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.

Advantages of GAC

One of the main advantages of GAC is its ability to handle imbalanced data. Kappa, on the other hand, can be biased toward high agreement when there is a large majority in one category.

Another advantage is that GAC can be used with nominal, ordinal, and interval scales, as long as the categories are mutually exclusive and exhaustive.

GAC is also relatively easy to calculate, and there are several software programs and online calculators available that can do the math for you.


Gwet`s Agreement Coefficient is a valuable tool for anyone working with categorical data and multiple raters. It provides a more accurate assessment of agreement than traditional methods such as Kappa, especially when the data is imbalanced.

As a professional, it is important to be familiar with statistical measures like GAC. Not only will it help you understand the data presented in articles, but it also makes for more efficient and accurate content development.


March 2024