How to Calculate True Negative Rate

The true negative rate (TNR) is a key metric in statistics and machine learning that measures how well a classification model correctly identifies negative cases. This guide explains how to calculate TNR, provides an interactive calculator, and offers practical interpretation.

What is True Negative Rate?

The true negative rate (TNR) is a performance metric that answers the question: "What proportion of actual negatives was identified correctly?" In other words, it measures the model's ability to correctly classify negative cases.

TNR is also known as specificity and is calculated as the number of true negatives divided by the total number of actual negatives. A high TNR indicates good performance at identifying negative cases.

Key Point: TNR is complementary to the true positive rate (TPR). While TNR focuses on negative cases, TPR focuses on positive cases.

How to Calculate True Negative Rate

To calculate the true negative rate, you need two key pieces of information:

The number of true negatives (TN) - cases correctly identified as negative
The total number of actual negatives (TN + false negatives, FN)

Formula

True Negative Rate (TNR) = (True Negatives / Total Actual Negatives) × 100%

Or mathematically: TNR = TN / (TN + FN)

Step-by-Step Calculation

Count the number of true negatives (TN) in your dataset
Count the total number of actual negatives (TN + FN)
Divide the number of true negatives by the total number of actual negatives
Multiply by 100 to get a percentage

Confusion Matrix

A confusion matrix helps visualize the components of TNR calculation:

	Predicted Positive	Predicted Negative
Actual Positive	True Positives (TP)	False Negatives (FN)
Actual Negative	False Positives (FP)	True Negatives (TN)

Worked Example

Let's calculate the TNR for a medical test that screens for a disease:

	Test Positive	Test Negative
Disease Present	120 (False Positives)	80 (False Negatives)
Disease Absent	30 (True Positives)	470 (True Negatives)

In this example:

True Negatives (TN) = 470
Total Actual Negatives = TN + FN = 470 + 80 = 550

Calculation

TNR = (470 / 550) × 100% ≈ 85.45%

This means the test correctly identified 85.45% of people who do not have the disease.

Interpreting the Result

The true negative rate provides several important insights:

Model Performance: A high TNR indicates the model is good at identifying negative cases
Error Analysis: A low TNR suggests the model is missing many negative cases
Comparison: You can compare TNR across different models or datasets

Practical Tip: Always consider TNR alongside other metrics like precision and recall for a complete picture of model performance.

FAQ

What is the difference between TNR and accuracy?: Accuracy measures overall correctness (TP+TN)/(TP+TN+FP+FN), while TNR specifically measures correctness for negative cases.
When is a high TNR important?: A high TNR is crucial when false negatives are particularly costly (e.g., missing a disease diagnosis).
Can TNR be 100%?: Yes, if all actual negatives are correctly identified as negative (TN = total actual negatives).
How does TNR relate to the false positive rate?: TNR and false positive rate (FPR) are complementary: TNR = 1 - FPR.
Is TNR the same as specificity?: Yes, TNR and specificity refer to the same concept in statistics.