Type I and Type II Errors
Hypothesis Testing
The Two Ways to Get It Wrong
Every statistical test carries risk of false positives (Type I) or false negatives (Type II). Understanding this tradeoff is essential for designing studies and interpreting results responsibly.
- Medicine — Balancing the risk of approving ineffective drugs versus withholding effective ones
- Criminal Justice — The presumption of innocence mirrors the null hypothesis framework
- Manufacturing — Setting inspection criteria that balance reject/accept error rates
There is no free lunch: reducing one error type increases the other.
In hypothesis testing, two types of mistakes are possible. Understanding them is essential for designing studies, choosing sample sizes, and interpreting results.
The Decision Matrix
Formal Definitions
The Fundamental Tradeoff
Consequences in Practice
| Domain | Type I Error (False Positive) | Type II Error (False Negative) |
|---|---|---|
| Medicine | Approving an ineffective drug | Missing a life-saving treatment |
| Criminal justice | Convicting an innocent person | Letting a guilty person go free |
| Quality control | Rejecting a good batch | Shipping defective products |
| Spam filtering | Blocking legitimate email | Allowing spam to reach inbox |
| Security | False alarm | Missing a real intrusion |