How Many People Must Be Approached to Obtain the Required Sample Size?

If You Need 300 Participants, How Many People Should You Invite?

Your sample-size calculation indicates that your study requires 300 participants. You plan to distribute an invitation to university students, but you know that not everyone will respond.

Some students may be ineligible. Others may decline participation, begin the questionnaire without completing it, or provide data that cannot be used for the intended analysis.

Should you invite 330 students, 500 students, or 1,000? Is it sufficient to divide the required sample by the expected response rate? What if eligibility and completion rates are calculated using different denominators?

Calculating how many people to approach requires a clear understanding of the recruitment process. The answer depends not simply on the required sample size, but on the probability that an approached individual will ultimately contribute the information the study needs.

Divide the Required Sample by the Expected Overall Recruitment Yield

Calculating Participant Contact Targets Correctly

Why Must You Approach More People Than the Required Sample?

The number of individuals approached is generally different from the number ultimately included in the analysis.

An invitation may not reach its intended recipient, an individual may fail screening, an eligible person may decline consent, or an enrolled participant may not provide the required data.

Each stage reduces the expected number available at the next stage.

Consequently, the required analytical sample should be translated into an appropriate contact target using plausible assumptions about recruitment yield.

This does not mean that every study should deliberately recruit more enrolled participants than necessary. Recruitment should be proportionate to the expected losses and consistent with the approved protocol.

What Is the Simplest Recruitment Calculation?

When a credible overall yield rate is available, the calculation is straightforward.

The overall yield must refer to the entire process from approach to usable data. A consent rate calculated only among eligible respondents cannot be substituted directly unless the preceding stages are also considered.

How Do You Calculate Recruitment When There Are Multiple Stages?

Many studies require separate assumptions for screening, eligibility, consent, and data completion.

The overall yield is obtained by multiplying conditional progression rates through the stages.

The formula follows the chain rule of conditional probabilities when the rates describe successive stages consistently. It does not require those stages to be statistically independent.

However, the estimated rates must be applicable to the population and recruitment procedure being planned.

Why Are Denominators So Important?

A percentage is meaningful only when the denominator is clear.

Consider a study in which 500 people are approached, 400 complete screening, 300 are eligible, 240 consent, and 216 provide usable data.

The 80% consent rate applies to eligible individuals, not everyone approached. Using 80% as the overall recruitment yield would substantially underestimate the contact requirement.

Researchers should record both the numerator and denominator for every recruitment rate.

What Is the Difference Between Response Rate and Consent Rate?

Response rate generally describes participation or response relative to a defined invitation or sampling denominator, although formal definitions differ across survey methods.

Consent rate describes the proportion of eligible individuals who agree to participate, when eligibility is established before consent.

A person may respond to an invitation but decline consent. Another may consent but fail to complete the required study activities.

Therefore, response, consent, and completion rates should not automatically be treated as interchangeable.

Researchers should specify the recruitment stages relevant to their design and avoid counting the same form of nonparticipation more than once.

How Do You Calculate Invitations for an Online Survey?

For a simple online survey, researchers may have reliable information about the proportion of invitations that produce usable questionnaires.

If the required sample is 400 and the anticipated overall usable-response rate is 25%, the expected invitation requirement is 400 / 0.25 = 1,600.

However, an online survey link distributed publicly may not provide a known denominator of unique individuals approached.

Page views, link clicks, and social media impressions are not necessarily equivalent to distinct eligible invitees.

Where the invitation denominator is unknown, researchers should not present a precise individual response rate without a defensible basis.

How Does Eligibility Affect the Number of Invitations?

Eligibility can substantially change the contact requirement.

Suppose 200 usable participants are needed and the overall yield after eligibility screening is 60% among eligible individuals.

If all approached individuals are eligible, approximately 334 contacts are needed.

If only half of those approached are eligible, approximately 667 contacts are needed, assuming the same subsequent 60% yield.

This illustrates why recruitment from a broad population may require many more contacts than recruitment from a verified eligible list.

The effects of eligibility, refusal, and attrition should be incorporated into planning rather than addressed only after recruitment falls behind.

How Should Attrition Be Incorporated?

Attrition affects the number of enrolled participants expected to contribute follow-up data.

If a longitudinal study requires 250 participants with final follow-up data and anticipates 20% attrition, the expected enrollment target is 250 / 0.80 = 312.5, rounded upward to 313.

Further adjustments may be necessary for eligibility and consent before enrollment.

However, attrition should not automatically be equated with complete analytical loss. Some designs use information from participants with incomplete follow-up under appropriate missing-data assumptions.

The calculation must reflect the sample-size method and planned analysis rather than applying a generic attrition percentage indiscriminately.

Why Is Adding 20% Different From Dividing by 80%?

A common mistake is to add the anticipated loss percentage directly to the required sample.

Suppose 100 completed observations are needed and 20% of enrolled participants are expected to be lost.

Adding 20% gives 120 enrolled participants, but retaining 80% of 120 yields only 96 completed observations on average.

Dividing by 0.80 gives 125 enrolled participants, whose expected retained count is 100.

The distinction matters because the loss rate applies to the initial enrolled group, not to the final required sample.

Should You Round at Every Stage?

For an overall expected contact calculation, it is usually clearest to retain unrounded intermediate values and round the final result upward.

For operational planning, however, each stage may require a whole-number target because partial participants cannot be screened or enrolled.

Sequential upward rounding can sometimes produce a slightly more conservative operational plan than rounding only the final combined calculation.

Researchers should state their rounding method and avoid claiming greater precision than the underlying rate assumptions support.

