QCE General Mathematics - Unit 3 - Bivariate data analysis 2

Association and Causation | QCE General Mathematics

Learn why association does not prove causation, including coincidence, confounding variables and cautious statistical communication.

Updated 2026-05-18 - 5 min read

An association means two variables appear to vary together. Causation means a change in one variable directly produces a change in the other. General Mathematics expects you to keep these ideas separate.

Why association is not enough

Suppose a dataset shows a positive association between ice cream sales and beach rescues. It would be weak reasoning to say ice cream causes rescues. A more sensible explanation is temperature: hot days can increase both ice cream sales and the number of swimmers.

Non-causal explanations include:

| Explanation | Meaning | |---|---| | Coincidence | the pattern appears in the sample by chance | | Common response | both variables respond to a third variable | | Confounding | another variable is mixed up with the explanatory variable | | Reverse causation | the assumed direction may be backwards |

How to write cautious conclusions

Use language such as "is associated with", "tends to", "is linked with" and "may be related to". Avoid "causes", "leads to" or "results in" unless the study design supports causation.

Good exam wording:

"The data suggest a positive association between weekly exercise time and sleep duration. This does not prove that exercise causes longer sleep because other variables, such as work schedule, health status or age, may influence both variables."

Worked example

Common traps

In modelling questions, the best answer often acknowledges both the observed pattern and its limitation. That is stronger than overclaiming.

Common response and lurking variables

A common response occurs when both variables respond to a third variable. A lurking variable is a variable not included in the analysis that may explain the association.

For example, suppose there is an association between sunscreen sales and ice-block sales. Sunscreen probably does not cause people to buy ice blocks. A warmer day can increase both. Temperature is a plausible lurking variable.

Stronger causal evidence

Evidence for causation is stronger when:

• there is a plausible mechanism
• the cause happens before the effect
• other explanations have been considered
• the relationship remains across different groups or repeated studies
• the data come from a suitable experimental or controlled design

General Mathematics questions usually do not require formal experimental design, but they do expect careful communication.

Better conclusion templates

Use this structure:

"The data show a [direction/strength/form] association between [variable A] and [variable B]. This does not prove causation because [possible non-causal explanation]."

For categorical data:

"The percentage of [outcome] is higher for [group 1] than [group 2], suggesting an association between [variables]. A possible non-causal explanation is [third variable]."

Depth: why association is not causation

An association shows that two variables vary together. Causation is a stronger claim: changing one variable directly produces a change in the other. General Mathematics questions often ask students to identify why a causal claim is not justified from an observational graph or table.

Three common explanations are:

| Issue | Meaning | Example | |---|---|---| | Confounding variable | another variable affects both variables being studied | temperature affects both ice-cream sales and beach attendance | | Reverse causation | the direction of cause may be the opposite | high stress may reduce sleep, but poor sleep may also increase stress | | Coincidence or common trend | both variables move together for unrelated reasons | two quantities both increase over time |

The safest conclusion is usually: "There is an association, but the data alone does not establish causation."

Stronger evidence for causation

Evidence for causation is stronger when:

• there is a plausible mechanism explaining how one variable affects the other
• the cause occurs before the effect
• confounding variables are controlled
• the association is seen repeatedly in different samples
• an experiment randomly assigns treatments where ethical and practical

In school data analysis, you often do not have all of this evidence. That does not make the analysis useless. It means the conclusion should be limited to association.

Writing balanced conclusions

This answer earns more than simply writing "correlation does not equal causation" because it names possible confounding variables in context.

Causal language to avoid

Avoid words such as:

• causes
• leads to
• makes
• results in
• because of

unless the study design supports causation. Use safer alternatives:

• is associated with
• tends to occur with
• is linked to
• has a relationship with
• is higher/lower for

The wording is not just style. It is part of the mathematical conclusion.

Quick check

Sources

• QCAA General Mathematics subject page
• QCAA General Mathematics 2025 syllabus
• QCAA General Mathematics 2025 formula book
• OpenStax Introductory Statistics: Correlation and Causation