How does statistical power influence sample size planning?

How does statistical power influence sample size planning?

• A. Higher power requires larger sample size to detect a given effect
• B. Power does not influence sample size
• C. Higher power requires smaller samples
• D. Power only affects p-values

Answer: (A)

Power is the probability of detecting a true effect if it exists. When planning a study, wanting higher power for a specific effect size means you need more data. Why? Increasing the sample size reduces the variability (standard error) of the estimated effect, which makes the test statistic larger for the same real effect. A larger test statistic makes it more likely to reject the null hypothesis at the chosen significance level, giving you higher power. If you accept lower power, you’d typically use a smaller sample, but you risk missing real effects (a higher chance of a false negative). Power also interacts with the significance level and data variability, so changing alpha or data spread can alter how many subjects you need to achieve the desired power. In short, to achieve greater power for detecting a given effect, you plan for a larger sample size.

Power is the probability of detecting a true effect if it exists. When planning a study, wanting higher power for a specific effect size means you need more data. Why? Increasing the sample size reduces the variability (standard error) of the estimated effect, which makes the test statistic larger for the same real effect. A larger test statistic makes it more likely to reject the null hypothesis at the chosen significance level, giving you higher power. If you accept lower power, you’d typically use a smaller sample, but you risk missing real effects (a higher chance of a false negative). Power also interacts with the significance level and data variability, so changing alpha or data spread can alter how many subjects you need to achieve the desired power. In short, to achieve greater power for detecting a given effect, you plan for a larger sample size.