How to Calculate False Negative Rate from Sensitivity and Specificity

by

False Negative Rate (FNR) Calculator

Calculate the miss rate and diagnostic accuracy from sensitivity and specificity values.

True Positive Rate (TPR)
True Negative Rate (TNR)

Results Breakdown

False Negative Rate 0%
False Positive Rate 0%

Understanding False Negative Rate

The False Negative Rate (FNR), often called the "miss rate," represents the probability that a positive case is incorrectly identified as negative by a diagnostic test. In medical and statistical contexts, this is a critical metric because it tells you how often the test fails to detect a condition when it is actually present.

How to Calculate FNR from Sensitivity

There is a direct mathematical inverse relationship between Sensitivity and the False Negative Rate. Because Sensitivity (True Positive Rate) and the False Negative Rate must add up to 100%, the formula is straightforward:

False Negative Rate (FNR) = 100% – Sensitivity

The Role of Specificity

While Specificity is not used to calculate the False Negative Rate, it is used to calculate the False Positive Rate (FPR). Just as Sensitivity relates to FNR, Specificity (True Negative Rate) relates to FPR:

False Positive Rate (FPR) = 100% – Specificity

Practical Example

Imagine a diagnostic test for a specific virus with the following characteristics:

  • Sensitivity: 94% (The test correctly identifies 94% of infected patients).
  • Specificity: 90% (The test correctly identifies 90% of healthy patients).

To find the False Negative Rate, you subtract the sensitivity from 100:

100% – 94% = 6% FNR. This means for every 100 infected people, 6 will receive a "false negative" result and be told they are healthy.

function calculateMetrics() { var sensitivity = parseFloat(document.getElementById('sensitivity').value); var specificity = parseFloat(document.getElementById('specificity').value); var resultsArea = document.getElementById('results-area'); var fnrOutput = document.getElementById('fnr-output'); var fprOutput = document.getElementById('fpr-output'); var interpretation = document.getElementById('interpretation'); // Validation if (isNaN(sensitivity) || sensitivity 100) { alert("Please enter a valid Sensitivity percentage between 0 and 100."); return; } // Calculate FNR var fnr = 100 – sensitivity; fnrOutput.innerHTML = fnr.toFixed(2) + "%"; // Handle Specificity if provided if (!isNaN(specificity) && specificity >= 0 && specificity <= 100) { var fpr = 100 – specificity; fprOutput.innerHTML = fpr.toFixed(2) + "%"; interpretation.innerHTML = "A sensitivity of " + sensitivity + "% means that " + fnr.toFixed(2) + "% of true positive cases are missed (False Negatives)."; } else { fprOutput.innerHTML = "N/A"; interpretation.innerHTML = "With " + sensitivity + "% sensitivity, the False Negative Rate is " + fnr.toFixed(2) + "%. Specificity is required to calculate False Positive Rate."; } resultsArea.style.display = 'block'; }

Leave a Comment