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Proportion · PROP-2I

Sample Size for Test of Two Independent Proportions

Plan sample sizes for comparing a binary outcome between two independent groups.

Enter percentage values, not decimals. For example, enter 20 for 20%, not 0.20.

1. Information obtained from previous studies or literature

Allowed range: 0.1% to 99.9%.

2. Information to be decided by the researcher

Enter the expected proportion in group 2, such as the case or exposed group.

Common planning value: 80%.

Common planning value: 5%.

Use 2 tails unless the protocol specifies a one-sided test.

Enter the group 2 to group 1 allocation ratio. Use 1 for equal groups.

Defaults to 10%. Enter 0 if no dropout adjustment is required.

3. Results

Enter the hypothesis-test assumptions and select Calculate to generate the group sample sizes and suggested sample-size wording.

4. Utilities

Optional helpers for planning values used in the two-proportion calculator.

P1 from P0 and odds ratio

Odds ratio from P0 and P1

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized surgical trial compares postoperative wound-infection proportions between a new prophylactic antibiotic regimen and standard care.

Formula and methodological note

The calculator preserves the established normal-approximation formula for comparing two independent proportions. It combines a pooled variance term at the selected Type I error with group-specific variance terms at the selected power.

The two groups must be independent, the endpoint must be binary, and the group proportions must represent the planning values for the same outcome definition. The allocation ratio is group 2 divided by group 1; a value of 1 gives equal allocation.

The established implementation rounds the difference between proportions to three decimal places before calculation. Group 1 is rounded upward first, group 2 is then derived from the allocation ratio and rounded upward, and dropout adjustment is applied separately to each rounded group size.

This method does not implement exact binomial methods or continuity correction and does not account for paired data, clustering, design effects, stratification, weighting, repeated measurements, or finite population correction. Rare or extreme proportions may require an alternative method and statistical review.

Method references

  1. Lemeshow S, Hosmer DW Jr, Klar J, Lwanga SK. Adequacy of Sample Size in Health Studies. Chichester: John Wiley & Sons; 1990.
  2. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Boca Raton: Chapman and Hall/CRC; 2017.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Test of Two Independent Proportions (PROP-2I).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/proportion/two-independent-proportions/.