What is statistical power and what factors influence it?

• A. Power is the probability of a Type I error
• B. Power is determined solely by the alpha level
• C. Power is the probability of detecting a true effect; influenced by effect size, sample size, alpha, and data variability
• D. Power increases when effect size decreases

Answer: (C)

Statistical power is the probability that a study will detect a true effect, meaning we correctly reject the null hypothesis when there is a real difference or association. It is equal to 1 minus the probability of a Type II error (failing to detect a real effect).

Power depends on several factors. A larger true effect size makes the signal easier to notice, so power increases. A bigger sample size reduces sampling error and gives a clearer signal, boosting power. The alpha level sets how leniently we judge results as significant; increasing alpha raises power but also raises the risk of a false positive. More variability in the data (noise) makes it harder to distinguish the real effect, decreasing power. In planning studies, power analyses help determine the required sample size to achieve a desired power (commonly around 0.80) given the expected effect size, alpha, and variability. If you test a one-tailed hypothesis instead of two-tailed, you can gain some extra power under the expected direction, because the rejection region is all in one tail.