# What is Complex Sampling? Part 4: Cluster Sampling

In this series, we’ve already talked about what a complex sample isn’t; why you’d ever bother with a complex sample; and stratified sampling.

All this is in support of our upcoming workshop: Introduction to the Analysis of Complex Survey Data Using SPSS.  If you want to learn a lot more on this topic, check that out.

In this article, we’re going to discuss another common design features of complex samples: cluster sampling.

### What is Cluster Sampling?

In cluster sampling, you split the population into groups (clusters), randomly choose a sample of clusters, then measure each individual from each selected cluster.

The most common and obvious example of cluster sampling is when school children are sampled.  An example I worked on recently in consulting was a survey of Florida high school students.  Included in this survey were questions about their smoking habits and cigarette marketing exposure.

Any time you want to sample students, it’s nearly impossible to sample them directly.  Lists with the contact information of high school students just don’t exist.

But lists of contact information of high schools do.

And the high schools have lists of students.

Even so, having that contact information for the schools isn’t going to help you take a simple random sample of students.

Imagine what that would take:

(1) you contact the thousands of high schools in Florida and ask each one for the list of all their students.

(2) After every single one complies with your request, you use a random sample generator to select a few students from each of 1000 schools (ranging from, say, 0 to 10).

(3) With the never-ending cooperation of the 1000 administrators, you send those surveys to the few kids from each school.

I imagine you see the problems.  As helpful as those administrators may want to be, they have their own legal and time constraints.  Nor is it reasonable for you to work with so many schools given your constraints, or to ask them to spend how many hours of time to get data from just a few students (even if they could).

It makes much, much more sense to sample fewer schools, and include all students from each selected school.  It maximizes resources all around.

And this is what cluster sampling does.

Instead of sampling the individuals (students), sample the clusters (the schools).

### The specific advantages of cluster sampling

• Costs: Cluster sampling can dramatically reduce survey costs (time, money, and energy) by concentrating the sampling units into small areas
• Feasibility: the list of population units may be defined only for the clusters and not the individual units

Both advantages are even more pronounced when the study is not just a survey, but there is some sort of intervention.  (Imagine you have to do a new teaching program for only 2 kids in one school, then 4 at another, and on and on at 1000 different schools).

### The specific statistical challenges of cluster sampling

So, once again, although there are overwhelmingly compelling practical advantages of cluster sampling, there are statistical challenges.

Since each individual in the population of all high school students in Florida didn’t have an equal chance of selection to the sample, the sample members don’t equally represent the population members.

So any statistics based on this unequal sampling will not be unbiased estimates of the population parameters.  And we really like unbiased estimates.

Particularly if clusters (schools) differ a lot, you’re going to need to take that into account when you calculate any statistics.

How?  Through weighting and specifying the sampling design.  This allows your stat software to accurately represent the population from your cluster sample.  More on those in upcoming articles and the workshop.

Analysis of Complex Sample Surveys Made Simple
Are you analyzing data from a nationally representative survey? Learn about the different types of sampling techniques and their effects on data analysis.