Gwet's gamma coefficient

Overview

The gamma coefficient is a chance-adjusted index for the reliability of categorical measurements. It estimates chance agreement using a hybrid (category- and distribution-based) approach. When applied to nominal categories, it is also called AC1, and when applied to non-nominal categories, it is also called AC2.

MATLAB Functions

• FAST_GAMMA %Calculate gamma using simplified formulas
• FULL_GAMMA %Calculate gamma using generalized formulas

Simplified Formulas

Use these formulas with two raters and two (dichotomous) categories:

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is the number of items both raters assigned to category

is the number of items both raters assigned to category

is the total number of items

is the number of items rater assigned to category

is the number of items rater assigned to category

is the number of items rater assigned to category

is the number of items rater assigned to category

Generalized Formulas

Use these formulas with multiple raters, multiple categories, and any weighting scheme:

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is the total number of categories

is the weight associated with two raters assigning an item to categories and

is the number of raters that assigned item to category

is the number of items that were coded by two or more raters

is the number of raters that assigned item to category

is the number of raters that assigned item to any category

is the total number of items

References

1. Gwet, K. L. (2008). Computing inter-rater reliability and its variance in the presence of high agreement. The British Journal of Mathematical and Statistical Psychology, 61(1), 29–48.
2. Gwet, K. L. (2014). Handbook of inter-rater reliability: The definitive guide to measuring the extent of agreement among raters (4th ed.). Gaithersburg, MD: Advanced Analytics.