Spearman's Rank Correlation Coefficient

Spearman's Rank Correlation Coefficient (denoted as ρ or r_s) is a non-parametric test that measures the strength and direction of the association between two ranked variables.

The formula is:

r_{s} = 1 - \frac{6 \sum d^{2}}{n (n^{2} - 1)}

Where:

d = difference between the ranks of each pair
n = number of pairs

Worked Example

Compare student ranks in Biology and Computer Science:

Student	Biology Rank	Computer Science Rank	d = B - C	d²
Daisy	1	2	-1	1
Poppy	2	1	1	1
Holly	3	4	-1	1
Sam	4	3	1	1
Σd²				4

Now apply the formula:

r_s = 1 − [6 × 4 / 4(4² − 1)] = 1 − 24/60 = 0.6

Practice Question

Estimate Spearman's rank correlation coefficient (rounded to 2 decimal places):

Your Answer: