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Compare simple random sampling, stratified, cluster, and systematic sampling methods.
Learn step-by-step with practice exercises built right in.
Simple Random Sample (SRS)
Stratified Random Sample
Cluster Sample
Explain the difference between a Simple Random Sample (SRS), a stratified sample, and a cluster sample. Give an example of when each would be appropriate.
Simple Random Sample (SRS):
Every possible subset of size has an equal chance of being selected. Use random methods (random number generator, lottery) with no systematic pattern.
Example: Select 100 voters from a list of 10,000 registered voters by numbering them and using random digits.
Pros: Unbiased, conceptually simple Cons: Requires complete list; doesn't guarantee representation of subgroups
Avoid these 3 frequent errors
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Systematic Sample
Multistage Sampling
Convenience Sample
Undercoverage: some population members cannot be selected
When to use each:
Check: Is population accessible? → SRS Check: Natural subgroups? → Stratified Check: Geographically dispersed? → Cluster Check: Ordered list? → Systematic
"Describe a sampling method" essays require: define the method, identify strata/clusters, explain how randomization is implemented, and discuss any bias risks.
Divide the population into strata (groups by characteristic), then randomly sample from each stratum.
Example: A university has 2,000 freshmen, 1,800 sophomores, 1,700 juniors, 1,500 seniors. To survey campus housing, randomly sample 40 from each class (proportional to size).
Pros: Ensures representation of each subgroup; more efficient for comparing groups Cons: Requires knowing strata beforehand; more complex
Cluster Sample:
Divide population into clusters (geographic or natural groups), randomly select a few clusters, then survey all or random sample within selected clusters.
Example: To survey 5,000 high school students across 50 schools, randomly select 5 schools, then survey all or random sample within those 5 schools.
Pros: Cost-efficient (less travel), practical for geographically dispersed populations Cons: May introduce bias if clusters are not representative; within-cluster similarity can distort results
When to use:
A pollster stands outside a shopping mall on a Saturday and surveys every 10th person who walks by. Is this a probability sampling method? Identify the potential bias.
Method type: This is systematic sampling (every 10th person) combined with convenience sampling (mall intercept). It appears to use a systematic rule but is actually non-probability because:
Potential biases:
Undercoverage: Missing people who don't visit malls (elderly, disabled, those who shop online, night-shift workers)
Temporal bias: Saturday shoppers differ from weekday shoppers (leisure vs. work-focused, different age/income mix)
Location bias: Mall shoppers differ from non-mall shoppers; may not represent the broader community
Voluntary response bias (if participation is optional): People willing to stop and answer differ from those in a hurry
Result: The sample is not representative. If surveying about shopping habits or product preferences, the results would overrepresent mall shoppers and be unreliable for the general population.
Better approach: Use true SRS from voter rolls or census data (if available) or conduct random-digit dialing for phone surveys.
A researcher wants to estimate average income in a city of 500,000. Evaluate three sampling plans: (A) SRS of 1,000 people, (B) Stratified sample (100 each from 10 neighborhoods), (C) Convenience sample (students from a local university). Which is best and why?
Plan A: SRS of 1,000
Pros:
Cons:
Plan B: Stratified sample (100 per neighborhood)
Pros:
Cons:
Plan C: Convenience sample (university students)
Pros:
Cons:
Best choice: Plan B (Stratified by neighborhood)
Reasoning:
Conclusion: C is obviously wrong (not representative). Between A and B, stratified sampling is more practical and achieves high precision with manageable data collection.