Which error refers to the failure to reject the null hypothesis when there is a difference?

The error that refers to the failure to reject the null hypothesis when there is indeed a significant difference present in the population is known as a Type II Error. This occurs when a researcher concludes that there is no effect or difference when, in truth, there is one, thus missing an opportunity to detect an important result.

In hypothesis testing, the null hypothesis is typically that there is no effect or no difference. If the null hypothesis is false but is not rejected, a Type II Error has occurred. This often relates to issues around the power of a test—the probability of correctly rejecting a false null hypothesis. Factors such as a small sample size, low effect size, or insufficient statistical power can contribute to an increased chance of committing this type of error.

Understanding Type II Error is crucial in research because it has important implications for decision making. It can lead to a failure to implement changes or interventions that could have been beneficial, as researchers mistakenly conclude that their findings do not support action when they do.

The other terms presented in the choices refer to different aspects of hypothesis testing or data interpretation: Type I Error pertains to rejecting a true null hypothesis (a “false positive”), false positives are synonymous with Type I Error, and sampling error relates to variability in sample statistics