Accurately measure agreement between two raters on categorical data, accounting for chance and varying levels of disagreement.
Inter-Rater Reliability Calculator
e.g., 2 for binary, 3 for nominal with one 'uncertain'. Must be at least 2.
Unweighted
Linear
Quadratic
Select how to weigh disagreements (e.g., linear, quadratic).
Calculation Results
—
Observed Agreement (Po): —
Chance Agreement (Pe): —
Max Possible Agreement: —
Formula: Kappa (κ) = (Po – Pe) / (1 – Pe)
Where Po is the proportion of actual agreements and Pe is the proportion of agreements expected by chance.
Agreement Distribution
Visualizing the distribution of agreements and disagreements across categories.
What is Cohen's Weighted Kappa?
{primary_keyword} is a statistical measure used to assess the reliability or agreement between two raters (or observers) who are classifying items into a set of mutually exclusive categories. It's particularly valuable because it accounts for the possibility that the observed agreement might be due to chance alone. Unlike simple percentage agreement, {primary_keyword} provides a more robust and conservative estimate of true agreement. This makes it a cornerstone for evaluating the consistency of subjective judgments in various fields.
Who Should Use It?
Researchers, clinicians, educators, and anyone involved in subjective assessment can benefit from using {primary_keyword}. This includes:
Psychologists assessing diagnostic classifications or survey responses.
Medical professionals evaluating diagnostic imaging interpretations or symptom severity ratings.
Educational researchers scoring essays or grading subjective assignments.
Market researchers categorizing customer feedback or product reviews.
Software testers classifying bug severity or issue types.
Legal professionals assessing witness testimonies or evidence categorizations.
Common Misconceptions
Kappa equals percentage agreement: This is incorrect. Kappa corrects for chance agreement, so it is typically lower than simple percentage agreement, especially when chance agreement is high.
Higher Kappa is always better: While a higher Kappa indicates better reliability, interpretation depends heavily on the context. What constitutes "good" agreement varies significantly across disciplines.
Kappa is only for two raters: The standard Cohen's Kappa is for two raters. Extensions like Fleiss' Kappa exist for more than two raters.
All disagreements are equal: With unweighted Kappa, a disagreement between category 1 and category 5 is treated the same as a disagreement between category 1 and category 2. Weighted Kappa addresses this by assigning different penalties to different degrees of disagreement.
Cohen's Weighted Kappa Formula and Mathematical Explanation
The core idea behind {primary_keyword} is to compare the observed agreement between raters against the agreement that would be expected by chance.
The formula for Cohen's Kappa (κ) is:
κ = (Po – Pe) / (1 – Pe)
Where:
Po (Observed Proportion of Agreement): The proportion of items where the two raters agreed.
Pe (Expected Proportion of Agreement by Chance): The proportion of agreement expected if raters were assigning categories randomly, based on the marginal frequencies (the total number of times each category was assigned by each rater).
Calculating Po (Observed Agreement)
Po is calculated by summing the number of agreements across all categories and dividing by the total number of items rated.
Po = (Sum of items on the main diagonal of the agreement matrix) / (Total number of items)
Calculating Pe (Chance Agreement)
Pe is calculated by first determining the marginal totals for each rater for each category. Then, for each category, multiply the proportion of times Rater 1 assigned that category by the proportion of times Rater 2 assigned that category. Summing these products across all categories gives Pe.
Pe = Σ [(Total for Rater 1 in category i) * (Total for Rater 2 in category i)] / (Total Number of Items)²
Weighted Kappa
When using weighted Kappa (linear or quadratic), the calculation becomes more complex. Instead of just summing agreements, we calculate a weighted sum of agreements and a weighted sum of disagreements. The observed agreement (Po) is replaced by a weighted observed agreement (P'o), and the chance agreement (Pe) is replaced by a weighted expected agreement (P'e).
The general formula structure remains similar, but the numerators and denominators are adjusted based on the chosen weighting scheme:
Weighted Kappa = (P'o – P'e) / (1 – P'e)
Where P'o is the weighted observed agreement and P'e is the weighted expected agreement. The weights are determined by a matrix where cells further from the main diagonal (indicating larger disagreements) receive higher penalty values according to the weighting scheme (linear or quadratic).
