DescTools (version 0.99.30)

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

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.

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 $$ \tau_{c} = \frac{m \cdot(P-Q)}{n^2 \cdot (m-1)}$$ 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.

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

# NOT RUN {
# 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)
# }