Random Sampling · 随机抽样
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| random sampling/ˈrændəm ˈsæmplɪŋ/ | 随机抽样 | suí jī chōu yàng |
| simple random sample/ˈsɪmpl ˈrændəm ˈsæmpl/ | 简单随机样本 | jiǎn dān suí jī yàng běn |
| stratified/ˈstrætɪfaɪd/ | 分层 | fēn céng |
| cluster/ˈklʌstə/ | 整群 | zhěng qún |
| systematic/ˌsɪstəˈmætɪk/ | 系统 | xì tǒng |
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.
为什么要随机选取？
- 随机抽样用机会来决定谁进入样本。
- 机会没有私心，所以能避开制造偏倚的人类倾向。
- 从长远看，随机样本往往看起来像总体。
- 随机性正是让公平推广成为可能的东西。
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.
简单随机样本
- 简单随机样本（SRS）让每一组 $n$ 个个体都有相等的机会。
- 执行方法：给总体编号，再抽取号码（随机数字或抓阄）。
- 每个个体——以及每种组合——都同样可能被选中。
- SRS 是其他方法赖以建立的黄金标准思想。
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.
分层、整群、系统
- **分层：**分成相似的组（层），再在每一层内取一个 SRS。
- **整群：**分成一些组（群），随机挑选整群，对其中所有人取样。
- **系统：**随机选一个起点，然后每隔 $k$ 个取一个个体。
- 分层是为了保证每个组都有代表；整群是在组分散时图方便。
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.
随机性使推广成为可能
- 因为随机方法没有偏倚，它的结果能推广到总体。
- 样本统计量因而成为总体值的可信估计。
- 非随机（“便利”）样本给不了你这样的保证。
- 后面各单元的推断公式假定样本是随机的。
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.
不要把分层和整群抽样弄混。分层：层是内部相似的，你从每一个层里取样（以保证每个都有代表）。整群：群是小型总体，你只抽取一部分整群。同样是“组”这个词，逻辑却相反——弄混它们是经典的考试失误。
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.
在一所学校的 $1000$ 名学生中调查 $100$ 名。
- **SRS：**给全部 $1000$ 人编号，抽 $100$ 个随机号码。
- **分层：**从每个年级（层）随机取 $25$ 人 → 每个年级都有代表。
- **整群：**随机挑 $4$ 个班（群），调查其中全部约 $100$ 名学生。
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.
随机抽样消除偏倚，使结果能推广。简单随机样本（SRS）让每一组 $n$ 个个体有相等的机会。分层在每一个相似的层内取样；整群抽取一部分整群；系统在随机起点后每隔 $k$ 个取一个。
Strata within a population · 总体内部的各层
Stratified sampling draws from every slice (stratum). · 分层抽样从每一块（层）中都取样。
A simple random sample (SRS) of size n gives an equal chance to... · 大小为 n 的简单随机样本（SRS）给予相等机会的是……
An SRS gives every group of n an equal chance. · SRS 让每一组 n 个个体都有相等机会。
Match each sampling method to its idea. · 把每种抽样方法与它的思想配对。
Stratify = all strata; cluster = some clusters; systematic = every k-th. · 分层 = 所有层；整群 = 部分群；系统 = 每隔 k 个。
Random sampling is what justifies generalizing the sample result to the population. · 随机抽样正是把样本结果推广到总体的依据。
A bias-free random method supports generalization. · 无偏的随机方法支持推广。
You take an SRS of 25 students from EACH grade. This is which method? · 你从每个年级各取 25 名学生的 SRS。这是哪种方法？
Sampling within every group (grade) is stratified sampling. · 在每个组（年级）内取样是分层抽样。
Choosing a random start and then taking every k-th individual is ___ sampling. · 选一个随机起点、然后每隔 k 个取一个个体，是 ___ 抽样（填英文一词）。
That every-k-th rule is systematic sampling. · 这种每隔 k 个的规则是系统抽样。