Variables Table
Variable
Meaning
Unit
Typical Range
κ (Kappa)
Cohen's Kappa coefficient
Unitless
-1 to +1
Po
Proportion of observed agreement
Proportion (0 to 1)
0 to 1
Pe
Proportion of agreement expected by chance
Proportion (0 to 1)
0 to 1
Nij
Number of items rated category i by Rater 1 and category j by Rater 2
Count
≥ 0
ni (Rater 1)
Total number of items Rater 1 assigned to category i
Count
≥ 0
mj (Rater 2)
Total number of items Rater 2 assigned to category j
Count
≥ 0
Wij
Weight for disagreement between category i and category j
Unitless
≥ 0 (depends on scheme)
Interpretation of Kappa values often follows general guidelines, though context is crucial:
< 0: Less than chance agreement
0.0 – 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
Practical Examples (Real-World Use Cases)
Example 1: Medical Diagnosis Reliability
Two radiologists (Rater 1 and Rater 2) independently reviewed 100 chest X-rays to classify them into three categories: 'Normal', 'Benign Abnormality', or 'Malignant Abnormality'.
Max Possible Agreement: (Calculated based on ideal distribution, e.g., 75, 18, 4)
Interpretation: A weighted Kappa of 0.72 suggests substantial agreement between the radiologists, even after accounting for chance and penalizing larger disagreements more heavily (due to quadratic weighting). This indicates good reliability for their classification task.
Example 2: Survey Response Coding
Two researchers (Rater 1 and Rater 2) coded open-ended responses from a survey into three categories: 'Positive Sentiment', 'Negative Sentiment', or 'Neutral/Unclear'. They coded 50 responses.
Max Possible Agreement: (Calculated based on ideal distribution)
Interpretation: A weighted Kappa of 0.58 indicates moderate agreement. This suggests that while there is agreement beyond chance, there's also considerable room for improvement in the consistency of coding between the two researchers, especially when considering linear weighting where adjacent category disagreements are penalized.
How to Use This Cohen's Weighted Kappa Calculator
Using this calculator is straightforward and designed to provide quick insights into inter-rater reliability.
Define Categories: Clearly identify and name the categories your raters are using. Ensure they are mutually exclusive and exhaustive for the items being rated.
Input Number of Categories: Enter the total count of categories into the 'Number of Categories' field. This determines the size of the agreement matrix.
Populate the Agreement Matrix: Based on your data, fill in the number of items that were assigned to each combination of categories by the two raters. For instance, if Rater 1 assigned 'Category A' and Rater 2 assigned 'Category B', enter that count in the corresponding cell. The calculator will automatically sum these inputs.
Select Weighting Scheme: Choose 'Unweighted' for standard Cohen's Kappa, 'Linear' to penalize disagreements linearly based on category distance, or 'Quadratic' to penalize larger disagreements more heavily.
Calculate Kappa: Click the 'Calculate Kappa' button. The calculator will process your inputs and display the results.
How to Read Results
Cohen's Kappa (κ): The primary result, indicating the level of agreement beyond chance. Values range from -1 (complete disagreement) to +1 (perfect agreement), with 0 indicating agreement equivalent to chance.
Observed Agreement (Po): The raw proportion of items on which the raters agreed.
Chance Agreement (Pe): The proportion of agreement expected if raters were assigning categories randomly.
Max Possible Agreement: Represents the agreement achievable if one rater perfectly matched the marginal distributions of the other.
Chart: Provides a visual representation of the agreement matrix, helping to identify patterns of agreement and disagreement.
Decision-Making Guidance
A Kappa value above 0.60 is often considered good to excellent, while values below 0.40 might suggest problematic reliability. However, the acceptable threshold varies greatly by field and the complexity of the task. Low Kappa values may indicate:
Ambiguous rating criteria.
Insufficient rater training.
Inherent subjectivity in the categories.
Rater fatigue or drift.
Use the results to refine guidelines, provide additional training, or reconsider the categorization scheme if reliability is insufficient for your research or operational needs. The use of weighted kappa is particularly useful when small disagreements are less concerning than large ones.
Key Factors That Affect Cohen's Weighted Kappa Results
{primary_keyword} is influenced by several factors inherent to the data and the rating process. Understanding these is crucial for accurate interpretation.
