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Named after Charles Spearman and denoted by a Greek letter ‘ρ’, Spearman correlation coefficient is a nonparametric data analysis technique. It is a measure the strength and direction of the statistical dependence of ranking between two variables.
It is an appropriate measure to use when the variables are being measure on a least ordinal scale.
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Spearman correlation does not have any assumption about the data distribution, but it is based on Pearson’s correlation assumptions.
A Pearson’s correlations is a statistical measure of strength between a linear relationship between the variables and its assumptions include:
As for the Spearman correlation coefficient, you can use it when your data does not have the above assumptions.
Let us first understand what monotonic function is. A monotonic function, irrespective of the increase in the independent variable, never increases or decreases itself. The graph shown below is the best representation of the monotonic function:
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n is the number of data points of the two variables
di is the difference in ranks of the “ith” element
The Spearman Coefficient (⍴) can take a value between +1 to -1
As closer as the ⍴ value comes to 0, the weaker the association between the two ranks gets.
It is important to rank the data before carrying out the Spearman correlation coefficient, just to observe that the increase in one variable is being followed by the other variable’s monotonous relation.
In order to understand the working of the Spearman correlation, let’s take an example and discuss the process step-by-step.
Example: the marks of students in the subjects English and Maths are given as data.
In our case, the highest mark obtained will be ranked as “1” and so on. The smallest marks will be given the lowest ranking. This should be done for both English and Maths marks.
The Spearman rank correlation for our data is 0.9
As mentioned above, the ⍴ value is nearing the +1, they have the perfect association of rank in the data.