StuartTauC: 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

a numeric vector or a table. A matrix will be treated as table.

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.

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

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

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

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. http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/freq_sect18.htm http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/freq_sect20.htm

Examples

Run this code

# 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)

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