Sample size: estimating a single prevalence
Estimate a single prevalence (one-group survey)
Use this tool when you want to estimate how common something is in a single population — e.g. prevalence of hypertension, vaccine coverage, or the proportion of patients with a complication. Defaults match a typical cross-sectional MMed survey.
As a proportion (e.g. 0.30 = 30 %). If unsure, use 0.50 — it gives the most conservative (largest) sample size.
How to justify this number
Use a recent local survey, registry, or systematic review. If no prior estimate exists, use p = 0.50 — this maximises p(1−p) and gives a conservative sample size.
In your protocol: "Based on Mokoena et al. (2023), the expected prevalence of hypertension in adult outpatients was 30%."
Half-width of the 95 % confidence interval. 0.05 = ± 5 percentage points.
How to justify this number
How precise do you need to be? For a prevalence near 30%, a margin of ± 5 percentage points (i.e. CI 25–35%) is usually acceptable. Tighter margins blow up your sample size quickly.
Rule of thumb: halving the margin of error quadruples the sample size.
Conventionally 95 %.
Tick this if you're sampling more than ~10 % of a known, finite population (e.g. all 800 patients on a ward register).
Tick this if you're sampling whole groups (clinics, classrooms, households) instead of individuals.
Inflate your target to allow for refusals, lost-to-follow-up, missing data.
You need
What does this calculation actually do?
For estimating a single proportion with a desired margin of error d:
n₀ = z² · p · (1 − p) / d²
With finite-population correction (when sampling fraction is non-negligible):
n = n₀ / (1 + (n₀ − 1) / N)
With clustering, inflate by the design effect:
DEff = 1 + (m − 1) · ρ
Finally inflate for expected drop-out: n_final = n / (1 − dropout).
References: Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies, WHO 1991. · Naing L et al. Arch Orofac Sci 2006;1:9–14.