Specialty › Precision & CI width

Difference between means

Precision-based sizing finds the per-group n that gives a confidence interval on a difference of means a target half-width, assuming equal σ.

What is Difference between means?

The two-sample mean-difference CI has SE = σ·√(2/n), so the per-group n is twice the single-mean n for the same half-width.

When should I use Difference between means?

  • Two-arm comparative study where the primary estimand is the mean difference, not a hypothesis test.

What data does it need?

σ + target half-width + confidence.

What does it report?

Required n per group.

Formula

n_per_group = 2 · (z_{1−α/2} · σ / E)²

How do I interpret the result?

Per-group n is 2× the single-mean n; cutting the half-width in half quadruples the required n.

See also