What does the power of a statistical test refer to?

The power of a statistical test refers to the probability of correctly rejecting the null hypothesis when it is false, which means declaring an effect or detecting a true positive result when it actually exists. This concept is critical in hypothesis testing because a high power indicates that the test is more likely to identify an effect if it is present.

Factors that influence the power of a statistical test include the sample size, the effect size, and the significance level (alpha). As the sample size increases or the effect size becomes more pronounced, the power of the test typically increases, enhancing its ability to detect real differences or effects.

By understanding that the power represents the likelihood of detecting an effect when there is one, analysts can better design their experiments and interpret their results. This knowledge is essential in fields where it is crucial to identify genuine effects or relationships, such as in forensic analysis or biomedical research.