What Is Power Analysis?
Statistical power analysis is the process of determining the sample size needed for a study to reliably detect an effect of a given size. Power (1 - β) is the probability that a test will correctly reject the null hypothesis when the alternative hypothesis is true. A study with inadequate power may fail to detect a real effect, wasting resources and potentially leading to incorrect conclusions.
Power analysis should ideally be performed during the study planning phase (a priori) to ensure adequate sample sizes. The four key components are: effect size, significance level (α), power (1 - β), and sample size. Given any three, the fourth can be calculated.
Sample Size Formula
For a two-sample t-test (two-tailed):
Where zα/2 is the critical z-value for the significance level, zβ is the z-value corresponding to the desired power, and d is Cohen's effect size.
Cohen's d Effect Size Guidelines
| Effect Size | Cohen's d | Typical n (per group, power=0.80) |
|---|---|---|
| Small | 0.2 | 393 |
| Medium | 0.5 | 64 |
| Large | 0.8 | 26 |
| Very Large | 1.2 | 12 |
Frequently Asked Questions
What power level should I use?
The standard convention is 0.80 (80%), meaning there is an 80% chance of detecting a true effect. For critical studies (e.g., clinical trials), 0.90 or even 0.95 may be appropriate. Higher power requires larger sample sizes but reduces the risk of Type II errors.
What if I don't know the effect size?
You can estimate effect size from pilot studies, prior research, or use Cohen's conventions (small=0.2, medium=0.5, large=0.8). If no prior information exists, a medium effect size (0.5) is a reasonable starting point. Conducting a sensitivity analysis across a range of effect sizes is also recommended.