Unit 3: Collecting Data

Sampling Methods

Evaluating simple random, stratified, and cluster sampling for bias.

Advanced20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Whether a Sample Actually Represents Its Population

A school prints a cafeteria-satisfaction survey in the student newspaper and asks anyone interested to mail it in. Before reading on: who is more likely to actually respond to this — students with strong opinions (especially unhappy ones), or the many students who are simply indifferent?

Definition — Sampling Methods and Bias

A simple random sample (SRS) gives every group of the intended size an equal chance of selection. Stratified sampling divides the population into groups (strata) and randomly samples separately within each. Cluster sampling divides the population into naturally occurring groups (clusters), then randomly selects entire clusters. Voluntary response sampling and convenience sampling both tend to produce biased samples — voluntary response overrepresents people with strong opinions; convenience sampling overrepresents whoever is easiest to reach.

Worked Example — Identifying Bias in a Sampling Method

The newspaper survey above is a voluntary response sample: only students who choose to respond are included, and people with the strongest feelings — especially strongly negative ones — are disproportionately motivated to respond. The resulting sample likely overrepresents extreme opinions and underrepresents the many students who are simply satisfied or indifferent, regardless of how large the response count ends up being.

Worked Example — Comparing Sampling Methods on the Same Population

A school of 1200 students (300 each of freshmen, sophomores, juniors, seniors) wants a sample of 120. An SRS numbers all 1200 students and randomly selects 120 — every student, and every possible group of 120, equally likely. A stratified sample instead selects 30 students at random from each of the 4 grade levels (30×4 = 120) — guaranteeing every grade is represented, useful if opinions plausibly differ by grade. A cluster sample splits the school into 40 existing homerooms of 30 students each and randomly selects 4 whole homerooms (4×30 = 120) — more practical logistically, but only as good as how representative each homeroom happens to be of the whole school.

Tip

A large sample size never fixes a biased sampling method — a huge voluntary response sample is still a voluntary response sample, systematically skewed in the same direction no matter how many people respond.

Common Mistakes

Assuming stratified and cluster sampling are the same thing since both involve groups.
Stratified sampling samples from every group; cluster sampling samples only a few whole groups and skips the rest entirely — they solve different problems and behave differently.
Treating a larger sample size as automatically making a sample more representative.
Sample size affects precision, not bias — a large biased sample is still biased; only the sampling method itself, not the sample size, determines whether bias exists.

Key Takeaways

SRS, stratified, and cluster sampling all use randomization but structure it differently, for different practical reasons.
Voluntary response and convenience sampling systematically favor certain kinds of respondents, producing bias no sample size can fix.
A sampling method's bias is a property of the method itself, independent of how large the resulting sample is.

Summary

Sampling methods determine whether a study's results generalize to a population. The next lesson turns to experiments — designed not just to describe a population, but to establish cause and effect.

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