Sample Size Calculator for Ophthalmology Theses: Prevalence, Two Proportions and Two Means

Last updated: November 2026

Every thesis protocol needs a sample size calculation, and ethics committees will ask how you got your number. Pick the design that matches your main question, enter the expected values from a previous study or pilot, and the calculator gives the number needed, inflated for dropouts. Show the formula and your sources in the protocol.

Formulas used

• One proportion: n = Z²_α/2 × p(1 − p) ÷ d², with finite population correction n′ = n ÷ (1 + (n − 1)/N) if the population is small.
• Two proportions (per group): n = [Z_α/2√(2p̄(1 − p̄)) + Z_β√(p₁(1 − p₁) + p₂(1 − p₂))]² ÷ (p₁ − p₂)², where p̄ is the average of p₁ and p₂.
• Two means (per group): n = 2(Z_α/2 + Z_β)² × SD² ÷ difference².
• Final n = n ÷ (1 − dropout). Round up.

Worked example: to compare IOP lowering of 2 mmHg between two drops when the SD is 4 mmHg, with α 0.05 and 80% power: 2 × (1.96 + 0.84)² × 16 ÷ 4 ≈ 63 eyes per group, or 70 per group allowing 10% dropout. If both eyes of a patient are included, the eyes are not independent: analyse one eye per patient or use methods that account for correlation, and say so in the protocol.

For paired designs, non-inferiority trials, survival outcomes or diagnostic accuracy studies, use a dedicated tool (for example G*Power or OpenEpi) or ask a statistician. See thesis topics and biostatistics for ophthalmologists.

For learning and quick checks only. Confirm any result that changes treatment against your own measurements, the device manufacturer's guidance and current local protocols.

Related: MS/DNB Ophthalmology Thesis: Choosing a Topic and Example Ideas, Biostatistics and Research Methods for Ophthalmologists, Landmark Trials in Ophthalmology: High-Yield Summary. See all eye calculators and tools.

Key sources

• Kirkwood BR, Sterne JAC. Essential Medical Statistics. 2nd ed. Blackwell; 2003
• Lwanga SK, Lemeshow S. Sample size determination in health studies: a practical manual. World Health Organization; 1991
• Armstrong RA. Statistical guidelines for the analysis of data obtained from one or both eyes. Ophthalmic Physiol Opt. 2013;33:7-14