Even a 99% accurate test can be wrong most of the time. Understanding this could save lives and reduce unnecessary anxiety.
Imagine a disease affects 1 in 1000 people. You take a test that's 99% accurate. It comes back positive. What's the chance you actually have the disease? Most people guess 99%. The real answer? Only about 9%!
| Actually Sick | Actually Healthy | |
|---|---|---|
| Test + | 10 | 99 |
| Test - | 0 | 9,891 |
The key insight is that when a disease is rare, there are far more healthy people being tested than sick people.
Even if the test is wrong only 1% of the time, 1% of a huge number (healthy people) can be larger than 99% of a tiny number (sick people).
In our example: 1% of 9,990 healthy people = ~100 false positives. But 99% of only 10 sick people = ~10 true positives.
So among positive results, false positives outnumber true positives about 10 to 1!
Medical Screening: This is why doctors often recommend confirmatory tests. A single positive result, especially for a rare condition, may not be as meaningful as it seems.
COVID-19 Testing: The false positive rate became important when testing asymptomatic populations during the pandemic.
Drug Testing: Workplace drug tests with 95% accuracy can produce many false positives in drug-free workforces.
Security Screening: Rare threat detection (terrorism, fraud) faces the same math - most alerts are false alarms.
The lesson: Base rates matter enormously. Always ask "How common is this condition?" before interpreting a positive result.