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Proportion · PROP-2P

Sample Size for Test of Paired Proportions

Plan the number of paired observations needed to compare a binary outcome measured in matched or dependent data.

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 an expected paired odds ratio greater than 0 and not equal to 1.

Common planning value: 80%.

Common planning value: 5%.

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

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

3. Results

Enter the paired-proportion assumptions and select Calculate to generate the required number of pairs and suggested sample-size wording.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

The proportion of patients with controlled blood pressure is recorded in the same clinic population before and after a quality-improvement programme.

Formula and methodological note

The calculator preserves the established normal-approximation formula for paired proportions. Sample-size information comes from the anticipated proportion of discordant pairs and the expected paired odds ratio, together with the selected Type I error and power.

The endpoint must be binary and observations must be paired or dependent, such as before-and-after measurements on the same participant or appropriately matched pairs. The discordant-pair proportion is the anticipated proportion of pairs with different outcomes; concordant pairs do not contribute to the paired comparison in the same way.

The required number of pairs is rounded upward. If anticipated dropout or non-response is entered, the rounded number of pairs is divided by 1 − r and rounded upward again.

This method does not implement an exact binomial method or continuity correction and does not apply to independent groups, clustered sampling, design effects, stratification, weighting, or repeated-measures structures beyond the specified paired comparison. Low discordance or an odds ratio close to 1 may require a large sample and methodological 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 Paired Proportions (PROP-2P).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/proportion/paired-proportions/.