The idea, step by step
What correlation can and cannot establish
A statistical association means values tend to vary together. Causation means changing one variable produces a change in another through a mechanism. Observational data can suggest a question, but a strong correlation alone does not establish the causal direction.
A third variable may affect both measurements. This is confounding. Reverse causation, selection effects and coincidence are other possible explanations.
Evaluate the study, not only its r-value
Ask how participants were selected, whether treatments were randomly allocated, what was controlled, and whether the explanation is plausible. Random allocation can strengthen causal inference by balancing confounders on average. A large sample reduces some sampling uncertainty but does not repair systematic bias.
Use cautious wording: “associated with” for an observational result. State a possible confounder or design a better study rather than announcing that all correlation is meaningless.
A common trap
A sample of 10,000 makes an observational correlation causal.
Instead: Sample size does not eliminate confounding or selection bias.
See the thinking
A common cause
A town observes that ice-cream sales and swimming rescues increase together. Does buying ice-cream cause rescues?
- The study is observational.
- Hot weather can increase both ice-cream purchases and swimming exposure.
- The observed association does not establish that ice-cream purchases cause rescues.
A stronger design
To test a revision strategy, volunteers are randomly assigned to use the strategy or their normal method for four weeks. Both groups sit the same assessment. Why is this stronger than comparing self-selected groups?
- Self-selection could place more motivated students in one group.
- Random assignment tends to balance such characteristics across groups.
- The common assessment and time window improve comparability, although adherence and chance still matter.
Check your understanding
Shoe size and reading ability are correlated among young children. Name a plausible confounder.
Show answer
Age.
Older children tend to have larger feet and more reading experience.
Your turn
6 questions · 18 marks · Work at your own pace.
Read the questions online
- Sales of heaters and cough medicine rise together. Give a plausible confounder.3 marks
- A survey finds students who seek tutoring have lower earlier scores. Does this prove tutoring reduces achievement?3 marks
- An online poll links sleep and concentration, but only volunteers respond. Name two limitations.3 marks
- A randomised experiment reports a mean improvement. Does random assignment guarantee every participant improves?3 marks
- Rewrite “Eating breakfast causes higher scores”, when the only evidence is an observational correlation.3 marks
- Explain why a plausible mechanism is helpful but does not by itself prove causation.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Sales of heaters and cough medicine rise together. Give a plausible confounder.3 marks
Seasonal conditions can increase both demand for heating and respiratory illness.
Cold weather or winter season. - A survey finds students who seek tutoring have lower earlier scores. Does this prove tutoring reduces achievement?3 marks
The direction can be reversed.
Compare appropriate baseline-adjusted outcomes using a better study design.
No. Earlier difficulty may cause students to seek tutoring. - An online poll links sleep and concentration, but only volunteers respond. Name two limitations.3 marks
Volunteers may not represent the population.
Other variables may affect both sleep and concentration.
Self-selection bias and uncontrolled confounding, such as workload or health. - A randomised experiment reports a mean improvement. Does random assignment guarantee every participant improves?3 marks
Individual responses vary.
The observed mean is an aggregate result.
No. It supports group-level comparison, not identical individual effects. - Rewrite “Eating breakfast causes higher scores”, when the only evidence is an observational correlation.3 marks
Remove the causal claim.
Keep the population/sample qualification.
In this sample, eating breakfast was associated with higher scores. - Explain why a plausible mechanism is helpful but does not by itself prove causation.3 marks
Evidence must distinguish competing explanations.
A story alone is not a controlled comparison.
A mechanism makes an explanation credible, but alternative causes and study bias still need to be addressed.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: statistical models. Original lessons and assessment practice; not an official SACE assessment.
Official curriculum source ↗