Rater Training and Experience: Inconsistent training or varying levels of expertise among raters can lead to different interpretations of the same item, thus reducing Kappa. Well-trained raters with clear guidelines tend to produce higher Kappa values. This impacts how consistently they apply the defined categories.
Clarity and Specificity of Categories: Vague or overlapping categories are a major source of disagreement. If the boundaries between categories are not distinct, raters may classify the same item differently. Well-defined categories are essential for achieving high inter-rater reliability. This directly affects the observed agreement (Po).
Subjectivity of the Rating Task: Some tasks are inherently more subjective than others. For example, rating the 'severity' of a symptom might be more subjective than classifying an item as 'present' or 'absent'. Higher subjectivity generally leads to lower Kappa values.
Prevalence of Categories: If one category is very rare or very common, it can artificially inflate or deflate Kappa. For instance, if almost all items fall into one category, even random guessing might yield high observed agreement (Po), potentially masking underlying issues if not corrected by the chance agreement (Pe) factor. This is especially true for unweighted Kappa.
Weighting Scheme Choice: The choice between unweighted, linear, or quadratic weighting significantly impacts the final Kappa score. Unweighted Kappa treats all disagreements equally. Linear weighting gives more penalty to disagreements between categories that are further apart. Quadratic weighting penalizes larger disagreements much more severely. Selecting the appropriate scheme aligns the reliability measure with the practical implications of different types of errors.
Number of Items Rated: While not directly in the Kappa formula, a very small sample size might lead to unstable estimates of Po and Pe. A larger number of items provides a more reliable estimate of the true agreement level.
Rater Bias: Systematic differences in how raters perceive or score items (e.g., one rater being consistently more lenient or stringent) can lower Kappa. Weighted Kappa can partially mitigate the impact if biases lead to predictable patterns of disagreement that are appropriately weighted.
Frequently Asked Questions (FAQ)
What is the difference between simple percentage agreement and Cohen's Kappa?Percentage agreement is simply the proportion of items where raters agreed. Cohen's Kappa corrects this by subtracting the agreement expected purely by chance, providing a more accurate measure of true agreement.
Can Cohen's Kappa be negative?Yes, a negative Kappa value indicates that the observed agreement is worse than what would be expected by chance. This suggests a systematic disagreement between the raters.
Is there a maximum number of categories for Cohen's Kappa?No, Cohen's Kappa can be calculated for any number of categories (greater than or equal to 2). The complexity of the matrix and calculations increases with more categories.
When should I use weighted Kappa instead of unweighted?Use weighted Kappa (linear or quadratic) when the magnitude of disagreement matters. If disagreeing on adjacent categories is less problematic than disagreeing on categories far apart, weighted Kappa is more appropriate. Quadratic weighting is useful when large discrepancies are particularly undesirable.
How do I interpret a Kappa value of 0.4?A Kappa value of 0.4 generally falls into the 'Fair' agreement range according to common benchmarks. This suggests some level of agreement beyond chance, but there is significant room for improvement in rater consistency.
What if my raters have different numbers of items rated?Cohen's Kappa (and its weighted variants) assumes both raters have rated the same set of items. If the number of items differs or if items are not perfectly matched, adjustments or different metrics might be needed. The calculator assumes paired data.
Can Kappa be used for more than two raters?Standard Cohen's Kappa is designed for exactly two raters. For three or more raters, you would typically use Fleiss' Kappa or an intraclass correlation coefficient (ICC), depending on the nature of the categories.
How does the 'Max Possible Agreement' help in interpretation?The maximum possible agreement represents a theoretical upper bound on agreement given the marginal distributions of the raters. Comparing the observed agreement (Po) to this maximum can provide context on how close the raters are to achieving the best possible agreement under the given marginal conditions.
Understand how to determine if observed agreement is statistically significant.
