# An ordinal measure of interrater absolute agreement

## TL;DR

This paper introduces a new measure for interrater agreement on ordinal scales that overcomes variance restriction issues, with proven statistical properties and demonstrated effectiveness through simulations and real data application.

## Contribution

A novel ordinal agreement measure based on dispersion index, with unbiased estimation, confidence interval construction, and validation through simulations and real case study.

## Key findings

- The new measure avoids variance restriction problems.
- Simulation studies confirm the measure's accuracy.
- Application to real data demonstrates practical utility.

## Abstract

A measure of interrater absolute agreement for ordinal scales is proposed capitalizing on the dispersion index for ordinal variables proposed by Giuseppe Leti. The procedure allows to avoid the problem of restriction of variance that sometimes affect traditional measures of interrater agreement in different fields of application. An unbiased estimator of the proposed measure is introduced and its sampling properties are investigated. In order to construct confidence intervals for interrater absolute agreement both asymptotic results and bootstrapping methods are used and their performance is evaluated. Simulated data are employed to demonstrate the accuracy and practical utility of the new procedure for assessing agreement. Finally, an application to a real case is provided.