Definition: A Type I error happens when a test rejects a true null hypothesis; its probability equals the significance level alpha chosen before the test.
What are the two errors?
A test can go wrong in two ways. A Type I error rejects H0 when it is actually true, a false alarm. A Type II error fails to reject H0 when it is actually false, a missed detection.
How are they linked?
The chance of a Type I error is alpha, the significance level. The chance of a Type II error is beta, and 1 – beta is the power. Lowering alpha makes Type I errors rarer but raises beta. A larger sample reduces both.
Worked example: a medical screening test is set at alpha = 0.01. If the patient is healthy (H0 true), there is a 1% chance of a false positive. Out of 2,000 healthy people tested, you would expect about 20 false alarms.
What do students confuse?
Mixing up which error is which. Mathbot’s tip: Type I is the “I” in “incorrectly rejecting.” Also, always describe each error in the context of the problem, not just by number.
Where to learn it
- Inference for Proportions: Intervals and Tests – lesson
- Inference for Means with t Procedures – lesson