An Alternative Interpretation of the Linearly Weighted Kappa Coefficients for Ordinal Data

When two (or more) observers are independently categorizing a set of observations, Cohen's kappa has become the most notable measure of interobserver agreement. When the categories are ordinal, a weighted form of kappa becomes desirable. The two most popular weighting schemes are the quadratic weights and linear weights. Quadratic weights have been justified by the fact that the corresponding weighted kappa is asymptotically equivalent to an intraclass correlation coefficient. This paper deals with linear weights and shows that the corresponding weighted kappa is equivalent to the unweighted kappa when cumulative probabilities are substituted for probabilities. A numerical example is provided.