Question

For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, you'll ask to get a list of all current members and contact 100 members at random. a) What kind of design have you used? b) What could go wrong with vour desion?

Short answer

a) Cluster sampling. b) Potential biases if selected churches aren't representative.

Step-by-step solution

Understand the Sampling Design

In the survey process, the selection of the sample involves choosing a subset of units from a larger population. In this exercise, the city has 17 Catholic churches, and you are picking 3 at random to survey their members. This initial step of selecting entire churches falls under the category of a cluster sampling design. Cluster sampling is used when it is difficult to conduct a simple random sample of the entire population because of logistical concerns. Here, churches serve as clusters.

Realize the Potential Biases

Cluster sampling might lead to biases if the clusters (churches) are not homogeneous or representative of the entire population. For instance, different churches may serve differing demographic or socio-economic groups. By selecting only 3 churches, there is a risk that the sample may not capture the full diversity of all church members in the city. Additionally, limiting the survey to 100 members from each of these 3 churches might not adequately represent larger or more densely populated churches.

Key concepts

Cluster Sampling

Cluster sampling is a type of sampling method used when populations are too large or dispersed to undertake a simple random sample easily. Instead of sampling individuals directly, we select larger groups, or "clusters," from within the population. These clusters should ideally represent the diversity of the whole population. In the example provided, the clusters are the Catholic churches within the city. Rather than attempting to compile a list of every individual church member, which could be logistically complex and time-consuming, three churches were selected at random to represent the entire population of church members. This method is efficient and cost-effective, especially when dealing with large populations. However, the goal is to ensure each church, or cluster, accurately mirrors the diversity of the overall group to avoid inaccuracies in the survey results.

Sampling Bias

Sampling bias occurs when the sample chosen is not representative of the population being studied, leading to skewed results. In the context of cluster sampling, bias can creep in if the selected clusters do not reflect the wider population's characteristics. In the exercise, choosing only three churches could introduce bias if these particular churches are not diverse. Each church might cater to different demographics in terms of age, income levels, or even cultural values. Without ensuring this diversity within chosen clusters, the survey results might misrepresent the preferences or opinions of all church members. To mitigate sampling bias, one could ensure the selected clusters vary by factors such as location, size, and membership demography, or consider increasing the number of clusters despite possible logistical challenges. This way, the sample can more accurately capture wider trends and viewpoints.

Survey Design

Survey design is crucial in gathering reliable and valid data from your selected sample. Designing an effective survey involves carefully choosing the sampling method, determining sample size, and formulating questions that yield clear, unbiased responses. For this exercise, the design starts with cluster sampling, isolating the churches as the primary units of selection. After randomly choosing three churches, the next step is to conduct random sampling within each selected church to pick 100 members. However, thoughtful survey design also involves weighing the trade-offs between feasibility and accuracy. While cluster sampling is practical, combining it with randomness at individual levels helps refine the results. Additionally, properly structuring survey questions plays a pivotal role. Questions must be clear and neutral to avoid misinterpretation or leading bias, ensuring the responses reflect true sentiments as much as possible. This holistic approach in survey design aids in achieving comprehensive and informative outcomes.