Goodman Kruskal's Gamma
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, ...)
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 |
conf.level |
confidence level of the interval. If set to |
... |
further arguments are passed to the function |
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 = (P-Q) / (P+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
Andri Signorell <andri@signorell.net>
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 GKgammaConDisPairs yields concordant and discordant pairs
Other association measures: KendallTauA (tau-a), KendallTauB (tau-b), cor (method="kendall") for tau-b, StuartTauC (tau-c), SomersDeltaLambda, GoodmanKruskalTau (tau), UncertCoef, MutInf
# 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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.