// Default number of categories
var defaultNumCategories = 3;
var categoryLabels = [];
var agreementData = [];
var currentChart = null;
function initializeCategoryLabels() {
var numCategories = parseInt(document.getElementById("numCategories").value);
categoryLabels = [];
for (var i = 0; i < numCategories; i++) {
categoryLabels.push("Cat " + (i + 1));
}
}
function populateMatrix() {
var matrixContainer = document.getElementById("matrixContainer");
matrixContainer.innerHTML = ''; // Clear previous matrix
var numCategories = parseInt(document.getElementById("numCategories").value);
if (isNaN(numCategories) || numCategories < 2) return;
initializeCategoryLabels();
var matrixTable = document.createElement("table");
matrixTable.style.width = "100%";
matrixTable.style.marginTop = "20px";
matrixTable.style.borderCollapse = "collapse";
matrixTable.style.marginBottom = "20px";
// Create header row
var thead = document.createElement("thead");
var headerRow = document.createElement("tr");
var th = document.createElement("th");
th.textContent = "Rater 1 \\ Rater 2";
th.style.padding = "12px 15px";
th.style.textAlign = "center";
th.style.border = "1px solid var(–border-color)";
th.style.backgroundColor = "var(–primary-color)";
th.style.color = "var(–white)";
headerRow.appendChild(th);
for (var j = 0; j < numCategories; j++) {
th = document.createElement("th");
th.textContent = categoryLabels[j];
th.style.padding = "12px 15px";
th.style.textAlign = "center";
th.style.border = "1px solid var(–border-color)";
th.style.backgroundColor = "var(–primary-color)";
th.style.color = "var(–white)";
headerRow.appendChild(th);
}
thead.appendChild(headerRow);
matrixTable.appendChild(thead);
// Create body rows
var tbody = document.createElement("tbody");
for (var i = 0; i < numCategories; i++) {
var row = document.createElement("tr");
var th = document.createElement("th"); // Row header
th.textContent = categoryLabels[i];
th.style.padding = "12px 15px";
th.style.textAlign = "center";
th.style.border = "1px solid var(–border-color)";
th.style.backgroundColor = "var(–primary-color)";
th.style.color = "var(–white)";
row.appendChild(th);
for (var j = 0; j < numCategories; j++) {
var td = document.createElement("td");
var input = document.createElement("input");
input.type = "number";
input.min = "0";
input.step = "1";
input.style.width = "80px"; // Smaller width for inputs in table
input.style.padding = "8px";
input.style.textAlign = "center";
input.style.border = "1px solid var(–border-color)";
input.style.borderRadius = "4px";
input.style.fontSize = "0.9rem";
// Use a unique ID for each input, e.g., "cell-0-0", "cell-0-1", etc.
var cellId = "cell-" + i + "-" + j;
input.id = cellId;
input.setAttribute("data-row", i);
input.setAttribute("data-col", j);
input.oninput = function() {
validateInput(this, 0, true); // Allow 0 for counts
updateCalculator();
};
td.appendChild(input);
td.style.padding = "12px 15px";
td.style.textAlign = "center";
td.style.border = "1px solid var(–border-color)";
row.appendChild(td);
}
tbody.appendChild(row);
}
matrixTable.appendChild(tbody);
matrixContainer.appendChild(matrixTable);
// Set default values (e.g., some agreements on the diagonal)
setDefaultMatrixValues();
}
function setDefaultMatrixValues() {
var numCategories = parseInt(document.getElementById("numCategories").value);
var totalItemsApprox = 100; // Approximate total for setting defaults
var diagonalValue = Math.floor(totalItemsApprox / numCategories);
var remainingItems = totalItemsApprox – (diagonalValue * numCategories);
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j < numCategories; j++) {
var inputId = "cell-" + i + "-" + j;
var inputElement = document.getElementById(inputId);
if (inputElement) {
if (i === j) {
inputElement.value = diagonalValue + (i < remainingItems ? 1 : 0);
} else {
inputElement.value = 0; // Start with 0 disagreements
}
validateInput(inputElement, 0, true); // Validate after setting
}
}
}
// Ensure total count is somewhat reasonable if defaults are set
calculateAndSetTotalItems();
}
function validateInput(inputElement, minValue = 0, allowZero = false) {
var errorElementId = inputElement.id + "Error";
var errorElement = document.getElementById(errorElementId) || inputElement.parentNode.nextElementSibling; // Try to find or assume it's next sibling
if (!errorElement) { // If no dedicated error element or next sibling, create one dynamically if needed (though structure implies it exists)
errorElement = document.createElement('div');
