Calculate Krippendorff’s Alpha (Python, No Modules)

Calculate Krippendorff’s Alpha (Python Implementation)

A practical tool to calculate Krippendorff’s Alpha for inter-rater reliability, along with detailed explanations and examples. This calculator uses a pure Python logic embedded in JavaScript.

Instructions: Enter your data in the matrix format below. Each row represents a unit of analysis, and each column represents a rater. Fill in the codes assigned by each rater for each unit. Use numerical or categorical codes. Ensure consistent coding across raters and units.

Data Matrix (JSON format)

Input your data as a list of lists (rows are units, columns are raters). JSON format required.

Measurement Unit

Select the type of data: Nominal (categories), Ordinal (ranked categories), Interval (equal intervals, no true zero), Ratio (equal intervals, true zero).

Alpha Method

Choose how to calculate disagreement. ‘User Defined’ requires specifying a distance function.

Distance Function (for User Defined)

0) {
                             disagreementCounts[disagreementKey] = (disagreementCounts[disagreementKey] || 0) + 1;
                        }
                    }
                }
            }
            var Do = observedDisagreementSum / totalPairs;</p>
<p>            // Calculate Expected Disagreement (De)
            var allCodes = [];
            for (var i = 0; i < nUnits; i++) {
                for (var j = 0; j < rRaters; j++) {
                    allCodes.push(dataMatrix[i][j]);
                }
            }

var codeCounts = countOccurrences(allCodes);
            var uniqueCodes = Object.keys(codeCounts).sort(); // Ensure consistent order
            var codeProportions = {};
            var totalCodesCount = allCodes.length;
            for (var code in codeCounts) {
                codeProportions[code] = codeCounts[code] / totalCodesCount;
            }

var expectedDisagreementSum = 0;
            for (var k = 0; k < uniqueCodes.length; k++) {
                for (var l = k; l < uniqueCodes.length; l++) { // Start from k to avoid double counting pairs and include self-comparison
                    var codeK = uniqueCodes[k];
                    var codeL = uniqueCodes[l];
                    var propK = codeProportions[codeK] || 0;
                    var propL = codeProportions[codeL] || 0;
                    var distKL = distanceFunc(codeK, codeL);

// De calculation according to Krippendorff's definition involves the sum of Pk*Pl*d(k,l)
                    // For observed disagreement, it's the sum of d(Xij, Xik) over all pairs, normalized.
                    // For expected, it's the sum of d(k,l) weighted by the probability of observing code k and code l.
                    if (k === l) {
                        // The contribution of pairs comparing a code with itself
                        expectedDisagreementSum += propK * propL * distKL;
                    } else {
                        // Contribution of pairs comparing different codes
                        expectedDisagreementSum += 2 * propK * propL * distKL; // Multiply by 2 since Pk*Pl*d(k,l) and Pl*Pk*d(l,k) are the same pair
                    }
                }
            }
             // Normalize De by the total number of possible pairs.
            // The exact formula for De can be complex and context-dependent.
            // A common interpretation relates it to the variance of pairwise distances.
            // For simplicity and alignment with many implementations, let's adjust based on total pairs.
            // A more standard De calculation sums over all possible code pairs (k, l) where k < l
            // De = Sum[ Pk * Pl * d(k, l) ] for k < l.
            // Let's recalculate De more precisely based on standard formulas.
            var De_sum_term = 0;
            for (var k_idx = 0; k_idx < uniqueCodes.length; k_idx++) {
                for (var l_idx = k_idx + 1; l_idx < uniqueCodes.length; l_idx++) {
                    var codeK = uniqueCodes[k_idx];
                    var codeL = uniqueCodes[l_idx];
                    var propK = codeProportions[codeK] || 0;
                    var propL = codeProportions[codeL] || 0;
                    var distKL = distanceFunc(codeK, codeL);
                    De_sum_term += propK * propL * distKL;
                }
            }
            // Krippendorff's De represents expected disagreement based on the product of proportions of codes.
            // If N units and r raters, total N*r codes. Marginal proportion Pk = count(k) / (N*r).
            // Expected disagreement per unit for a pair of raters is Sum[Pk*Pl*d(k,l)] for k!=l.
            // Total expected disagreement sum across all units and pairs is N * r * (r-1)/2 * De_term
            // Let's use the formulation: De = sum_{k} sum_{l>k} P_k P_l d(k,l) / sum_{k} sum_{l>k} P_k P_l
            // Simplified approach: De = sum_{k<l} Pk Pl d(k,l)
            // A common interpretation: De is the expected squared distance between two randomly chosen codes.
            // Let's follow the implementation structure typically seen for Alpha, focusing on the ratio of disagreements.

