Do the Data Tell the Truth? · 数据说的是真话吗？
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| bias/ˈbaɪəs/ | 偏差 | piān chā |
| representative/ˌreprɪˈzentətɪv/ | 有代表性的 | yǒu dài biǎo xìng de |
| population/ˌpɒpjʊˈleɪʃn/ | 总体 | zǒng tǐ |
| generalization/ˌdʒenərəlaɪˈzeɪʃn/ | 推广 | tuī guǎng |
Can we trust the data?
- Before any graph or calculation, ask: were the data collected honestly and well?
- The method of collection decides what conclusions are even possible.
- Bad data can't be rescued by clever analysis — "garbage in, garbage out."
- Unit 3 is about getting good data, so Units 4–9 can trust them.
我们能相信这些数据吗？
- 在任何作图或计算之前，先问：数据是否诚实、良好地收集到的？
- 收集的方法决定了哪些结论才有可能成立。
- 糟糕的数据无法靠巧妙的分析拯救——“垃圾进，垃圾出”。
- 第 3 单元讲的是获取好数据，好让第 4–9 单元能信任它们。
Bias: a lopsided method
- Bias 偏差 is a systematic tendency to miss the truth in the same direction.
- A biased method favors certain outcomes no matter how much data you gather.
- It's different from random error, which averages out; bias does not average out.
- The danger: a sample that isn't representative 有代表性的 of the population 总体.
偏倚：一个偏斜的方法
- 偏倚是一种系统性的、朝同一方向偏离真相的倾向。
- 有偏的方法总偏向某些结果，不管你收集了多少数据。
- 它不同于随机误差——随机误差会互相抵消；偏倚不会抵消。
- 危险在于：样本对总体不有代表性。
When can we generalize?
- A generalization 推广 extends a sample's finding to the whole population.
- This is only justified when the sample was gathered without bias (ideally at random).
- Data from a lopsided method describe only that lopsided group — not everyone.
- "Who was actually reached?" decides how far a conclusion can travel.
什么时候可以推广？
- 推广是把样本的发现扩展到整个总体。
- 只有当样本是无偏（理想情况下随机）收集的，这才有依据。
- 来自偏斜方法的数据只描述那个偏斜的群体——而非所有人。
- “实际上触及了谁？”决定了一个结论能走多远。
Plan before you collect
- Good data collection is planned in advance, not patched up afterward.
- Decide the population, the sampling method, and the questions before gathering.
- A careful plan is the cheapest way to avoid bias you can't fix later.
- Analysis is only as trustworthy as the collection that fed it.
先规划，再收集
- 好的数据收集是事先规划的，不是事后打补丁。
- 在收集之前就定好总体、抽样方法和问题。
- 周密的计划是避免日后无法修复的偏倚的最省钱办法。
- 分析的可信度，不会超过喂给它的那份收集。
A bigger sample does not fix bias. If the method systematically misses part of the population, collecting more responses the same flawed way just gives you a more precise wrong answer. Size fights random error; only a better method fights bias. Always ask how the data were collected before trusting any conclusion.
更大的样本并不能修复偏倚。如果方法系统性地漏掉了总体的一部分，用同样有缺陷的方式收集更多回应，只会给你一个更精确的错误答案。样本量对抗的是随机误差；只有更好的方法才能对抗偏倚。信任任何结论之前，先问数据是怎么收集的。
A radio host asks listeners to call in whether they support a new law.
- Only motivated, opinionated listeners call — not a representative sample.
- The result is biased; it describes callers, not the population.
- Getting $10{,}000$ callers instead of $100$ makes it no less biased.
一位电台主持人请听众打电话说是否支持一项新法律。
- 只有积极、有强烈意见的听众才会打进来——不是有代表性的样本。
- 结果是有偏的；它描述的是打电话的人，而非总体。
- 得到 $10{,}000$ 个来电而不是 $100$ 个，也丝毫不会减少偏倚。
The method of data collection determines what we can conclude. Bias is a systematic error that makes a sample unrepresentative of the population, and it does not shrink with a larger sample. Only bias-free (ideally random) collection justifies a generalization — so plan collection carefully before analyzing.
数据收集的方法决定了我们能得出什么结论。偏倚是一种系统性误差，使样本对总体不有代表性，而且它不会随样本增大而缩小。只有无偏（理想情况随机）的收集才能为推广提供依据——所以在分析之前就要仔细规划收集。
A biased sample over-represents one group · 有偏样本过度代表了某一组
When one slice dominates, the sample isn't representative of the population. · 当某一块占据主导时，样本就不能代表总体。
Collecting a much larger sample using the same flawed method will remove the bias. · 用同样有缺陷的方法收集大得多的样本，就能消除偏倚。
Size fights random error, not bias — a flawed method stays biased at any size. · 样本量对抗随机误差，而非偏倚——有缺陷的方法在任何规模下都仍有偏。
A radio call-in poll mainly reaches motivated listeners. Its result is... · 一个电台来电投票主要触及积极的听众。它的结果是……
Self-selected callers aren't representative — the poll is biased. · 自我选择的来电者不具代表性——这个投票有偏。
A systematic tendency to miss the truth in the same direction is called ___. · 一种系统性地朝同一方向偏离真相的倾向叫做 ___（填英文一词）。
Bias is systematic, directional error that doesn't average out. · 偏倚是系统性、有方向的误差，不会互相抵消。
Extending a sample's finding to the whole population is justified only when the sample is... · 只有当样本……时，把样本的发现推广到整个总体才有依据。
Only bias-free collection supports generalization. · 只有无偏的收集才支持推广。
The method of data collection determines what conclusions are possible. · 数据收集的方法决定了哪些结论有可能成立。
Good conclusions require good collection — plan it before analyzing. · 好的结论需要好的收集——在分析前就要规划。