sampbasics() — Populations & sampling

Who you study (the population) versus the slice you actually measure (the sample) — and how to pick it fairly.

population → sample

Key idea

• Population = the ENTIRE group you want to describe; sample = the smaller part you actually measure. (e.g. all 50,000 students vs 500 surveyed)
• A census measures the whole population; a survey / sample survey measures a sample instead — faster and cheaper. (e.g. census = everyone; survey = a sample)
• Target population = exactly who you want to describe; the sampling frame is the actual list you draw from (ideally it matches the target). (e.g. target: all adults · frame: the phone book)
• Sampling units are the individual things you draw (people, households, items). (e.g. one household = one unit)
• A sample chart is built from sample data; a population chart from the whole population — the sample chart ESTIMATES the population one.
• Bias = a systematic error that tilts results away from the truth; an unbiased sample represents the population fairly. (e.g. too-high or too-low every time)
• Common sources of bias: undercoverage (the frame misses people), non-response, voluntary (self-selected) response, and leading question wording.
• Simple random sampling (SRS): every unit — and every possible group — has an equal chance. The fairness benchmark. (e.g. names from a hat)
• With replacement, the same unit can be drawn again; without replacement, each unit is drawn at most once. (e.g. dice rolls vs dealt cards)
• Stratified sampling: split the population into homogeneous strata (one group = a stratum) and randomly sample WITHIN each. (e.g. sample within each grade level)
• Cluster sampling: split into clusters, then randomly pick whole clusters and survey everyone in them. (e.g. pick 10 schools, survey all pupils)
• Systematic sampling: order the list and take every k-th unit after a random start. (e.g. every 20th person on the roll)

Where you'd use it

• A polling company wants to know how a country of 40 million will vote (the population). A census is impossible, so they take a random sample of about 1,000 people and report the result with a margin of error.
• A factory cannot test every one of 100,000 bulbs (that would be a destructive census), so it draws a simple random sample of 200 to estimate the defect rate.
• A school surveys students by randomly choosing a few whole classes (cluster sampling) instead of a few students from every class, because it is far easier to administer.
• A health study splits people into age strata and samples within each (stratified sampling) so every age group is properly represented.

Frequently asked questions

What is the difference between a population and a sample?

The population is the whole group you want to describe (every voter, bulb, patient); the sample is the smaller part you actually measure. You use the sample to estimate the population.

When should I do a census instead of a sample?

A census measures everyone — worth it only when the population is small, the stakes are high, or testing is cheap and non-destructive. Usually a sample is faster, cheaper, and accurate enough.

What is a sampling frame, and why does it matter?

The frame is the actual list you draw from. If it doesn’t match the target population (e.g. a phone list misses people without phones), you get undercoverage bias no matter how big the sample.

What exactly is bias?

A systematic error that pushes results the same wrong way every time. Unlike random error, it does not shrink as you collect more data — only better design fixes it.

Does a bigger sample remove bias?

No. A large but skewed sample just gives a confidently wrong answer — the 1936 Literary Digest poll asked 2.4 million people and still got it wrong. Randomness, not size, fights bias.

What makes a sample “simple random”?

Every unit — and every possible group of units — has an equal chance of being chosen, like drawing names from a hat. It’s the fairness benchmark other methods are judged against.

With replacement vs without replacement?

With replacement, a unit can be drawn more than once (like rolling a die); without replacement, each unit appears at most once (like dealing cards). Surveys almost always sample without replacement.

Stratified vs cluster sampling — what’s the difference?

Stratified: split into similar groups (strata) and sample within each so every group is represented. Cluster: split into groups (clusters) and randomly pick whole clusters — cheaper, but each cluster must resemble the population.

What is systematic sampling?

Order the list and take every k-th unit after a random start (e.g. every 20th name). Simple and fast, but it can fail if the list has a hidden repeating pattern matching k.