A null hypothesis being not rejected, but later found to be false, is an example of what type of error?

A null hypothesis being not rejected, yet later determined to be false, represents a type II error. This type of error occurs when a statistical test fails to identify a difference or effect that actually exists. In the context of hypothesis testing, the null hypothesis typically posits no effect or relationship within the data. When this hypothesis is not rejected, it suggests that the evidence is insufficient to support an alternative hypothesis, even if the alternative is true.

In essence, a type II error reflects a missed opportunity to detect an effect when one is present. For example, if a new treatment is genuinely effective in reducing a disease but research fails to reject the null hypothesis due to limitations in sample size or variability, researchers conclude that there is no significant benefit from the treatment, potentially delaying its acceptance and use in clinical practice. This kind of misunderstanding can have meaningful implications in healthcare decisions, making it a critical aspect of statistical analysis.

Other types of errors, while important in their own right, do not pertain to this scenario. A type I error, for instance, involves rejecting a true null hypothesis, leading to a false positive conclusion. Types III and IV errors are less commonly referenced in standard statistical literature but generally involve issues related to misdirection or incorrect interpretation of