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 |

`conf.level` |
confidence level of the interval. If set to |

`...` |
further arguments are passed to the function |

### 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} = \frac{2 m \cdot(P-Q)}{n^2 \cdot (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.

### 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)
```

*DescTools*version 0.99.54 Index]