Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 | ```
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 <[email protected]>

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`

1 2 3 4 5 6 7 8 9 10 | ```
# 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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