Probability Sampling Methods: Multistage, Multiphase, and Cluster Samples

Probability Sampling

Imagine that you are a psychologist and a large school district has hired you to design a study testing the health and wellness of 9th graders in their district because the school district officials want to know how fit their students are.

You know that you need to find out how healthy the 9th graders in the district are, but the problem is that there are so many 9th graders that you won't have the time or budget to measure the fitness of all of them. How should you proceed? How do you choose which 9th graders to test?

The sample of a study is the group of participants in the study, and it is chosen in a process known as sampling. One of the main types of sampling techniques is probability sampling, which involves choosing your sample randomly.

Let's look closer at three different types of probability sampling: cluster, multistage, and multiphase sampling.

Cluster

Ok, so you want to measure the fitness of 9th graders in a large school district, but first you have to choose which 9th graders to test. One way that you might do this is through cluster sampling, or choosing a random sample of clusters to test.

Clusters are just natural divisions. For example, one natural division in a school district is at the school level: School A, School B, and so on. Each school becomes a cluster.

Let's say that you decide to choose four of the high schools in the district and use all of the 9th graders in those four schools as your sample. You'd choose the high schools randomly, by flipping a coin or drawing names out of a hat or using a computer program. Once you've chosen your clusters, or schools, you have your sample. Every 9th grader at those four schools will be in your study.

Cluster sampling works well wherever there are natural divisions, or clusters, in a population. Towns in a county, counties in a state, churches in a town - all of these are examples of naturally occurring clusters.

Multistage

Cluster sampling is a simple and elegant way to choose a sample, but it might not always work well. For example, what if the four schools that you happen to choose are made up of kids from the richer side of town? Their parents can afford to buy them organic food and expose them to more extracurricular sports. As a result, they might be healthier than the other schools in the district.

Another way to draw your sample is through multistage sampling, which involves randomly choosing clusters and then randomly choosing subjects from each cluster. It is known as 'multistage' because there are multiple stages, or steps, to creating the sample. The first stage in multistage sampling is the same as cluster sampling. In our example, we would flip a coin to choose which schools we're working with. We can choose more schools than in cluster sampling, so maybe we will choose eight instead of four schools.

But then, instead of measuring every subject in every cluster we choose, we'd randomly choose a sample from each cluster. For example, remember that in cluster sampling, we used every 9th grade student at each of the schools that we chose. In multistage sampling, we will only take a portion of the 9th graders at each school. For example, maybe we randomly choose several 9th grade homeroom classes from each school.

The advantage of multistage sampling is that it allows us to choose more clusters. Instead of four schools, we drew students from eight schools. We wouldn't be measuring every student at each of those schools, so we are free to choose more schools. This, in turn, could lead to a more representative sample.

Multiphase

So far, we've looked at two ways that we can choose a sample - cluster and multistage sampling. Both of those assume that we are using the same measurement tool on all of our subjects. For example, maybe we are distributing a survey asking about fitness activities and nutrition.

But what if we wanted to also take measurements like blood pressure, resting heart rate, or other physical indicators of fitness? Those tests are expensive and more difficult to administer than a simple survey, so we might not be able to do them on a large sample.