Does the Formula Guarantee That the Required Sample Will Be Obtained?

No. The formula calculates an expected number of usable participants.

Actual eligibility, consent, and completion outcomes vary, even when the assumed rates are correct on average.

For example, approaching 500 individuals with a true overall yield probability of 60% produces an expected 300 usable participants, but the actual number may fall below or exceed 300.

If the study requires a specified probability of achieving at least the target, a probabilistic planning calculation may be needed.

Under a simplified model with independent and identically distributed individual outcomes, the usable count could be modeled using a binomial distribution. Clustered recruitment, unequal rates, and other dependencies require more appropriate models.

How Can You Plan for a High Probability of Meeting the Target?

Researchers can distinguish between an expected-yield target and an assurance-based contact target.

Under a simple binomial model, the number of usable participants X among n approached individuals follows X ~ Binomial(n, p), where p is the overall usable-data probability.

A researcher seeking at least 95% probability of obtaining the required sample can choose the smallest n satisfying the following condition:

The required number can be obtained using binomial probability calculations or suitable statistical software.

However, the result remains conditional on the assumed yield probability and independence model. Uncertainty in p should be considered separately.

How Do You Account for Uncertain Recruitment Rates?

When rates are uncertain, calculate the contact requirement under several plausible assumptions.

For a required sample of 300, consider three possible overall yields:

These values are hypothetical and calculated by dividing 300 by each assumed yield and rounding upward.

The difference demonstrates why a recruitment plan based on an unsupported optimistic rate may be operationally fragile.

A sensitivity analysis of recruitment assumptions can help determine whether the study remains feasible under less favorable conditions.

What If Different Recruitment Channels Have Different Yields?

Recruitment through institutional email, classroom announcements, professional networks, and public advertisements may produce different participation patterns.

A single overall yield can conceal important differences.

For example, a targeted institutional invitation may reach fewer people but produce a higher proportion of eligible participants than a broad public advertisement.

Researchers can estimate contacts separately for each channel, then combine expected usable participants across channels.

However, duplicate contacts must be identified appropriately, and the sampling consequences of each channel should be considered.

How Should Contact Targets Be Allocated Across Sites?

Site-specific planning should account for eligible population size, expected yield, recruitment capacity, and the study's analytical requirements.

If a multi-site study requires representation from each institution, the recruitment calculation may need separate targets rather than a pooled overall estimate.

For example, one university may have a high eligibility rate but limited available participants, while another may have a larger pool with a lower consent rate.

The planning of recruitment by study site should reflect these differences.

Simply dividing the overall contact target equally among institutions may not be feasible or methodologically appropriate.

What If the Accessible Population Is Smaller Than the Contact Target?

Suppose the calculation indicates that 800 people should be approached, but only 500 eligible or potentially eligible individuals are accessible.

The recruitment plan cannot create additional people within the defined population.

Researchers should reassess the assumptions, available sites, study duration, and statistical or methodological objectives.

They may need to expand the recruitment setting, revise the study design, or accept lower precision or power with transparent justification.

The problem of an eligible population smaller than the required sample should be addressed before recruitment begins whenever possible.

Should You Invite Everyone at Once?

Not necessarily. A staged invitation strategy may help manage recruitment and avoid enrolling substantially more participants than needed.

For example, researchers may invite an initial batch, evaluate the response and eligibility rates, and then issue further invitations if required.

However, staged recruitment can introduce selection or calendar effects if later invitees differ systematically from earlier invitees.

The approach should be planned in advance where possible and remain consistent with the sampling design and approved protocol.

Researchers should not manipulate invitation timing to obtain a preferred result or exclude less convenient participants.

What Is the Difference Between Inviting More People and Overrecruiting?

Inviting more people than the required sample may be necessary because not every invitation produces an enrolled participant.

Overrecruitment concerns enrolling or collecting data from more participants than the study needs or can justify.

The two are related but not identical.

Researchers should manage invitation batches, enrollment ceilings, and expected response delays to reduce unnecessary participant burden.

The decision about unnecessary overrecruitment and participant burden should consider the approved protocol and the value of additional information.

How Should the Calculation Be Reported?

The methodology should state the required analytical sample, assumed recruitment rates, sources of those assumptions, and resulting contact target.

It should distinguish the anticipated number approached from the planned enrollment and analysis samples.

After recruitment, researchers should report actual counts and reasons for nonparticipation where available and appropriate.

The STROBE statement recommends reporting participant numbers at relevant stages of observational studies and considering a flow diagram.

Transparent reporting allows readers to distinguish recruitment feasibility from statistical sample-size adequacy.

Calculating Invitations for 300 Usable Survey Responses

The figure of 618 represents the minimum expected contact target under the stated assumptions, not a guaranteed number sufficient to produce 300 usable responses.

If the researcher requires a high probability of meeting the target rather than merely an expected yield of 300, an additional assurance-based calculation would be appropriate.

Common Mistakes in Recruitment Number Calculations

Calculate Contacts Using the Actual Recruitment Process

Identify the number of usable participants required, then map the stages between an initial approach and inclusion in the intended analysis.

Calculate the expected yield using consistent conditional denominators and evaluate whether the resulting contact target is feasible.

The final contact number should be presented as a planning estimate supported by transparent assumptions.

Actual recruitment progress should be monitored so that emerging shortfalls can be addressed before the study becomes infeasible.

Before Finalizing How Many People to Approach

Frequently Asked Questions About Recruitment Contact Calculations

Calculate Recruitment Contacts From the Expected Yield, Not the Sample Size Alone

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