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Mean · MEAN-1S

Sample Size for Test of One Mean

Plan a one-sample mean test for a prespecified detectable difference, power, and Type I error rate.

1. Information obtained from previous studies or literature

Enter the planning SD in the same outcome units as the detectable difference.

2. Information decided by the researcher

Enter the smallest mean difference the study should be able to detect, in outcome units.

3. Results

Enter the hypothesis-test assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher tests whether mean haemoglobin concentration among pregnant women receiving supplementation differs from a clinically relevant reference mean.

Formula and methodological note

The calculator uses the normal-approximation one-sample mean-test formula: n = (SD / Δ)² × (zα + zβ)², followed by the calculator’s established small-sample correction and final ceiling. Here Δ is the detectable mean difference, zα is determined by the selected one- or two-sided Type I error, and zβ is determined by the requested power.

It is intended for one independent continuous, approximately normally distributed outcome. The planning SD and detectable difference must use the same outcome units.

It does not account for clustering, design effects, stratification, repeated measurements, non-normal outcomes, non-inferiority/equivalence designs, or interim monitoring.

Method references

  1. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman and Hall/CRC; 2017.
  2. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Test of One Mean (MEAN-1S).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/mean/one-mean/.