Kendall's W coefficient of concordance

Native implementation of Kendall's W (Kendall & Smith, 1939, Eq. 2) for assessing concordance among m rankings of n objects. Each column of observations is one rater's ordering; values are ranked within each column (rank() with average ties), so either raw scores or already-assigned ranks may be passed. The tie correction (Kendall & Smith 1939, footnote on p. 277; modern textbook formula) is applied automatically when ties are present.

Usage

reliability_kendall_w(observations)

Arguments

observations

A subjects x raters matrix or data.frame. Rows are objects/units being ranked; columns are raters. Must not contain NA.

Value

A list with elements:

method

"kendall_w".

value

Numeric – W on the interval [0, 1].

ci_lower, ci_upper

NA_real_ (W has no closed-form CI).

per_value

NULL (Kendall's W has no per-category breakdown).

n_observers

Number of raters (m).

n_units

Number of objects ranked (n).

n_pairable

m * n.

chi_squared

Friedman chi-square statistic, m(n-1)W (Kendall & Smith 1939, Eq. 5).

df

Degrees of freedom for the chi-square test (n - 1).

p_value

Upper-tail p-value from the chi-square distribution.

S

Sum of squared deviations of rank sums from their mean (Kendall & Smith 1939, Eq. 2 numerator / 12).

References

Kendall, M. G., & Babington Smith, B. (1939). The problem of m rankings. Annals of Mathematical Statistics, 10(3), 275-287. doi:10.1214/aoms/1177732186

Kendall, M. G., & Gibbons, J. D. (1990). Rank Correlation Methods (5th ed.), Chapter 6. Oxford University Press.