BUILT-IN MATHEMATICA SYMBOL

# KendallTau

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

KendallTau[m]
gives Kendall's rank correlation coefficients for the matrix m.

KendallTau[m1, m2]
gives Kendall's rank correlation coefficients for the matrices and .

KendallTau[dist]
gives Kendall's rank correlation matrix for the multivariate symbolic distribution dist.

KendallTau[dist, i, j]
gives the Kendall rank correlation for the multivariate symbolic distribution dist.

## DetailsDetails

• KendallTau[v1, v2] gives Kendall's rank correlation coefficient between and .
• Kendall's is a measure of monotonic association based on the relative order of consecutive elements in the two lists.
• Kendall's between and is given by , where is the number of concordant pairs of observations, is the number of discordant pairs, is the number of ties involving only the variable, and is the number of ties involving only the variable.
• A concordant pair of observations and is one such that both and or both and . A discordant pair of observations is one such that and or and .
• The tie-corrected version of Kendall's returned is sometimes referred to as Kendall's Tau-b.
• The arguments and can be any real-valued vectors of equal length.
• For a matrix m with columns, KendallTau[m] is a × matrix of the rank-correlations between columns of m.
• For an × matrix and an × matrix , KendallTau[m1, m2] is a × matrix of the rank-correlations between columns of and columns of .
• KendallTau[dist, i, j] is the probability of concordance minus the probability of discordance Probability[(x1-x2)(y1-y2)>0, {{x1, y1}disti, j, {x2, y2}disti, j}]-Probability[(x1-x2)(y1-y2)<0, {{x1, y1}disti, j, {x2, y2}disti, j}] where is the marginal of dist.
• KendallTau[dist] gives a matrix where the entry is given by KendallTau[dist, i, j].

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Kendall's for two vectors:

 Out[2]=

Kendall's for a matrix:

 Out[2]//MatrixForm=

Kendall's for two matrices:

 Out[3]//MatrixForm=

Compute Kendall's for a bivariate distribution:

 Out[2]//MatrixForm=

Compare to a simulated value:

 Out[3]//MatrixForm=