A null hypothesis was not rejected, and later it was found that the results were false. This is an example of what type of error?

The situation described involves the failure to reject the null hypothesis when, in fact, the alternative hypothesis is true. This scenario exemplifies a type II error, also known as a "false negative." In essence, a type II error occurs when a test fails to detect an effect or difference that is actually present.

In hypothesis testing, the null hypothesis typically posits that there is no effect or difference, while the alternative hypothesis suggests that there is. When researchers do not reject the null hypothesis and conclude there is no significant effect or difference, yet later discover that the effect does exist, they have committed a type II error.

This understanding is crucial in statistics because it highlights the importance of power in hypothesis testing—the ability of a test to correctly reject a false null hypothesis. A higher power reduces the likelihood of committing a type II error. Recognizing this concept allows researchers and practitioners to design studies with adequate sample sizes and effect sizes to minimize the risk of missing real differences or effects.