Cohen's Kappa Calculator
This Cohen's Kappa calculator computes the inter-rater agreement coefficient, accounting for agreement occurring by chance. It provides the kappa value, standard error, z-score, p-values, confidence interval, and interpretation according to Landis & Koch guidelines.
Further Information
Cohen's Kappa (κ) is a statistical measure of inter-rater reliability for categorical items. It measures the agreement between two raters who each classify N items into C mutually exclusive categories.
What Makes Kappa Special?
Unlike simple percent agreement, Cohen's Kappa accounts for the agreement occurring by chance. For example, if two raters are classifying items into categories purely at random, they would still achieve some level of agreement. Kappa removes this chance agreement to give a more accurate measure of true consensus.
The Kappa Formula:
κ = (Po - Pe) / (1 - Pe)
Where:
Po = Observed agreement (proportion of times raters agree)
Pe = Expected agreement (agreement by chance)
Requirements
- Two raters classifying the same set of items
- Categorical data (nominal or ordinal)
- Same categories used by both raters
- Independent classifications (raters don't influence each other)
- At least 2 items classified
Landis & Koch Interpretation Scale
The following scale (Landis & Koch, 1977) provides guidelines for interpreting kappa values:
| Kappa Value | Level of Agreement |
|---|---|
| < 0 | Poor (less than chance agreement) |
| 0.00 – 0.20 | Slight agreement |
| 0.21 – 0.40 | Fair agreement |
| 0.41 – 0.60 | Moderate agreement |
| 0.61 – 0.80 | Substantial agreement |
| 0.81 – 1.00 | Almost perfect agreement |
Understanding Kappa Values
- κ = 1: Perfect agreement between raters
- κ = 0: Agreement is no better than chance
- κ < 0: Agreement is worse than chance (rare)
When to Use Cohen's Kappa
Use Cohen's Kappa when:
- Comparing classifications from two raters/judges
- Working with categorical data
- You want to account for chance agreement
- Assessing reliability of diagnostic tests
- Evaluating consistency in coding qualitative data
Cohen's Kappa vs. Other Measures
| Measure | Use When |
|---|---|
| Cohen's Kappa | Two raters, categorical data, chance correction needed |
| Fleiss' Kappa | Three or more raters |
| Weighted Kappa | Ordinal data with ordered disagreement categories |
| Percent Agreement | Simple reporting, but doesn't account for chance |
| Intraclass Correlation (ICC) | Continuous or ordinal data, multiple raters |
Limitations
- Kappa is sensitive to the prevalence of categories (prevalence problem)
- Kappa is sensitive to bias between raters (bias problem)
- Does not distinguish between types of disagreement
- Weighted Kappa should be used for ordinal data where some disagreements are more serious than others
References
- Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37-46.
- Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159-174.