# Evaluating statistical claims on the SAT: the two-switch method

> Random sampling and random assignment are independent switches. The 2x2 that tells you which SAT conclusions are justified, with two worked examples.

Published 2026-06-05 | Math | StudyHall

Canonical: https://trystudyhall.com/blog/sat-evaluating-statistical-claims

The SAT’s study-design questions rarely ask you to calculate anything. They hand you a study and ask which conclusion is justified, and the answer turns on two decisions made before any data existed: who got into the study, and who got which treatment. Random sampling and random assignment sound like one idea. They are two independent switches, and each licenses a different conclusion.

**Key takeaways:**
- **Random sampling** (who is in the study) lets you generalize to the population sampled.
- **Random assignment** (who gets the treatment) lets you conclude cause and effect.
- The switches are **independent**: a study can have both, either, or neither.
- On "which conclusion is best supported," eliminate every choice claiming more than the design earned.

## Two switches, two permissions

**Random sampling is about recruitment.** Was every member of the population equally likely to end up in the study? If yes, the sample is a fair miniature, and results generalize to that population (with the precision described by the [margin of error](https://trystudyhall.com/blog/sat-margin-of-error)). If the participants were volunteers or one classroom, the results describe the participants and nobody else.

**Random assignment is about treatment.** Once people are in, did chance decide who got the treatment and who was the comparison group? If yes, the groups start out statistically alike, so a difference at the end points at the treatment: that’s an experiment, and causal language is earned. If people chose their own group, whatever made them choose rides along as a hidden variable, and the honest conclusion is an association. That’s an observational study.

## The 2x2 of justified conclusions

|  | Random assignment | No random assignment |
| --- | --- | --- |
| **Random sampling** | Cause and effect, generalizable to the population | Association only, generalizable to the population |
| **No random sampling** | Cause and effect, for the participants only | Association only, for the participants only |
*Find the study’s box first; the justified conclusion reads straight off it.*

## How the SAT words it

Correct answers about observational studies sound deliberately deflating: "there is an association," "students who exercise *tend to* sleep more," often with an explicit "but no cause-and-effect relationship can be established." That deflation is precision, and the SAT rewards it. Wrong answers smuggle in *causes* or *improves*, or quietly widen "the participants" into "all teenagers." So run the elimination: cross out every choice claiming causation without random assignment, then every choice generalizing without random sampling. The survivor is usually the humblest sentence on the screen.

## Try one: pick the justified conclusion

**Example: Evaluating statistical claims.**

> Researchers recruited 200 adult volunteers and randomly assigned half to an eight-week meditation program; the rest continued their usual routines. At the end, the meditation group reported significantly lower stress than the comparison group.

Which conclusion is best supported by the study’s results?

- A) Meditation reduces stress for all adults.
- B) The meditation program likely caused the lower stress levels among the participants in this study.
- C) Meditation is associated with lower stress, but no cause-and-effect relationship can be established.
- D) No conclusion can be drawn, because the participants were volunteers.

**Answer:** B. Run the switches. Assignment: random, so causal language is earned. Sampling: volunteers, so the conclusion stays inside the study. That’s the second choice: cause and effect, participants only. "All adults" flips a generalization switch the study never had; the association-only choice throws away the causal license random assignment paid for; and "no conclusion" is too strict, since volunteer studies still support conclusions about the volunteers.

## Try one: design the study

**Example: Evaluating statistical claims.**

> A nutritionist wants to determine whether a new free-breakfast program causes improved attendance among students at a large high school.

Which study design would best allow the nutritionist to draw a cause-and-effect conclusion?

- A) Compare the attendance of students who choose to join the program with that of students who decline.
- B) Select a random sample of students and survey them about their breakfast habits and attendance.
- C) Randomly assign students to participate in the program or not, then compare the two groups' attendance.
- D) Offer the program to every student and compare the school’s attendance with the previous year’s.

**Answer:** C. Cause and effect requires random assignment, and only one design has it: chance splits students into program and no-program groups, so a later attendance gap points at the program. Letting students choose invites self-selection: joiners may already attend more. The random survey is sampling, not assignment; it can only find an association. And the year-over-year comparison has no comparison group, so anything else that changed between years competes as an explanation.

- ✗ **The trap:** Pick the most satisfying conclusion, the one with "causes" and "all students," because the study *suggests* it.
- ✓ **The move:** Pick the conclusion the design paid for. No random assignment, no "causes." No random sampling, no "all."

**[Practice statistical claims](https://trystudyhall.com/learn/statistical-claims)**: Drill study-design questions with a tutor that makes you name both switches before you touch the conclusions.

## FAQ

### What is the difference between random sampling and random assignment?

Random sampling decides who gets into the study and controls whether results generalize to the population. Random assignment decides who gets the treatment within the study and controls whether you can conclude cause and effect. They are independent decisions.

### When can you conclude cause and effect on the SAT?

Only when participants were randomly assigned to treatment and comparison groups, which makes the study an experiment. Without random assignment, the justified conclusion is an association, however striking the difference between groups.

### Why do correct SAT answers say "associated with" instead of "causes"?

Because most studies in these questions are observational, and association is all that design can establish. The SAT offers stronger-sounding causal conclusions as traps; the deflating, carefully hedged sentence is usually the justified one.

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