SpearmanRho

SpearmanRho[v1, v2]
gives Spearman's rank correlation coefficient for the vectors and .

SpearmanRho[m]
gives Spearman's rank correlation coefficient for the matrix m.

SpearmanRho[m1, m2]
gives Spearman's rank correlation coefficient for the matrices and .

SpearmanRho[dist]
gives Spearman's rank correlation matrix for the multivariate symbolic distribution dist.

SpearmanRho[dist, i, j]
gives the ^(th) Spearman rank correlation for the multivariate symbolic distribution dist.

DetailsDetails

  • SpearmanRho[v1, v2] gives Spearman's rank correlation coefficient between and .
  • Spearman's is a measure of association based on the rank differences between two lists which indicates how well a monotonic function describes their relationship.
  • Spearman's is given by , where n=Length[xlist], is the rank difference between and , is the correction term for ties in , and is the correction term for ties in .
  • SpearmanRho[{v11, v12, ...}, {v21, v22, ...}] is equivalent to Correlation[{r11, r12, ...}, {r21, r22, ...}] where is the tie-corrected ranking corresponding to .
  • The arguments and can be any real-valued vectors of equal length.
  • For a matrix m with columns SpearmanRho[m] is a × matrix of the rank correlations between columns of m.
  • For an × matrix and an × matrix SpearmanRho[m1, m2] is a × matrix of the rank correlations between columns of and columns of .
  • SpearmanRho[dist, i, j] is 12 Expectation[F[x]G[y], {x, y}Distributeddisti, j] - 3 where F[x] and G[y] are the CDFs of the i^(th) and j^(th) marginals of dist, respectively, and is the ^(th) marginal of dist.
  • SpearmanRho[dist] gives a matrix where the ^(th) entry is given by SpearmanRho[dist, i, j].

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Spearman's for two vectors:

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Spearman's for a matrix:

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Spearman's for two matrices:

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Compute Spearman's for a bivariate distribution:

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Compare to a simulated value:

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