What does it mean if a statistical test has a high power?

A statistical test having high power means that there is a high probability of correctly rejecting a false null hypothesis. In hypothesis testing, the null hypothesis is a statement that there is no effect or no difference, and the power of a test is the likelihood that the test will detect an effect when there is one, thereby allowing researchers to make accurate conclusions based on their data.

High power is critical in practical applications because it indicates the test's effectiveness in identifying true positives. A powerful test minimizes the chance of missing a true effect, which is essential for drawing valid conclusions in research. Consequently, a high-powered statistical test provides more confidence in the results being reported, especially when testing hypotheses relevant to healthcare, where the implications of research findings can significantly impact patient care and treatment strategies.

Understanding the concept of power is vital for researchers when designing studies, as it directly influences sample size requirements and the overall reliability of test results. Conducting power analyses helps ensure that studies are adequately equipped to detect meaningful differences or relationships if they exist.