What is an example of a statistical type II error?

A statistical type II error occurs when the null hypothesis is false, but the test fails to reject it, leading to the incorrect conclusion that there is no effect or difference when one actually exists. This type of error is particularly significant because it implies that a researcher may miss identifying a real effect or relationship in the data, which could have implications for further research or practical applications.

In the context of hypothesis testing, the null hypothesis typically represents a position of no effect or no difference. Resolving whether to accept or reject this hypothesis based on sample data is essential for drawing valid conclusions. When a type II error occurs, it means the test's sensitivity was not strong enough to detect an effect, thus resulting in the incorrect acceptance of the null hypothesis.

Understanding type II error is crucial in fields where detecting true positive effects is necessary, as it underscores the importance of sample size, effect size, and power in study design. A well-designed study seeks to minimize the risk of type II errors by ensuring adequate statistical power, allowing researchers to better identify true effects when they exist.