False Negative

A test result that says something is not there when it is — a true case the test misses.

Visual intuition

3 in 100

before new evidence

A false negative is one of the 3 the test lets slip

The 3 highlighted people truly have the condition. Each one the test wrongly clears is a false negative — the miss rate is 1 minus sensitivity, so a 99%-sensitive test misses about 1 true case in 100.

Formula

false-negative rate = 1 - sensitivity

Example

If 10 of 10,000 screened people truly have a condition and the test is 99% sensitive, it usually catches all 10 — but at 80% , about 2 of the 10 walk away wrongly reassured.

How It Works

A false negative is the miss: the person has the condition, the test says they do not. Misses come only from the group that truly has the condition, at a rate of 1 minus — a 99%-sensitive test misses 1 true case in 100. False negatives and false positives trade off: lower the alarm threshold to miss fewer cases and you flag more healthy people; raise it and the reverse. Which error costs more depends on the stakes — missing a cancer is not priced like a false fire alarm. In hypothesis testing the same miss — failing to detect a real effect — is a type II error, the concern behind statistical power.