Gwet`s Agreement Coefficient: A Comprehensive Guide

Gwet`s Agreement Coefficient is a statistical measure used to determine the reliability of agreement between two or more raters when assessing categorical data. It is particularly useful in situations where there are multiple categories with imbalanced distribution.

Developed by Kilem L. Gwet, Ph.D., in 2008, the Gwet`s Agreement Coefficient (GAC) is considered an improvement over the traditional Kappa statistic, which has some limitations when dealing with imbalanced data.

How does GAC work?

GAC is based on the concept of observed agreement and takes into account random agreement. Unlike Kappa, which is based on the difference between observed and expected agreement, GAC calculates random agreement based on the distribution of categories and the marginal totals.

To calculate GAC, you need to have the following information:

1. The number of raters you have (n)

2. The number of categories you are assessing (k)

3. The observed agreement between raters (o)

4. The marginal distribution of categories for each rater (pi)

Once you have these values, you can use the following formula to calculate GAC:

GAC = (o – e) / (1 – e)

where e = ∑ (pi^2)

The resulting value ranges from -1 to 1, with 1 indicating perfect agreement and -1 indicating perfect disagreement.