Number of negative events incorrectly labeled as positive.
Number of negative events correctly labeled as negative.
False Alarm Rate (Probability):0.000
False Alarm Rate (%):0.00%
Specificity (True Negative Rate):0.00%
Total Negative Conditions:0
What is False Alarm Rate?
The False Alarm Rate, also known as the False Positive Rate (FPR), is a critical metric used in Signal Detection Theory, Machine Learning (binary classification), and medical diagnostics. It measures the probability that a "false alarm" will occur—meaning a negative condition is incorrectly identified as positive.
In statistical terms, it represents the ratio of negative instances that are incorrectly classified as positive (Type I errors) to the total number of actual negative instances.
The Formula
The False Alarm Rate is calculated using the values from a confusion matrix:
FA Rate = FP / (FP + TN)
Where:
FP (False Positives): The number of negative instances wrongly categorized as positive (the "False Alarms").
TN (True Negatives): The number of negative instances correctly categorized as negative.
FP + TN: The total number of actual negative instances.
Understanding the Metrics
To fully utilize the FA Rate Calculator, it helps to understand the relationship between the variables:
Predicted Positive
Predicted Negative
Actual Positive
True Positive (TP)
False Negative (FN)
Actual Negative
False Positive (FP) (False Alarm)
True Negative (TN) (Correct Rejection)
Real-World Examples
1. Radar Technology:
A radar system is scanning for aircraft. If the radar blips indicating an aircraft is present when the sky is actually empty, this is a False Alarm (False Positive). If this happens 5 times out of 100 scans of empty sky, the FA Rate is 5%.
2. Medical Testing:
In a test for a specific virus, a False Alarm occurs if a healthy patient tests positive. If 10 healthy patients test positive (FP) and 990 healthy patients correctly test negative (TN), the calculation is:
The False Alarm Rate is mathematically the inverse of Specificity (also known as the True Negative Rate). While FA Rate measures the error of falsely identifying negatives, Specificity measures the accuracy of correctly identifying negatives.
Specificity = 1 – FA Rate
A lower False Alarm Rate generally indicates a more reliable system regarding negative rejection, though this must often be balanced against the Hit Rate (True Positive Rate) using tools like ROC (Receiver Operating Characteristic) curves.
function calculateFARate() {
// Get input elements by ID
var fpInput = document.getElementById('fpInput');
var tnInput = document.getElementById('tnInput');
var resultBox = document.getElementById('fa-result');
var errorBox = document.getElementById('error-display');
// Parse values
var fp = parseFloat(fpInput.value);
var tn = parseFloat(tnInput.value);
// Reset error and result display
errorBox.style.display = 'none';
resultBox.style.display = 'none';
errorBox.innerHTML = ";
// Validation logic
if (isNaN(fp) || isNaN(tn)) {
errorBox.innerHTML = 'Please enter valid numbers for both False Positives and True Negatives.';
errorBox.style.display = 'block';
return;
}
if (fp < 0 || tn < 0) {
errorBox.innerHTML = 'Values cannot be negative.';
errorBox.style.display = 'block';
return;
}
// Total Negatives (Denominator)
var totalNegatives = fp + tn;
// Check for division by zero
if (totalNegatives === 0) {
errorBox.innerHTML = 'Total Negatives (FP + TN) cannot be zero. Division by zero is undefined.';
errorBox.style.display = 'block';
return;
}
// Calculation Logic
var faRate = fp / totalNegatives;
var specificity = 1 – faRate;
// Formatting results
var faRateDecimal = faRate.toFixed(4);
var faRatePercent = (faRate * 100).toFixed(2) + '%';
var specificityPercent = (specificity * 100).toFixed(2) + '%';
// DOM Manipulation to display results
document.getElementById('res-prob').innerHTML = faRateDecimal;
document.getElementById('res-percent').innerHTML = faRatePercent;
document.getElementById('res-specificity').innerHTML = specificityPercent;
document.getElementById('res-total').innerHTML = totalNegatives;
// Show result box
resultBox.style.display = 'block';
}