Sample size: comparing two means

Fast, MMed-friendly sample-size calculator for comparing two independent means (two-sample t-test). Plain-language inputs, citations, and a copy-ready methods paragraph.

Compare two means (two-sample t-test)

Use this tool when your outcome is continuous (e.g. blood pressure, BMI, length of stay) and you want to compare two independent groups. Defaults are tuned for a typical MMed-level study.

Mean in Group 1 (control / reference) μ₁

The expected average outcome in your reference group.

How to justify this number

Sources, in order of strength:

1. A recent local study in a similar setting.
2. A systematic review or meta-analysis.
3. A pilot of 30–50 of your own records.

In your protocol: "Based on Smith et al. (2024), the mean systolic BP in our cohort was approximately 120 mmHg."

Mean in Group 2 (intervention / comparison) μ₂

The expected mean in the comparison group.

How to justify this number

Two valid framings:

• Expected mean based on prior trials.
• Minimum clinically important difference (MCID) — the smallest change that would change practice. Often more defensible.

Cite an MCID from clinical guidelines (e.g. 5 mmHg for systolic BP per SEMDSA hypertension guideline 2018).

Standard deviation (pooled) σ

Spread of the outcome — assumed roughly equal in both groups.

How to justify this number

The hardest input to pin down. Best sources:

• SD reported in the same paper you used for the means.
• Width of a 95 % CI: SD ≈ √n × (CI width) / 3.92.
• Range / 4 if only min–max is reported (rough).
• Pilot data (n ≥ 30) from your own records.

If unsure, run sensitivity at ± 25 % around your best guess and report it.

Significance level α

Acceptable false-positive rate. Two-sided test.

0.01 (stricter — confirmatory trials) 0.05 (standard) 0.10 (exploratory / pilot only)

How to justify this number

α = 0.05 is the universal default. Cite: ICH E9 (1998) Statistical Principles for Clinical Trials.

Power 1 − β

Probability of detecting the effect if it really exists.

0.80 (standard) 0.85 0.90 (more conservative) 0.95 (large / high-stakes trials)

Allocation ratio k = n₂ / n₁

Equal groups = 1. Set to 2 for a 2:1 design (e.g. one control to two cases).

1 (equal groups) 2 (1:2) 3 (1:3) 0.5 (2:1)

You need

— in Group 1

— in total

Adjust the inputs to see your sample size.

What does this calculation actually do?

For a two-sample t-test with allocation ratio k, the required sample size in Group 1 is approximately:

n₁ = (1 + 1/k) · σ² · (z₁₋α/₂ + z₁₋β)² / (μ₁ − μ₂)²
n₂ = k · n₁

Cohen's effect size d = (μ₁ − μ₂) / σ. We add 1 to each group as a small-sample correction (Snedecor & Cochran 1989) — this matches power.t.test() in base R closely for n ≥ 20.

Assumptions: independent observations, approximately normal outcomes (or n ≥ 30 per group via the central limit theorem), roughly equal variances. Inflate by your expected drop-out rate before recruiting.

References: Snedecor GW, Cochran WG. Statistical Methods, 8th ed. 1989. · Cohen J. Statistical Power Analysis 1988. · Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies, WHO 1991.