Direct comparison
Type I vs Type II Error: Definitions, Examples & How to Reduce | CASRAI
Type I error is a false positive — rejecting a true null hypothesis. Type II error is a false negative — failing to reject a false null hypothesis. Both relate to statistical power and significance level.
Side-by-side comparison
| Dimension | Type I error | Type II error |
|---|---|---|
| Definition | Rejecting a true null hypothesis — a false positive. | Failing to reject a false null hypothesis — a false negative. |
| Symbol | α (alpha) — the significance level. | β (beta) — related to statistical power (1 − β). |
| Decision error | Concluding an effect exists when it does not. | Concluding no effect exists when one does. |
| Controlled by | Setting a lower significance threshold (e.g. α = 0.01). | Increasing sample size and statistical power. |
| Clinical example | A test says a patient has a disease; they do not. | A test says a patient is healthy; they have the disease. |
| Research example | Concluding a drug works when it has no real effect. | Concluding a drug has no effect when it genuinely does. |
| Trade-off | Reducing α raises the bar to reject the null. | This makes it harder to detect real effects, increasing β. |
| Multiple testing | Inflated by running many tests (Bonferroni correction applies). | Bonferroni correction can increase Type II errors. |
Common questions
FAQ
Which error type is worse?+
It depends on context. In clinical drug approval, a Type I error (approving an ineffective drug) wastes resources and may expose patients to side effects, while a Type II error (missing an effective treatment) denies patients a benefit. In screening for a serious disease, a Type II error (missing a case) may be more dangerous. Researchers must weigh the costs of each in their specific domain.
How does statistical power relate to Type II error?+
Power is 1 − β: the probability of correctly detecting a true effect. A study with 80% power has a 20% Type II error rate (β = 0.20). Power increases with larger sample sizes, larger true effect sizes, and higher significance thresholds. A power analysis before data collection ensures the study is adequately sized to detect a meaningful effect.
What is the Bonferroni correction and when is it needed?+
When a researcher runs multiple statistical tests simultaneously, each at α = 0.05, the probability of making at least one Type I error by chance rises above 5%. The Bonferroni correction divides α by the number of tests (e.g. 0.05/20 = 0.0025), keeping the family-wise error rate controlled. The trade-off is reduced power — a higher risk of Type II errors.
Going deeper