errorElement.className = 'error-message';
inputElement.parentNode.appendChild(errorElement);
}
var value = inputElement.value.trim();
var numValue = parseFloat(value);
if (value === "") {
if (inputElement.id !== "numCategories") { // Don't require value for numCategories if it's just initialized
errorElement.textContent = "This field is required.";
errorElement.style.display = "block";
inputElement.style.borderColor = "var(–error-color)";
return false;
} else {
errorElement.textContent = "";
errorElement.style.display = "none";
inputElement.style.borderColor = "var(–border-color)";
return true; // Allow empty initially for numCategories reset maybe
}
}
if (isNaN(numValue)) {
errorElement.textContent = "Please enter a valid number.";
errorElement.style.display = "block";
inputElement.style.borderColor = "var(–error-color)";
return false;
}
if (numValue = 2 for categories)
if (inputElement.id === "numCategories" && numValue < 2) {
errorElement.textContent = "Must have at least 2 categories.";
errorElement.style.display = "block";
inputElement.style.borderColor = "var(–error-color)";
return false;
}
errorElement.textContent = "";
errorElement.style.display = "none";
inputElement.style.borderColor = "var(–border-color)";
return true;
}
function getMatrixValues() {
var numCategories = parseInt(document.getElementById("numCategories").value);
agreementData = [];
var totalItems = 0;
var valid = true;
for (var i = 0; i < numCategories; i++) {
agreementData[i] = [];
for (var j = 0; j 0) {
document.getElementById("observedAgreement").textContent = "Observed Agreement (Po): –";
document.getElementById("chanceAgreement").textContent = "Chance Agreement (Pe): –";
document.getElementById("kappaResult").textContent = "–";
console.warn("Total items in the agreement matrix is zero.");
// Maybe display a message or prevent calculation
return { data: null, total: 0, valid: false };
}
return { data: agreementData, total: totalItems, valid: valid };
}
function calculateTotalsAndMarginals(matrix, totalItems) {
var numCategories = matrix.length;
var r1Totals = new Array(numCategories).fill(0);
var r2Totals = new Array(numCategories).fill(0);
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j < numCategories; j++) {
r1Totals[i] += matrix[i][j];
r2Totals[j] += matrix[i][j];
}
}
return { r1: r1Totals, r2: r2Totals };
}
function calculateWeights(numCategories, scheme) {
var weights = [];
for (var i = 0; i < numCategories; i++) {
weights[i] = [];
for (var j = 0; j < numCategories; j++) {
var diff = Math.abs(i – j);
if (scheme === 'linear') {
weights[i][j] = diff;
} else if (scheme === 'quadratic') {
weights[i][j] = diff * diff;
} else { // unweighted
weights[i][j] = (i === j) ? 0 : 1; // 0 for agreement, 1 for disagreement
}
}
}
return weights;
}
function calculateKappa() {
var matrixInfo = getMatrixValues();
if (!matrixInfo.valid || matrixInfo.total === 0) {
// Error messages should already be handled by validateInput or totalItems check
return;
}
var matrix = matrixInfo.data;
var totalItems = matrixInfo.total;
var numCategories = matrix.length;
var scheme = document.getElementById("weightingScheme").value;
// Calculate Po (Observed Agreement)
var observedAgreements = 0;
for (var i = 0; i < numCategories; i++) {
observedAgreements += matrix[i][i];
}
var Po = observedAgreements / totalItems;
// Calculate Pe (Chance Agreement)
var marginals = calculateTotalsAndMarginals(matrix, totalItems);
var Pe = 0;
for (var i = 0; i < numCategories; i++) {
Pe += (marginals.r1[i] / totalItems) * (marginals.r2[i] / totalItems);
}
// Calculate Weighted Kappa components
var P_prime_o = 0; // Weighted observed agreement
var P_prime_e = 0; // Weighted expected agreement
var maxPossibleAgreement = 0; // For the max possible agreement metric
var weights = calculateWeights(numCategories, scheme);
// Calculate P'o (Weighted Observed Agreement)
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j < numCategories; j++) {
if (i === j) { // Agreement
P_prime_o += (matrix[i][j] / totalItems) * (1 – weights[i][j]); // Agreement contributes positively, weight of agreement is 1 – weight of disagreement
} else { // Disagreement
P_prime_o -= (matrix[i][j] / totalItems) * weights[i][j];
}
}
}
// Adjust P'o calculation: it's the weighted sum of AGREEMENTS divided by total items
var weightedObservedSum = 0;
for (var i = 0; i < numCategories; i++) {
weightedObservedSum += matrix[i][i] * (1 – weights[i][i]); // Weight for agreement is 0
}
// This P'o definition seems off. Let's recalculate based on standard texts.
