KendallW: Kendall's Coefficient of Concordance W In DescTools: Tools for Descriptive Statistics

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

 `1` ```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.

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

Examples

 ``` 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) ```

Example output

```[1] 0.5396569

Kendall's coefficient of concordance Wt

data:  anxiety
Kendall chi-squared = 30.76, df = 19, subjects = 20, raters = 3,
p-value = 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 chi-squared = 13.778, df = 7, subjects = 8, raters = 3, p-value
= 0.05528
alternative hypothesis: W is greater 0
sample estimates:
W
0.6560847

Friedman rank sum test

data:  as.matrix(d.att[, -1])
Friedman chi-squared = 13.778, df = 7, p-value = 0.05528
```

DescTools documentation built on June 17, 2021, 5:12 p.m.