How to Calculate True Negative From Confusion Matrix

What is True Negative?

A true negative (TN) occurs when a classification model correctly predicts the negative class. For example, in a medical test that identifies a disease, a true negative would be a healthy person correctly identified as not having the disease.

True negatives are important because they show the model's ability to correctly identify negative cases, which is often as important as identifying positive cases in many applications.

Confusion Matrix Basics

A confusion matrix is a 2x2 table that summarizes the performance of a classification algorithm. It has four components:

• True Positives (TP): Correctly predicted positive cases
• True Negatives (TN): Correctly predicted negative cases
• False Positives (FP): Incorrectly predicted positive cases (Type I error)
• False Negatives (FN): Incorrectly predicted negative cases (Type II error)

The matrix looks like this:

True negatives are found in the bottom-right cell of this matrix.

Calculating True Negative

The true negative count is simply the number of negative cases that the model correctly identified. It's one of the four components of the confusion matrix.

Formula

In practice, you would:

1. Count all negative cases in your dataset
2. Count how many of these were correctly identified by your model
3. This count is your true negative value

Common Pitfalls

• Confusing true negatives with true positives
• Misinterpreting false negatives as true negatives
• Assuming a high true negative rate means the model is perfect

Practical Examples

Let's look at two examples to illustrate how to calculate true negatives.

Example 1: Medical Test

Suppose a disease test was given to 1000 people:

• 500 people actually have the disease (positive cases)
• 500 people do not have the disease (negative cases)

The test results were:

• 450 people correctly identified as having the disease (TP)
• 50 people incorrectly identified as having the disease (FP)
• 400 people correctly identified as not having the disease (TN)
• 50 people incorrectly identified as not having the disease (FN)

In this case, the true negative count is 400.

Example 2: Spam Detection

For a spam detection system processing 10,000 emails:

• 2,000 emails are spam (positive cases)
• 8,000 emails are not spam (negative cases)

The system's performance was:

• 1,800 spam emails correctly identified (TP)
• 200 non-spam emails incorrectly marked as spam (FP)
• 7,800 non-spam emails correctly identified (TN)
• 200 spam emails incorrectly marked as non-spam (FN)

Here, the true negative count is 7,800.