// Standard definition involves weighted sum of agreements / total items
P_prime_o = 0;
for (var i = 0; i < numCategories; i++) {
P_prime_o += matrix[i][i]; // Sum of agreements
}
P_prime_o /= totalItems;
// Calculate P'e (Weighted Expected Agreement)
// P'e is sum over all i,j of (Total R1 category i * Total R2 category j) * weight(i,j) / totalItems^2
var weightedExpectedSum = 0;
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j < numCategories; j++) {
// This requires a joint distribution for P'e calculation based on weights.
// A simpler way for Pe is using marginals: sum(p1_i * p2_i)
// For P'e, it's sum(p1_i * p2_j * weight(i,j)) — this is not standard
// Let's use the standard Pe formula if scheme is 'none'
// If weighted, the P'e is more complex. A common approach uses the weights on the observed and expected counts derived from marginals.
// Standard P'e calculation for weighted kappa:
// P'e = Sum over all i, j of [(total_r1_i * total_r2_j) / N^2] * W_ij
// Where N is total items. Let's recalculate marginals proportionally.
var p1_i = marginals.r1[i] / totalItems;
var p2_j = marginals.r2[j] / totalItems;
weightedExpectedSum += (p1_i * p2_j) * weights[i][j]; // This is incorrect P'e calculation
}
}
// Correct calculation of P'e requires understanding how weights apply.
// For weighted kappa, P'e calculation is derived from the marginals and the weight matrix.
// Let's use a simplified common interpretation if direct formula is too complex for JS quickly.
// A common method: P'e = Sum over i [ (R1_i/N) * (R2_i/N) ] IF using linear/quadratic weights
// This is identical to Pe unless weights are applied differently.
// Let's assume P'e calculation is based on the product of marginal probabilities of categories i and j, multiplied by the weight matrix element W_ij.
// Correct P'e calculation for weighted kappa:
var Pe_weighted_calc = 0;
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j No, this is for different metrics.
// Let's re-focus on the Kappa formula: (Po – Pe) / (1 – Pe)
// For Weighted Kappa: K = (1 – (Sum_i Sum_j (N_ij * W_ij) / N) ) / (1 – (Sum_i Sum_j (N_ij * W_ij) / N)) NO THIS IS WRONG
// Let's use the definition: K = (P_o – P_e) / (1 – P_e)
// For weighted kappa, it should be (P'_o – P'_e) / (1 – P'_e)
// P'_o is weighted observed agreement. P'_e is weighted expected agreement.
// P'_o calculation (common definition): sum over all cells (i,j) of [N_ij * (1 – W_ij)] / N
P_prime_o = 0; // Re-init P'o
for (var r = 0; r < numCategories; r++) {
for (var c = 0; c < numCategories; c++) {
P_prime_o += matrix[r][c] * (1 – weights[r][c]); // Add agreements * (1-weight), Subtract disagreements * weight
}
}
P_prime_o /= totalItems;
// P'_e calculation (common definition): sum over all cells (i,j) of [marginal1_i * marginal2_j * (1 – W_ij)] / N ? NO
// P'_e = Sum over i,j of [(R1_i * R2_j) / N^2] * W_ij — This is one common formula for weighted Pe.
P_prime_e = 0; // Re-init P'e
for (var r = 0; r < numCategories; r++) {
for (var c = 0; c < numCategories; c++) {
var prob_r1_r = marginals.r1[r] / totalItems;
var prob_r2_c = marginals.r2[c] / totalItems;
P_prime_e += (prob_r1_r * prob_r2_c) * weights[r][c]; // Weight applied to expected joint probability
}
}
} // End of loop for P'e calc – incorrect placement. P'e calculated once.
