The idea, step by step
A pattern is not a mechanism
Association means two variables vary together in the observed data. Causation means a change in one produces a change in the other. An observational scatterplot, even with a very strong pattern, does not by itself show that one variable caused the other.
A third variable may influence both measurements. This is a confounding explanation. The direction of influence can also be reversed, or the observed pattern may reflect selection, measurement or chance.
Match the conclusion to the design
A well-designed randomised experiment can give stronger causal evidence because treatment groups are assigned rather than self-selected. Ethical and practical limits often mean only observational evidence is available.
You can still use observational data responsibly: describe the association, consider alternative explanations and state the limits. Do not turn a sensible caution into the claim that data can never contribute to causal understanding.
A common trap
If correlation is high, the cause is proven.
Instead: A strong association can still arise through confounding or selection; the study design matters.
See the thinking
Ice creams and sunburn
A beach survey finds that ice-cream purchases and sunburn cases both rise on some days. Does buying ice cream cause sunburn?
- The measurements are associated.
- Hot, sunny days may increase both beach activity/ice-cream purchases and sun exposure.
- The survey has not isolated the effect of buying ice cream.
Revision app comparison
Students choosing a revision app score higher than students not using it. Give an alternative explanation.
- Students selected their own groups.
- Motivation, previous attainment or extra study time may differ.
- A random assignment with comparable conditions would better isolate the app's effect.
Check your understanding
Older children tend to have larger vocabularies and larger shoes. Does shoe growth cause vocabulary growth?
Show answer
No.
Age and development plausibly influence both.
Your turn
6 questions · 15 marks · Work at your own pace.
Read the questions online
- Umbrella sales and rainfall rise together. Which is a plausible direction of causation?2 marks
- Towns with more fire engines report more total fire damage. Why is reducing fire engines not justified by this association?3 marks
- Coffee drinkers in a survey sleep less. Name a possible confounder.2 marks
- Why does random assignment help a treatment comparison?3 marks
- Write a cautious conclusion: more exercise is associated with lower reported stress in a voluntary survey.2 marks
- A company claims its product caused improvement because users improved over a month, with no comparison group. Give two alternative explanations.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Umbrella sales and rainfall rise together. Which is a plausible direction of causation?2 marks
The context supports rain influencing purchases.
Sales alone do not cause weather.
Rainfall can increase demand for umbrellas. - Towns with more fire engines report more total fire damage. Why is reducing fire engines not justified by this association?3 marks
Fire severity can influence both engine numbers and damage.
The observed pattern does not isolate engines' protective effect.
Larger/more severe fires call out more engines. - Coffee drinkers in a survey sleep less. Name a possible confounder.2 marks
Shift work/workload may affect both coffee use and sleep.
The survey alone cannot separate these effects.
For example, shift work or workload. - Why does random assignment help a treatment comparison?3 marks
Participants do not choose their treatment.
Other influences are less likely to align systematically with treatment.
It reduces systematic group differences on average. - Write a cautious conclusion: more exercise is associated with lower reported stress in a voluntary survey.2 marks
Retain the observed direction.
State sample and design limits.
In this voluntary sample, more exercise is associated with lower reported stress; causation is not established. - A company claims its product caused improvement because users improved over a month, with no comparison group. Give two alternative explanations.3 marks
Time, other support or natural changes could contribute.
Without a suitable comparison, the product effect is not isolated.
Practice effects and other changes over the month, for example.
Curriculum reference & lesson scope
Australian Curriculum v 9 and SA Curriculum Mathematics
Year 10 continuous distributions, bivariate data, two-way categorical tables, bias and investigations, with the approved percentile and standard-deviation content included in the normal chapter.
Official curriculum source ↗