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 |

`direction` |
direction of the calculation. Can be |

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

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

### 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(C|R) = \frac{P-Q}{\frac{1}{2} \cdot n \cdot (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)
```

*DescTools*version 0.99.55 Index]