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Stratified, Cluster, and Systematic Sampling
Comparing Three Sampling Designs
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Sampling methods help statisticians learn about a large population without measuring every single member. Choosing the right method matters because it affects cost, speed, and how well the sample represents the whole group. Stratified, cluster, and systematic sampling are three common methods that each organize the population in a different way before selecting data. Understanding their differences helps students decide which method fits a real study.
Stratified sampling divides a population into meaningful subgroups and samples from each subgroup. Cluster sampling divides the population into natural groups and then selects whole groups to study. Systematic sampling chooses members at regular intervals after a random starting point. These methods can all be useful, but they do not produce the same strengths, weaknesses, or sources of bias.
Key Facts
- Stratified sampling: divide the population into strata, then randomly sample within each stratum.
- Cluster sampling: divide the population into clusters, then randomly select one or more clusters and sample all or many members in them.
- Systematic sampling: choose every -th member after a random start, where .
- In proportional stratified sampling, sample from each stratum using n_h = (N_h/N)n.
- A good stratified sample represents all important subgroups, while a good cluster sample uses clusters that resemble the population.
- Systematic sampling can be biased if the list has a repeating pattern that matches the sampling interval k.
Vocabulary
- Population
- The full set of individuals or items that a study wants to describe.
- Sample
- A smaller group taken from the population and actually measured.
- Stratum
- A subgroup in stratified sampling whose members share an important characteristic.
- Cluster
- A natural group in cluster sampling, such as a classroom, city block, or school.
- Sampling interval
- The fixed step size k used in systematic sampling to select every k-th member.
Common Mistakes to Avoid
- Confusing strata with clusters, because strata are formed to separate similar types while clusters are natural groups that each should reflect the population. Mixing them up leads to choosing the wrong sampling plan.
- Using systematic sampling without a random start, because starting at the first item can create predictable bias. A random starting point is needed before taking every k-th member.
- Assuming cluster sampling always gives a representative sample, because selected clusters may differ from one another a lot. If clusters are unusual, the sample can be biased.
- Ignoring subgroup sizes in stratified sampling, because taking equal numbers from very different sized strata can distort the overall sample. Proportional allocation is often needed when estimating population-wide results.
Practice Questions
- 1 A school has 120 ninth graders, 180 tenth graders, and 300 eleventh graders. A researcher wants a stratified sample of 60 students proportional to grade level. How many students should be sampled from each grade?
- 2 A factory has 1,200 products on a conveyor list and wants a systematic sample of 100 products. Find the sampling interval k. If the random start is 7, list the first five sampled positions.
- 3 A city wants to survey households by randomly choosing 8 apartment buildings and surveying every household in those buildings. Is this stratified, cluster, or systematic sampling, and what is one advantage and one possible drawback of this method?