Understand the idea.
What correlation can and cannot establish
Association means measurements tend to vary together. A causal claim says that changing one factor produces a change in another. An observational correlation alone cannot distinguish direct causation from reverse causation, a shared cause, selection effects or coincidence.
A confounder is a third factor that can affect both variables and provide another explanation for their association. Name the factor and explain both links; simply saying “there might be other factors” does not show how the observed pattern could arise.
Evaluate the study, not only its r-value
Inspect how the study was conducted. Random allocation of treatments tends to balance pre-existing characteristics between groups, strengthening causal comparisons. A shared assessment and similar conditions also matter. Random sampling instead concerns which population the findings may represent.
A larger observational sample can improve precision without removing systematic bias or confounding. Report an observational finding as “associated with”, then discuss plausible explanations. A well-designed randomised experiment can support a causal claim, subject to adherence, chance and study limitations.
See the method in action.
A common cause
A town observes that ice-cream sales and swimming rescues increase together. Does buying ice-cream cause rescues?
Worked solution
- 1
Identify the type of evidence.
The town observed sales and rescues; it did not randomly assign ice-cream purchases or control swimming conditions.
- 2
Give a common explanation for both increases.
More swimming exposure can produce more rescues, while the same weather increases demand for ice-cream.
- 3
Limit the conclusion to what the evidence supports.
Hot weather is a plausible confounder. The association does not establish that buying ice-cream causes rescues.
Hot weather is a plausible confounder.
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?
Worked solution
- 1
Identify a weakness of self-selection.
Students choosing the strategy might differ in motivation, prior achievement or study time, so group results could reflect those differences.
- 2
Explain the role of random allocation.
Assignment by chance tends to distribute such characteristics across both groups rather than systematically concentrating them in the strategy group.
- 3
Check the remaining comparison conditions.
Both groups study for four weeks and sit the same assessment. These common conditions improve comparability, although adherence and chance imbalances still require attention.
- 4
State why the design is stronger.
Random allocation reduces confounding compared with self-selection, giving stronger evidence about the strategy's effect among the volunteers.
Random allocation reduces confounding compared with self-selection.
Try it yourself.
Check your understanding
Shoe size and reading ability are correlated among young children. Name a plausible confounder.
Show answer & reasoning
Age.
Age can affect both measurements: older children tend to have larger feet and more reading experience. It can therefore explain a shoe-size/reading association without shoe size causing reading ability.
Keep practising
6 worksheet questions · 18 marks
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 ↗