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BUILT-IN MATHEMATICA SYMBOL
GoodmanKruskalGamma
GoodmanKruskalGamma[v1, v2]
gives the Goodman-Kruskal 
coefficient for the vectors 
and 
.
GoodmanKruskalGamma[m]
gives the Goodman-Kruskal 
coefficients for the matrix m.
GoodmanKruskalGamma[m1, m2]
gives the Goodman-Kruskal 
coefficients for the matrices 
and 
.
GoodmanKruskalGamma[dist]
gives the 
coefficient matrix for the multivariate symbolic distribution dist.
GoodmanKruskalGamma[dist, i, j]
gives the 
coefficient for the multivariate symbolic distribution dist.
Details
- GoodmanKruskalGamma[v1, v2] gives the Goodman-Kruskal coefficient
between 
and 
. - Goodman-Kruskal
is a measure of monotonic association based on the relative order of consecutive elements in the two lists. - Goodman-Kruskal
between 
and 
is given by 
, where 
is the number of concordant pairs of observations and 
is the number of discordant pairs. - 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 
. - If no ties are present,
is equivalent to KendallTau. - The arguments
and 
can be any real-valued vectors of equal length. - For a matrix m with
columns, GoodmanKruskalGamma[m] is a 
×
matrix of the 
-coefficients between columns of m. - For an
×
matrix 
and an 
×
matrix 
, GoodmanKruskalGamma[m1, m2] is a 
×
matrix of the 
-coefficients between columns of 
and columns of 
. - GoodmanKruskalGamma[dist, i, j] gives
where 
is equal to Probability[(x1-x2)(y1-y2)>0, {{x1, y1}
disti, j, {x2, y2}disti, j}] and 
is equal to Probability[(x1-x2)(y1-y2)<0, {{x1, y1}disti, j, {x2, y2}disti, j}] where 
is the 
marginal of dist. - GoodmanKruskalGamma[dist] gives a matrix
where the 
entry is given by GoodmanKruskalGamma[dist, i, j].
Examplesopen all
Basic Examples (4)
New in 9
