What occurs when a false null hypothesis is not rejected?

A Type II error occurs when a false null hypothesis is not rejected, meaning that the test fails to identify a true effect or difference when one actually exists. In hypothesis testing, the null hypothesis typically posits that there is no effect or relationship. When researchers fail to reject this null hypothesis despite there being evidence that it is false, they miss the opportunity to detect the true condition, leading to a Type II error.

This situation can arise from various factors, including insufficient sample size, inadequate experimental design, or low statistical power. Power is the probability that a test will correctly reject a false null hypothesis, so when power is low, the risk of committing a Type II error increases. Thus, recognizing and understanding Type II errors is crucial for researchers aiming to accurately interpret their findings and ensure that they are sensitive enough to detect real effects in their studies.