Inter Rater Agreement Calculator

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Inter-Rater Agreement Calculator (Cohen's Kappa)

Enter the number of instances where Rater A and Rater B agreed or disagreed on two categories (e.g., "Yes" vs "No" or "Pass" vs "Fail").

Rater B: Category 1
Rater B: Category 2
Rater A: Category 1
Rater A: Category 2

Results

Observed Agreement (Po): 0%
Expected Agreement (Pe): 0%
Cohen's Kappa (κ): 0.00
Interpretation: N/A
function calculateKappa() { var aa = parseFloat(document.getElementById('aa_val').value) || 0; var ab = parseFloat(document.getElementById('ab_val').value) || 0; var ba = parseFloat(document.getElementById('ba_val').value) || 0; var bb = parseFloat(document.getElementById('bb_val').value) || 0; var total = aa + ab + ba + bb; if (total === 0) { alert("Please enter some numerical data."); return; } // Observed Proportion of Agreement var po = (aa + bb) / total; // Probability of 'Yes' by chance var probRaterAYes = (aa + ab) / total; var probRaterBYes = (aa + ba) / total; var probBothYes = probRaterAYes * probRaterBYes; // Probability of 'No' by chance var probRaterANo = (ba + bb) / total; var probRaterBNo = (ab + bb) / total; var probBothNo = probRaterANo * probRaterBNo; // Expected Proportion of Agreement var pe = probBothYes + probBothNo; // Kappa calculation var kappa = 0; if (pe < 1) { kappa = (po – pe) / (1 – pe); } else { kappa = 1; } // Display Results document.getElementById('result-section').style.display = 'block'; document.getElementById('obs-agreement').innerText = (po * 100).toFixed(2) + "%"; document.getElementById('exp-agreement').innerText = (pe * 100).toFixed(2) + "%"; document.getElementById('kappa-score').innerText = kappa.toFixed(4); var interp = ""; if (kappa < 0) interp = "Less than chance agreement (Poor)"; else if (kappa <= 0.20) interp = "Slight agreement"; else if (kappa <= 0.40) interp = "Fair agreement"; else if (kappa <= 0.60) interp = "Moderate agreement"; else if (kappa <= 0.80) interp = "Substantial agreement"; else interp = "Almost perfect agreement"; document.getElementById('interpretation-text').innerText = interp; document.getElementById('result-section').scrollIntoView({ behavior: 'smooth' }); }

Understanding Inter-Rater Agreement and Cohen's Kappa

In research and data analysis, Inter-Rater Agreement (also known as inter-rater reliability) measures the degree to which two or more coders or observers agree when categorizing the same items. While simple percentage agreement is easy to calculate, it often overestimates reliability because it doesn't account for agreement occurring purely by random chance.

What is Cohen's Kappa?

Cohen's Kappa (κ) is a statistical metric used to measure inter-rater reliability for qualitative (categorical) items. It is generally thought to be a more robust measure than simple percent agreement calculation, as κ takes into account the possibility of the agreement occurring by chance.

The Math Behind the Calculator

Our calculator uses the standard Cohen's Kappa formula:

κ = (Po – Pe) / (1 – Pe)
  • Po (Observed Agreement): The proportion of items where both raters agreed.
  • Pe (Expected Agreement): The theoretical proportion of agreement if both raters made their choices completely at random based on the frequency of each category.

How to Interpret Your Results

Landis and Koch (1977) provided a widely used scale for interpreting Kappa values:

Kappa Value Strength of Agreement
< 0.00 Poor (Less than chance)
0.01 – 0.20 Slight
0.21 – 0.40 Fair
0.41 – 0.60 Moderate
0.61 – 0.80 Substantial
0.81 – 1.00 Almost Perfect

Practical Example

Imagine two doctors (Rater A and Rater B) evaluating 100 X-rays for a specific condition (Present/Absent).

  • Both agree it's "Present" in 45 cases.
  • Both agree it's "Absent" in 40 cases.
  • Rater A says Present, but Rater B says Absent in 10 cases.
  • Rater A says Absent, but Rater B says Present in 5 cases.

In this case, the observed agreement is 85%. However, after calculating the probability of them agreeing by luck, the Kappa score will give a more realistic view of how much the doctors actually agree on the diagnostic criteria versus just making similar guesses.

When to Use This Tool

This calculator is ideal for binary classifications. If you have more than two categories or more than two raters, you might require Fleiss' Kappa or an Intra-class Correlation Coefficient (ICC). Use this Cohen's Kappa calculator for:

  • Medical diagnosis consistency checks.
  • Content analysis in social science research.
  • Machine Learning model validation against human "gold standard" labels.
  • Quality control in manufacturing audits.

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