How Is Sample Size Calculated?
Sample size is calculated before a study begins using a priori power analysis, and it rests on four inputs: the statistical test you will use, the expected effect size (from the literature or a pilot study), the significance level (usually α = 0.05), and the target power (usually 0.80, often 0.90 in health research). Once these four are set, the minimum number of participants is computed with tools like G*Power — this is exactly the “sample size justification” ethics committees ask for.
This guide explains the logic and the steps. Send us your study details and we'll run the calculation and deliver it with a justification paragraph you can paste straight into your ethics application.
Who is this guide for?
Researchers whose ethics application requires a sample size justification
Students preparing a thesis proposal who need to know how many participants are required
Authors told by reviewers that a power analysis is missing
Anyone who has already collected data and wonders if the sample was sufficient (post-hoc power)
The four steps of the calculation
- 01
Fix the test
The calculation depends on the analysis: formulas differ for t-tests, ANOVA, correlation, regression and chi-square. Decide the analysis first.
- 02
Choose the effect size
Take the effect size from similar published studies; if none exist, choose Cohen's small-medium-large benchmark appropriate to your field and justify it.
- 03
Set α and power
The common convention: α = 0.05, power = 0.80. Clinical studies and fields demanding strong evidence raise power to 0.90.
- 04
Compute and add attrition
Calculate with G*Power (free). For surveys and follow-up studies add a 10-20% attrition margin to set the recruitment target.
Cohen's effect size benchmarks
Widely accepted reference values when the literature offers none:
| Analysis | Measure | Small | Medium | Large |
|---|---|---|---|---|
| t-test (two groups) | Cohen's d | 0.20 | 0.50 | 0.80 |
| ANOVA | f | 0.10 | 0.25 | 0.40 |
| Correlation | r | 0.10 | 0.30 | 0.50 |
| Multiple regression | f² | 0.02 | 0.15 | 0.35 |
| Chi-square | w | 0.10 | 0.30 | 0.50 |
Example: required samples for common scenarios
Approximate values for α = 0.05, power = 0.80, two-tailed (computed with G*Power):
| Scenario | Effect size | Total n required |
|---|---|---|
| Independent t-test, medium effect | d = 0.50 | 128 (64 per group) |
| Independent t-test, large effect | d = 0.80 | 52 (26 per group) |
| One-way ANOVA, 3 groups, medium effect | f = 0.25 | 159 (53 per group) |
| Correlation, medium effect | r = 0.30 | 84 |
| Multiple regression, 5 predictors, medium effect | f² = 0.15 | 92 |
Why ethics committees reject: common mistakes
Unjustified numbers: “a similar study used 100, so we did too” — that isn't a power analysis, and most committees won't accept it
Calculating independently of the test: basing the number on survey length or a population table, then running a different analysis
Choosing an effect size without a source — “a medium effect was assumed” alone is insufficient; grounds are expected
Forgetting attrition: applying with the bare minimum and finishing the study underpowered
Presenting post-hoc power instead of an a priori calculation — committees want the pre-study computation
If the data is already collected: post-hoc power
After a study is complete, “was my sample sufficient?” is answered with post-hoc (observed) power analysis: the achieved power is computed from the actual sample, the observed effect size and α. Reviewers sometimes request this; its interpretation needs care — for a non-significant finding, low post-hoc power is used to distinguish “there is no effect” from “there wasn't enough power to see the effect.” Our reports state this distinction explicitly.
Frequently asked questions
Do you run sample size calculations for ethics applications?
Yes — it's one of our most requested services. Send your study design and planned analysis; we run the calculation and deliver it with a justification paragraph (test, effect size source, α, power, computed n and attrition margin) ready to paste into the application form.
I have no pilot study — where do I get an effect size?
First look at publications using similar scales or comparisons; effect sizes can be computed from their reported means and standard deviations. If nothing exists, Cohen's medium benchmark is used with a written justification — committees accept this approach.
Can I use G*Power myself?
Yes — it's free and widely used. The difficulty is usually not the software but selecting the right test family, tails and effect size type; a wrong choice yields a seriously different answer. If unsure, send us your inputs and we'll check the calculation.
Does the calculation change when the population is finite (e.g. nurses at one hospital)?
Yes. A finite population correction applies and reduces the required sample. For cross-sectional prevalence studies, proportion-estimation formulas (population, expected rate, margin of error) are used instead of power analysis — we determine which fits your design.
Is the study worthless if I can't reach the computed number?
No, but it must be reported as a limitation. There are also defensible options such as recalculating power under a larger assumed effect or simplifying the analysis plan — we'll frame the most honest version for your situation.
Leave the sample size calculation to us
Send your study design — we'll deliver the calculation plus a ready ethics-committee justification text.
Last updated: July 8, 2026