Sampling, experiments and justified claims
Separate representative sampling from random assignment before judging a population or causal conclusion.
What you will tackle
- Evaluate observational studies and controlled experiments
- Identify populations and limits on generalisation
- Distinguish random sampling from random assignment
- Explain causal and noncausal conclusions with confounders
Sampling and assignment solve different problems
Random sampling chooses who enters a study and helps represent a source population. Random assignment allocates included participants to treatments and helps balance confounding differences. A randomised experiment can support a causal comparison for the studied conditions; broad population generalisation still depends on recruitment and context.
Observation alone leaves alternative explanations
An association between tutoring and grades can reflect prior achievement, motivation or resources. Following an outcome after a policy change also needs a comparison and consideration of other simultaneous changes. Distinguish a measured difference, a causal interpretation and a claim about a wider population.
Build your notes, then practise
Work on paper before opening an explanation. Guided tasks provide a starting point; independent tasks remove the scaffolding; application tasks ask you to justify a method or interpretation in context.
Guided practice
Guided 1
Students who choose a breakfast club score higher on a test. Does this show that the club caused the difference? Describe one confounder and a stronger design.
Show a starting hint
Ask what else differs between the two groups.
Compare with the explained answer
- Membership was chosen rather than randomly assigned.
- Motivation or previous attainment could affect both membership and score.
- Random assignment of consenting students to a club offer and a comparison condition would strengthen a causal comparison.
Answer / response criteria: No; self-selection can confound the association. A randomised comparison would be stronger.
Independent practice
Independent 1
A city randomly samples 500 residents, then observes their commute choices and stress. Which population is represented, and is a causal effect of cycling established?
Compare with the explained answer
- The sampling frame is the city's residents, subject to response and coverage limitations.
- Commute choices were observed, not assigned.
- Health, route length and work conditions could confound any association.
Answer / response criteria: The city's represented resident population; a causal cycling effect is not established.
Application practice
Application 1
Forty volunteers are randomly assigned to two study apps; app A improves the measured score more. Explain the strongest causal and population claims supported.
Compare with the explained answer
- Random assignment strengthens attributing the score difference to the app under the experiment's conditions.
- The participants were volunteers, not a random sample of all students.
- Generalising to every student or to different tasks would require further evidence.
Answer / response criteria: Evidence for an app effect in the experimental setting; limited population generalisation.
What can you explain now?
Forty volunteers are randomly assigned to two study apps; app A improves the measured score more. Explain the strongest causal and population claims supported.
Compare with the explanation
Evidence for an app effect in the experimental setting; limited population generalisation.
Explain the reasoning before comparing. This review records your self-assessment rather than an official score or mastery decision.
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Source and review status
Coverage follows the named requirements and examples in the 2026–2027 ACT test guide and subject descriptions. That guide explicitly does not list every possible topic. The broader coded College and Career Readiness Standards are also mapped to conceptual teaching and practice; this does not calibrate a learner to a score band. The separate scientific-background context list and reading-complexity rubric have their own stated limits.
Original teaching and explained self-check practice are available. Specialist review and difficulty calibration remain pending. Essays require self-check or teacher review and are not automatically marked or awarded official scores.
Official source specification / guide