 Type I and type II errors

For a null hypothesis $H_0$, a type I error rejects $H_0$ when it is true, while a type II error does not reject $H_0$ when the alternative is true. If a test does not reject $H_0$ on an event $A$, their conditional probabilities are $\alpha =P_0(A^c)$ and $\beta =P_1(A)$. Nonrejection does not establish the truth of the null hypothesis.

Type I and Type II errors are concepts in statistics that describe the potential errors that can occur when testing a hypothesis. 1. **Type I Error (False Positive)**: This occurs when a null hypothesis (H0) is rejected when it is actually true. In simpler terms, it means that the test indicates a significant effect or difference when there actually is none.