R: Kendall's Coefficient of Concordance W

KendallW {DescTools} | R Documentation

## 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

`cor`, `KappaM`, `CronbachAlpha`, `ICC`, `friedman.test`

### 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)

[Package DescTools version 0.99.38 Index]