GoodmanKruskalGamma
Goodman Kruskal's Gamma
Calculate Goodman Kruskal's Gamma statistic, a measure of association for ordinal factors in a twoway table. The function has interfaces for a table (matrix) and for single vectors.
 Keywords
 nonparametric, multivar
Usage
GoodmanKruskalGamma(x, y = NULL, conf.level = NA, ...)
Arguments
 x
 a numeric vector or a contingency table. A matrix will be treated as a table.
 y
 NULL (default) or a vector with compatible dimensions to
x
. If y is provided,table(x, y, ...)
is calculated.  conf.level
 confidence level of the interval. If set to
NA
(which is the default) no confidence intervals will be calculated.  ...
 further arguments are passed to the function
table
, allowing i.e. to set useNA. This refers only to the vector interface.
Details
The estimator of $gamma$ is based only on the number of concordant and discordant pairs of observations. It ignores tied pairs (that is, pairs of observations that have equal values of X or equal values of Y). Gamma is appropriate only when both variables lie on an ordinal scale.
It has the range [1, 1]. If the two variables are independent, then the estimator of gamma tends to be close to zero.
For $2 x 2$ tables, gamma is equivalent to Yule's Q (YuleQ
).
Gamma is estimated by $$ G = \frac{PQ}{P+Q}$$ where P equals twice the number of concordances and Q twice the number of discordances.
Value

a single numeric value if no confidence intervals are requested,
and otherwise a numeric vector with 3 elements for the estimate, the lower and the upper confidence interval
References
Agresti, A. (2002) Categorical Data Analysis. John Wiley & Sons, pp. 5759.
Goodman, L. A., & Kruskal, W. H. (1954) Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732764.
Goodman, L. A., & Kruskal, W. H. (1963) Measures of association for cross classifications III: Approximate sampling theory. Journal of the American Statistical Association, 58, 310364.
See Also
There's another implementation of gamma in vcdExtra GKgamma
ConDisPairs
yields concordant and discordant pairs
Other association measures:
KendallTauA
(taua), KendallTauB
(taub), cor
(method="kendall") for taub, StuartTauC
(tauc), SomersDelta
Lambda
, GoodmanKruskalTau
(tau), UncertCoef
, MutInf
Examples
# example in:
# http://support.sas.com/documentation/cdl/en/statugfreq/63124/PDF/default/statugfreq.pdf
# pp. S. 1821
tab < as.table(rbind(
c(26,26,23,18, 9),
c( 6, 7, 9,14,23))
)
GoodmanKruskalGamma(tab, conf.level=0.95)