What is statistical power?

• A. The probability of correctly rejecting a false null hypothesis (1 - Type II error)
• B. The probability of failing to reject a false null hypothesis
• C. The probability of making a Type I error
• D. The probability of observing a large p-value

Answer: (A)

Statistical power is the probability that a study will detect an effect when there actually is one. It equals 1 minus the probability of a Type II error, which is failing to reject a false null hypothesis. In practical terms, if there is a real effect, power tells you how often your test will yield a statistically significant result. Power increases with a larger true effect, a larger sample size, and lower variability in the data, and it can also rise with a higher alpha level (though that also raises the chance of a false positive). A typical target is about 0.8, meaning about 80% of real effects would be detected.

The other ideas describe different concepts: the probability of failing to reject a false null is the Type II error itself, not power; the probability of making a Type I error is alpha (the false positive rate); and the probability of observing a large p-value is not what power measures—power is about correctly detecting real effects, which tends to align with smaller p-values when a real effect exists.