What is power in hypothesis testing?

• A. The probability of correctly rejecting a false null hypothesis.
• B. The probability of a Type I error.
• C. The probability of failing to reject a true null hypothesis.
• D. The probability of observing a sample mean equal to the population mean.

Answer: (A)

Power is the probability of correctly rejecting a false null hypothesis. In other words, when there really is an effect, power tells you how likely your test is to detect it as statistically significant. It’s equal to 1 minus beta, where beta is the chance of failing to detect that effect (a Type II error). Power grows when the true effect is larger, the sample size is bigger, data are less variable, or you use a more lenient significance level (higher alpha). This is why researchers plan studies to achieve adequate power so a real effect isn’t missed. The other ideas described by the options refer to a Type I error rate (alpha), failing to reject a true null (Type II error), or a specific sample outcome, none of which capture the test’s ability to detect an actual effect like power does.