Type I and Type II errors
A Type I error is rejecting a true null (a false alarm). Its probability is alpha. A Type II error is failing to reject a false null (a missed effect). Its probability is beta.
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Analogy
A smoke alarm that rings with no fire is Type I. One that stays silent during a fire is Type II.
Example
H0: patient is healthyTest says ill, patient healthy:Type I errorTest says healthy, patient ill:Type II error
In practice
Medical screening has to balance false alarms against missed cases.
Practice
Flashcards
- What is a Type I error?Rejecting a true null hypothesis. Its chance is alpha.
Interview questions
- Explain Type I and Type II errors using a medical screening example, and say how sample size affects them.
- Type I is a false alarm
- Type II is a missed case
- Alpha is the Type I rate
- More data raises power
- Lowering alpha raises beta
Questions people ask
Can I reduce both types of error at the same time?
Not by changing alpha alone, since lowering alpha makes Type II errors more likely. The way to cut both is more data, which sharpens the test, or a better measurement. This is why sample size planning matters before the study starts.
Which error is worse, Type I or Type II?
It depends on the cost. Convicting an innocent person is a Type I error and is treated as worse. Missing a cancer in screening is a Type II error and can be worse. Choose alpha with the consequences in mind.