Sampling, margin of error and causal claims
| English | 中文 | Pinyin |
|---|---|---|
| margin of error/ˈmɑːdʒɪn ɒv ˈerə/ | 误差范围 | wù chā fàn wéi |
| random assignment/ˈrændəm əˈsaɪnmənt/ | 随机分组 | suí jī fēn zǔ |
A decision before an answer
- Randomly choosing students from a school and randomly assigning a treatment do different jobs: one supports population inference, the other a causal comparison.
- Your goal: Interpret a sample estimate and its stated margin of error.
Read the relationship
- A sample statistic estimates a population quantity. A reported estimate of 58% with margin of error 4 percentage points gives an interval from 54% to 62% under the stated procedure. It does not mean 58% of respondents answered with an error of four percent, nor does it guarantee that every individual sample contains the true value.
- Distinguish random sampling from random assignment.
Estimate 46% ±3 percentage points gives:
Subtract and add three points.
Use the defining rule
- A representative random sample helps generalise to the population from which it was drawn. Convenience or voluntary-response samples can be biased even when large. Increasing a well-designed sample generally reduces sampling variability and margin of error at the same confidence level, but cannot automatically cure a systematically excluded group.
- Identify the population and causal scope supported by a study.
Which supports causal comparison?
Assignment addresses competing differences between groups.
Check the conditions
- Random assignment distributes participants among treatment groups and supports causal inference by balancing competing factors on average. Random sampling selects who participates. A randomised experiment conducted only with volunteers may support a treatment effect for its participants without establishing that all people share the same effect.
- Identify the population and causal scope supported by a study.
A random sample of 400 school students yields 58% support ±4 percentage points: stated interval 54%–62%. This estimates the sampled school population, not all students worldwide. If volunteers are randomly assigned to two revision methods, a controlled outcome difference can support a causal comparison among participants; volunteer selection still limits wider generalisation.
Estimate 71% with margin 5 points has upper endpoint ____%.
71+5=76.
Apply the task format
- An observational study measures existing differences without assigning treatment; association can reflect confounding. A comparison of students who choose extra tutoring against those who do not may mix tutoring with motivation or prior attainment. To judge a claim, identify selection, assignment, comparison, measured outcome and the exact population before accepting causation or broad generalisation.
- Identify the population and causal scope supported by a study.
Sample size, random selection and random assignment are not interchangeable. A narrow margin does not remove selection bias.
Which answer fits this case?
Interpret a sample estimate and its stated margin of error
A large convenience sample automatically eliminates selection bias.
More observations do not repair a systematically unrepresentative selection.
Keep the distinctions
- margin of error 误差范围 — A stated sampling-uncertainty allowance around an estimate.
- random assignment 随机分组 — Allocation of participants to treatment groups by chance.
- Interpret a sample estimate and its stated margin of error.
- Distinguish random sampling from random assignment.
- Identify the population and causal scope supported by a study.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.