Utility of weights for weighted kappa as a measure of interrater agreement on ordinal scale

Kappa statistics, unweighted or weighted, are widely used for assessing interrater agreement. The weights of the weighted kappa statistics in particular are defined in terms of absolute and squared distances in ratings between raters. It is proposed that those weights can be used for assessment of interrater agreements. A closed form expectations and variances of the agreement statistics referred to as AI₁ and AI₂, functions of absolute and squared distances in ratings between two raters, respectively, are obtained. AI₁ and AI₂ are compared with the weighted and unweighted kappa statistics in terms of Type I Error rate, bias, and statistical power using Monte Carlo simulations. The AI₁ agreement statistic performs better than the other agreement statistics.