DescTools: GoodmanKruskalTau – R documentation

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GoodmanKruskalTau

Goodman Kruskal's Tau

Description

Calculate Goodman Kruskal's tau 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

GoodmanKruskalTau(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 `x`. If y is provided, `table(x, y, ...)` is calculated.
`direction`	direction of the calculation. Can be `"row"` (default) or `"column"`, where `"row"` calculates Goodman Kruskal's tau-a (R\|C) ("column dependent").
`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

Goodman-Kruskal tau measures association for cross tabulations of nominal level variables. Goodman-Kruskal tau is based on random category assignment. It measures the percentage improvement in predictability of the dependent variable (column or row variable) given the value of other variables (row or column variables). Goodman-Kruskal tau is the same as Goodman-Kruskal lambda except the calculations of the tau statistic are based on assignment probabilities specified by marginal or conditional proportions. Misclassification probabilities are based on random category assignment with probabilities specified by marginal or conditional proportion.

Goodman Kruskal tau reduces to φ^2 (see: Phi) in the 2x2-table case.

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>, based on code from Antti Arppe <antti.arppe@helsinki.fi>

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.

Somers, R. H. (1962) A New Asymmetric Measure of Association for Ordinal Variables, American Sociological Review, 27, 799-811.

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.

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. 24–30

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)))

# Goodman Kruskal's tau C|R
GoodmanKruskalTau(tab, direction="column", conf.level=0.95)
# Goodman Kruskal's tau R|C
GoodmanKruskalTau(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)))

GoodmanKruskalTau(tab, direction="row", conf.level=0.95)
GoodmanKruskalTau(tab, direction="column", conf.level=0.95)
# reduce both to:
Phi(tab)^2

DescTools

Tools for Descriptive Statistics

v0.99.41

GPL (>= 2)

Authors

Andri Signorell [aut, cre], Ken Aho [ctb], Andreas Alfons [ctb], Nanina Anderegg [ctb], Tomas Aragon [ctb], Chandima Arachchige [ctb], Antti Arppe [ctb], Adrian Baddeley [ctb], Kamil Barton [ctb], Ben Bolker [ctb], Hans W. Borchers [ctb], Frederico Caeiro [ctb], Stephane Champely [ctb], Daniel Chessel [ctb], Leanne Chhay [ctb], Nicholas Cooper [ctb], Clint Cummins [ctb], Michael Dewey [ctb], Harold C. Doran [ctb], Stephane Dray [ctb], Charles Dupont [ctb], Dirk Eddelbuettel [ctb], Claus Ekstrom [ctb], Martin Elff [ctb], Jeff Enos [ctb], Richard W. Farebrother [ctb], John Fox [ctb], Romain Francois [ctb], Michael Friendly [ctb], Tal Galili [ctb], Matthias Gamer [ctb], Joseph L. Gastwirth [ctb], Vilmantas Gegzna [ctb], Yulia R. Gel [ctb], Sereina Graber [ctb], Juergen Gross [ctb], Gabor Grothendieck [ctb], Frank E. Harrell Jr [ctb], Richard Heiberger [ctb], Michael Hoehle [ctb], Christian W. Hoffmann [ctb], Soeren Hojsgaard [ctb], Torsten Hothorn [ctb], Markus Huerzeler [ctb], Wallace W. Hui [ctb], Pete Hurd [ctb], Rob J. Hyndman [ctb], Christopher Jackson [ctb], Matthias Kohl [ctb], Mikko Korpela [ctb], Max Kuhn [ctb], Detlew Labes [ctb], Friederich Leisch [ctb], Jim Lemon [ctb], Dong Li [ctb], Martin Maechler [ctb], Arni Magnusson [ctb], Ben Mainwaring [ctb], Daniel Malter [ctb], George Marsaglia [ctb], John Marsaglia [ctb], Alina Matei [ctb], David Meyer [ctb], Weiwen Miao [ctb], Giovanni Millo [ctb], Yongyi Min [ctb], David Mitchell [ctb], Franziska Mueller [ctb], Markus Naepflin [ctb], Daniel Navarro [ctb], Henric Nilsson [ctb], Klaus Nordhausen [ctb], Derek Ogle [ctb], Hong Ooi [ctb], Nick Parsons [ctb], Sandrine Pavoine [ctb], Tony Plate [ctb], Luke Prendergast [ctb], Roland Rapold [ctb], William Revelle [ctb], Tyler Rinker [ctb], Brian D. Ripley [ctb], Caroline Rodriguez [ctb], Nathan Russell [ctb], Nick Sabbe [ctb], Ralph Scherer [ctb], Venkatraman E. Seshan [ctb], Michael Smithson [ctb], Greg Snow [ctb], Karline Soetaert [ctb], Werner A. Stahel [ctb], Alec Stephenson [ctb], Mark Stevenson [ctb], Ralf Stubner [ctb], Matthias Templ [ctb], Duncan Temple Lang [ctb], Terry Therneau [ctb], Yves Tille [ctb], Luis Torgo [ctb], Adrian Trapletti [ctb], Joshua Ulrich [ctb], Kevin Ushey [ctb], Jeremy VanDerWal [ctb], Bill Venables [ctb], John Verzani [ctb], Pablo J. Villacorta Iglesias [ctb], Gregory R. Warnes [ctb], Stefan Wellek [ctb], Hadley Wickham [ctb], Rand R. Wilcox [ctb], Peter Wolf [ctb], Daniel Wollschlaeger [ctb], Joseph Wood [ctb], Ying Wu [ctb], Thomas Yee [ctb], Achim Zeileis [ctb]

Initial release

2021-04-09