Suppose that you wanted to sample from the entire United States as a whole.
Can you perform a simple random sample (SRS)?
You'd have to somehow account for every person in the United States, and maybe assign them a number, and pull numbers out of a hat, or use some kind of random sampling procedure. This would be too difficult to assign to everyone.
Can you perform a stratified random sample?
Strata, in this case, are still too big. You might take a few people from Maine, and a few people from Minnesota, and a few people from North Dakota, etc., and it would still be too large. Plus, it really wouldn't be cost effective, commuting to all these different places.
Can you perform a cluster sample of states?
If you identified states as clusters, you would randomly select some of the clusters and then sample everyone within that cluster. You'd be sampling entire states. For example, everyone in North Carolina would be in the sample if you select that state as a cluster, which simply isn't feasible.
Therefore, none of those really make any sense. The way out of the box here is a multi-stage design.
Multi-stage sampling is a common sampling procedure utilized when the population is very, very large. With multi-stage sampling, you continue zooming in from larger areas to smaller and smaller areas until you can find a small enough sample of the people you need.
To perform a multi-stage sampling, first select clusters, then take a simple random sample from each cluster.
Let's take a look at an example:
[MUSIC PLAYING] Suppose you want to sample the United States as a whole. Because of geographic simplicity, states make the most sense as clusters. If every state needs to be represented, a stratified random sample should be performed. However, it's not realistic or feasible to sample everyone within each state. So in this instance, you can randomly select five states to make up the clusters for your multi-stage sample. Of these five states, you pick one to begin the process.
Let's say you start with Minnesota. And because it's equally unrealistic to sample everyone in a state, you continue to narrow down your population with a random selection of counties. You once again select five. If you were able to sample everyone in these counties, you can stop. But if you still need a smaller sample size, randomly choose just one, such as Carver County. Then you can randomly select three towns within that county.
Again, if those are small enough units, you can stop. However, if the sample size is still too large, continue to narrow it down by selecting just one town, like Chaska. Within Chaska, for example, you can sample some neighborhoods.
Typically, by the time you get to the neighborhood level, it's easy enough to walk around and get almost everybody within that neighborhood. This method of drilling down from state to county to town to neighborhood would give you a multi-stage sample of your first cluster, Minnesota. Then it's on to the next cluster, where you would repeat the process with the remaining four to achieve a multi-stage sampling of the United States.
Now you can move onto the next cluster where you would repeat this process with the remaining four states.
Source: SOURCE: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS. MN MAP: HTTPS://EN.WIKIPEDIA.ORG/WIKI/LIST_OF_COUNTIES_IN_... CARVER COUNTY: HTTPS://EN.WIKIPEDIA.ORG/WIKI/LIST_OF_COUNTIES_IN_...