Multistage Sample vs Cluster Sample
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Multistage sample
Collecting data and study design
A multistage sample is selected in two or more stages, sampling large groups first and then sampling units within the groups that were chosen.
Multistage sampling is what large national surveys do when no list of every individual exists. For example, you might randomly select 30 school districts, then randomly select 4 schools within each chosen district, then randomly select 25 students within each chosen school. Every stage uses a random mechanism, and the stages often mix methods, such as cluster sampling followed by a simple random sample inside each cluster. The AP course names four random sampling methods (simple random, stratified, cluster, and systematic), so describe a multistage design stage by stage rather than with one label.
Cluster sample
Collecting data and study design
A cluster sample divides the population into groups called clusters, randomly selects whole clusters, and includes every individual in the chosen clusters.
Cluster sampling is used when the population naturally falls into groups that are each meant to resemble the whole population. For example, to survey a school district you might randomly choose 5 schools and then survey every student in those 5 schools. Unlike strata, clusters are ideally diverse within and similar to one another, and you sample entire clusters rather than individuals. It is often cheaper because you only travel to a few locations.