In statistics, which statement best defines the power of a study?

• A. The probability of incorrectly rejecting a true null hypothesis (Type I error)
• B. The probability of correctly rejecting a false null hypothesis (1 - beta)
• C. The p-value of the study
• D. The confidence interval width

Answer: (B)

Power of a study is the probability that the statistical test will detect a true effect, meaning it will correctly reject a false null hypothesis. This is equal to 1 minus beta, where beta is the probability of a Type II error (failing to reject a false null). Power increases with larger effect size, larger sample size, less variability, and a reasonable significance level.

The other statements describe different concepts: the chance of rejecting a true null hypothesis is the Type I error rate (alpha); the p-value is the probability of obtaining data as or more extreme than observed under the null; and confidence interval width reflects precision, not the ability to detect an effect. Thus, the best definition is the probability of correctly rejecting a false null hypothesis, i.e., 1 minus beta.