GoodmanKruskalGamma.Rd
Calculate Goodman Kruskal's Gamma statistic, a measure of
association for ordinal factors in a two-way table.
The function has interfaces for a contingency table (matrix) and for single vectors (which will then be tabulated).
GoodmanKruskalGamma(x, y = NULL, conf.level = NA, ...)
a numeric vector or a contingency table. A matrix will be treated as a table.
NULL (default) or a vector with compatible dimensions to x
. If y is provided, table(x, y, ...)
is calculated.
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 control the handling of NAs
by setting the useNA
argument. This refers only to the vector interface, the dots are ignored if x
is a contingency table.
The estimator of γ 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 2×2 tables, gamma is equivalent to Yule's Q (YuleQ
).
Gamma is estimated by G=P−QP+Q where P equals twice the number of concordances and Q twice the number of discordances.
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
Agresti, A. (2002) Categorical Data Analysis. John Wiley & Sons, pp. 57-59.
Brown, M.B., Benedetti, J.K.(1977) Sampling Behavior of Tests for Correlation in Two-Way Contingency Tables, Journal of the American Statistical Association, 72, 309-315.
Goodman, L. A., & Kruskal, W. H. (1954) Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732-764.
Goodman, L. A., & Kruskal, W. H. (1963) Measures of association for cross classifications III: Approximate sampling theory. Journal of the American Statistical Association, 58, 310-364.
There's another implementation of gamma in vcdExtra GKgamma
ConDisPairs
yields concordant and discordant pairs
Other association measures: KendallTauA
(tau-a), KendallTauB
(tau-b), cor
(method="kendall") for tau-b, StuartTauC
(tau-c), SomersDelta
Lambda
, GoodmanKruskalTau
(tau), UncertCoef
, MutInf