Sample Size for Two Means

n per group
Total n
Attrition-adjusted total

What this answers

This planner answers "how many participants do I need per group, before I collect any data, to reliably detect a difference of the size I expect between two independent groups?" A study with too few participants can genuinely miss a real effect, not because the effect does not exist, but because the study never had enough power to detect it.

How it is calculated

This calculator uses a normal-approximation formula for the independent two-sample design, documented here rather than the more exact iterative noncentral-t solution some specialized software computes. This approximation is standard and widely used, giving results that closely match the more exact calculation in typical cases, and this calculator states its method explicitly rather than presenting an unstated approximation as an exact answer.

Worked example

For an expected effect size of Cohen's d equal to .5 (a conventionally "medium" effect), alpha of .05, and 80% power: the required sample size is 63 per group, 126 total, a widely cited reference value for this exact combination that closely matches published statistical software output.

Assumption audit

Calculated from your data: the required sample size per group and in total, given your stated effect size, alpha, and power.

Evidence to review: how plausible your assumed effect size actually is. An overly optimistic assumed effect size will lead to an underpowered study if the true effect turns out to be smaller.

You must verify: that your planned recruitment can actually reach the recommended sample size, and that random assignment to groups is genuinely feasible for your study design.

Common mistakes

A common mistake is assuming an optimistic effect size just because it is the effect the study hopes to find, rather than one grounded in prior research or a pilot study; an inflated assumed effect size understates the true sample size needed. Another is ignoring the attrition field when real-world dropout is expected; a study that starts with exactly the recommended n and then loses participants to follow-up ends up underpowered by the time it finishes. A third is treating the recommended n as a hard guarantee of finding a real effect; it only sets the probability of detecting the assumed effect size at the stated power, not a certainty.

Limitations

This calculator assumes equal variance between groups and, by default, equal group sizes. It also assumes a two-sided test; a one-sided test would require a smaller sample for the same power, a distinction worth being explicit about before reporting a required n.