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KendallW

Kendall's Coefficient of Concordance W


Description

Computes Kendall's coefficient of concordance, a popular measure of association. It is an index of interrater reliability of ordinal data. The coefficient could be corrected for ties within raters.

Usage

KendallW(x, correct = FALSE, test = FALSE, na.rm = FALSE)

Arguments

x

k x m matrix or dataframe, k subjects (in rows) m raters (in columns).

correct

a logical indicating whether the coefficient should be corrected for ties within raters.

test

a logical indicating whether the test statistic and p-value should be reported.

na.rm

logical, indicating whether NA values should be stripped before the computation proceeds. If set to TRUE only the complete cases of the ratings will be used. Defaults to FALSE.

Details

The test for Kendall's W is completely equivalent to friedman.test. The only advantage of this test over Friedman's is that Kendall's W has an interpretation as the coefficient of concordance. The test itself is only valid for large samples.
Kendall's W should be corrected for ties, if raters did not use a true ranking order for the subjects.

Value

Either a single value if test is set to FALSE or else

a list with class “htest” containing the following components:

statistic

the value of the chi-square statistic.

p.value

the p-value for the test.

method

the character string “Kendall's coefficient of concordance W”.

data.name

a character string giving the name(s) of the data.

estimate

the coefficient of concordance.

parameter

the degrees of freedom df, the number of subjects examined and the number of raters.

Note

This function was previously published as kendall() in the irr package and has been integrated here without logical changes, but with some adaptations in the result structure.

Author(s)

Matthias Gamer <m.gamer@uke.uni-hamburg.de>

References

Kendall, M.G. (1948) Rank correlation methods. London: Griffin.

See Also

Examples

anxiety <- data.frame(rater1=c(3,3,3,4,5,5,2,3,5,2,2,6,1,5,2,2,1,2,4,3),
                      rater2=c(3,6,4,6,2,4,2,4,3,3,2,3,3,3,2,2,1,3,3,4),
                      rater3=c(2,1,4,4,3,2,1,6,1,1,1,2,3,3,1,1,3,3,2,2))

KendallW(anxiety, TRUE)

# with test results
KendallW(anxiety, TRUE, test=TRUE)

# example from Siegel and Castellan (1988)
d.att <- data.frame(
  id        = c(4,21,11),
  airfare   = c(5,1,4),
  climate   = c(6,7,5),
  season    = c(7,6,1),
  people    = c(1,2,3),
  program   = c(2,3,2),
  publicity = c(4,5,7),
  present   = c(3,4,6),
  interest  = c(8,8,8)
)

KendallW(t(d.att[, -1]), test = TRUE)

# which is perfectly the same as
friedman.test(y=as.matrix(d.att[,-1]), groups = d.att$id)

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

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