§-Syllabus dot point

WAMathematics ApplicationsSyllabus dot point

Why does a strong association not prove that one variable causes the other?

Distinguish association from causation, identify confounding and coincidence, and place bivariate analysis within the statistical investigation process.

How to separate association from causation, explain confounding and coincidental correlation, and work through the four-step statistical investigation process for bivariate data.

Generated by Claude Opus 4.87 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Association is not causation
Confounding variables
The statistical investigation process
Coincidental correlation

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 $r$ both measure. Causation means that changing one variable directly produces a change in the other. The leap from a high $r$ to a causal claim is the most common error in the whole topic.

There are four explanations for an observed correlation between variables $x$ and $y$ .

A causes B. Changing $x$ really does change $y$ (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 $x$ and $y$ 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.

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.

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 $r^2$ , any prediction with its interpolation or extrapolation status, and an explicit note on whether causation can be claimed.

Worked example

Judging a claim from a correlation

A council reports that across $30$ suburbs the number of parks ( $x$ ) and median house price ( $y$ ) have correlation $r = 0.78$ , and claims that building parks raises house prices.

State what r tells you

With $r = 0.78$ , there is a moderate-to-strong positive linear association between number of parks and median price. The coefficient of determination is $r^2 = 0.78^2 = 0.61$ , so about $61\%$ 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 $r$ 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 ( $r = 0.78$ , $r^2 = 0.61$ ), 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 $r$ is necessary but not sufficient evidence of a real relationship; a plausible mechanism must also exist.

Exam-style practice questions

Practice questions written in the style of SCSA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WACE 20224 marksA study finds a strong positive correlation (

r = 0.86

) 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 $r$ 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 $r$ does not imply causation and naming a plausible confounder that affects both variables.

WACE 20245 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, $r$ 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 $r$ 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.