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Calculate Goodman Kruskal's Gamma statistic, a measure of association for ordinal factors in a two-way table. The function has interfaces for a table (matrix) and for single vectors.
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 set useNA. This refers only to the vector interface.
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
The estimator of YuleQ
).
Gamma is estimated by
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
# NOT RUN {
# 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)
# }
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