The probability that a negative case is correctly identified as negative.
The probability that a positive case is correctly identified as positive.
Used to demonstrate the number of misdiagnoses.
False Positive Rate (Type I Error)
0%
False Negative Rate (Type II Error)
0%
Total Accuracy (Assuming balanced classes)
0%
Understanding False Positive Rate (FPR)
In statistical hypothesis testing and medical diagnostics, the False Positive Rate (FPR) is a critical metric that indicates the probability of falsely rejecting the null hypothesis. In simpler terms, it represents the percentage of healthy individuals (negatives) who incorrectly receive a positive test result.
FPR is directly related to Specificity. While Specificity measures how good a test is at identifying negatives, the False Positive Rate measures how often the test fails in that regard.
The Calculation Formula
The relationship between False Positive Rate and Specificity is complementary. If you know the specificity of a test, calculating the FPR is straightforward using the following formula:
FPR = 1 – Specificity
Similarly, the False Negative Rate (FNR) is derived from Sensitivity:
FNR = 1 – Sensitivity
Input Definitions
Specificity (True Negative Rate): The ability of a test to correctly identify those without the disease (e.g., a 95% specificity means 95% of healthy people test negative).
Sensitivity (True Positive Rate): The ability of a test to correctly identify those with the disease (e.g., an 80% sensitivity means 80% of sick people test positive).
Real-World Example
Imagine a medical screening for a rare condition with the following parameters:
Specificity: 98%
Sensitivity: 90%
To find the False Positive Rate:
FPR = 100% – 98% = 2%
This means that for every 100 healthy individuals tested, statistically 2 will receive a "false alarm" indicating they have the condition when they actually do not.
Why Does This Matter?
Understanding the trade-off between Sensitivity and Specificity (and consequently FPR and FNR) is vital for setting thresholds in diagnostic tests:
High FPR Risks: Leads to unnecessary stress, expensive follow-up procedures, and potential treatment of healthy individuals (overdiagnosis).
High FNR Risks: Leads to missed diagnoses, delayed treatment, and potentially severe health consequences for patients who are actually sick.
function calculateFPR() {
// 1. Get input values
var specificityInput = document.getElementById('specificity').value;
var sensitivityInput = document.getElementById('sensitivity').value;
var populationInput = document.getElementById('population').value;
// 2. Validate inputs
if (specificityInput === "" || sensitivityInput === "") {
alert("Please enter both Specificity and Sensitivity values.");
return;
}
var specificity = parseFloat(specificityInput);
var sensitivity = parseFloat(sensitivityInput);
var population = parseFloat(populationInput) || 1000;
// Validate range
if (specificity 100 || sensitivity 100) {
alert("Please enter percentages between 0 and 100.");
return;
}
// 3. Perform Calculations
// FPR = 1 – Specificity
var fpr = 100 – specificity;
// FNR = 1 – Sensitivity
var fnr = 100 – sensitivity;
// Simple Accuracy (Assuming 50/50 split for estimation purposes in this basic calc)
// Accuracy = (True Positives + True Negatives) / Total
// In percentage terms: (Sensitivity + Specificity) / 2
var estAccuracy = (sensitivity + specificity) / 2;
// Population Impact Calculation (Assuming 50% prevalence for illustration)
// Using 50/50 split allows us to show raw numbers easily
var negativePop = population / 2;
var positivePop = population / 2;
var falsePositivesCount = Math.round((fpr / 100) * negativePop);
var falseNegativesCount = Math.round((fnr / 100) * positivePop);
// 4. Update the DOM
document.getElementById('fpr-result').innerHTML = fpr.toFixed(2) + "%";
document.getElementById('fnr-result').innerHTML = fnr.toFixed(2) + "%";
document.getElementById('accuracy-result').innerHTML = estAccuracy.toFixed(2) + "%";
// Dynamic Explanation
var explanation = "Given a Specificity of " + specificity + "%, the test will incorrectly flag " + fpr.toFixed(2) + "% of healthy individuals as positive.";
document.getElementById('fpr-explanation').innerHTML = explanation;
// Population Impact Text
var impactHTML = "Scenario Analysis:";
impactHTML += "In a balanced group of " + population + " people (half healthy, half with condition):";
impactHTML += "• You would expect approximately " + falsePositivesCount + " False Positives (Healthy people told they are sick).";
impactHTML += "• You would expect approximately " + falseNegativesCount + " False Negatives (Sick people told they are healthy).";
document.getElementById('population-impact').innerHTML = impactHTML;
// Show results
document.getElementById('results-area').style.display = 'block';
}