Calculating False Positive Rate

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False Positive Rate (FPR) Calculator

Calculate the probability of incorrectly identifying a negative case as positive.

Incorrectly flagged as positive
Correctly identified as negative
Resulting False Positive Rate:
0%

Understanding False Positive Rate

In statistics and binary classification, the False Positive Rate (FPR)—also known as the fall-out—is the probability that a false alarm will be raised, meaning a negative result is incorrectly classified as positive.

The Mathematical Formula

FPR = False Positives / (False Positives + True Negatives)

Key Definitions

  • False Positives (FP): The number of instances where the test predicted "Positive" but the actual condition was "Negative".
  • True Negatives (TN): The number of instances where the test correctly predicted "Negative".
  • Specificity: This is the True Negative Rate. FPR is simply 1 minus Specificity.

Example Scenario

Imagine a medical screening for a rare condition conducted on 1,000 healthy individuals. If 50 of those healthy individuals receive a positive test result, while 950 correctly receive a negative result:

  • False Positives = 50
  • True Negatives = 950
  • Total Negatives = 1,000
  • FPR = 50 / 1,000 = 0.05 or 5%
function calculateFPR() { var fp = parseFloat(document.getElementById('falsePositives').value); var tn = parseFloat(document.getElementById('trueNegatives').value); var resultBox = document.getElementById('fpr-result-box'); var resultDisplay = document.getElementById('fpr-value'); var interpretationDisplay = document.getElementById('fpr-interpretation'); if (isNaN(fp) || isNaN(tn) || fp < 0 || tn < 0) { alert("Please enter valid non-negative numbers for both inputs."); return; } var totalActualNegatives = fp + tn; if (totalActualNegatives === 0) { alert("The sum of False Positives and True Negatives must be greater than zero."); return; } var fpr = (fp / totalActualNegatives) * 100; var specificity = 100 – fpr; resultBox.style.display = 'block'; resultDisplay.innerHTML = fpr.toFixed(2) + "%"; var message = "This means for every 100 negative cases, " + fpr.toFixed(2) + " will be incorrectly flagged as positive. Your test specificity is " + specificity.toFixed(2) + "%."; interpretationDisplay.innerHTML = message; // Scroll to result resultBox.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }

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