Who enters a study and how treatment is assigned answer different questions. Check both before accepting a population or causal claim.
A statistical claim is only as broad as the study design supports. Random sampling helps a study represent a population. Random assignment to treatment groups supports causal interpretation in a well-designed experiment. These are different steps.
Worked example: an observational association
These examples are original teaching exercises, not released SAT questions. A school survey finds that students who report more nightly sleep tend to have higher test scores. Students choose their own sleep habits; the researchers do not assign them.
The result establishes an association in the observed data. It does not by itself show that additional sleep caused higher scores. Other factors, such as health or study routines, could differ between the groups. Stating an alternative explanation shows why the causal conclusion needs more support; it does not prove that sleep has no effect.
Worked example: random assignment
A study recruits 80 volunteers and randomly assigns 40 to use study method A and 40 to use method B. Both groups study the same material for the same duration and take the same assessment. This design provides a basis for comparing the effects of the methods under the study conditions.
The volunteers were not a random sample of all students. A causal interpretation for the participants does not automatically support a claim that the result generalises to every student. Random assignment helps control systematic group differences; it does not guarantee identical groups or remove every practical issue such as noncompliance.
Worked example: random sampling without an experiment
A city selects a random sample of residents and asks how they travel to work. The survey can estimate travel patterns for the sampled population under the sampling assumptions. Because it does not assign travel methods, it cannot establish that cycling to work causes a particular health outcome.
Read the study's limits
| Design feature | What it helps support | What it does not automatically establish |
|---|---|---|
| Random sample | Population estimates | A treatment caused an outcome |
| Random assignment | A comparison of treatment effects | Representation of every population |
| Large sample | More precise estimates under comparable methods | Absence of selection bias |
Also check the outcome measured, duration, comparison group, and wording of the conclusion. A study measuring one assessment cannot establish every long-term learning outcome. “Associated with” and “caused by” make different claims.
A compact practice routine
Underline who was selected and how, then underline how treatments were assigned, if any. State the narrowest conclusion that answers the question. Reject an answer that silently changes the population or converts correlation into causation.
For estimating proportions and interpreting uncertainty, read sample statistics and margin of error.
Official sources
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