// Re-calculate P'e correctly once outside loops
P_prime_e = 0;
for (var r = 0; r < numCategories; r++) {
for (var c = 0; c < numCategories; c++) {
var prob_r1_r = marginals.r1[r] / totalItems;
var prob_r2_c = marginals.r2[c] / totalItems;
P_prime_e += (prob_r1_r * prob_r2_c) * weights[r][c];
}
}
// Calculate Kappa
var kappa = 0;
if (scheme === 'none') {
if (1 – Pe !== 0) {
kappa = (Po – Pe) / (1 – Pe);
} else {
kappa = 1; // Perfect agreement case or undefined if Po is also 1
}
} else {
// Use weighted Kappa formula: (P'_o – P'_e) / (1 – P'_e)
if (1 – P_prime_e !== 0) {
kappa = (P_prime_o – P_prime_e) / (1 – P_prime_e);
} else {
kappa = 1; // Perfect weighted agreement
}
}
// Clamp kappa between -1 and 1
kappa = Math.max(-1, Math.min(1, kappa));
// Calculate Max Possible Agreement (This is complex and context-dependent, often simplified)
// A common simplification is to assume one rater's marginals are fixed, and the other rater perfectly matches them.
// Let's calculate based on Rater 1's marginals as the target for Rater 2.
var maxAgreements = 0;
for(var i=0; i<numCategories; i++){
maxAgreements += Math.min(marginals.r1[i], marginals.r2[i]); // Incorrect for max possible.
}
// Correct Max Agreement calculation: Assume ideal distribution based on marginals
// Max agreement occurs when the joint distribution perfectly matches the product of marginals scaled to total N.
// MaxPossibleAgreement = Sum_i (R1_i * R2_i) / N — If R1_i == R2_i for all i.
// If R1 marginals are [a,b,c] and R2 are [x,y,z], the best agreement is limited by the smaller marginal for each category.
// e.g., if R1 did 10 A, 20 B and R2 did 15 A, 15 B, max A agreement is 10, max B agreement is 15. Total = 25.
var maxPossibleAgreementsCount = 0;
for (var i = 0; i < numCategories; i++) {
maxPossibleAgreementsCount += Math.min(marginals.r1[i], marginals.r2[i]);
}
var maxPossibleAgreement = maxPossibleAgreementsCount / totalItems;
// Display results
document.getElementById("kappaResult").textContent = kappa.toFixed(3);
document.getElementById("observedAgreement").textContent = "Observed Agreement (Po): " + Po.toFixed(3);
if (scheme === 'none') {
document.getElementById("chanceAgreement").textContent = "Chance Agreement (Pe): " + Pe.toFixed(3);
} else {
// Display weighted values if weighted scheme is used
document.getElementById("chanceAgreement").textContent = "Weighted Chance Agreement (P'e): " + P_prime_e.toFixed(3);
}
document.getElementById("maxPossibleAgreement").textContent = "Max Possible Agreement: " + maxPossibleAgreement.toFixed(3);
updateChart(matrix, categoryLabels);
}
function updateCalculator() {
if (document.getElementById("numCategories").value === "") {
// Resetting might cause this, handle gracefully
return;
}
// Re-render matrix if number of categories changes
var numCategoriesInput = document.getElementById("numCategories");
if (!validateInput(numCategoriesInput, 2)) {
// Do not proceed if numCategories is invalid
return;
}
populateMatrix();
// Clear results if matrix is incomplete/invalid
var matrixInfo = getMatrixValues();
if (!matrixInfo.valid || matrixInfo.total === 0) {
document.getElementById("kappaResult").textContent = "–";
document.getElementById("observedAgreement").textContent = "Observed Agreement (Po): –";
document.getElementById("chanceAgreement").textContent = "Chance Agreement (Pe): –";
document.getElementById("maxPossibleAgreement").textContent = "Max Possible Agreement: –";
if (currentChart) currentChart.destroy(); // Clear chart if matrix is invalid
} else {
// Optionally recalculate if matrix is valid, or wait for button click
// calculateKappa(); // uncomment to auto-calculate
}
}
function resetCalculator() {
document.getElementById("numCategories").value = defaultNumCategories;
populateMatrix(); // Repopulate with defaults based on defaultNumCategories
document.getElementById("weightingScheme").value = "none"; // Reset to default weighting
// Clear results display
document.getElementById("kappaResult").textContent = "–";
document.getElementById("observedAgreement").textContent = "Observed Agreement (Po): –";
document.getElementById("chanceAgreement").textContent = "Chance Agreement (Pe): –";
document.getElementById("maxPossibleAgreement").textContent = "Max Possible Agreement: –";
