How to Calculate True Negative Rate

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True Negative Rate (Specificity) Calculator

The number of negative cases correctly identified as negative.
The number of negative cases incorrectly identified as positive.
function calculateTNR() { var tn = parseFloat(document.getElementById('trueNegatives').value); var fp = parseFloat(document.getElementById('falsePositives').value); var resultDiv = document.getElementById('tnrResult'); if (isNaN(tn) || isNaN(fp)) { resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.color = '#721c24'; resultDiv.innerHTML = 'Error: Please enter valid numbers for both fields.'; return; } if (tn < 0 || fp < 0) { resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.color = '#721c24'; resultDiv.innerHTML = 'Error: Values cannot be negative.'; return; } var totalActualNegatives = tn + fp; if (totalActualNegatives === 0) { resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#f8d7da'; resultDiv.style.color = '#721c24'; resultDiv.innerHTML = 'Error: Total actual negatives (TN + FP) cannot be zero.'; return; } var tnr = tn / totalActualNegatives; var tnrPercentage = tnr * 100; resultDiv.style.display = 'block'; resultDiv.style.backgroundColor = '#d4edda'; resultDiv.style.color = '#155724'; resultDiv.innerHTML = '

Results

' + 'True Negative Rate (Specificity): ' + tnr.toFixed(4) + " + '' + tnrPercentage.toFixed(2) + '%' + 'This means ' + tnrPercentage.toFixed(2) + '% of all actual negative cases were correctly identified.'; }

Understanding the True Negative Rate (Specificity)

In the world of statistics, data science, and medical testing, the True Negative Rate (TNR)—often referred to as Specificity—is a critical metric used to evaluate the performance of a binary classification test. It measures the ability of a test to correctly identify individuals or instances that do not have a specific condition or characteristic.

The Formula for True Negative Rate

To calculate the True Negative Rate, you need two specific values from your confusion matrix:

  • True Negatives (TN): The count of cases that were negative and were correctly predicted as negative.
  • False Positives (FP): The count of cases that were negative but were incorrectly predicted as positive (also known as a Type I error).

TNR = TN / (TN + FP)

Why is Specificity Important?

While Sensitivity (True Positive Rate) tells us how good a test is at finding the "sick" people, Specificity tells us how good the test is at identifying the "healthy" people. High specificity is crucial when the cost of a False Positive is high. For example:

  • Medical Diagnosis: If a test for a rare disease has low specificity, many healthy patients will receive a scary diagnosis and potentially undergo unnecessary, invasive treatments.
  • Spam Filters: If a spam filter has low specificity, it will flag important personal emails as spam, causing users to miss vital information.
  • Security Systems: A high specificity in a security alarm ensures that the alarm doesn't go off every time a house cat moves (minimizing false alarms).

Practical Example

Imagine a diagnostic test used to screen 1,000 people for a condition. Out of these, 900 people are actually healthy (Negative).

  • The test correctly identifies 855 of them as healthy (True Negatives).
  • The test incorrectly flags 45 of them as having the condition (False Positives).

Using the formula:

TNR = 855 / (855 + 45) = 855 / 900 = 0.95

In this scenario, the test has a 95% Specificity. This means it correctly identifies 95% of healthy individuals, while 5% receive a false alarm.

True Negative Rate vs. False Positive Rate

It is important to note that the True Negative Rate and the False Positive Rate (FPR) are complementary. They will always add up to 1 (or 100%):

  • TNR + FPR = 1
  • If your Specificity is 95%, your False Positive Rate is 5%.

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