# StuartTauC: Stuart Tau-c In DescTools: Tools for Descriptive Statistics

## 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

 `1` ```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 = 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.

## 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.

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, `SomersDelta`
`Lambda`, `GoodmanKruskalTau`, `UncertCoef`, `MutInf`

## Examples

 ```1 2 3 4 5 6 7``` ```# 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) ```

### Example output

```     tauc    lwr.ci    ups.ci
0.4110953 0.2546754 0.5675151
```

DescTools documentation built on June 17, 2021, 5:12 p.m.