Which type of error occurs when a decision is made to retain a null hypothesis that should have been rejected?

A Type II error occurs when a decision is made to retain a null hypothesis that should have been rejected, meaning that the test fails to identify a difference or effect that actually exists. In hypothesis testing, the null hypothesis typically posits no effect or no difference, and when the true state of affairs is that an effect does exist, but the test concludes otherwise, this is classified as a Type II error.

Understanding the implications of Type II errors in research is crucial, as they can lead to missed opportunities for recognizing significant results or effects that could be important for further investigation or application. This contrasts with other types of errors, such as Type I, which involves incorrectly rejecting a true null hypothesis, leading to false positives. The other terms like cluster error or sampling error pertain to different aspects of study design or data collection rather than hypothesis testing specifically.