Question

For each of the following ​situations, explain how you could select a sample using the named sampling procedure.

A. There are 100 kindergarten classes in the school system. You want to use multistage cluster sampling to select a sample of 100 children.

B. There are 220 principals in the school​ system, and you want to use simple random sampling to select a random sample of 40 participants.

C. There are 240 principals in the school​ system, and there are approximately twice as many secondary principals as elementary principals. You want to use stratified sampling to select a sample of 45 principals to ensure proportional representation.

D.  You have a directory that lists the names and addresses of​ 12,000 teachers. You want to use systematic sampling to select a sample of​ 2,400 teachers.

E. You want to survey the attitudes of parents affiliated with one elementary school. What would be an example of using convenience sampling to select a​ sample?

F. You want to sample principals who are known for supporting multicultural diversity in their schools. What would be an example of using snowball sampling to select a​ sample?

Answer 1

There are several methods of sampling from the population. Each method has its advantages and disadvantages. We have to choose a method which reduces the cost of sampling as well as reduces the sampling bias. Various methods are discussed below:

A. Multistage cluster sampling: Divide the 100 classes into clusters of 100 children each. If the last cluster has less than 100 children, discard this cluster. This is the first stage of multistage clustering. Randomly choose one cluster from the clusters formed. Sample all the children from this cluster.

B. Simple Random Sampling: Prepare a list of the 220 principals. Ensure that each principal has an equal chance of getting selected. Randomly choose 40 principals from this list.

C. Stratified Sampling: Divide the principals into two groups of elementary and secondary principals. From the elementary principals, randomly choose 15 principals. From the secondary principals, randomly choose 30 principals. So, the total sample size is 15+30=45 and the ratio of the principals is also maintained.

Note: When choosing from each group, any of the other sampling methods can be used.

D. Systemic sampling: From a list of 12,000 teachers, we have to select 2,400 teachers. For the starting point, we randomly select one teacher from the entire list. Since 12,000/2,400 = 5, we then select every 5th teacher from that list. Note that we circle back on reaching the end of the list.

E. Convenience Sampling: A sampling of only those who attend a parents-teachers meeting is an example of convenience sampling of parents affiliated with one elementary school.

F. Snowball Sampling: In snowball sampling, the first principal is chosen randomly. Then, that principal is asked for references of other principals. Those principals are surveyed next and the process continues till the desired sample size is reached.