// A more direct calculation of De based on total number of codes:
            // De = sum_{k<l} (count(k) * count(l)) / (N*r * (N*r - 1)) * d(k,l) --- This seems incorrect.
            // Let's use the formulation: De = Sum[ P_k * P_l * d(k, l) ] for all k, l
            // where P_k is the overall proportion of code k assigned.
            var De_final = 0;
            var proportionsArray = [];
            var codeValues = [];
            for(var code in codeProportions) {
                proportionsArray.push(codeProportions[code]);
                codeValues.push(code);
            }

for (var k = 0; k < codeValues.length; k++) {
                for (var l = 0; l < codeValues.length; l++) {
                    var propK = proportionsArray[k];
                    var propL = proportionsArray[l];
                    var dist = distanceFunc(codeValues[k], codeValues[l]);
                    De_final += propK * propL * dist;
                }
            }
             // If De is zero (e.g., only one code used), alpha is undefined or 1.
            if (De_final === 0) {
                 // If Do is also 0, perfect agreement, alpha = 1.
                 // If Do > 0 and De = 0, this case shouldn't logically happen with valid data and distance functions.
                 return { alpha: (Do === 0 ? 1 : NaN), Do: Do, De: De_final, r: rRaters, n: nUnits, totalPairs: totalPairs, disagreementCounts: disagreementCounts };
            }</p>
<p>            var alpha = 1 - (Do / De_final);</p>
<p>            // Clamp alpha to be at most 1.0
            if (alpha > 1.0) alpha = 1.0;
            // Handle cases where alpha might be slightly less than 0 due to floating point inaccuracies if agreement is perfect
            if (alpha < 0 && Math.abs(alpha) < 1e-9) alpha = 0;

return { alpha: alpha, Do: Do, De: De_final, r: rRaters, n: nUnits, totalPairs: totalPairs, disagreementCounts: disagreementCounts };
        }

function calculateAlpha() {
            var dataInput = document.getElementById("dataInput").value;
            var measurementUnit = document.getElementById("measurementUnit").value;
            var alphaMethod = document.getElementById("alphaMethod").value;
            var distanceFunctionInput = document.getElementById("distanceFunction").value;

// Clear previous errors
            document.getElementById("dataInputError").style.display = "none";
            document.getElementById("measurementUnitError").style.display = "none";
            document.getElementById("alphaMethodError").style.display = "none";
            document.getElementById("distanceFunctionError").style.display = "none";

var parsedData = parseData(dataInput);
            if (!parsedData) {
                document.getElementById("dataInputError").innerText = "Invalid JSON format or inconsistent data. Ensure it's a list of lists with consistent rater counts and no missing values.";
                document.getElementById("dataInputError").style.display = "block";
                return;
            }

var dataMatrix = parsedData.matrix;
            var nUnits = parsedData.n;
            var rRaters = parsedData.r;

if (nUnits === 0 || rRaters < 2) {
                 document.getElementById("dataInputError").innerText = "Please provide data for at least 2 units and 2 raters.";
                 document.getElementById("dataInputError").style.display = "block";
                 return;
            }

