Differentiate simple random sampling, stratified sampling, and cluster sampling; provide use cases.

Differentiate simple random sampling, stratified sampling, and cluster sampling; provide use cases.

• A. Simple random gives every unit equal chance; Stratified divides into subgroups with random samples; Cluster samples intact groups for cost efficiency; use to ensure representation and reduce variance or cost.
• B. Stratified sampling is always cheaper than simple random sampling.
• C. Cluster sampling samples individuals randomly across the population.
• D. Simple random sampling requires identical subgroup sizes.

Answer: (A)

The main idea is how different sampling designs trade off representativeness, precision, and cost, depending on how the population is organized and what you want to learn. Simple random sampling gives every unit an equal chance of being selected, and each draw is independent. This minimizes bias when the population is fairly homogeneous and you have a complete list of units. It’s a straightforward way to estimate overall characteristics without assuming anything about subgroups. Stratified sampling starts by dividing the population into subgroups that are internally similar but differ on the characteristic of interest across groups. Then you take random samples from each subgroup. This ensures that important subgroups are represented in the final sample and can reduce the overall estimator variance, especially when there are known differences between subgroups. You can allocate samples proportionally to subgroup size or use equal or Neyman allocations depending on goals and variance. Cluster sampling packages the population into intact groups, or clusters, and you sample whole clusters (one-stage) or sample within selected clusters (two-stage). This design is especially useful when the population is large and dispersed, making it costly or impractical to list every unit. It offers cost and logistical advantages, though it can increase sampling error if units within a cluster are more alike than the population as a whole. In the example, the description aligns well: random selection with equal chance for each unit; division into subgroups with random draws from each; and keeping intact groups to choose clusters for cost efficiency, with the aim of representing the population well while controlling costs. The other statements clash with how these methods actually work—for instance, stratified sampling isn’t inherently cheaper than simple random sampling, and cluster sampling isn’t described as drawing individuals randomly across the entire population, nor does simple random sampling require identical subgroup sizes.

The main idea is how different sampling designs trade off representativeness, precision, and cost, depending on how the population is organized and what you want to learn.

Simple random sampling gives every unit an equal chance of being selected, and each draw is independent. This minimizes bias when the population is fairly homogeneous and you have a complete list of units. It’s a straightforward way to estimate overall characteristics without assuming anything about subgroups.

Stratified sampling starts by dividing the population into subgroups that are internally similar but differ on the characteristic of interest across groups. Then you take random samples from each subgroup. This ensures that important subgroups are represented in the final sample and can reduce the overall estimator variance, especially when there are known differences between subgroups. You can allocate samples proportionally to subgroup size or use equal or Neyman allocations depending on goals and variance.

Cluster sampling packages the population into intact groups, or clusters, and you sample whole clusters (one-stage) or sample within selected clusters (two-stage). This design is especially useful when the population is large and dispersed, making it costly or impractical to list every unit. It offers cost and logistical advantages, though it can increase sampling error if units within a cluster are more alike than the population as a whole.

In the example, the description aligns well: random selection with equal chance for each unit; division into subgroups with random draws from each; and keeping intact groups to choose clusters for cost efficiency, with the aim of representing the population well while controlling costs. The other statements clash with how these methods actually work—for instance, stratified sampling isn’t inherently cheaper than simple random sampling, and cluster sampling isn’t described as drawing individuals randomly across the entire population, nor does simple random sampling require identical subgroup sizes.