What Should You Do When the Expected Prevalence Is Unknown for Sample-Size Planning?

How Can You Calculate Sample Size Without Knowing the Expected Prevalence?

You want to estimate how common a particular characteristic, condition, or behavior is in a population. Perhaps you are studying the proportion of university students experiencing academic burnout, the prevalence of a health condition in a community, or the percentage of teachers using generative AI for instructional preparation.

Before collecting data, you need to determine how many participants to recruit. Yet the sample-size formula requires an anticipated prevalence, and reliable information about that prevalence may not exist.

Should you assume 50%, conduct a pilot survey, borrow an estimate from another population, or calculate sample sizes under several possible values? The appropriate choice depends on the research objective, available evidence, and sampling design.

Use 50% as a Conservative Starting Point When No Better Estimate Exists

Choosing a Prevalence Assumption When Reliable Prior Data Are Unavailable

What Does Expected Prevalence Mean in Sample-Size Planning?

Prevalence is the proportion of a defined population that has a specified condition or characteristic at a particular point or during a specified period. In sample-size planning, expected prevalence is the value researchers provisionally assume for that population proportion.

It is usually represented by p, with values ranging from zero to one. For example, an expected prevalence of 30% is expressed as p = 0.30.

The assumption is needed because the sampling variance of a binary outcome depends on the underlying population proportion. For independent Bernoulli observations, the variance of the individual binary indicator is p(1 − p).

Expected prevalence should not be confused with the prevalence eventually observed in the study. The former is a planning input; the latter is an estimate obtained from the collected data.

Why Does the Prevalence Assumption Affect Sample Size?

For a simple random sample from a sufficiently large population, a commonly used approximate sample-size formula for estimating one proportion is:

The formula assumes that the normal approximation is suitable and that the desired precision is expressed as an absolute difference in percentage points. Different interval procedures or precision objectives may require different calculations.

Why Is 50% Called the Conservative Prevalence Assumption?

The expression p(1 − p) reaches its maximum value of 0.25 when p = 0.50. As p moves toward zero or one, this variance term becomes smaller.

Because the conventional sample-size formula is directly proportional to p(1 − p), using 50% produces the largest required sample size for a fixed confidence level and absolute margin of error under that formula.

These values use 95% confidence, an absolute margin of error of five percentage points, and the same large-population normal approximation. Values are rounded upward independently.

The table also illustrates why p = 0.50 can be unnecessarily demanding when credible evidence indicates that the characteristic is uncommon.

Conversely, assuming a low prevalence merely to reduce the required sample size is not defensible when that assumption lacks evidence.

Does Conservative Mean That 50% Is Always the Safest Choice?

No. The conservative property is specific to the variance term in the conventional absolute-precision formula. It does not automatically extend to every statistical objective.

For rare conditions, a margin of error of ±5 percentage points may be too broad to be useful. If the true prevalence is 1%, a confidence interval with several percentage points of uncertainty may provide little information about the quantity researchers actually need.

Rare-prevalence studies may instead require a narrower absolute margin of error, a relative precision target, or a minimum number of observed cases.

Furthermore, exact binomial, Wilson, and other interval procedures have operating characteristics that differ from the simple Wald approximation, especially near the boundaries of zero and one.

Thus, the appropriate planning question is not simply which value produces the largest n, but how precisely the prevalence needs to be estimated for the research purpose.

Where Should You Look Before Assuming 50%?

Before adopting the maximum-variance assumption, examine whether credible information about prevalence already exists.

Potential sources include population-based surveys, official statistical reports, disease registries, previous epidemiological studies, institutional records, and systematic reviews.

When evaluating an estimate, consider whether its definition of the characteristic matches yours. Prevalence of diagnosed depression, for example, is not necessarily interchangeable with prevalence of elevated scores on a screening instrument.

Also examine the sampling frame, geographical setting, age distribution, measurement period, and the date of the evidence.

An estimate from a different population or research context may be informative, but it should not be transferred without considering comparability. Although that distinction also arises in effect-size planning, prevalence has its own population-specific interpretation.

