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BUILT-IN MATHEMATICA SYMBOL
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 
Spearman rank correlation for the multivariate symbolic distribution dist.
Details
- 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}
disti, j] - 3 where F[x] and G[y] are the CDFs of the i
and j
marginals of dist, respectively, and 
is the 
marginal of dist. - SpearmanRho[dist] gives a matrix where the
entry is given by SpearmanRho[dist, i, j].
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