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Mean · MEAN-2I

Sample Size for Test of Two Independent Means

Plan a comparison of two independent group means using a prespecified detectable difference, allocation ratio, power, and Type I error rate.

1. Information obtained from previous studies or literature

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

2. Information decided by the researcher

Enter the smallest between-group difference the study should be able to detect.

A value of 1 gives equal allocation.

3. Results

Enter the hypothesis-test assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized trial compares mean postoperative pain scores between patients receiving a new analgesic and those receiving standard treatment.

Formula and methodological note

The calculator uses the normal-approximation two-independent-means formula with the selected allocation ratio, Type I error, and power. The continuous requirement is converted to whole participants per group before the dropout/non-response adjustment is applied separately to each group.

It assumes independent observations, a continuous approximately normally distributed outcome, a common planning SD in both groups, and the specified allocation ratio. The detectable difference and SD must use the same outcome units.

It does not account for clustering, design effects, covariate adjustment, repeated measurements, paired data, 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 Two Independent Means (MEAN-2I).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/mean/two-independent-means/.