- Recognize Type I and Type II errors and their consequences.
Errors
Errors sometimes arise in hypothesis testing. This is because we are reaching a conclusion about the entire population based on a sample. We cannot eliminate hypothesis testing errors entirely.
Sometimes, due to chance, the result of the hypothesis test does not align with reality.
errors in hypothesis testing
If we reject a correct null hypothesis, we are committing a type I error. If we do not reject a null hypothesis that is actually incorrect, we are committing a type II error.
| Reject the null hypothesis | Do not reject the null hypothesis | |
| Null hypothesis is correct | Type I error | No error |
| Null hypothesis is incorrect | No error | Type II error |
- [latex]α[/latex] = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
[latex]α[/latex] is also known as the significance level of the hypothesis test. - [latex]β[/latex] = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.
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