Type I and type II errors
Type I: rejecting a true H₀ (false alarm). Type II: keeping a false H₀.
Worked example
H₀: the drug has no effect. What is a type II error here?
Worked solution
- 1.Type I error (α): rejecting H₀ although it is true.
- 2.Type II error (β): not rejecting H₀ although it is false.
Typical mistake: Swapping the two error types; memory aid: type I = false alarm.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task 1 of 3Hypothesis test
Task
H₀: the defendant is innocent. What is a type II error here?
Type II error
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- 1. State H₀ and H₁, choose α
- 2. Test statistic: z = (x̄ − μ₀) / (σ / √n) or t = (x̄ − μ₀) / (s / √n)
- 3. Compare with the critical value (two-sided |z|, one-sided only in the direction of H₁)
- 4. Decide: reject or do not reject H₀
Typical mistake: Swapping the two error types; memory aid: type I = false alarm.
Frequently asked questions
What is the typical mistake in "Type I and type II errors"?
Swapping the two error types; memory aid: type I = false alarm.
What is a type I error?
Rejecting H₀ although it is true; its probability is at most α.