How many participants do you need? Power analysis in G*Power
How to calculate sample size before collecting data, what you need to decide up front, and example numbers for the common analyses.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
"How many participants do I need?" is one of the first questions supervisors ask. The professional answer is called a power analysis, and it's done before collecting data.
Four things to decide up front
- The statistical test you'll run (t-test, ANOVA, correlation, regression).
- The significance level (α): almost always .05.
- Power: the chance of finding an effect if it really exists. The convention is .80.
- The expected effect size: the hardest to set, and the most influential.
How to set the effect size
The best option is to rely on similar previous studies. If there are none, use Cohen's conventions:
| Measure | Small | Medium | Large |
|---|---|---|---|
| d (difference between two groups) | 0.20 | 0.50 | 0.80 |
| f (ANOVA) | 0.10 | 0.25 | 0.40 |
| r (correlation) | .10 | .30 | .50 |
| f² (regression) | 0.02 | 0.15 | 0.35 |
The smaller the expected effect, the larger the sample you need.
Example numbers (α = .05, power = .80, two-tailed)
| Analysis | Effect size | Required sample |
|---|---|---|
| t-test, two groups | d = 0.50 | 64 per group (128 in total) |
| Pearson correlation | r = .30 | 84 |
| One-way ANOVA, 3 groups | f = 0.25 | 159 in total |
| Multiple regression, 3 predictors | f² = 0.15 | 77 |
How to do it in G*Power
G*Power is free software. Choose:
- Test family: for example t tests or F tests.
- Statistical test: the exact test.
- Type of power analysis: A priori.
Then enter the effect size, α and power, and click Calculate. The result is the Total sample size.
How to report it in the method chapter
Sample size was determined with a power analysis in GPower 3.1. To detect a medium effect (f*² = 0.15) in a multiple regression with three predictors, with power of .80 and a significance level of .05, 77 participants were required.
And if you can't reach that number?
It happens, especially with hard-to-reach populations. State it honestly as a limitation, report effect sizes and confidence intervals, not only significance, and treat non-significant results with caution: the sample may simply have been too small to detect the effect.
Next steps
The effect size for a power analysis comes from previous studies - how to read and report it: effect sizes. The number goes into the participants section, and the test you calculated for must match the test you chose. Note that SEM and latent-variable models usually need much larger samples.
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