The Null Hypothesis and Error Types
Statistical hypothesis testing error types include Type I and Type II. These error types have been used beyond hypothesis testing in areas such as etymology, inventory control, computer security, spam filtering, optical character recognition, bio-metrics, medical screening, and paranormal investigation.
A statistical test can either reject or fail to reject a null hypothesis. i.e., it can prove the hypothesis to be false or not prove it to be false–it can’t prove it to be true.
Null Hypothesis: a general statement or default position that states there is no relationship between two measured phenomena. Generally assumed to be true until evidence indicates otherwise.
The two types of errors are:
Type I: Incorrect rejection of a true null hypothesis
Type 2: Failure to reject a false null hypothesis
Below are some informal interpretations that might help clarify the two types of errors, but it is important to remember that, by convention, a null hypothesis usually asserts there is no relationship. This tends to confuse things because, while a Type 1 error means we have incorrectly rejected a true hypothesis, this shakes out to mean we have assigned a relationship that does not exist.
- Type 1 Error
- Error of the first kind
- α (alpha)
- H0 (H-nought) is true but is rejected
- Asserting something is true that is false
- Convicting an innocent person
- A false hit
- Crying wolf
What it really means: if you have made a Type I error, you have said there is a relationship between two measured phenomena when there isn’t.
- Type 2 Error
- Error of the second kind
- β (beta)
- H0 (H-nought) is false but is accepted
- Saying there is no relationship between two measured phenomena when there is
- Asserting something is false that is true
- Letting a guilty person go
- A missed hit
- Missing the wolf
What it really means: if you have made a Type II error, you have said there is no relationship between two measured phenomena when there is.
I hope this helps you the next time you are running a statistical analysis and can’t remember which error type is which.
See you next time…