Type I Error (False Positive)
You reject a true null hypothesis — you conclude something is happening when it actually isn’t.
Example:
A medical test says a patient has a disease, but they actually don’t.
Type II Error (False Negative)
You fail to reject a false null hypothesis — you miss a real effect.
Example:
A medical test says a patient does not have a disease, but they actually do.
🧪 Medical Example (Classic)
Let the null hypothesis be:
H₀: The patient does NOT have the disease.
| Outcome | What it means | Error type |
|---|---|---|
| Test says “disease present” but patient is healthy | False alarm | Type I |
| Test says “no disease” but patient is sick | Missed detection | Type II |
This exact framing appears in the Wikipedia example.
🔢 Probabilities: α and β
α (alpha) = probability of a Type I error
This is the significance level you choose (often 0.05).
β (beta) = probability of a Type II error
🧠 Intuition
Think of a courtroom:
Type I error: Convicting an innocent person
Type II error: Letting a guilty person go free
You can tighten the rules to avoid one type of error, but that usually increases the other.
⚖️ Trade‑off
Reducing Type I errors (making α smaller) makes it harder to detect real effects → increases Type II errors.
Increasing power (reducing β) makes it easier to detect real effects → increases risk of Type I errors.
This tension is why study design and sample size matter.