Comparing Categorical Groups · 比较分类各组
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| conditional distributions/kənˈdɪʃənl ˌdɪstrɪˈbjuːʃnz/ | 条件分布 | tiáo jiàn fēn bù |
| independent/ˌɪndɪˈpendənt/ | 独立 | dú lì |
| causation/kɔːˈseɪʃn/ | 因果关系 | yīn guǒ guān xì |
| confounding variable/kənˈfaʊndɪŋ ˈveərɪəbl/ | 混杂变量 | hùn zá biàn liàng |
Comparing groups fairly
- To see if two categorical variables are related, compare conditional distributions 条件分布 across groups.
- A conditional distribution is the set of proportions for one variable within a single group.
- "What does the subject breakdown look like for girls vs for boys?"
- Using proportions (not raw counts) makes the comparison fair when groups differ in size.
公平地比较各组
- 要看两个分类变量是否相关，就跨各组比较条件分布。
- 条件分布是某个变量在某一个组内的一组比例。
- “女生的科目构成和男生的相比是什么样的？”
- 用比例（而非原始计数）在各组人数不同时仍能公平比较。
Association vs. independence
- If the conditional distributions are the same across groups, the variables appear independent 独立.
- If they differ, the variables show an association — knowing one tells you something about the other.
- The bigger the difference between groups, the stronger the association.
- "Same proportions everywhere" is the picture of no relationship.
关联还是独立
- 如果各组的条件分布相同，这两个变量看起来是独立的。
- 如果它们不同，两个变量就存在关联——知道一个就能了解另一个的一些信息。
- 组间差异越大，关联越强。
- “处处比例相同”就是没有关系的画面。
Differences in proportions
- Quantify the association with a difference in proportions: e.g. $60\%$ of girls vs $40\%$ of boys chose science.
- That $20$-percentage-point gap is the evidence of a relationship, stated in context.
- Always report which group is higher and by how much.
- A tiny difference may just be sampling noise; a large one signals real association.
比例之差
- 用比例之差来量化关联：例如 $60\%$ 的女生对 $40\%$ 的男生选了科学。
- 那 $20$ 个百分点的差距，就是关系的证据，需结合语境陈述。
- 总要说清哪个组更高、高多少。
- 微小的差异可能只是抽样噪声；巨大的差异则预示真实的关联。
Association is still not causation
- Even a strong association between two categorical variables does not prove causation 因果关系.
- A hidden confounding variable 混杂变量 could drive both.
- Observational data can reveal association but rarely establishes cause.
- Only a well-designed experiment (Unit 3) can support a causal claim.
关联仍然不是因果
- 即使两个分类变量之间关联很强，也不能证明因果关系。
- 一个隐藏的混杂变量可能同时驱动两者。
- 观察性数据能揭示关联，但很少能确立原因。
- 只有设计良好的实验（第 3 单元）才能支持因果主张。
To judge association, always compare conditional proportions, never raw counts — a group with more people will have bigger counts everywhere even with no relationship. And "$60\%$ vs $40\%$" is an association, not proof that being a girl causes choosing science: a confounding variable could explain the gap.
判断关联时，始终比较条件比例，绝不用原始计数——人数更多的组在哪里计数都更大，即使没有任何关系。而且“$60\%$ 对 $40\%$”是一种关联，并不能证明身为女生导致了选择科学：一个混杂变量也许能解释这个差距。
Do exercise habits relate to sleeping well? Survey results:
- Of exercisers: $70\%$ sleep well. Of non-exercisers: $45\%$ sleep well.
- The conditional distributions differ ($70\%$ vs $45\%$) → an association.
- But maybe healthy people both exercise and sleep well — a confounder. No causation proven.
锻炼习惯和睡得好有关系吗？调查结果：
- 锻炼者中：$70\%$ 睡得好。不锻炼者中：$45\%$ 睡得好。
- 两个条件分布不同（$70\%$ 对 $45\%$）→ 存在关联。
- 但也许健康的人既锻炼又睡得好——一个混杂因素。并未证明因果。
Compare conditional distributions across groups: if they're the same, the variables look independent; if they differ, there's an association, measured by a difference in proportions (stated in context). Association still does not prove causation — a confounding variable may be at work.
跨各组比较条件分布：若它们相同，变量看起来独立；若它们不同，就存在关联，用比例之差（结合语境）来度量。关联仍不能证明因果关系——可能有混杂变量在起作用。
One group's conditional distribution · 某一组的条件分布
Within one group, the slices are its conditional distribution. · 在一个组内，各分块就是它的条件分布。
Two categorical variables appear independent when their conditional distributions are... · 当两个分类变量的条件分布……时，它们看起来是独立的。
Same conditional distributions → no association → independence. · 条件分布相同 → 无关联 → 独立。
70% of exercisers vs 45% of non-exercisers sleep well. What is the difference in proportions, in percentage points? · 锻炼者中 70% 睡得好，不锻炼者中 45% 睡得好。比例之差是多少个百分点？
70 − 45 = 25 percentage points. · 70 − 45 = 25 个百分点。
You should compare raw counts, not proportions, to judge association between categorical variables. · 判断分类变量间的关联时，应比较原始计数而非比例。
Compare conditional proportions — counts are unfair when groups differ in size. · 要比较条件比例——当各组人数不同时，计数并不公平。
A hidden variable that could drive both variables and explain an association is a ___ variable. · 一个可能同时驱动两个变量并解释关联的隐藏变量，叫做 ___ 变量。
A confounding variable offers an alternative explanation. · 混杂变量提供了另一种解释。
Which statements about association vs. causation are correct? · 关于关联与因果，哪些说法正确？
Even strong association never by itself proves causation. · 即使很强的关联，本身也永远不能证明因果。