Statistical Power
Hypothesis Testing
The Probability of Finding Real Effects
Statistical power is the probability of correctly rejecting a false null hypothesis — the chance of detecting a real effect when it exists. Low power means wasting resources on studies destined to fail.
- Clinical Trials — Ensuring studies are large enough to detect meaningful treatment effects
- Grant Applications — Justifying sample sizes with power analysis calculations
- A/B Testing — Avoiding underpowered tests that waste advertising budgets
Power analysis is the difference between good science and expensive guessing.
Factors Affecting Power
The Power Function
The power is a monotone increasing function of , , and , and a monotone decreasing function of .
A Priori Power Analysis
Cohen's Effect Size Conventions
| Effect Size () | Interpretation |
|---|---|
| 0.2 | Small |
| 0.5 | Medium |
| 0.8 | Large |