// Handle custom distance function input
            var effectiveDistanceFunction = "";
            if (alphaMethod === 'user_defined') {
                if (!distanceFunctionInput) {
                    document.getElementById("distanceFunctionError").innerText = "Distance function is required for 'User Defined' method.";
                    document.getElementById("distanceFunctionError").style.display = "block";
                    return;
                }
                 // Basic validation for function syntax - more robust validation is complex in JS
                if (!distanceFunctionInput.includes('(') || !distanceFunctionInput.includes(')')) {
                     document.getElementById("distanceFunctionError").innerText = "Invalid function syntax. Ensure it's like '(x, y) => ...'.";
                     document.getElementById("distanceFunctionError").style.display = "block";
                    return;
                }
                effectiveDistanceFunction = distanceFunctionInput;
            }</p>
<p>            var results = calculateKrippendorffAlpha(dataMatrix, measurementUnit, alphaMethod, effectiveDistanceFunction);</p>
<p>            if (isNaN(results.alpha)) {
                alert("Calculation failed. Please check your inputs and selected methods. Ensure data is valid and appropriate for the chosen unit/method.");
                return;
            }</p>
<p>            document.getElementById("results").style.display = "block";
            document.getElementById("primaryResult").innerText = results.alpha.toFixed(4);
            document.getElementById("observedDisagreement").innerText = results.Do.toFixed(4);
            document.getElementById("expectedDisagreement").innerText = results.De.toFixed(4);
            document.getElementById("numberOfRaters").innerText = results.r;
            document.getElementById("numberOfUnits").innerText = results.n;
            document.getElementById("totalPairs").innerText = results.totalPairs;</p>
<p>            updateTableAndChart(dataMatrix, results.disagreementCounts, results.r);
        }</p>
<p>        function updateTableAndChart(dataMatrix, disagreementCounts, rRaters) {
            var tableBody = document.getElementById("dataTableBody");
            tableBody.innerHTML = ""; // Clear previous table content</p>
<p>            for (var i = 0; i < dataMatrix.length; i++) {
                var row = document.createElement("tr");
                var unitCell = document.createElement("td");
                unitCell.innerText = "Unit " + (i + 1);
                row.appendChild(unitCell);

for (var j = 0; j < dataMatrix[i].length; j++) {
                    var raterCell = document.createElement("td");
                    raterCell.innerText = dataMatrix[i][j];
                    row.appendChild(raterCell);
                }
                tableBody.appendChild(row);
            }

// Update table header if number of raters changed
            var headerRow = document.querySelector("#dataTable thead tr");
            while(headerRow.cells.length > 1) { // Keep 'Unit' header cell
                headerRow.deleteCell(headerRow.cells.length - 1);
            }
            for(var j=0; j < rRaters; j++) {
                var th = document.createElement("th");
                th.innerText = "Rater " + (j + 1);
                headerRow.appendChild(th);
            }

// Update Chart Data
            updateDisagreementChart(disagreementCounts);
        }

function updateDisagreementChart(disagreementCounts) {
            var ctx = document.getElementById('disagreementChart').getContext('2d');

// Prepare data for the chart
            var labels = Object.keys(disagreementCounts).sort();
            var dataValues = labels.map(function(label) {
                return disagreementCounts[label];
            });

// Destroy previous chart instance if it exists
            if (chartInstance) {
                chartInstance.destroy();
            }

// Create new chart
            chartInstance = new Chart(ctx, {
                type: 'bar', // Use bar chart for discrete disagreement counts
                data: {
                    labels: labels,
                    datasets: [{
                        label: 'Number of Disagreements',
                        data: dataValues,
                        backgroundColor: 'rgba(0, 74, 153, 0.6)', // Primary color tint
                        borderColor: 'rgba(0, 74, 153, 1)',
                        borderWidth: 1
                    }]
                },
                options: {
                    responsive: true,
                    maintainAspectRatio: false, // Allow custom aspect ratio
                    scales: {
                        y: {
                            beginAtZero: true,
                            title: {
                                display: true,
                                text: 'Frequency'
                            }
                        },
                        x: {
                            title: {
                                display: true,
                                text: 'Rater Code Pair (e.g., 1-2)'
                            }
                        }
                    },
                    plugins: {
                        legend: {
                            display: false // Hide legend as we only have one dataset
                        },
                        title: {
                            display: true,
                            text: 'Distribution of Disagreements Between Rater Pairs'
                        }
                    }
                }
            });
        }

