Free tool
Sample size calculator
How many participants to recruit, and the paragraph that justifies it to your ethics committee, IRB or supervisor.
Sample size calculator, with the paragraph for your ethics application
Get the number to recruit and a justification paragraph that names the four numbers a committee checks: the test, the effect size and its source, alpha and power, plus drop-out.
Effect size you want to detect (Cohen's d)
What the paragraph needs, and why
A sample size justification is judged on four numbers: the test it was calculated for, the effect size and where it comes from, alpha and power. Leave one out, or give an effect size with no source, and the application comes back with a question.
The calculator writes all four into the paragraph and tells you when one is weak. Once you have run the study, report the analysis with the matching guide, for example how to report a power analysis in APA or how to calculate sample size for a survey.
Methods: exact noncentral t, F and chi-square (as G*Power 3.1), Fisher’s z for correlation, Fleiss for two proportions, Cochran (1977) for surveys. Results are rounded up to whole participants.
Questions
What effect size should I use?
The one a comparable study found: a meta-analysis first, then a similar published study, then your own pilot. Cohen’s small, medium and large are a last resort, and committees often ask why you chose one. Overestimating the effect is the most common fault: in one study of 50 trials, 80% planned for a larger effect than they found.
What do ethics committees and IRBs check in a sample size justification?
Four numbers and where they come from: the effect size and its source, alpha, power, and the test the sample size was calculated for. Most also expect an allowance for drop-out or non-response.
How is drop-out added?
By dividing, not by adding a percentage. To keep 128 participants with 10% drop-out you recruit 128 / 0.9 = 143, not 128 × 1.1 = 141.
Does this give the same numbers as G*Power?
Yes for t-tests, ANOVA, regression and chi-square, which use the same exact methods; we check them against G*Power’s published values. Correlation uses Fisher’s z, which gives about one more participant than G*Power’s exact method.
How big should a survey sample be?
For a ±5% margin of error at 95% confidence you need 385 responses when the percentage is unknown (50%). With a small population, the finite population correction lowers that: 278 for a population of 1,000.