Clustered Sampling Versus Clustered Assignment

Two Different Ways a Study Can Be Clustered

A data set may contain many individual records but much less independent information than its row count suggests. To understand why, it helps to ask two separate questions: How were the observations sampled? And at what level was the intervention assigned? These questions describe different parts of a study design, even when both involve groups such as schools, clinics, or households.

In clustered sampling, investigators select groups or settings and then observe multiple people or other units within them. In clustered assignment, the intervention or condition is assigned to a group, so its members share the same assigned condition. A study can have either feature or both. The distinction matters because shared environments can make outcomes similar, while group assignment limits which units provide treatment comparisons.

Clustered Sampling: Groups Enter Through Selection

Suppose investigators select schools and then record information on students in those schools. The schools are sampling units at the first stage, and the students are observed within the selected schools. Students in one school share teachers, facilities, policies, and local circumstances. Such shared conditions can make their outcomes more alike than outcomes from students in different schools. In regression terms, observations within a school may therefore be dependent.

That dependence is not created by assigning students to an intervention. There may be no intervention at all. It arises because observations are grouped in shared settings, and the sampling design selects those settings as part of how the data are obtained. If the scientific goal is to describe a broader population of schools or students, the sampled schools are important sources of information about that population.

The number of individual records still matters: it describes how many measurements were collected. But it does not turn every person into a separate independent draw when people share sampled settings. The relevant count of primary sampling units is the number of independently selected clusters under the stated sampling assumptions. A sampling design that selects a fixed number of groups without replacement can itself make selection indicators dependent; the exact design should not be replaced with an assumption of independent selection.

Clustered Assignment: Groups Receive the Condition

In an experiment, assignment is clustered when a condition is allocated to a group rather than separately to each person. For example, a service might be introduced at the clinic level, with every participating patient at a clinic receiving the clinic's assigned service. The clinic is then the assignment unit; the patient is an outcome-measurement unit.

This design has a direct consequence for treatment comparisons: patients within one clinic do not provide separate, independently randomized assignments. They all inherit the clinic's assignment. The number of people measured can be much larger than the number of assignment units. That does not mean the assignment indicators for different clinics are necessarily independent; their dependence is determined by the randomization scheme.

For example, assigning exactly half of a fixed set of clinics to each condition constrains the assignment of any one clinic once the assignments of others are known. The clinics are still the units to which treatment was assigned, but the indicators recording their assignments are dependent. It is therefore important to distinguish the number of assignment units from the number of independent randomization decisions.

Why the Two Counts Answer Different Questions

The sampling design and the assignment design identify different routes by which information can be limited. Sampling units concern how the observed settings enter the data and, in a sampling-based analysis, how well those settings represent a wider population. Assignment units concern which units received randomized conditions and therefore where treatment variation was introduced.

These counts should not be substituted for one another. A study might sample a large number of people from a small number of schools, or it might randomize a small number of clinics while measuring many patients at each clinic. In the first case, the number of sampled schools is central to the sampling structure. In the second, the number of randomized clinics is central to the assignment structure. Neither count alone completely describes the dependence or the precision of every possible regression estimate.

A useful short justification is to trace how a shared source enters the design. If two records share the same selected school, they share a sampled setting; their errors or outcomes may therefore be related. If two people share the same clinic-level assignment, their treatment indicators are identical because one clinic condition applies to both. In either case, treating the records as unrelated simply because they occupy different rows ignores a feature of how the data were generated.

When Sampling and Assignment Both Occur

Many experiments contain both structures. Investigators may first sample settings from a population and then randomize an intervention to groups within those settings. In that case, the same label—for example, “clinic”—may describe a sampling unit and an assignment unit, or the two levels may differ. The study description must establish which role each group plays.

The following hypothetical design makes the distinction explicit. Assume six regions are independently selected as primary sampling units. Two hospitals are included in each region, and within each region a random procedure assigns exactly one hospital to a new program and the other to usual care. The pairwise randomizations in different regions are performed independently. Thirty patients are measured per hospital.

Common Mistake: Treating Every Cluster as an Independent Assignment

A frequent error is to say, “There are eight clinics, so there are eight independent treatment assignments.” The first part may correctly count the clinic-level assignment units, but the conclusion about independence does not follow. In a fixed allocation of four of eight clinics to treatment, any two clinic indicators have joint treatment probability \(3/14\), not \(1/4\). The allocation rule creates dependence.

The correction is to report the design precisely: eight cluster-level assignment units, with assignment indicators dependent under a fixed four-of-eight allocation. If a study uses independent random assignment at the cluster level, say so; if it uses a constraint, matching, or another allocation rule, describe that rule instead. Do not infer independence from the number of groups.

A related mistake is to treat a sampling cluster as though it must also be an assignment unit. A survey of students sampled within schools has school-level sampling but no treatment assignment at all. Conversely, an experiment can randomize clinics even if the participating clinics were not selected through a probability sample. Identify the role from the actual design, not from the group name.