function resetCalculator() {
            document.getElementById("dataInput").value = '[[1, 1, 2, 1], [1, 2, 2, 2], [3, 3, 3, 3], [1, 1, 1, 2]]';
            document.getElementById("measurementUnit").value = "nominal";
            document.getElementById("alphaMethod").value = "nominal";
            document.getElementById("distanceFunction").value = "";
            document.getElementById("distanceFunctionGroup").style.display = "none"; // Hide custom function input

document.getElementById("results").style.display = "none";
            document.getElementById("dataTableBody").innerHTML = ""; // Clear table
             // Clear chart
            if (chartInstance) {
                chartInstance.destroy();
                chartInstance = null;
            }
            document.getElementById('disagreementChart').getContext('2d').clearRect(0, 0, 1, 1); // Clear canvas visually

// Clear errors
             document.getElementById("dataInputError").style.display = "none";
             document.getElementById("measurementUnitError").style.display = "none";
             document.getElementById("alphaMethodError").style.display = "none";
             document.getElementById("distanceFunctionError").style.display = "none";
        }

function copyResults() {
            var primaryResult = document.getElementById("primaryResult").innerText;
            var observedDisagreement = document.getElementById("observedDisagreement").innerText;
            var expectedDisagreement = document.getElementById("expectedDisagreement").innerText;
            var numberOfRaters = document.getElementById("numberOfRaters").innerText;
            var numberOfUnits = document.getElementById("numberOfUnits").innerText;
            var totalPairs = document.getElementById("totalPairs").innerText;
            var measurementUnit = document.getElementById("measurementUnit").value;
            var alphaMethod = document.getElementById("alphaMethod").value;

if (!primaryResult) {
                alert("No results to copy yet.");
                return;
            }

var textToCopy = "Krippendorff's Alpha Calculation Results:\n\n" +
                             "Krippendorff's Alpha: " + primaryResult + "\n" +
                             "Observed Disagreement (Do): " + observedDisagreement + "\n" +
                             "Expected Disagreement (De): " + expectedDisagreement + "\n" +
                             "Number of Raters (r): " + numberOfRaters + "\n" +
                             "Number of Units (n): " + numberOfUnits + "\n" +
                             "Total Possible Pairs: " + totalPairs + "\n\n" +
                             "Assumptions:\n" +
                             "Measurement Unit: " + measurementUnit + "\n" +
                             "Alpha Method: " + alphaMethod + "\n";

navigator.clipboard.writeText(textToCopy).then(function() {
                alert("Results copied to clipboard!");
            }).catch(function(err) {
                console.error("Failed to copy text: ", err);
                alert("Failed to copy results. Please copy manually.");
            });
        }

// Initial setup for method selection
        document.getElementById("measurementUnit").addEventListener("change", function() {
             var methodSelect = document.getElementById("alphaMethod");
             var selectedUnit = this.value;
             var selectedMethod = methodSelect.value;

// If unit is nominal, ensure method isn't ordinal/interval/ratio unless explicitly chosen
             if (selectedUnit === "nominal" && (selectedMethod === "ordinal" || selectedMethod === "interval" || selectedMethod === "ratio")) {
                 methodSelect.value = "nominal"; // Default back to nominal
             }
             // If unit is ordinal, interval, or ratio, nominal method is still valid, but others might be more appropriate.
             // The logic here is mainly to guide users. The calculator core handles actual calculation.
        });

// Add Chart.js library dynamically or assume it's available
        // For this example, we'll assume Chart.js is available globally.
        // In a real-world scenario, you'd include it via CDN or local file.
        // Example: <script src="https://cdn.jsdelivr.net/npm/chart.js"></script></p>
<p>        // Placeholder for Chart.js inclusion if needed<br />
        // If not already loaded, add this line within the <head> or before the script block:<br />
        // <script></script></p>
<p>        // Initial call to potentially set default state if needed, or let user interact<br />
        // resetCalculator(); // Call reset on load to set defaults</p>
<p>    </script><br />
    <br />
    <script></script><br />
</body><br />
</html></p>
		</div>

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