What is the formula for calculating inter-rater reliability?

There isn’t just one formula for calculating inter-rater reliability. The right one depends on your data type (e.g., nominal data, ordinal data) and the number of raters.

  • Cohen’s kappa (κ) is commonly used for two raters
  • Fleiss’ kappa is typically used for three or more raters
  • The Intraclass Correlation Coefficient (ICC) is used for continuous data (interval or ratio). This is based on analysis of variance (ANOVA)

The most used formula (for Cohen’s kappa) is:
\kappa = \dfrac{{{P}_o}-{{P}_e}}{{1}-{P_e}}
Po is the observed proportion of agreement, and Pe stands for the expected agreement by chance.