Can You Use a Plausible Prevalence Range Instead of One Value?

Yes. If the available evidence suggests that prevalence might fall between 10% and 30%, calculate sample sizes across that range rather than pretending that one value is known precisely.

For the conventional formula, p(1 − p) increases as p approaches 0.50 from below. Therefore, the largest sample-size requirement across the assumed 10% to 30% range occurs at 30%.

If the plausible range includes 50%, that value produces the maximum requirement under the same assumptions.

This approach can be more informative than selecting a single unsupported estimate. It also makes the consequences of uncertainty visible.

A structured plausible-assumptions analysis can examine prevalence alongside other uncertain design inputs.

Should You Conduct a Pilot Survey to Estimate Prevalence?

A pilot survey may help evaluate whether participants understand the questions, whether the outcome can be measured consistently, and whether recruitment procedures are feasible.

It may also produce a preliminary prevalence estimate. However, estimates from small pilots can be highly uncertain, particularly when the characteristic is rare.

For example, observing no cases among 20 pilot participants does not establish that the population prevalence is zero.

Using a small pilot's observed prevalence directly in a sample-size formula may lead to an unjustifiably small main study, especially if the pilot happens to underestimate the true prevalence.

The broader concern resembles the difficulty of using uncertain pilot estimates as fixed planning inputs. Pilot information should be interpreted alongside its uncertainty and other relevant evidence.

How Does a Finite Population Change the Calculation?

When sampling without replacement from a known, finite population, a finite population correction may reduce the required sample size.

For the conventional initial estimate n₀, an approximate adjustment is:

The correction is most consequential when the sample represents a substantial fraction of the finite population. It may be negligible when the population is very large relative to the sample.

What If Participants Are Sampled Through Schools, Clinics, or Communities?

Participants selected from the same school, clinic, classroom, or geographical cluster may resemble one another more closely than independently sampled participants.

Such dependence can reduce the effective information contributed by a given number of observations.

A commonly used approximate design effect for equal-sized clusters is:

Unequal cluster sizes, stratification, survey weights, and complex selection probabilities can alter the design effect. Researchers should use calculations appropriate to the actual sampling strategy.

Importantly, a larger sample does not correct selection bias or nonresponse bias. Precision and representativeness are different properties.

How Should Nonresponse Be Incorporated?

The statistical sample-size requirement generally refers to the number of usable observations needed for analysis, not necessarily the number of people who must be invited.

If the anticipated usable-response proportion is r, a simple recruitment calculation is:

Number to approach ≈ required completed sample / r.

For example, if 385 completed responses are needed and 80% of approached eligible participants are expected to provide usable data, approximately 482 people must be approached.

This adjustment addresses expected recruitment yield. It does not guarantee unbiased estimates when nonrespondents differ systematically from respondents.

Researchers should therefore plan both adequate recruitment and procedures for evaluating potential nonresponse bias.

Estimating the Prevalence of Generative AI Use Among University Students

The resulting sample-size plan is defensible only to the extent that the assumptions match the actual survey. The 50% prevalence assumption protects against underestimating the variance term in the conventional formula, but it does not protect against coverage error, nonresponse bias, or an inappropriate sampling design.

Common Misconceptions About Unknown Prevalence

Select a Prevalence Assumption That Fits Your Estimation Objective

Begin by specifying the population, the characteristic being measured, and the precision required for the intended use of the estimate. Only then should you choose the prevalence assumption.

The distinction between an overall population estimate and estimates for subgroups is especially important. A sample adequate for university-wide prevalence may be too small to estimate prevalence separately for each academic program.

Where prevalence uncertainty materially affects the required sample, a sample-size sensitivity analysis should be considered before finalizing recruitment.

It is also worth checking whether the planned confidence-interval width will answer the research question. A mathematically defensible sample size may still produce an estimate too imprecise for the decision researchers intend to make.

Before Calculating Sample Size With Unknown Prevalence

Frequently Asked Questions About Sample Size When Prevalence Is Unknown

Unknown Prevalence Does Not Prevent Defensible Sample-Size Planning

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