How does increasing sample size affect statistical power?

How does increasing sample size affect statistical power?

• A. Increasing sample size generally increases power
• B. Increasing sample size decreases power
• C. Power is unaffected by sample size
• D. Power is maximized at very small samples

Answer: (A)

Power is the probability of detecting a true effect if it exists. When you increase the sample size, the standard error shrinks, making the estimated effect more precise. This makes the test statistic under the true effect more likely to exceed the threshold needed to reject the null, so the chance of detecting the effect (power) rises. This relationship holds for a given effect size and alpha level; larger samples give you more information and reduce random variability, especially important for small effects. While power grows with sample size, the gains can level off at very large N, but the general direction is clear: bigger samples generally increase power.

Power is the probability of detecting a true effect if it exists. When you increase the sample size, the standard error shrinks, making the estimated effect more precise. This makes the test statistic under the true effect more likely to exceed the threshold needed to reject the null, so the chance of detecting the effect (power) rises. This relationship holds for a given effect size and alpha level; larger samples give you more information and reduce random variability, especially important for small effects. While power grows with sample size, the gains can level off at very large N, but the general direction is clear: bigger samples generally increase power.