R: Kendall's Tau-a

KendallTauA {DescTools} | R Documentation

## Kendall's Tau-a

### Description

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.

### Usage

    KendallTauA(x, y = NULL, direction = c("row", "column"), conf.level = NA, ...)

### Arguments

`x` | a numeric vector or a table. A matrix will be treated as table.
`y` | NULL (default) or a vector with compatible dimensions to `x`. If y is provided, `table(x, y, ...)` is calculated.
`direction` | direction of the calculation. Can be `"row"` (default) or `"column"`, where `"row"` calculates Kendall's tau-a (R|C) ("column dependent").
`conf.level` | confidence level of the interval. If set to `NA` (which is the default) no confidence interval will be calculated.
`...` | further arguments are passed to the function `table`, allowing i.e. to set useNA. This refers only to the vector interface.

### Details

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.)

### 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

### Author(s)

Andri Signorell <andri@signorell.net>

### References

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

### See Also

`ConDisPairs` yields concordant and discordant pairs
Other association measures:
`cor (method="kendall")` for Tau b, `StuartTauC`, `GoodmanKruskalGamma`
`Lambda`, `UncertCoef`, `MutInf`

### Examples

    # 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)

[Package DescTools version 0.99.32 Index]