Should Sample Size Be Based on Participants or Clusters?

Do You Need More Participants, More Clusters, or Both?

Suppose you are planning an educational intervention involving 600 students. You could recruit those students from six classrooms containing 100 students each or from 30 classrooms containing 20 students each.

Both designs include 600 students. However, if classrooms are independently randomized to intervention conditions, they do not provide the same amount of independent treatment replication.

Alternatively, suppose you want to estimate the average academic engagement of students in a region using a sample of schools. In this case, both the number of schools and the number of students selected within each school may affect the precision of your estimate.

Should sample size calculations therefore use the number of students, the number of classrooms, or some combination of the two? The answer depends on what you intend to estimate and how the observations are selected, assigned, and analyzed.

Plan the Number of Clusters and Participants Together

How Participants and Clusters Contribute Differently to Statistical Power

What Is a Cluster in Sample Size Planning?

A cluster is a group of observational units connected through a shared sampling, assignment, organizational, biological, or environmental structure.

Examples include students within classrooms, patients within hospitals, employees within organizations, households within communities, and repeated measurements within participants.

In cluster-randomized trials, entire groups are independently assigned to treatment conditions. In multistage surveys, groups may be selected first and individuals subsequently sampled within them.

Although both designs contain clusters, their sample size requirements differ because the inferential objectives and assignment mechanisms differ.

Researchers should therefore identify how clustering enters the research design before selecting a sample size formula.

Why Is the Number of Clusters Important?

Clusters provide information about variation between groups. When treatment is independently assigned to groups, they also provide the independent assignment replication needed to estimate the treatment contrast.

Suppose an instructional intervention is randomized across eight classrooms. Measuring 50 students in each classroom produces 400 individual outcomes, but only eight independently randomized classrooms.

Increasing the number of students within those same classrooms may improve the precision of classroom outcome estimates. It does not increase the number of independently assigned classrooms.

This distinction becomes especially important when treatment effects vary across groups or when between-group variation is substantial.

A large individual sample cannot automatically compensate for too few independent treatment assignments.

Why Does the Number of Participants per Cluster Also Matter?

Participants within clusters provide information about individual outcomes and the characteristics of their groups.

For example, a classroom mean achievement score estimated from 30 students may be more precise than one estimated from five students, assuming comparable measurement and sampling conditions.

Additional participants can reduce within-cluster sampling uncertainty and improve estimation of certain individual-level relationships.

However, participants within the same cluster may share teachers, policies, environments, or other influences that create correlated outcomes.

Consequently, each additional participant may contribute less new information than an independent participant recruited from another cluster.

The extent of this reduction depends on the intracluster correlation and the estimand.

What Is the Intracluster Correlation Coefficient?

The intracluster correlation coefficient, or ICC, summarizes similarity among observations within the same cluster under a specified model.

For a simple random-intercept model with a continuous outcome, it can be expressed as:

A larger positive ICC indicates that observations within the same cluster tend to resemble one another more strongly.

ICC values depend on the outcome, population, measurement context, and statistical model. An ICC estimated for student achievement should not automatically be used for student satisfaction or attendance.

For binary outcomes and more complex models, ICC definitions and interpretations require additional care.

How Does ICC Affect Sample Size?

For a simple equal-cluster-size design with exchangeable within-cluster correlation, a common design-effect approximation is:

The formula is useful for understanding the consequences of clustering, but it should not replace a design-specific sample size calculation.

Unequal cluster sizes, covariate adjustment, repeated measurements, stratification, and complex assignment procedures may require different calculations.

Can Two Studies With the Same Number of Participants Have Different Precision?

Yes. The distribution of participants across clusters can materially affect precision.

Consider two hypothetical designs with 600 students and ICC = 0.05.

For a simple overall mean under the equal-size approximation, Design A has an independent-observation equivalent of approximately 101, compared with approximately 308 for Design B.

These calculations illustrate how distributing participants across more clusters can improve precision when intracluster correlation is positive.

They do not establish the relative power of every possible regression or intervention analysis. Treatment-effect power also depends on allocation, group-level variation, covariates, and the proposed estimator.

Does More Clusters Always Mean Better Research?

Not automatically. More clusters can improve independent group coverage and statistical precision, but other design characteristics remain important.

For example, recruiting 30 conveniently selected schools does not automatically produce a representative sample of all schools.

Likewise, very small numbers of participants per cluster may produce imprecise group-level outcome measures.

The appropriate balance depends on the scientific objective, recruitment costs, population structure, and available resources.

The practical question is how additional groups or individuals contribute to the specific quantity the study seeks to estimate.

How Does Sample Size Planning Differ Between Cluster Sampling and Cluster Randomization?

Cluster sampling and cluster randomization should not be treated as equivalent designs.

In cluster sampling, groups are selected to obtain observations from a population. Sample size planning concerns the precision of population estimates or relationships under the sampling design.

In cluster randomization, groups are independently assigned to treatment conditions. Planning must account for the number of randomized groups and the precision of the treatment contrast.

For example, a survey estimating regional student engagement may require design-based calculations incorporating selection probabilities, clustering, and stratification.

A classroom-randomized intervention instead requires a power calculation reflecting treatment allocation, outcome variance, ICC, cluster sizes, and the intended effect.

Using a survey design effect as the entire power calculation for a cluster-randomized trial may overlook important features of treatment assignment.

What If the Outcome Is Individual-Level but Treatment Is Group-Level?

This is common in educational and clinical intervention studies.

For example, schools may be randomized to instructional programs while academic achievement is measured for individual students.

The student is the outcome measurement unit, but the school is the independent randomization unit.

Both levels matter for sample size planning.

Researchers should distinguish group-level treatment assignment from individual-level outcome measurement and ensure that the calculation corresponds to the intended treatment-effect estimand.

