Kendall's W

Kendall's concordance analysis (after Maurice George Kendall ) is a non-parametric statistical method for quantifying the agreement between multiple raters ( raters ). This is Kendall's concordance coefficient W is an alternative to

• Kappa statistics - which are designed for nominal scaled data - and

• Rank correlation coefficients for ordinal data (such as Spearman's and Kendall's ) - which are mainly intended for two judge -

Dar.

The concordance coefficient W is similar to Cronbach's alpha to determine the reliability, for example, a test procedure. It takes values ​​between 0 and 1.

Formula

If appraisers bring the cases ( = objects to observe people, characteristics) in a rank order, each case receives from each judge a rank order; the sum of all assigned rankings for a case is then:

If a judge a case no clear rank order (1,2,3, ... N) assigns, but, for example, several cases have to share a rank order, one speaks of "rank binding ". The number of cases that each share a specific rank place in a judge, called rank bond length.

Of course, multiple rank bonds can also occur with a judge when cases are judged equal. The total number of bonds is at a rank raters:

Kendall's W is it calculated as follows:

In which

And

W is the Friedman - coefficient (English article) as well as the rank correlation coefficient of Spearman directly related:

And

,

Where the average of all rank correlations between the possible combinations representing each of two raters.

Literature and sources

• Bortz, J., Lienert, GA & Boehnke, K. ( 1990): Distribution -free methods in biostatistics. Chap. 9 Berlin: Springer.
• MG Kendall, Babington Smith, B.: The problem of m rankings. In: The Annals of Mathematical Statistics. 10, No. 3 Sep 1939 p 275-287.

• Descriptive Statistics