Understand how random sampling affects generalizing results to a population.
Random sampling lets you generalize findings to the population sampled.
核心知识
When a sample is randomly selected from a population, findings from the sample can be generalized to that population. Without random sampling, results apply only to those studied.
深入理解
Random sampling and random assignment answer different questions:
- Random sampling → Can we generalize to a larger population?
- Random assignment → Can we claim cause and effect?
If you randomly select 500 registered voters from a state, your findings can represent all registered voters in that state. Each voter had an equal chance of being chosen, so the sample should reflect the population's characteristics.
But if you survey 500 people who happened to walk past a mall on a Tuesday afternoon, your findings describe only those 500 people. They might skew toward people who are unemployed, retired, or work non-traditional hours. You can't extend the results to all residents of the city.
The SAT frequently sets traps here. A study might have excellent random assignment (making it a true experiment) but use volunteers instead of a random sample. In that case, you can say the treatment caused an effect — but only for people like the volunteers, not for the general population.
分步讲解
- Identify how participants were selected. Were they randomly chosen from a defined population, or were they volunteers/convenience samples?
- If randomly sampled from a population → results generalize to that population.
- If volunteers or a convenience sample → results apply only to the participants themselves (or people similar to them).
常见误解
- Thinking random assignment also gives you generalizability. It doesn't. Random assignment handles causation; random sampling handles generalization. They're separate.
- Assuming any large sample can be generalized. A large biased sample is still biased.
- Overlooking the specific population the sample was drawn from.
示例解析
A health organization randomly selected 1,200 adults from a national database of all adults aged 25–65. Participants completed a survey about their exercise habits and were asked to report their stress levels. The organization found that adults who exercised at least 3 times per week reported lower stress levels. To which population can the results of this study most reasonably be generalized?
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