Association, causation and the statistical investigation process in WACE Mathematics Applications Unit 3
“Distinguish association from causation, identify confounding and coincidence, and place bivariate analysis within the statistical investigation process.”
A correlation measures only that two variables move together; it never proves that one causes the other. A strong association can arise from a genuine cause, a reverse cause, a confounding third variable, or pure coincidence. SCSA asks you to recognise these alternatives and to place the whole bivariate analysis inside the four-step statistical investigation process: pose a question, collect data, analyse, and interpret in context.
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What this dot point is asking
You must explain why association is not causation, name and describe confounding and coincidence, and set out the statistical investigation process so that your interpretation stays inside what the data can support.
Association is not causation
Two variables are associated when knowing one tells you something about the likely value of the other, which a scatterplot and the correlation coefficient both measure. Causation means that changing one variable directly produces a change in the other. The leap from a high to a causal claim is the most common error in the whole topic.
A correlation coefficient near or shows a strong linear association. Causation is a separate, stronger claim: it says one variable drives the other. Observational data, where nothing is controlled, can support association but cannot by itself establish causation.
There are four explanations for an observed correlation between variables and .
- A causes B. Changing really does change (for example, hours of fertiliser raising crop yield).
- B causes A. The arrow runs the other way to the assumed direction.
- A confounder causes both. A hidden third variable drives and together.
- Coincidence. With enough variables, some pairs correlate by chance with no real link at all.
Confounding variables
A confounding variable is a third variable that influences both of the variables being studied, creating an association between them that is not causal.
Ice-cream sales and drownings are strongly positively correlated. Neither causes the other; the confounder is hot weather, which raises both ice-cream sales and the number of swimmers (and so drownings). Whenever you see a strong association between two unrelated-seeming variables, look for a confounder that plausibly drives both.
To argue causation you must rule out confounders, which in practice means a controlled experiment where the explanatory variable is changed while everything else is held fixed. SCSA Mathematics Applications works almost entirely with observational data, so a defensible conclusion stops at "there is a strong association" plus a comment that causation is not established.
The statistical investigation process
Every bivariate task sits inside a four-step cycle. Naming the steps and saying what happens at each is directly examinable.
- Pose a clear statistical question about two variables.
- Collect appropriate data (sample design, response and explanatory variables).
- Analyse with a scatterplot, the correlation coefficient , the coefficient of determination , and the least-squares line.
- Interpret the analysis in context and report, staying within what the data supports.
The interpretation step is where marks are won or lost. A complete interpretation reports the direction, form and strength of the association, the proportion of variation explained by , any prediction with its interpolation or extrapolation status, and an explicit note on whether causation can be claimed.
Judging a claim from a correlation
A council reports that across suburbs the number of parks () and median house price () have correlation , and claims that building parks raises house prices.
State what r tells you
With , there is a moderate-to-strong positive linear association between number of parks and median price. The coefficient of determination is , so about of the variation in median price is explained by the linear relationship with park count.
Test the causal claim
The data is observational, so the claim is not justified from alone. A confounder fits well: wealthier, established suburbs tend to have both more parks and higher house prices, so suburb affluence drives both variables.
Report safely
A defensible conclusion is: there is a moderate-to-strong positive association between parks and median price (, ), but because the data is observational and affluence is a likely confounder, the data does not show that parks cause higher prices.
Coincidental correlation
With many variables measured over time, some pairs will correlate strongly by chance even though no mechanism links them. These coincidental (or "spurious") correlations are a reminder that a large is necessary but not sufficient evidence of a real relationship; a plausible mechanism must also exist.
- Reading causation into a correlation
- A strong supports association only. Never write "x causes y" from observational data.
- Forgetting to name a confounder
- Questions that ask "why is the claim not justified" expect a specific, plausible third variable, not just "correlation is not causation".
- Skipping the context in the conclusion
- Interpret in the variables of the question (parks, prices, drownings), not in abstract symbols.
- Treating as a percentage of data points
- is the proportion of variation in the response variable explained by the linear relationship, not the fraction of points on the line.
Exam-style questions
Questions in the style of SCSA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
WACE 2022-style4 marksA study finds a strong positive correlation () between the number of lifeguards on a beach and the number of drownings recorded that day. A newspaper claims that lifeguards cause drownings. Explain why this claim is not justified and identify a possible confounding variable.Show worked answer →
A high measures only the strength of the linear association, not the direction of any cause.
The claim is not justified because correlation does not establish causation. The two variables move together, but a third variable can drive both. (2 marks)
A confounding variable here is the number of beachgoers (or hot weather). On hot, busy days more people swim, so more lifeguards are rostered and more drownings occur. The beachgoer count explains both, so the lifeguard-drowning link is non-causal. (2 marks)
Markers reward stating that does not imply causation and naming a plausible confounder that affects both variables.
WACE 2024-style5 marksDescribe the four steps of the statistical investigation process, then explain which step is where a researcher must be careful not to overstate a causal claim from an observed correlation.Show worked answer →
The statistical investigation process has four stages.
Step 1, pose a clear statistical question. Step 2, collect or obtain appropriate data. Step 3, analyse the data with displays and numerical summaries such as a scatterplot, and the least-squares line. Step 4, interpret the results and report a conclusion in context. (3 marks)
The risk of overstating causation arises at Step 4, interpretation. A strong supports an association only; claiming one variable causes the other requires a controlled experiment or elimination of confounders, not an observational correlation. (2 marks)
Markers reward all four named steps and locating the causation caution at the interpretation stage.