Description Usage Arguments Details Value Note Author(s) References See Also Examples
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.
1 
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 pvalue should be reported. 
na.rm 
logical, indicating whether 
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.
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 chisquare statistic. 
p.value 
the pvalue 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. 
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.
Matthias Gamer <m.gamer@uke.unihamburg.de>
Kendall, M.G. (1948) Rank correlation methods. London: Griffin.
cor
, KappaM
, CronbachAlpha
, ICC
, friedman.test
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  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)

[1] 0.5396569
Kendall's coefficient of concordance Wt
data: anxiety
Kendall chisquared = 30.76, df = 19, subjects = 20, raters = 3,
pvalue = 0.04288
alternative hypothesis: Wt is greater 0
sample estimates:
Wt
0.5396569
Kendall's coefficient of concordance W
data: t(d.att[, 1])
Kendall chisquared = 13.778, df = 7, subjects = 8, raters = 3, pvalue
= 0.05528
alternative hypothesis: W is greater 0
sample estimates:
W
0.6560847
Friedman rank sum test
data: as.matrix(d.att[, 1])
Friedman chisquared = 13.778, df = 7, pvalue = 0.05528
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