Written by Dackohn; last reviewed November 2026.
Statistical power is the probability that a study detects an effect that really exists. With 80% power, a true effect of the assumed size is found four times out of five. Power rises with sample size, effect size and the significance level. To detect a medium effect (d = 0.5) with 80% power, you need 64 people per group.
Power and the two kinds of error
A test can go wrong in two ways. A Type I error is a false alarm, with a probability of α, usually 5%. A Type II error is a miss: a real effect goes undetected, with a probability called β. Power is 1 − β. If power is 80%, then β is 20%. See Type I and Type II errors for more on the pair.
The four things that control power
- Sample size. More data means less noise. This is the factor you control most directly.
- Effect size. Larger effects are easier to detect. Halving the effect roughly quadruples the sample you need.
- Significance level. A stricter α (.01 rather than .05) lowers power.
- Variability. Less noise in the measurement raises power. Paired designs often gain power this way.
How many participants do you need?
For two independent groups, at α = .05 two-sided:
| Effect size (Cohen’s d) | Per group for 80% power | Total |
|---|---|---|
| 0.2 (small) | 394 | 788 |
| 0.3 | 176 | 352 |
| 0.5 (medium) | 64 | 128 |
| 0.8 (large) | 26 | 52 |
Moving from 80% to 90% power at d = 0.5 raises the requirement from 64 to 86 per group.
Worked example: an underpowered study
A researcher compares two teaching methods with 30 students in each group and expects a medium effect (d = 0.5). The power is only 48%, so even if the effect is real the study is more likely to miss it than find it. A non-significant result here says very little. With 64 per group, the same study would have 80% power.
Why low power is worse than it looks
Underpowered studies miss real effects, and the effects they do detect tend to be overestimates, because only unusually large sample estimates reach significance. This is one reason published effects often shrink when studies are repeated.
Common mistakes
- Calculating power after the study from the observed effect. This only restates the p-value. Report a confidence interval instead.
- Treating a non-significant result as proof of no effect when power was low.
- Using an optimistic effect size from a small pilot, which leads to an underpowered study. Plan around the smallest effect that would matter.
Try it yourself
Statistical Power Calculator →Find the sample size you need or the power your study has. Effect Size Visualizer →See what d = 0.2, 0.5 and 0.8 look like.Frequently asked questions
What is a good statistical power?
80% is the usual minimum. Use 90% or more when missing a real effect would be costly.
How do you increase statistical power?
Collect more data, reduce measurement noise, use a paired design where possible, or study a larger effect. Raising alpha also increases power but adds false positives.
What is the difference between power and significance?
Significance (alpha) is the false-positive rate when there is no effect. Power is the chance of detecting an effect that does exist.
Related reading: Effect size explained · Type I and Type II errors · How to calculate sample size
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.