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Kendall’s coefficient of concordance (W)

Kendall’s W measures how much several judges agree when rating or ranking the same items. It goes from 0 (no agreement) to 1 (full agreement). In theses it is widely used for expert judgment, alongside Aiken’s V or the CVC. Paste the ratings from Excel: one row per item and one column per judge. If your table has judges in rows, change it in the selector.

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How it’s calculated

Each judge’s ratings are turned into ranks: 1 for the item with the lowest rating. Ties get the average rank.

The ranks of each item are added up (Rᵢ) and S is the sum of squared differences between each Rᵢ and their mean.

W = 12S / (k²(n³ − n) − kΣT), where k is the number of judges, n the number of items and T corrects each judge’s ties.

Significance comes from χ² = k(n − 1)W with n − 1 degrees of freedom, as in SPSS.

How to read the result

  • p < 0.05: the judges agree more than you would expect by chance.
  • A common guide (Landis and Koch): up to 0.20 slight, 0.21 to 0.40 fair, 0.41 to 0.60 moderate, 0.61 to 0.80 substantial and above 0.80 almost perfect.
  • With fewer than 7 items the chi-square is only approximate; report it with care.

Frequently asked questions

Does it match SPSS?
Yes. In SPSS it is Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples > Kendall’s W. There each row is a judge and each column an item: choose "Rows = judges" if you paste your table that way.
Kendall’s W, Aiken’s V or CVC?
Aiken’s V and the CVC tell you whether each item is valid. Kendall’s W tells you whether the judges agree with each other across the instrument. Many theses report one of the first two plus W.
How many judges do I need?
At least 2, though theses usually have 3 to 7.
Does it work if judges answered yes or no?
For yes/no answers the binomial test is a better fit, and it is also in these tools.

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