# Learn How to Calculate Spearman's Rank Correlation - Tutorial

## Calculate Spearman's Rank Correlation - Definition, Formula and Example

##### Definition:

Spearman's rank correlation is a technique which is used to examine the power and direction of the relation among any two set of variables. Spearman correlation of +1 or -1 arises when every variable is a monotone function of other variable.

#### Formula:

R = 1 - ( (6 X σd2) / (n3 - n) )
###### Where,

σ = Sumation of differences d = Differences n = Number of Datas R = Rank Value

##### Example:

Assume that there are two sets available namely, A and B.Values entered for Set A are '1, 5, 2, 5, 2' and values given for Set B are '2, 2, 3, 1, 3'. Calculate the Spearman rank correlation for the given values?

##### Given, ##### To Find,

Spearman Rank Correlation Value (R)

##### Solution: Substitute the given values in the Rank Value (R) formula, Rank Value (R) = 1 - ( (6 X σd2) / (n3 - n) ) = 1 - ( (6 X 26.5) /(125-5)) = 1 - 1.325 R = -0.325

##### Conclusion:

The result is a negative value. So according to the below table, the value -0.325 is considered as a weak negative correlation value.

Table of Rank value and its correlation conclusion
R Value Correlation Conclusion
-1 Perfect negative
between -1 and -0.5 Strong negative
between -0.5 and 0 Weak negative
0 No correlation
between 0 and 0.5 Weak positive
between 0.5 and 1 Strong positive
1 Perfect positive