Adding students to existing schools does not create additional randomized schools.

What If Treatment Is Assigned Individually Within Selected Groups?

Individual randomization within schools or hospitals creates a different design from cluster randomization.

For example, students within each classroom might be independently assigned to receive one of two learning resources.

Here, students are independently randomized, although their outcomes may still be correlated because of classroom membership.

Sample size planning should reflect the individual assignment structure, possible clustering, and any treatment interference.

The number of groups may still matter for generalizability and modeling contextual effects, but it does not serve the same role as the number of randomized clusters in a cluster-randomized trial.

How Do Unequal Cluster Sizes Affect Sample Size?

Groups rarely contain exactly the same number of participants.

One school may contribute 20 students while another contributes 100. Unequal cluster sizes can affect the precision of estimates and the relative influence of groups.

For many simple clustered designs, greater cluster-size variation reduces efficiency relative to equally sized clusters with the same total number of participants.

However, the precise consequences depend on the estimator, allocation procedure, weighting, and correlation structure.

Researchers should consider expected cluster-size variation during planning rather than relying solely on an average group size.

When group size is associated with outcomes, the distinction between individual-average and cluster-average estimands becomes particularly important.

What If Some Clusters Drop Out?

Cluster loss can be especially consequential when the study already contains few independent groups.

For example, losing two schools from a trial with 12 randomized schools removes a substantial proportion of the independent assignment units.

Cluster dropout may also introduce bias if withdrawal relates to treatment condition or potential outcomes.

Sample size planning should therefore consider plausible cluster-level attrition separately from individual-level missing outcomes.

Recruiting extra individuals within remaining schools cannot fully replace lost randomized schools.

Researchers should document anticipated attrition assumptions and evaluate their sensitivity to different loss scenarios.

How Many Clusters Are Enough?

There is no universal minimum number of clusters that guarantees adequate power or valid inference.

The requirement depends on the expected effect size, ICC, cluster sizes, allocation ratio, outcome type, analysis, and acceptable uncertainty.

Trials with few clusters can be particularly sensitive to between-cluster variation and the assumptions of conventional statistical procedures.

Some analytical methods rely on approximations that perform better with larger numbers of independent clusters.

Small-sample corrections or randomization-based methods may be useful in suitable designs, but they do not create information that the assignment structure lacks.

Researchers should conduct a design-specific power or precision assessment rather than adopting an arbitrary cluster-count threshold.

Should You Use the Same Sample Size Formula for Every Outcome?

No. Different outcomes may have different variances, ICC values, distributions, and expected intervention effects.

For example, academic achievement, attendance, and student satisfaction may exhibit different degrees of classroom clustering.

Binary outcomes may require different calculations from continuous outcomes, and time-to-event outcomes introduce additional considerations.

When a study has several primary outcomes, sample size planning should address the relevant inferential objectives and any multiplicity requirements.

Researchers should not assume that a calculation suitable for one outcome automatically provides adequate power for every other outcome.

Can Baseline Measurements Improve Precision?

Yes. Baseline outcome measurements and strongly predictive covariates can improve precision in some clustered designs.

For example, measuring student achievement before an instructional intervention may help explain variation in post-intervention achievement.

However, the magnitude of the improvement depends on baseline-posttest relationships, the analysis, and the clustering structure.

Sample size calculations should reflect the planned covariate adjustment when sufficient evidence supports the assumed precision gain.

Researchers should avoid assuming an unrealistically large benefit from baseline adjustment merely to reduce the required number of clusters.

When Is Simulation-Based Sample Size Planning Useful?

Simulation can be useful when the design is too complex for simple analytical formulas.

Examples include unequal cluster sizes, repeated measurements, multiple nesting levels, nonnormal outcomes, complex randomization, and anticipated missingness.

A simulation-based approach generates hypothetical datasets under specified assumptions and evaluates how frequently the planned analysis achieves its inferential objective.

Its usefulness depends on the plausibility of the assumptions and the accuracy of the simulated data-generating process.

Researchers should vary uncertain inputs, especially ICC, effect size, cluster-size distribution, and attrition, rather than presenting one optimistic scenario.

How Should Clustered Sample Size Be Reported?

Report the planned and observed numbers of clusters and participants separately.

Describe the expected and actual cluster-size distribution, assumed ICC, target effect size, outcome variance, statistical power or precision objective, and analytical method.

When relevant, report adjustments for unequal cluster sizes, attrition, stratification, baseline measurements, and allocation ratio.

For cluster-randomized trials, the CONSORT extension provides reporting guidance concerning study size, allocation, clustering, and statistical analysis.

The objective is to make the calculation reproducible and demonstrate that it corresponds to the actual research design.

Choosing Between More Students and More Classrooms

The 30-classroom design would often be preferable for this type of cluster-randomized comparison, assuming comparable implementation quality and recruitment feasibility.

However, the design-effect calculations alone do not establish that 30 classrooms provide adequate power. Nor do they demonstrate that six classrooms are sufficient or insufficient for every possible intervention effect.

The correct decision requires a treatment-effect-specific calculation using defensible assumptions.

The example illustrates why choosing a total student count before deciding how many classrooms to recruit can lead to an underpowered design.

Common Misconceptions About Participants and Clusters

How to Plan the Right Combination of Participants and Clusters

Start by defining the estimand and identifying the level of independent sampling or treatment assignment. Then determine the number of groups and individuals required to achieve the desired precision or statistical power.

Sample size should not be chosen solely by targeting a convenient total number of respondents. The relevant information comes from how those respondents are organized and how their observations support the intended comparison.

What to Verify Before Calculating Clustered Sample Size

Frequently Asked Questions About Participants and Clusters

Plan for Independent Groups and the People Within Them

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