# Identify which type of sampling is used?

## 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. A sample consists of every 49th student from a group of 496 students. An education researcher randomly selects 48 middle schools and interviews all the teachers at each school. A researcher interviews 19 work colleagues who work in his building.

##### 1 Answer
Jul 20, 2017

Keep in mind that Statistics isn't my strong suit; I just looked up these definitions and am using my intuition here.

1) Since subgroups of students are selected (each labeled sophomore, junior, or senior), and samples are selected proportional to the subgroup size, this is stratified sampling.

2) This is quite systematic, because "every 49th" student is selected.

3) This may be a bit confusing, but the word "random" is a decent indication that it is random sampling. To distinguish this from cluster sampling, we note that there is only one level of selection: choose the sample and go with it.

We can also see that "all the teachers at each school" were interviewed, rather than "all the teachers at random schools from these 48", so this is not cluster sampling.

4) Since colleagues were chosen from the researcher's own building, this is convenience sampling. Not much trekking needed!

• Random sampling is the most basic kind, and is when we select a sample (a chunk from the entire group) out of a population (the entire group).

It is literally random picking, but at a single level of selection.

• Stratified sampling is when a population is divided into particular subgroups (or strata), and samples are selected proportionally from these subgroups. (So, if a subgroup has more people in it, a larger sample will be selected.)

In identifying this, it helps to know that this has two levels of selection: the initial subgroup, and then the samples chosen (with actual thought!) from these subgroups.

• Systematic sampling has a certain pattern to it, and is a consistent method. For example, you could select only every $5$th person you see on the same street at the same time each weekday, and that is quite systematic.

Keywords to look for are "every", "each", and anything that indicates a consistent pattern.

• Cluster sampling is when you form groups (clusters) from the population, and then randomly choose clusters from that set. This is not a particularly precise method, especially if the sample sizes are similar.

This has two levels of selection: choosing the clusters/groups, and then randomly selecting which clusters to use.

• Convenience sampling is what it sounds like.

You pick people near you, because it's easy and you may be lazy. :)