Final answer:
To select a multi-stage cluster sample of first-year English students, one must define the population, create clusters of colleges, randomly select clusters, create sub-clusters within the chosen institutions, randomly select sub-clusters, and finally select the individuals within these sub-clusters.
Step-by-step explanation:
Steps Involved in Selecting a Multi-Stage Cluster Sample
To select a multi-stage cluster sample of students taking first-year English in U.S. colleges and universities, follow these steps:
- Define the population: Identify the complete set of U.S. colleges and universities offering first-year English courses.
- First-stage clustering: Group the colleges and universities into clusters. Clusters can be based on various characteristics, such as geographical location, size, or type of institution (public, private, community college, etc.).
- Randomly select clusters: Use a simple random sampling technique to select a number of these clusters for the study.
- Second-stage clustering: Within each selected college or university, create sub-clusters based on classes or sections of the first-year English course.
- Randomly select sub-clusters: From each selected college or university, again use simple random sampling to choose specific classes or sections that represent the sub-clusters.
- Select individuals: Finally, choose all the students within the selected classes or sections to form your sample. Alternatively, a further stage of random sampling could be performed within each sub-cluster if the classes are too large.
Applying the multi-stage cluster sampling method ensures a diverse and representative sample, while also allowing researchers to manage practical constraints, such as time and resources.