Calculate False Negative Rate From Sensitivity

What is False Negative Rate?

The false negative rate (FNR) is a statistical measure that represents the probability of a test incorrectly indicating that a condition is absent when it is actually present. It is calculated from the sensitivity (also known as true positive rate) of a diagnostic test.

False negatives occur when a test fails to detect a true condition, which can have serious consequences in medical testing, quality control, and other fields where accurate detection is critical.

How to Calculate False Negative Rate

To calculate the false negative rate from sensitivity, you need to understand the relationship between these two metrics. Sensitivity measures the proportion of actual positives that are correctly identified by the test, while the false negative rate measures the proportion of actual positives that are incorrectly identified as negatives.

The false negative rate is simply the complement of sensitivity. If a test has a sensitivity of 90%, it means 90% of true cases are correctly identified, and the false negative rate would be 10%.

Formula

Where:

• Sensitivity is the proportion of actual positives correctly identified by the test (expressed as a decimal between 0 and 1).

For example, if a test has a sensitivity of 0.9 (90%), the false negative rate would be 1 - 0.9 = 0.1 (10%).

Example Calculation

Let's say a diagnostic test for a particular disease has a sensitivity of 95%. This means that 95% of people who actually have the disease test positive, and 5% test negative (false negatives).

Using the formula:

So, the false negative rate for this test is 5%. This means that 5% of people with the disease will not be correctly identified by the test.