Which statement best describes how statistical power changes with sample size and effect size?

Which statement best describes how statistical power changes with sample size and effect size?

• A. Increasing sample size has no effect on power.
• B. Power depends only on the effect size, not on sample size.
• C. Increasing sample size or increasing the true effect size increases power.
• D. Power is maximized when effect size is zero.

Answer: (C)

Power is the probability that a statistical test will detect a true effect when it exists. It grows when the true effect size is larger and when you have more data. Why this happens: a bigger sample reduces sampling variability, so the observed difference is less likely to be swamped by random noise and more likely to cross the significance threshold. A larger true effect makes the difference you’re trying to detect bigger relative to the noise, also making it easier to declare significance. So the statement that increasing either the sample size or the true effect size increases power is the best description. The other views don’t fit. Increasing sample size does affect power, so saying it has no effect is incorrect. Power depends on both effect size and sample size, not on effect size alone. And power is not maximized when the true effect is zero; with no real effect, there’s nothing to detect and the chance of a false positive is just the chosen alpha, not a high power.

Power is the probability that a statistical test will detect a true effect when it exists. It grows when the true effect size is larger and when you have more data. Why this happens: a bigger sample reduces sampling variability, so the observed difference is less likely to be swamped by random noise and more likely to cross the significance threshold. A larger true effect makes the difference you’re trying to detect bigger relative to the noise, also making it easier to declare significance. So the statement that increasing either the sample size or the true effect size increases power is the best description.

The other views don’t fit. Increasing sample size does affect power, so saying it has no effect is incorrect. Power depends on both effect size and sample size, not on effect size alone. And power is not maximized when the true effect is zero; with no real effect, there’s nothing to detect and the chance of a false positive is just the chosen alpha, not a high power.