This tool calculates Cohen's Kappa and Percent Agreement to measure the consistency of a single observer across two different time points or trials. Enter the number of observations for each category pairing below.
(Count of consistent "Yes" or "Category A" results)
(Count of consistent "No" or "Category B" results)
(Disagreement: Positive then Negative)
(Disagreement: Negative then Positive)
Calculation Results
Percent Agreement
0%
Cohen's Kappa (κ)
0.00
Understanding Intra-Rater Reliability
Intra-rater reliability is a statistical measure used to determine the consistency of a single person's measurements or observations over time. Unlike inter-rater reliability (which compares two different people), intra-rater reliability asks: "If the same person assesses the same subject twice, will they give it the same score?"
Why Use Cohen's Kappa?
While Percent Agreement is straightforward, it is often criticized because it doesn't account for the agreement that might happen purely by chance. Cohen's Kappa (κ) is a more robust metric because it subtracts the probability of random agreement from the observed agreement. It is the gold standard for binary or categorical data in clinical research and psychology.
Interpreting the Results
According to the widely cited Landis & Koch (1977) scale, Kappa values can be interpreted as follows:
< 0.00: Poor (Less than chance agreement)
0.01 – 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
Example Calculation
Imagine a radiologist reviews 100 X-rays on Monday and marks 45 as "Normal" and 55 as "Abnormal." Two weeks later, the same radiologist reviews the same 100 X-rays. If they mark 42 of the original "Normal" ones as "Normal" again, but change their mind on 3, those 3 are disagreements. Our calculator takes these counts and provides the specific Kappa coefficient to validate the radiologist's internal consistency.
function calculateReliability() {
// Get values from inputs
var a = parseFloat(document.getElementById('cell_aa').value) || 0;
var b = parseFloat(document.getElementById('cell_ab').value) || 0;
var c = parseFloat(document.getElementById('cell_ba').value) || 0;
var d = parseFloat(document.getElementById('cell_bb').value) || 0;
var total = a + b + c + d;
if (total === 0) {
alert("Please enter at least one observation count.");
return;
}
// Observed Agreement (Po)
var po = (a + d) / total;
// Expected Agreement (Pe)
// Row Marginals
var row1Total = a + b;
var row2Total = c + d;
// Column Marginals
var col1Total = a + c;
var col2Total = b + d;
var pe = ((row1Total / total) * (col1Total / total)) + ((row2Total / total) * (col2Total / total));
// Cohen's Kappa
var kappa = 0;
if (pe !== 1) {
kappa = (po – pe) / (1 – pe);
} else {
kappa = 1; // Perfect agreement where expected is also perfect
}
// Display Percent Agreement
document.getElementById('percent_agree_res').innerText = (po * 100).toFixed(2) + "%";
// Display Kappa
document.getElementById('kappa_res').innerText = kappa.toFixed(3);
// Interpret Kappa
var interpretation = "";
var description = "";
if (kappa < 0) {
interpretation = "Poor Agreement";
description = "The rater's consistency is worse than what would be expected by random chance.";
} else if (kappa <= 0.20) {
interpretation = "Slight Agreement";
description = "There is a very small degree of consistency in the rater's observations.";
} else if (kappa <= 0.40) {
interpretation = "Fair Agreement";
description = "The rater shows a fair level of consistency, but there is significant room for improvement.";
} else if (kappa <= 0.60) {
interpretation = "Moderate Agreement";
description = "The rater is moderately consistent over time.";
} else if (kappa <= 0.80) {
interpretation = "Substantial Agreement";
description = "The rater shows a high level of consistency across trials.";
} else {
interpretation = "Almost Perfect Agreement";
description = "The rater is extremely consistent, with very few contradictory observations.";
}
document.getElementById('interpretation_res').innerText = "Interpretation: " + interpretation;
document.getElementById('description_res').innerText = description;
// Show results area
document.getElementById('results_area').style.display = 'block';
}