lowest rank. For example, if we have a series of numbers such as 20, 24,
33, 40, and 15 appearing three times, we will assign rank 1 to 65 (the
highest), rank 2 to 20 (the second-highest), rank 3 to 18 (the third-highest),
rank 4 to both 40 and 33 (the fourth-highest), rank 5 to 24 (the fifth-highest),
rank 6 to 15 (the lowest).
Calculation
The formula to calculate Spearman's rank correlation coefficient is:
1 - (6?d2)/n(n2-1)
where ?d2 is the sum of the squared differences between the ranks of each
variable, n is the total number of observations, and m is the number of times
a particular value has tied up or stand off.
Example
Let's consider an example where we have two judges who have scored 5
participants on a scale of 1 to 10. The data is as follows:
7, 6, 8, 9, 6
8, 7, 6, 9, 10
To calculate the ranks, we combine the data and assign ranks as discussed
earlier:
10 (rank 1), 9 (rank 2), 8 (rank 3), 7 (rank 4), 7 (rank 4), 6 (rank 6), 6 (rank 6)
Now, we can calculate the Spearman's rank correlation coefficient:
sum of d = (1-2) + (2-1) + (3-5) + (4-4) + (4-4) + (6-6) + (6-6) = 10
n = 7, m = 2
Spearman's rank correlation coefficient = 1 - (6(10))/(7(7-1)) = 0.6 (rounded
off to one decimal place)
Therefore, there is a moderate positive correlation between the judges'
Spearman's rank correlation coefficient is a method used to measure the
strength and direction of the relationship between two variables. It is more
suitable in cases where the data is not normally distributed, unlike Pearson's
coefficient of correlation. In this blog, we will focus on Spearman's rank
correlation and how to calculate it.
Ranking Strategy
To calculate Spearman's rank correlation, first, we need to rank the data. We
can assign ranks to data by giving the highest number the lowest rank or the
lowest number the highest rank. The highest number should always be given
the lowest rank. For example, if we have a series of numbers such as 20, 24,
33, 40, and 15 appearing three times, we will assign rank 1 to 65 (the
highest), rank 2 to 20 (the second-highest), rank 3 to 18 (the third-highest),
rank 4 to both 40 and 33 (the fourth-highest), rank 5 to 24 (the fifth-highest),
rank 6 to 15 (the lowest).
Calculation
The formula to calculate Spearman's rank correlation coefficient is:
1 - (6?d2)/n(n2-1)
where ?d2 is the sum of the squared differences between the ranks of each
variable, n is the total number of observations, and m is the number of times
a particular value has tied up or stand off.
Example
Let's consider an example where we have two judges who have scored 5
participants on a scale of 1 to 10. The data is as follows:
7, 6, 8, 9, 6
8, 7, 6, 9, 10
To calculate the ranks, we combine the data and assign ranks as discussed
earlier:
10 (rank 1), 9 (rank 2), 8 (rank 3), 7 (rank 4), 7 (rank 4), 6 (rank 6), 6 (rank 6)
Now, we can calculate the Spearman's rank correlation coefficient:
sum of d = (1-2) + (2-1) + (3-5) + (4-4) + (4-4) + (6-6) + (6-6) = 10
n = 7, m = 2
Spearman's rank correlation coefficient = 1 - (6(10))/(7(7-1)) = 0.6 (rounded
off to one decimal place)
Therefore, there is a moderate positive correlation between the judges'
