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Spearman Correlation formula

What is the definition of the Spearman Correlation test?

ρ=rs=1−6∑d2in(n2−1)

  • 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:

ρ=∑i(xi−ˉx)(yi−ˉy)√∑i(xi−ˉx)2∑i(yi−ˉy)2

  • x : value of x
  • x̄ : mean of x
  • y : value of y
  • ȳ : mean of y

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