Explain a type II error in hypothesis testing.

A type II error, also known as a "false negative," occurs in hypothesis testing when a researcher fails to reject a null hypothesis that is actually false. This means that even though there is evidence to suggest that the alternative hypothesis is true, the statistical test concludes that it is not. As a result, the researcher incorrectly accepts that there is no effect or difference when, in fact, one exists.

In practical terms, this could mean missing an important discovery in a healthcare context. For example, if a new treatment for a disease is truly effective but the test fails to demonstrate this, the result could lead to the continued use of an ineffective treatment, potentially affecting patient outcomes.

Understanding type II errors is crucial in research design, as it underscores the importance of having sufficient statistical power to detect an effect when it exists, thereby reducing the likelihood of making such an error.