Statistical Power and Sample Size
Statistical power measures a test's ability to detect a true effect, preventing costly false negatives.
Defining Statistical Power
Statistical power is the probability of correctly rejecting a false null hypothesis. It represents a test's ability to detect a real effect when one actually exists in the population. High power reduces the risk of committing a Type II error, which occurs when a false null hypothesis fails to be rejected.
1 - \beta = P(\text{Reject } H_0 \mid H_0 \text{ is false})Drivers of Power
Power depends primarily on three factors: sample size, effect size, and the significance level. Larger sample sizes reduce standard error, making subtle effects easier to detect and boosting power. Similarly, larger effect sizes or higher significance thresholds naturally increase the likelihood of detecting a true effect.
\text{SE} = \frac{\sigma}{\sqrt{n}}Determining Sample Size
Before collecting data, researchers perform a power calculation to determine the minimum sample size required for their study. By setting target levels for power and significance, they can solve for required sample size based on an estimated effect size. This prevents studies from being underpowered or unnecessarily expensive.
n \approx \left( \frac{z_{\alpha/2} + z_{\beta}}{\text{Effect Size}} \right)^2Flashcard
The statistical power of a hypothesis test.
Check your understanding
A medical researcher wants to increase the statistical power of a clinical trial without changing the significance level or the underlying effect size. Which adjustment should the researcher make?