DescTools (version 0.99.30)

GoodmanKruskalGamma: Goodman Kruskal's Gamma

Description

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.

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.

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

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 $2\times 2$ tables, gamma is equivalent to Yule's Q (YuleQ). Gamma is estimated by $$G=\frac{P-Q}{P+Q}$$ where P equals twice the number of concordances and Q twice the number of discordances.

References

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.

See Also

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

Examples

# 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)
# }