Fleiss’ kappa statistic without paradoxes

The Fleiss’ kappa statistic is a well-known index for assessing the reliability of agreement between raters. It is used both in the psychological and in the psychiatric field. Unfortunately, the kappa statistic may behave inconsistently in case of strong agreement between raters, since this index assumes lower values than it would have been expected. The aim of this paper is to propose a new method to avoid this paradox through permutation techniques. Furthermore, we study the problem of kappa confidence intervals and, in particular, we suggest to use Bootstrap confidence intervals free of paradoxes.