Cluster Sampling

It’s not just costly to survey 50,000 households from aroun stratified sampling a country; it’s flat-out logistically unfeasible. That’s where cluster sampling comes in: break down your population into clusters, pick a few random clusters out of the bunch, and then analyze your data within these clusters only.

That’s not all, however, since the technique carries a very specific disadvantage. The good news is that this guide explains everything about cluster sampling, including what you give up when using it, how to quantify this disadvantage, and when it is worth doing.

What Is Cluster Sampling?

The cluster sampling procedure involves dividing a population into smaller groups or clusters. Some of the selected clusters are randomly sampled for further analysis.

In this case, a cluster is a naturally occurring subdivision of a population into groups prior to research rather than an artificially created division. For instance, a population can be divided into schools, counties, hospitals, wards, blocks of households. The task of a researcher is to examine the existing population structure rather than to create new subdivisions.

A well-organized cluster is expected to be a mini-version of the whole population. In order to provide such a representation, each group must possess an internal heterogeneity; that is, all sub-populations represented in the sample must occur in clusters as well. Otherwise, if each of the selected clusters contains households with similar incomes, the research will provide little information on the distribution of income levels. In other words, internal heterogeneity distinguishes cluster sampling from stratified sampling.

How Cluster Sampling Works — Step by Step

However, in reality, the procedure gets divided into four stages. While the theory is neat and clear, it’s at the judgment stage for each that research gets it wrong.

For this particular section, one example is used consistently – a national study of diabetes prevalence.

Step 1 — Define Your Population

The target population must be defined first before any groups are identified. “Adults in a particular country” is too broad to formulate a sampling frame out of. “Adults aged 18 years old and above permanently residing in the country at the time of conducting the study” is an example of a clear population definition.

The definition you come up with will help identify your clusters; if not done clearly, you risk selecting clusters from an inappropriate sampling frame.

Step 2 — Divide into Clusters

For a cluster to be considered a proper cluster, there need to be two requirements: first, there should be no overlap among the clusters, and secondly, all the clusters combined must cover the whole of the population. In the study about the diabetic prevalence, the first step may be to break the country into districts – that is, to consider all 500 of them as possible clusters.

But the most important thing at this stage will be the diversity within the cluster; and this means that if all people in a single cluster are the same regarding the criterion under discussion, then that particular cluster will have no value at all. This is indicated by the intraclass correlation coefficient, or ICC, which we will discuss later.

Step 3 — Randomly Select Clusters

Label the clusters with numbers and draw your sample randomly. All the clusters will have an equal chance of being selected. In the case of the study on diabetes, you may select 30 districts out of 500 randomly with the help of a random number generator.

This one aspect that is rarely mentioned in introductions is: When there is a marked difference between the sizes of the clusters, then equal probability sampling will yield an unrepresentative sample. The solution to this problem is usually probability proportionate to size (PPS).

Step 4 — Collect Data

When conducting one-stage sampling, you observe every individual in the selected clusters. On the other hand, when using two-stage or multi-stage sampling techniques, you randomly choose individuals from within the selected clusters. It is how you conduct your sampling that determines how precise your results will be.

The 3 Types of Cluster Sampling

Honestly, the three types are often taught as minor procedural variations. They’re not. Each one reflects a different tradeoff between cost, fieldwork complexity, and statistical accuracy.

Single-Stage Cluster Sampling

The clusters are picked randomly, and then you survey each and every single individual within them.

That’s it.

The World Health Organization’s Expanded Program on Immunization developed such a design – 30 randomly selected geographic clusters, seven eligible children in the age group 12-23 months in each cluster for a total of 210 children – to gauge vaccine coverage in developing countries where there is no registry of the population. It was purposefully designed to be easy to conduct since it was assumed that field workers would not have access to any computer program or statistician. In 1982, an analysis of the technique was done based on results collected from surveys in 25 countries. 

Use single-stage whenever you can realistically survey all individuals in your cluster, and when simplicity outweighs efficiency gains from a more complicated design.

Two-Stage Cluster Sampling

First, you will have to choose the clusters and then draw random samples from each cluster chosen and not study all the members within the cluster.

With the second phase of sampling, you will have complete control over the size of your sample irrespective of the size of each cluster. For example, thirty clusters are picked out; and within each of them, 200 are drawn out randomly; the sample remains the same even if the cluster contains 40,000 members or 400,000 members.

Multi-Stage Cluster Sampling

Multi-stage sampling involves even more stages of selection, whereby at each stage the size of the sample decreases. Multi-stage sampling is used by the US National Health Interview Survey, where counties are first selected, followed by census tracts from the counties, then households from the tracts, then people from the households.

There is really no other way if you need to conduct a survey for an entire country with millions of respondents. Statistical programs for analyzing complex survey data are necessary, and normal regression programs will give you too small standard errors.

Cluster Sampling vs. Stratified Sampling — Which Should You Use?

This is the question people actually want answered, and to be fair, the two methods sound similar until you look at what each one requires.

In cluster sampling, the groups selected are randomly chosen while the others are completely disregarded. The groups must have variety among themselves but be homogenous relative to each other.

In stratified sampling, samples must be drawn from all groups, with no exclusion at all. The characteristic used for classifying into different groups must be a common one — age group, income level, region, etc.

Rule of thumb regarding which method to use: use cluster sampling if your clusters resemble little populations. On the other hand, use stratified sampling if your clusters represent some specific segments that need comparison.

