R: Stuart Tau C

StuartTauC {DescTools} | R Documentation

## Stuart Tau C

### Description

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.

### Usage

    StuartTauC(x, y = NULL, 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.
`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

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 = m / n^2 * (P-Q) / (m-1)

where P equals twice the number of concordances and Q twice 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.

### 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.

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

`ConDisPairs` yields concordant and discordant pairs
Other association measures:
`GoodmanKruskalGamma`, `KendallTauA` (tau-a), `cor` (method="kendall") for tau-b, `SomersDelta`
`Lambda`, `GoodmanKruskalTau`, `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)))

    StuartTauC(tab, conf.level=0.95)

[Package DescTools version 0.99.24 Index]