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Most measures of agreement are chance-corrected. They differ in three dimensions: their definition of chance agreement, their choice of disagreement function, and how they handle multiple raters. Chance agreement is usually defined in a pairwise manner, following either Cohen's kappa or Fleiss's kappa. The disagreement function is usually a nominal, quadratic, or absolute value function. But how to handle multiple raters is contentious, with the main contenders being Fleiss's kappa, Conger's kappa, and Hubert's kappa, the variant of Fleiss's kappa where agreement is said to occur only if every rater agrees. More generally, multi-rater agreement coefficients can be defined in a g-wise way, where the disagreement weighting function uses g raters instead of two. This paper contains two main contributions. (a) We propose using Fréchet variances to handle the case of multiple raters. The Fréchet variances are intuitive disagreement measures and turn out to generalize the nominal, quadratic, and absolute value functions to the case of more than two raters. (b) We derive the limit theory of g-wise weighted agreement coefficients, with chance agreement of the Cohen-type or Fleiss-type, for the case where every item is rated by the same number of raters. Trying out three confidence interval constructions, we end up recommending calculating confidence intervals using the arcsine transform or the Fisher transform. [ABSTRACT FROM AUTHOR]

Several measures of agreement, such as the Perreault–Leigh coefficient, the AC 1 , and the recent coefficient of van Oest, are based on explicit models of how judges make their ratings. To handle such measures of agreement under a common umbrella, we propose a class of models called guessing models, which contains most models of how judges make their ratings. Every guessing model have an associated measure of agreement we call the knowledge coefficient. Under certain assumptions on the guessing models, the knowledge coefficient will be equal to the multi-rater Cohen's kappa, Fleiss' kappa, the Brennan–Prediger coefficient, or other less-established measures of agreement. We provide several sample estimators of the knowledge coefficient, valid under varying assumptions, and their asymptotic distributions. After a sensitivity analysis and a simulation study of confidence intervals, we find that the Brennan–Prediger coefficient typically outperforms the others, with much better coverage under unfavorable circumstances. [ABSTRACT FROM AUTHOR]