For instance, when investigating school performance on a national level, one may employ cluster sampling since each individual school reflects all categories of students found throughout the entire population. However, when evaluating health status based on different income levels, stratified sampling should be preferred since it is impossible to exclude any segment due to randomization.

Generally, cluster sampling is cheaper but less accurate than stratified.

Real-World Examples of Cluster Sampling

What is rather strange is that most writings on the subject stick to imaginary illustrations – for instance, seventh graders, fictitious cities, and unspecified polling firms. Illustrations that have appeared in research papers tend to be more helpful; here are three.

Public Health — WHO’s EPI Vaccination Coverage Surveys

The World Health Organization’s Expanded Programme on Immunization employs a survey of thirty clusters to determine vaccination rates among children in communities without any national system for registering births. A random selection is made of thirty geographic regions, and field staff then surveys seven sequential homes within each region. The end result, a total of 210 homes surveyed, is a sufficiently small survey size but yet adequate enough to draw valid conclusions from. It is not the precision, but rather the practicality, that makes this survey effective.

Education — The National Assessment of Educational Progress (NAEP)

The NAEP, organized by the National Center for Education Statistics, involves multi-stage cluster sampling in the US. First come geographic regions (PSUs consisting of one or several counties); next, schools located within PSUs form clusters on stage two; and third, students are randomly chosen from schools that make up the sample. There is no need to create an exhaustive national list of all students. Thus, a sample-based representative national portrait of achievement emerges.

Market Research — Regional Store Audits

There is a supermarket chain that has a total of 600 outlets in 50 regions. The auditing of all outlets in the supermarket is extremely expensive. In this case, you may proceed as follows: treat each of the 50 regions as a cluster, select 15 such clusters randomly, then audit all stores within the selected 15 clusters. You would have analyzed about 180 stores.

Advantages and Disadvantages of Cluster Sampling

Advantages

The key feature of cost efficiency is legitimate, as studying scattered communities is costly as it requires contacting individuals one by one. Sampling by clusters minimizes the costs of travel and logistics as all activities take place in certain places. Moreover, such an approach may be applied when there is no population frame available at the individual level but only at the cluster level.

It means that the researcher does not need a list of people but only the list of clusters: communities, institutions, regions.

Disadvantages

Which sounds obvious until it isn’t: the disadvantage is a measurable loss in statistical precision, not just a vague reduction in quality.

The design effect (DEFF) is the number that captures this. It tells you how much larger your cluster sample needs to be to match the precision of a simple random sample. The formula is DEFF = 1 + (n − 1) × ICC, where n is average cluster size and ICC is the intraclass correlation coefficient.

The multiplier for the sample size depends entirely upon the design effect; a DEFF of 2.0, which is the design effect that the WHO EPI surveys had taken as a baseline value, means that double the number of observations is required to achieve accuracy equivalent to that obtained by simple random sampling. This is the real consequence. It is not just that the estimates are less precise. There is a definite multiplier depending upon cluster size and ICC that can be calculated even prior to conducting the study.

Common Mistakes in Cluster Sampling

I’ve seen four versions of these mistakes described across methodology courses and published critiques, and the fourth one gets underplayed in almost every introductory treatment.

Mistake 1 — Clusters That Are Too Homogeneous

However, if individuals within a cluster resemble each other a lot (in terms of high ICC), then your actual sample size would be less than indicated by the numbers. If you have twenty clusters consisting of households with almost the same earnings, then you get much less statistical information than what the number indicates. The simple answer to the dilemma is that you should calculate your ICC before you make the final design decision.

Mistake 2 — Too Few Clusters

To reduce costs, it may be common for researchers to reduce the number of clusters and balance that out with increasing the number of individuals sampled from each cluster. But it would be a mistake. The main source of variance in cluster sampling is the number of clusters included, not the individuals sampled within those clusters.

Mistake 3 — Ignoring the Design Effect in Sample Size Calculations

Sample size calculators assume simple random samples by default. Put your required precision into a calculator without accounting for the DEFF factor, and you’ll end up with a smaller sample size than needed. All sample sizes designed for cluster sampling should have that taken into account at the outset.

Mistake 4 — Analyzing Clustered Data as Though It Were a Simple Random Sample

More researchers have performed this procedure than the literature implies. The standard errors, which have been calculated without any corrections for clustering, are too low; the p-values are too high; and the confidence intervals are too narrow. There must be proper techniques used, such as multilevel models, survey weights, and software for analyzing complex surveys. Not taking this step into account not only reduces precision but results in errors.

When to Use (and When NOT to Use) Cluster Sampling

That’s kind of the whole point of learning this method: the choice should be deliberate, not a default because the population happens to be large.

Use cluster sampling when:

• Your population is extensive, and it is scattered throughout the geographical area.
• There is no individual listing available, but there is clustering available.
• The costs involved in transportation and logistics do not allow individual sampling.
• There is sufficient diversity in natural clusters to cover the entire population.

Do not use cluster sampling when:

• Your clusters have homogenous structure within them; you will experience high value for design effect and be unhappy with your effective sample
• You already have a small sample size; the design effect will work to diminish statistical precision quickly
• Statistical precision is critical (medical trials, drug efficacy studies, etc.)
• You require reliable estimates for various sub-groups; stratified sampling guarantees all sub-groups will be covered; cluster sampling leaves that up to chance

Frequently Asked Questions

Closing

It is not the scientists who know the definition of cluster sampling by heart that conduct it in a good manner, but those who figured out the design effect before selecting even a single respondent, selected clusters that actually reflect the entire population, and made up their mind about the precision compromise beforehand.

Do select the technique depending on your research needs, and not simply because it sounds easier to explain.