Which statement correctly describes the relationship between power and sample size?

Which statement correctly describes the relationship between power and sample size?

• A. Power is unaffected by sample size.
• B. Power is the probability of making a Type II error.
• C. Power determines the magnitude of the treatment effect.
• D. Power generally increases with larger sample size.

Answer: (D)

Power is the probability of correctly rejecting the null hypothesis when there is a real effect. As sample size increases, the estimates become more precise because the standard error shrinks. This makes the test statistic more likely to exceed the critical value under the true effect, so the chance of detecting that effect rises. In other words, larger samples give you more reliable evidence and raise power, holding the true effect size and the chosen significance level constant. That’s why researchers often plan studies with enough participants to achieve adequate power. The other statements don’t fit: power is not the probability of a Type II error (that probability is beta, and power is 1 minus beta). Power also does not determine how large the treatment effect is—the actual effect size is a property of the data, while power reflects how likely you are to detect that effect given your sample size and variability.

Power is the probability of correctly rejecting the null hypothesis when there is a real effect. As sample size increases, the estimates become more precise because the standard error shrinks. This makes the test statistic more likely to exceed the critical value under the true effect, so the chance of detecting that effect rises. In other words, larger samples give you more reliable evidence and raise power, holding the true effect size and the chosen significance level constant. That’s why researchers often plan studies with enough participants to achieve adequate power.

The other statements don’t fit: power is not the probability of a Type II error (that probability is beta, and power is 1 minus beta). Power also does not determine how large the treatment effect is—the actual effect size is a property of the data, while power reflects how likely you are to detect that effect given your sample size and variability.