Kendall's W Coefficient of Concordance

Kendall's W coefficient of concordance measures how closely several raters agree when ranking the same set of objects, from 0 for no agreement to 1 for identical rankings.

Kendall의 W 일치계수는 여러 평가자가 같은 대상들에 매긴 순위가 얼마나 일치하는지를 0(일치 없음)부터 1(완전 일치)까지로 나타내는 지수입니다.

Five judges ranked the same eight entries; do they agree with each other?

심사위원 다섯 명이 같은 작품 여덟 개에 순위를 매겼는데, 서로 의견이 일치한다고 볼 수 있나요?

Kendall's W compares the spread of the rank sums each object receives with the largest spread possible, so it reaches 1 when all raters give the same ranking and 0 when rank sums are equal. The statistic m(n − 1)W follows approximately a chi-square distribution with n − 1 degrees of freedom and equals the Friedman statistic.

When to use Kendall's W Coefficient of Concordance

• Several judges rank or score the same set of objects and you want one agreement index.
• You need an effect size to report alongside a Friedman test.
• Ratings are ordinal and averaging raw scores across raters would be inappropriate.

When to use something else

• Only two raters are compared; use Spearman correlation or weighted kappa.
• Ratings are on an interval scale and you want absolute agreement; use the intraclass correlation.

Assumptions and requirements

• Each rater ranks (or scores) the same set of objects.
• Raters judge independently of each other.
• Scores are at least ordinal; tied values receive average ranks.

What the analysis reports

• W with optional tie correction
• Chi-square statistic, degrees of freedom and p value
• Mean Spearman correlation among all pairs of raters
• Rank sum and mean rank of each object

How to report it

Agreement among [m] raters ranking [n] objects was W = [value] (mean Spearman ρ = [value]), χ²([df], N = [m]) = [value], p = [value].

Related methods

• Friedman Test
• Intraclass Correlation (ICC)
• Kendall's Tau

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