Kendall's Coefficient of Agreement

Kendall's u coefficient of agreement between judges.

kendall.u(M, correct = TRUE)

Arguments

M	a square matrix or a data frame consisting of absolute choice frequencies; row stimuli are chosen over column stimuli
correct	logical, if TRUE (default) a continuity correction is applied when computing the test statistic (by subtracting one from the sum of agreeing pairs)

Details

Kendall's u (Kendall and Babington Smith, 1940) takes on values between min.u (minimum agreement) and 1 (maximum agreement). The minimum min.u equals \(-1/(m - 1)\), if \(m\) is even, and \(-1/m\), if \(m\) is odd, where \(m\) is the number of subjects (judges).

The null hypothesis in the chi-square test is that the agreement between judges is by chance.

It is assumed that there is an equal number of observations per pair and that each subject judges each pair only once.

Value

u

Kendall's u coefficient of agreement

min.u

the minimum value for u

chi2

the chi-square statistic for a test that the agreement is by chance

df

the degrees of freedom

p.value

the p-value of the test

References

Kendall, M.G., & Babington Smith, B. (1940). On the method of paired comparisons. Biometrika, 31, 324--345. doi: 10.1093/biomet/31.3-4.324

See also

schoolsubjects, eba, strans, circular.

Examples

data(schoolsubjects)
lapply(schoolsubjects, kendall.u)  # better-than-chance agreement
#> $boys
#> 
#> Kendall's u coefficient of agreement
#> 
#> u = 0.1866, minimum u = -0.04762
#> chi2 = 412.22, df = 90.75, p-value = 1.721e-42
#> alternative hypothesis: between-judges agreement is not by chance
#> continuity correction has been applied
#> 
#> 
#> $girls
#> 
#> Kendall's u coefficient of agreement
#> 
#> u = 0.08218, minimum u = -0.04
#> chi2 = 180.12, df = 62.38, p-value = 2.307e-13
#> alternative hypothesis: between-judges agreement is not by chance
#> continuity correction has been applied
#> 
#>