Inference and Experiments · 推断与实验
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| random assignment/ˈrændəm əˈsaɪnmənt/ | 随机分配 | suí jī fēn pèi |
| random selection/ˈrændəm sɪˈlekʃn/ | 随机选择 | suí jī xuǎn zé |
| statistically significant/stəˈtɪstɪkli sɪɡˈnɪfɪkənt/ | 统计显著 | tǒng jì xiǎn zhù |
| scope of inference/skəʊp ɒv ˈɪnfərəns/ | 推断范围 | tuī duàn fàn wéi |
Two kinds of randomness, two payoffs
- Statistics uses randomness in two different places, with two different rewards.
- Random assignment 随机分配 (to treatments) → lets you claim cause-and-effect.
- Random selection 随机选择 (of units from a population) → lets you generalize to that population.
- Knowing which one a study used tells you what its results can support.
两种随机，两种回报
- 统计学在两个不同的地方使用随机性，带来两种不同的回报。
- 随机分配（到各处理）→ 让你能宣称因果。
- 随机选取（从总体中选单位）→ 让你能推广到那个总体。
- 知道一项研究用了哪一种，就知道它的结果能支撑什么。
Random assignment → causation
- Randomly assigning units to treatments balances all other variables across groups.
- So any difference in the response can be pinned on the treatment itself.
- This is why experiments — and only experiments — can prove cause.
- Without random assignment, a confounder could always be the real cause.
随机分配 → 因果
- 把单位随机分配到各处理，会把所有其他变量在各组间平衡开。
- 于是响应上的任何差异都能归到处理本身。
- 这就是为什么实验——且只有实验——能证明因果。
- 没有随机分配，混杂因素总可能才是真正的原因。
Random selection → generalization
- Randomly selecting units from the population makes the sample representative.
- So the conclusion generalizes to that whole population.
- Without random selection, results apply only to the units actually studied.
- Selection is about who's in the study; assignment is about what they get.
随机选取 → 推广
- 从总体中随机选取单位，使样本具有代表性。
- 于是结论能推广到那整个总体。
- 没有随机选取，结果只适用于实际研究的那些单位。
- 选取关乎谁在研究中；分配关乎他们接受什么。
Significance and scope
- A difference is statistically significant 统计显著 if it's too large to be reasonably explained by chance.
- The scope of inference 推断范围 = what the two randomizations jointly permit.
- Random assignment + random selection → cause-and-effect that generalizes (the strongest scope).
- Only assignment → cause but not generalizable; only selection → generalizable association, not cause.
显著性与范围
- 如果一个差异大到无法用机会合理解释，它就是统计显著的。
- 推断范围 = 两次随机化共同允许的东西。
- 随机分配 + 随机选取 → 可推广的因果（最强的范围）。
- 只有分配 → 有因果但不可推广；只有选取 → 可推广的关联，但非因果。
Two separate randomizations, two separate conclusions. Random assignment buys causation; random selection buys generalization. A study can have one, both, or neither — and its scope of inference is exactly what those two choices allow. Don't claim cause without random assignment, or generalization without random selection.
两次独立的随机化，两个独立的结论。随机分配换来因果；随机选取换来推广。一项研究可能有其一、两者兼有，或都没有——它的推断范围恰好是这两个选择所允许的。没有随机分配就别宣称因果，没有随机选取就别宣称推广。
$60$ volunteers are randomly assigned to a new study method or the old one; scores rise significantly.
- Random assignment → the method caused the gain (a valid causal claim).
- But they were volunteers, not randomly selected → can't generalize to all students.
- Scope: cause-and-effect for these subjects, not a population-wide claim.
$60$ 名志愿者被随机分配到一种新学习法或旧学习法；分数显著上升。
- 随机分配 → 该方法导致了提升（一个有效的因果主张）。
- 但他们是志愿者，不是随机选取的 → 无法推广到所有学生。
- 范围：****对这些受试者的因果，而非全体总体的主张。
Random assignment to treatments licenses a cause-and-effect claim; random selection of units licenses generalization to the population. A difference is statistically significant when it's implausibly large for chance alone. The scope of inference is set by which randomizations a study used.
对各处理的随机分配允许因果主张；对单位的随机选取允许推广到总体。当一个差异大到单凭机会难以出现时，它就是统计显著的。推断范围由一项研究使用了哪些随机化来决定。
Random assignment to treatments · 随机分配到各处理
Random assignment balances other variables across treatment groups. · 随机分配把其他变量在各处理组间平衡开。
Match each randomization to what it permits. · 把每种随机化与它所允许的东西配对。
Assignment → causation; selection → generalization. · 分配 → 因果；选取 → 推广。
Volunteers are randomly assigned to two study methods and one wins significantly. You can conclude... · 志愿者被随机分配到两种学习法，其中一种显著胜出。你可以得出……
Random assignment gives causation; volunteers block generalization. · 随机分配给出因果；志愿者阻碍推广。
A difference too large to be reasonably explained by chance is called statistically ___. · 一个大到无法用机会合理解释的差异，被称为统计 ___（填英文一词）。
That's the meaning of statistically significant. · 这就是统计显著的含义。
Random selection of units from a population is what allows you to generalize the results to that population. · 从总体中随机选取单位，正是让你能把结果推广到那个总体的原因。
Random selection buys generalization. · 随机选取换来推广。
A study with random assignment but NO random selection supports... · 一项有随机分配但没有随机选取的研究支持……
Assignment → cause; without selection it doesn't generalize. · 分配 → 因果；没有选取则不可推广。