Stuart Tau-c
Calculate Stuart's tau-c 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.
StuartTauC(x, y = NULL, conf.level = NA, ...)
x |
a numeric vector or a table. A matrix will be treated as 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 |
Stuart's tau-c makes an adjustment for table size in addition to a correction for ties. Tau-c is
appropriate only when both variables lie on an ordinal scale.
It is estimated by
tau_c = 2m * (P-Q) / (n^2 (m-1))
where P equals the number of concordances and Q the number of discordances, n is the total amount of observations and m = min(R, C). The range of tau-c is [-1, 1].
See http://support.sas.com/documentation/cdl/en/statugfreq/63124/PDF/default/statugfreq.pdf, pp. 1739 for the estimation of the asymptotic variance.
The use of Stuart's Tau-c versus Kendall's Tau-b is recommended when the two ordinal variables under consideration have different numbers of values, e.g. good, medium, bad versus high, low.
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.
ConDisPairs yields concordant and discordant pairs
Other association measures: GoodmanKruskalGamma, KendallTauA (tau-a), cor (method="kendall") for tau-b, SomersDeltaLambda, GoodmanKruskalTau, 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))) StuartTauC(tab, conf.level=0.95)
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