Lấy mẫu, sai số biên và tuyên bố nhân quả
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| margin of error/ˈmɑːdʒɪn ɒv ˈerə/ | Sai số biên |
| population/ˌpɒpjʊˈleɪʃn/ | The entire set of individuals, items or outcomes about which a statistical study seeks information. |
| random assignment/ˈrændəm əˈsaɪnmənt/ | Phân nhóm ngẫu nhiên |
A survey says…
- A survey of 400 randomly chosen voters in one city finds 54% support a new park, with a margin of error 误差范围 of 5%. A newspaper writes: "Most people in the country support new parks."
- The SAT tests what a study can and cannot conclude: about which population 总体, with what precision, and whether it shows cause.
Margin of error
- 54% ± 5% means the true proportion in the population is plausibly between 49% and 59%. So "a majority supports the park" is not certain: 49% is possible.
- Larger random samples give smaller margins of error; the margin does not fix bias in how the sample was chosen.
54% ± 5% gives a range of 49% to 59%, which includes 50%
A random sample estimates that 38% of a town's residents cycle to work, with a margin of error of 4%. Which statement is best supported?
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Estimate ± margin gives the plausible range for that town.
A larger random sample generally gives a smaller margin of error.
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More data make the estimate more precise.
Who does the result apply to?
- Results generalise only to the population the sample was randomly selected from: voters in that city, not the whole country.
- A voluntary online poll is biased: the people who choose to answer are not representative.
A random sample of students at one school supports conclusions about all teenagers in the country.
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The population is the students of that school.
Cause needs random assignment 随机分组
- Random sampling → you can generalise to the population. Random assignment to treatment groups → you can conclude cause and effect.
- An observational study ("students who sleep more get better grades") shows association only.
Researchers randomly assign 100 volunteers to take a new vitamin or a placebo; the vitamin group has fewer colds. Cause can be concluded, but only for people like these volunteers, because they were not randomly sampled.
What can this study conclude?
Match a study design to the conclusions it supports.
Which study design allows a conclusion about cause and effect?
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Random assignment is needed for a causal conclusion.
To conclude cause and effect, a study needs random ____ to groups.
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Random assignment, not just random sampling.
Traps
- Over-generalising from one city, one school or volunteers to everyone.
- Treating the estimate as exact: with the margin of error, 54% may not mean "a majority".
Recap
- Estimate ± margin of error gives a range of plausible values; bigger random samples shrink it.
- Random sampling → generalise; random assignment → cause. Neither → association within the sample.