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Spearman Correlation formula
What is the definition of the Spearman Correlation test?
\[\rho = r_s = 1 - \frac{6\sum{d^2_i}}{n(n^2-1)}\]
- p : Spearman correlation
- rs : Spearman correlation
- di : rg(Xi) - rg(Yi): difference between the two ranks of each observation (for example, one can have the second best score on variable X, but the ninth on variable Y.)
- n : number of scores
Note: if there are tied ranks, the following method can be used to calculate the Spearman Correlation:
\[\rho = \frac{\sum_i (x_i - \bar{x})(y_i - \bar{y})}{\sqrt {\sum_i (x_i - \bar{x})^2 \sum_i (y_i - \bar{y})^2}}\]
- x : value of x
- x̄ : mean of x
- y : value of y
- ȳ : mean of y
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