Kendall's Tau-a
Calculate Kendall's tau-a 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.
KendallTauA(x, y = NULL, direction = c("row", "column"), 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 |
direction |
direction of the calculation. Can be |
conf.level |
confidence level of the interval. If set to |
... |
further arguments are passed to the function |
Kendall's tau coefficient (sometimes called "Kendall rank correlation coefficient"), is a statistic used to measure the association between two measured quantities. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
Kendall's tau-a is computed as
tau_a = 2 * (P-Q) / (n * (n-1))
where P equals twice the number of concordances and Q twice the number of discordances. Its range is [-1, 1].
(Note that Kendall tau-a does not take into consideration any ties, which makes it unpractical. Consider using KendallTauB (Tau-b) when ties are present.)
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.
Hollander, M, Wolfe, D. A., Chicken, E. (2014) Nonparametric Statistical Methods, Third edition, Wiley,
Liebetrau, A. M. (1983) Measures of Association, Sage University Papers Series on Quantitative Applications in the Social Sciences, 07-004. Newbury Park, CA: Sage, pp. 49-56
ConDisPairs yields concordant and discordant pairs
Other association measures: cor (method="kendall") for Tau b, StuartTauC, GoodmanKruskalGammaLambda, 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))) # Kendall's tau-a C|R KendallTauA(tab, direction="column", conf.level=0.95) # Kendall's tau-a R|C KendallTauA(tab, direction="row", conf.level=0.95) # http://support.sas.com/documentation/cdl/en/statugfreq/63124/PDF/default/statugfreq.pdf # pp. 1814 (143) tab <- as.table(cbind(c(11,2),c(4,6))) KendallTauA(tab, direction="row", conf.level=0.95) KendallTauA(tab, direction="column", conf.level=0.95) # Liebetrau, pp. 52 x <- c(1,2,2,3,3,3,4,5) y <- c(1,3,2,1,5,3,4,5) ConDisPairs(table(x, y)) KendallTauA(x, y, conf.level=0.95)
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