Cohen’s quadratically weighted kappa is higher than linearly weighted kappa for tridiagonal agreement tables

Cohen’s weighted kappa is a popular descriptive statistic for measuring the agreement between two raters on an ordinal scale. Popular weights for weighted kappa are the linear weights and the quadratic weights. It has been frequently observed in the literature that the value of the quadratically weighted kappa is higher than the value of the linearly weighted kappa. In this paper, this phenomenon is proved for tridiagonal agreement tables. A square table is tridiagonal if it has nonzero elements only on the main diagonal and on the two diagonals directly adjacent to the main diagonal.