Random Sampling
Introduced| English | Meaning |
|---|---|
| random sampling/ˈrændəm ˈsæmplɪŋ/ | random sampling |
| simple random sample/ˈsɪmpl ˈrændəm ˈsæmpl/ | simple random sample |
| stratified/ˈstrætɪfaɪd/ | Describing sampling that divides a population into groups and samples within each group. |
| cluster/ˈklʌstə/ | Describing sampling that selects whole groups from a population and studies members within the selected groups. |
| systematic/ˌsɪstəˈmætɪk/ | Describing sampling that selects members at a fixed interval after a starting point, usually chosen randomly. |
Why randomize the choice?
- Random sampling 随机抽样 uses chance to decide who gets into the sample.
- Chance has no agenda, so it avoids the human tendencies that create bias.
- A random sample tends to look like the population in the long run.
- Randomness is what makes a fair generalization possible.
The simple random sample
- A simple random sample (SRS) 简单随机样本 gives every group of $n$ individuals an equal chance.
- Carry it out: number the population, then draw numbers (random digits or a hat).
- Every individual — and every combination — is equally likely.
- The SRS is the gold-standard idea the others build on.
Random outcomes: dice make each face equally likely under fair conditions
Stratified, cluster, systematic
- Stratified 分层: split into similar groups (strata), then take an SRS within each.
- Cluster 整群: split into groups (clusters), randomly pick whole clusters, sample everyone in them.
- Systematic 系统: pick a random start, then take every $k$-th individual.
- Stratify to guarantee representation of each group; cluster for convenience when groups are scattered.
Randomness enables generalization
- Because a random method has no bias, its results generalize to the population.
- The sample statistic becomes a trustworthy estimate of the population value.
- Non-random ("convenience") samples give you no such guarantee.
- Later units' inference formulas assume the sample was random.
Don't confuse stratified and cluster sampling. Stratified: strata are internally similar, and you sample from every stratum (to guarantee each is represented). Cluster: clusters are mini-populations, and you sample only some whole clusters. Same word "groups," opposite logic — mixing them up is the classic exam slip.
Survey $100$ of a school's $1000$ students.
- SRS: number all $1000$, draw $100$ random numbers.
- Stratified: take $25$ at random from each grade (the strata) → every grade represented.
- Cluster: randomly pick $4$ homeroom classes (clusters) and survey all $\approx 100$ students in them.
Random sampling removes bias so results generalize. A simple random sample (SRS) gives every group of $n$ an equal chance. Stratified samples within every similar stratum; cluster samples some whole clusters; systematic takes every $k$-th after a random start.
Write from a stratified sample
- The population is split into year groups.
- A random sample is taken inside each year group.
What sampling method is this?
Strata are groups, and each group is sampled.
What is a random sample inside each year group?
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Sampling within every group is stratification.
Strata within a population
Stratified sampling draws from every slice (stratum).
A simple random sample (SRS) of size n gives an equal chance to...
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An SRS gives every group of n an equal chance.
Match each sampling method to its idea.
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Stratify = all strata; cluster = some clusters; systematic = every k-th.
Random sampling is what justifies generalizing the sample result to the population.
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A bias-free random method supports generalization.
You take an SRS of 25 students from EACH grade. This is which method?
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Sampling within every group (grade) is stratified sampling.
Choosing a random start and then taking every k-th individual is ___ sampling.
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That every-k-th rule is systematic sampling.