Spearman’s Rank Correlation Coefficient - CCEA
Purpose: To test the strength of the correlation (relationship) between two variables.
Equation: rs = 1 - 6∑d2
n3-n
Where:
 rs = Spearman’s Rank Value
 ∑ = the sum of
 d = difference in rank of the values of each matched pair
 n = number of ranked pairs
Null Hypothesis: There is no statistically significant relationship between
______________ and _______________.
Alternative Hypothesis: There is a statistically significant relationship between
______________ and _______________.
2) Rank your “x” data, giving the largest measurement the lowest
rank. If some measurements have the same value, give them the
average of the ranks. Repeat this procedure to rank the “y” data.
3) Calculate the difference
between “Rank x” & “Rank y”.
1) Place your values for “x”
(independent) and “y” (dependent
variable) into the table.
n
1
2
3
4
5
6
7
8
9
10
11
12
Variable x
x
Rank x (Rx)
Tip: If the sum of Rx – Ry = 0
then the ranking is correct
Variable y
y
Rank y (Ry)
∑ Rx – Ry = ________
difference
d (Rx-Ry)
4) Square the
difference.
difference2
d2
5) Calculate ∑d2 = __________
Field Studies Council Derrygonnelly
6) Using the formula below, calculate Spearman’s Rank Coefficient (rs).
rs = 1 - 6∑d2
n3-n
=
Critical Values Table
Degrees of
Freedom
4
5
6
7
8
9
10
11
12
15
20
25
30
40
50
0.05 (5%)
0.01 (1%)
0.88
0.83
0.80
0.77
0.72
0.68
0.64
0.60
0.57
0.50
0.47
0.44
0.39
0.35
0.31
1.00
0.96
0.91
0.87
0.84
0.80
0.77
0.74
0.71
0.65
0.59
0.54
0.48
0.43
0.38
7) Determine your degrees of freedom (n-2) and
use this number to determine your corresponding
critical value from the Critical Values Table.
Spearman’s Rank Coefficient (rs) =
________________________________
Critical Value =
________________________________
If the absolute value of the Spearman’s Rank Coefficient (rs) is less than the critical
value, you accept the null hypothesis.
If the absolute value of the Spearman’s Rank Coefficient (rs) is greater than the critical
value, you reject the null hypothesis.
Write a sentence explaining your result. Include whether you accept or reject your
null hypothesis, the rs value, the critical value, significance level and degrees of
freedom.
Field Studies Council Derrygonnelly