Weighted kappa is higher than Cohen’s kappa for tridiagonal agreement tables

Cohen’s kappa and weighted kappa are two popular descriptive statistics for measuring agreement between two observers on a nominal scale. It has been frequently observed in the literature that, when Cohen’s kappa and weighted kappa are applied to the same agreement table, the value of weighted kappa is higher than the value of Cohen’s kappa. This paper proves this phenomenon for tridiagonal agreement tables.