Question

Imagine that you had to gather a random sample $(N=300)$ of the student body at your school. How would you acquire a list of the population? Would the list be complete and accurate? What procedure would you follow in selecting cases (that is, simple or systematic random sampling)? Would cluster sampling be an appropriate technique (assuming that no list was available)? Describe in detail how you would construct a cluster sample.

Short answer

Gather a complete student list from school records. Use simple or systematic random sampling if the list is available. If not, use cluster sampling by selecting entire homerooms or classes randomly.

Step-by-step solution

Title - Obtain the Population List

First, gather a list of the entire student body. This list can be obtained from the school administration, typically from the registrar’s office or student records department. Ensure that the list is up-to-date and comprehensive, including all students currently enrolled.

Title - Verify Completeness and Accuracy

Check the list for completeness and accuracy. This involves verifying that there are no duplicate entries, missing students, or outdated information. Cross-checking with attendance records or recent class lists may help to ensure everything is accurate.

Title - Choose Sampling Method

Decide on the sampling method. If you have a complete and accurate list, you can use simple random sampling or systematic random sampling. Simple random sampling involves randomly selecting 300 students from the population list. Systematic random sampling requires selecting a starting point randomly and then selecting every kth student, where k is the population size divided by 300.

Title - Simple or Systematic Random Sampling Procedure

For simple random sampling, use a random number generator to select 300 students from the list. For systematic random sampling, first calculate the interval k (total number of students / 300). Then select a random starting point between 1 and k, and include every kth student in your sample.

Title - Cluster Sampling Consideration

If no complete list of students is available, consider using cluster sampling. Cluster sampling involves dividing the population into clusters (e.g., classes, grade levels, or homerooms) and then randomly selecting entire clusters. Each selected cluster will then be included in the sample.

Title - Constructing a Cluster Sample

To create a cluster sample, first identify natural clusters within the school, such as homerooms. Randomly select a certain number of these clusters (e.g., 10 homerooms if each homeroom has about 30 students). Once selected, include all students from these clusters in your sample.

Key concepts

Random Sampling

Random sampling is a method where each individual in a population has an equal chance of being selected. Imagine placing every student's name in a hat and drawing 300 names randomly. This approach ensures that every student has the same probability of being part of the sample. Random sampling is excellent for minimizing bias. It gives a fair representation of the entire student body because each selection is entirely by chance. For our task, this would involve using a computer program to randomly select 300 students from our complete and accurate list.

Systematic Sampling

Systematic sampling involves selecting every kth individual from a list, where k is a constant interval. Starting from a randomly chosen point on the list, you would select every kth student. For example, if your school has 3,000 students and you need a sample of 300, k would be 10 (since 3000/300 = 10). You would pick a random number between 1 and 10 to start, and then select every 10th student from the chosen starting point. Systematic sampling is simple and quick but requires an accurate, up-to-date student list to ensure nobody is missed or counted twice.

Cluster Sampling

Cluster sampling is a technique where the population is divided into naturally occurring groups, or clusters. In a school setting, clusters could be homerooms, grade levels, or clubs. After identifying the clusters, you would randomly select a few clusters and include every student within those selected clusters in your sample. This method is particularly helpful if a complete student list isn't available. For example, if there are 100 homerooms and you need a sample of 300 students, you could randomly choose 10 homerooms, assuming each homeroom has around 30 students. Cluster sampling can be efficient but may introduce bias if the clusters differ significantly from each other.

Student Population List

The student population list is crucial for any sampling method. This list includes all students enrolled in the school and is typically maintained by the school's administration office. It's essential to ensure this list is complete and accurate before selecting a sample. Any mistakes or omissions in the list could lead to a biased sample. You can verify the list by cross-checking with other records such as attendance logs or class rosters. Ensuring the list’s accuracy is the first step towards drawing a representative sample, whether using random, systematic, or cluster sampling methods.