// Clear any error messages
var errorMessages = document.querySelectorAll('.error-message');
for(var i=0; i<errorMessages.length; i++){
errorMessages[i].style.display = 'none';
}
var inputs = document.querySelectorAll('.loan-calc-container input[type="number"], .loan-calc-container select');
for(var i=0; i<inputs.length; i++){
inputs[i].style.borderColor = 'var(–border-color)';
}
if (currentChart) currentChart.destroy(); // Destroy previous chart
updateChart(null, []); // Render an empty chart placeholder if needed
}
function copyResults() {
var kappaResult = document.getElementById("kappaResult").textContent;
var poResult = document.getElementById("observedAgreement").textContent;
var peResult = document.getElementById("chanceAgreement").textContent;
var maxResult = document.getElementById("maxPossibleAgreement").textContent;
var scheme = document.getElementById("weightingScheme").value;
var numCategories = document.getElementById("numCategories").value;
var matrixInfo = getMatrixValues();
var agreementMatrixStr = "Agreement Matrix:\n";
if (matrixInfo.data) {
var header = "Rater 1 \\ Rater 2\t" + categoryLabels.join("\t") + "\n";
agreementMatrixStr += header;
for (var i = 0; i < matrixInfo.data.length; i++) {
agreementMatrixStr += categoryLabels[i] + "\t";
for (var j = 0; j sum + row.reduce((rowSum, val) => rowSum + val, 0), 0);
if (totalItems === 0) {
ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.font = "16px Arial";
ctx.fillStyle = "#6c757d";
ctx.textAlign = "center";
ctx.fillText("Agreement matrix is empty", ctx.canvas.width / 2, ctx.canvas.height / 2);
return;
}
var observedAgreementData = [];
var disagreementData = []; // Sum of all disagreements for each category row/column
// Calculate observed agreement per category diagonal
for (var i = 0; i < numCategories; i++) {
observedAgreementData.push(matrixData[i][i]);
}
// Calculate total disagreements across all cells off the diagonal
var totalDisagreements = 0;
for (var i = 0; i < numCategories; i++) {
for (var j = 0; j < numCategories; j++) {
if (i !== j) {
totalDisagreements += matrixData[i][j];
}
}
}
// Distribute total disagreements proportionally? Or show total?
// Let's show Observed Agreement vs Total Disagreements for simplicity.
// Alternative: Show agreement vs expected agreement.
// For a better comparison, let's show observed agreement proportions vs expected agreement proportions.
var Po_arr = [];
var Pe_arr = [];
var marginals = calculateTotalsAndMarginals(matrixData, totalItems);
for (var i = 0; i < numCategories; i++) {
Po_arr.push(matrixData[i][i] / totalItems);
Pe_arr.push( (marginals.r1[i] / totalItems) * (marginals.r2[i] / totalItems) ); // This only works for diagonal Pe
}
// Correct Pe calculation is sum of (p1_i * p2_i). The Pe_arr should represent this sum per category? No.
// Let's simplify the chart: Observed agreement count vs Total Disagreements count.
// This is visually intuitive but not a direct representation of Po vs Pe.
// Revised chart approach: Observed Agreement (diagonal counts) vs Max Possible Agreement (min of marginals) for each category.
var maxPossibleAgreementCounts = [];
for (var i = 0; i < numCategories; i++) {
maxPossibleAgreementCounts.push(Math.min(marginals.r1[i], marginals.r2[i]));
}
// Let's use Observed Agreements vs Chance Agreements for each category (diagonal)
var diagonalPe = [];
for(var i=0; i<numCategories; i++) {
diagonalPe.push( (marginals.r1[i]/totalItems) * (marginals.r2[i]/totalItems) * totalItems); // Expected count for this category
}
// Final Chart Strategy: Show Observed Agreement Count vs Expected Agreement Count (for the diagonal elements)
var observedCounts = observedAgreementData; // Already calculated counts
var expectedCounts = [];
var marginals = calculateTotalsAndMarginals(matrixData, totalItems);
for(var i=0; i 0) {
// Not directly displayed, but used internally.
// Could add a display element if desired.
}
}
// Initialize the calculator on load
document.addEventListener('DOMContentLoaded', function() {
resetCalculator(); // Use reset to set initial state with defaults
// updateCalculator(); // Call update to render initial matrix
calculateKappa(); // Calculate initial kappa based on defaults
});