Getting n right: two-arm sample size basics

Sample size trades the chance of a false alarm and the chance of missing a real effect against the smallest difference you care about. For an equal two-arm design, a normal approximation is a first pass a statistician can refine.

Worked example, means. Two arms, alpha 0.05 two-sided, 80 percent power, shared standard deviation 1, and a meaningful mean difference of 0.5. With Z values about 1.96 and 0.84, n per arm is about 2 times (1.96 + 0.84) squared times sigma squared, divided by delta squared, which is about 63 people who finish per arm, about 126 before dropouts.

Common mistakes. Picking the difference from a hopeful target instead of pilot data or the literature. Forgetting people who do not finish. Mixing one-sided and two-sided cutoffs between the plan and the calculator.

Compute n per arm: https://nexamedtech.com/tools/sample-size-calculator