Which statement about power is true?

Which statement about power is true?

• A. It is the probability of rejecting the null hypothesis when the null is true
• B. It is the probability of failing to detect an effect when there is an effect
• C. It is the probability of rejecting the null hypothesis when the alternative is true
• D. It is unaffected by sample size

Answer: (C)

Power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. This means that, if there is a real effect, higher power increases the chance you’ll detect it. Why this is the best answer: power directly quantifies the test’s ability to identify a real effect, given the true state of the world, and it depends on factors like effect size, sample size, variability, and the chosen significance level. Larger samples and larger true effects generally raise power, while a more stringent significance level or more variable data can lower it. Why the other statements aren’t correct: rejecting the null when the null is true is the Type I error rate, not power. Failing to detect an effect when there is one describes a Type II error, and power is 1 minus that probability. Finally, power does depend on sample size; increasing sample size usually increases power.

Power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. This means that, if there is a real effect, higher power increases the chance you’ll detect it.

Why this is the best answer: power directly quantifies the test’s ability to identify a real effect, given the true state of the world, and it depends on factors like effect size, sample size, variability, and the chosen significance level. Larger samples and larger true effects generally raise power, while a more stringent significance level or more variable data can lower it.

Why the other statements aren’t correct: rejecting the null when the null is true is the Type I error rate, not power. Failing to detect an effect when there is one describes a Type II error, and power is 1 minus that probability. Finally, power does depend on sample size; increasing sample size usually increases power.