Quick answer: Sample size is decided by a power analysis, not by lab convention: with the expected effect size, α (usually 0.05) and desired power (usually 0.8), the analysis returns the minimum n — the number of biological units, not subsamples. Underpowered studies chase noise; overpowered ones spend animals and budget to confirm trivia. This guide shows the calculation, the inputs, and the honest workarounds when n can’t be reached. Replication rules first: study design and sampling.
Table of Contents
The four inputs (and the one people guess wrong)
| Input | Where it comes from | Typical value |
|---|---|---|
| Effect size | Pilot data or the smallest effect that would matter scientifically | d = 0.5–0.8, or from prior literature |
| Significance level α | Field convention | 0.05 |
| Power (1 − β) | Field convention | 0.80–0.90 |
| Test type | Design: t-test, ANOVA, proportions | Two-sided t-test for two groups |
Worked example: expecting a medium effect (d = 0.5) between two treatment groups at α = 0.05 and power = 0.80, a two-sided t-test needs about n = 64 per group. Halve the expected effect to d = 0.25 and the requirement jumps to ~250 per group — effect size drives everything, which is why pilots are worth their cost. Free tools: G*Power, the pwr package in R, or jamovi’s power module — menu-driven, no code (see the jamovi first-analysis guide).
When n can’t be reached: honest options
- Sharpen the measurement: paired designs and repeated measures slash variance — a paired t-test needs roughly half the n of a two-group design for the same power.
- Reduce noise, not ambition: randomize blocks (batches, cages, days) so known variance sources stop inflating the error term.
- Reframe the claim: if only n = 15 per group is feasible, the study demonstrates the large effects only — say so in the limitations, with the detectable effect size stated.
- Never iterative stopping: adding units until p < .05 inflates false positives; the testing logic that punishes this is in the hypothesis testing guide.
Report power thinking in the methods: expected effect, α, power, achieved n — the transparency reviewers increasingly demand. The measurement machinery behind effect sizes is in the effect size guide, and the p-value/power partnership in the p-value explainer. For one-to-one help planning a thesis study before the first sample, Ampersand Academy teaches biostatistics one-to-one.
Official documentation
For the full reference behind this guide, read the NIST/SEMATECH e-Handbook page on hypothesis and power. It is the source the details above are drawn from, and the first place to check when an option or attribute name changes.
Frequently asked questions
How do I calculate the sample size for my experiment?
Run a power analysis: combine the expected effect size, your alpha (usually 0.05), target power (usually 0.8) and the planned test. Tools like G*Power, R’s pwr package or jamovi modules return the minimum n per group.
Why does a smaller expected effect need a much larger sample?
Small effects are harder to see through random noise. Halving the effect size roughly quadruples the required n, which is why pilots and literature-based estimates matter before data collection.
Is 0.8 power a strict rule?
It is convention: an 80 percent chance of detecting a real effect of the assumed size. Studies that can afford 0.9 should use it; the honest failure mode is stating the achieved power in limitations.
Does a paired design really need fewer subjects?
Usually yes. Pairing removes between-subject variance from the comparison, so the same power is reached with roughly half the participants or animals of an independent-groups design.
Can I check power after the study instead of before?
Post hoc power calculated from your own p-value is circular and uninformative. What reviewers accept is the detectable effect size at your achieved n, stated in the limitations.
Last updated on · Written by Dinesh Kumar R
