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Module 5 · L04 of 8 ~30 min MST-12-S2-08 ⚡ +70 XP available

Causation and Correlation

A study found that countries with more TVs per household had lower infant mortality, did TVs save babies? No: wealth drives both TV ownership and healthcare quality. This lesson teaches you to spot the hidden third variable (the confounding variable) that makes correlation misleading.

Think first, Ice cream sales and drowning rates both rise in summer. Does eating ice cream cause drowning? If not, what explains both rising at the same time?
0/5QUESTS
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Orient to causation and correlation

Connect association, causation and confounding variables.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Think First, recall from memory
+5 XP warm-up

Ice cream sales and drowning rates both rise in summer. Does eating ice cream cause drowning? If not, what variable explains why both rise at the same time?

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02
The big idea, association is not causation
+5 XP to read

Correlation shows association it tells you that two variables tend to move together. It does NOT tell you that one causes the other.

A confounding variable (also called a lurking variable) is a third variable that influences both x and y, creating an apparent correlation between them.

Even r = +1 does not prove causation. You need a controlled experiment to establish cause-and-effect.

Correlation ≠ Causation
High r → association, not proof of cause
Ask: is there a third variable?
When you see a correlation, ask "what else could be driving both variables?" Temperature drives both ice-cream sales and drowning rates.
Spurious correlation
A strong correlation between completely unrelated variables (e.g. Nicolas Cage film releases and pool drownings) is called spurious, it's coincidence, not causal.
What proves causation?
Randomised controlled experiments with proper controls, not correlation alone. Statistics can suggest; experiments confirm.
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What you will learn
Know

Key facts

  • The difference between causation and correlation
  • What a confounding (lurking) variable is
  • Examples of real-world spurious correlations
Understand

Concepts

  • Why a high r value does not prove causation
  • How a confounding variable creates an apparent correlation
  • Why headlines about correlation are often misleading
Can do

Skills

  • Identify the confounding variable in a given scenario
  • Explain why a given correlation does not prove causation
  • Evaluate a news headline that confuses correlation and causation
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Key terms, causation and correlation
CausationOne variable directly causes a change in another, established by controlled experiments, not correlation alone.
Confounding variableA third variable that influences both x and y, creating an apparent (but not causal) correlation between them.
Lurking variableAnother name for a confounding variable, it is "hidden" in the data and not one of the two variables being studied.
Spurious correlationA strong correlation between two variables that has no causal or logical connection, due to coincidence or a shared third variable.
AssociationA statistical relationship between two variables, weaker claim than causation; does not imply one causes the other.
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Distinguish causal claims

Separate evidence of association from evidence that one variable causes another.

05
Causation vs correlation, the core distinction
MST-12-S2-08 core

Correlation means that two variables tend to move together. Causation means that changing one variable directly produces a change in the other.

Correlation can exist without causation in three ways:

  1. Reverse causation: Maybe y causes x, not x causing y. More hospitals in a city may correlate with more deaths, but sick people go to hospitals, not the other way around.
  2. Confounding variable: A third variable Z causes both x and y to change, making x and y appear related. Temperature (Z) drives both ice-cream sales (x) and drowning rates (y).
  3. Coincidence: By chance, two unrelated things fluctuate together over the same time period.
Key rule: No matter how strong the correlation ($r$), you cannot conclude causation from a scatterplot or correlation coefficient alone. You need experimental evidence.

Correlation is an association between two variables; causation means one variable directly produces a change in the other. High correlation does not prove causation, a third factor may explain both trends.

Pause, copy the core distinction: correlation (a statistical association measured by r) does not imply causation (a direct cause-and-effect mechanism), and note the exam phrase "association does not imply causation" into your book.

Quick check: Ice cream sales and drowning rates both rise in summer ($r = 0.87$). What is the most likely explanation?

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Identify confounders

Find hidden third variables that can drive both measured variables.

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Confounding variables, the hidden third driver
MST-12-S2-08 core

Correlation, even strong r values, does not prove that one variable causes the other. When two variables appear strongly related but neither causes the other directly, a confounding (lurking) variable is usually driving both simultaneously: for example, age drives both shoe size and reading speed in children, creating a spurious association between those two variables.

A confounding variable is one that is not being measured in the study but influences both the x and y variables, creating a misleading correlation.

Classic examples:

  • TVs and infant mortality: Countries with more TVs have lower infant mortality. Confounding variable: wealth. Wealthier countries can afford both TVs and better healthcare.
  • Shoe size and reading ability in children: Bigger shoes → better reading. Confounding variable: age. Older children have bigger feet and are better readers.
  • Hospitals and death rate: More hospitals in a suburb correlates with more deaths. Confounding variable: population size. More people means both more hospitals and more deaths.

To identify the confounding variable, ask: "What third factor could independently cause both x and y to change?"

A confounding variable is a hidden third factor that influences both variables being studied, producing a spurious correlation. To establish causation, a controlled experiment (randomised, with a control group) is required.

Pause, copy the confounding variable definition (a third variable that influences both x and y, creating a spurious correlation), a real example (age confounding shoe size and reading speed), and note that controlled experiments control for confounders into your book.

Which does NOT belong? Examples of confounding variables in research:

4

Evaluate causal evidence

Judge whether study design supports a causal conclusion.

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Evaluating causal claims, how to spot the difference
MST-12-S2-08 core

A confounding variable explains many spurious correlations, but examiners also ask you to evaluate causal claims. Four criteria help: Is the association strong and consistent? Does A always precede B in time? Is there a plausible mechanism? Does removing A reduce B? Meeting all four is much stronger evidence of causation than a high r value alone.

Many news headlines confuse correlation with causation. Here is a checklist for evaluating claims:

  1. Is this an experiment or an observation? Correlation studies observe, they cannot prove causation. Only controlled experiments (where one variable is deliberately changed) can show cause-and-effect.
  2. Is there a plausible confounding variable? If yes, the apparent correlation may be explained by the third variable, not a direct link.
  3. Could the direction be reversed? Does A cause B or does B cause A?
  4. Is the sample size large enough? Small samples can produce random correlations that disappear with more data.

Example headline: "Students who eat breakfast get better grades." This is a correlation. Confounding variable: socio-economic status, students from wealthier families are more likely to eat breakfast AND to attend well-resourced schools. The breakfast itself may not cause better grades.

To evaluate a causal claim: check whether a controlled experiment was used, look for plausible confounders, consider whether the relationship makes biological/physical sense, and look for dose-response patterns.

Pause, copy the four causal-claim criteria: strong and consistent association, temporal order (cause precedes effect), plausible mechanism, and dose-response (removing cause reduces effect) into your book.

Complete: A correlation coefficient of $r = 0.91$ between two variables shows a strong but does NOT prove .

5

Work causation examples

Compare three claims and trace the evidence behind each one.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · IDENTIFY THE CONFOUNDER

A study finds that municipalities with more fire stations have more deaths from house fires. Identify the confounding variable and explain why this correlation is not causal.

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Apparent correlation: more fire stations → more fire deaths. This seems backwards.
Intuitively fire stations should reduce deaths. Something else must explain the pattern.
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PROBLEM 2 · EVALUATE A NEWS HEADLINE

"Study shows people who drink coffee live longer." The study surveyed 10 000 adults about coffee consumption and tracked their longevity. Evaluate whether this is evidence of causation.

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Is this an experiment? No, it is an observational study (survey). No variable was deliberately changed.
Observational studies can show correlation but cannot prove causation.
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PROBLEM 3 · EXPLAIN WHY r ≠ CAUSATION

A researcher finds $r = 0.91$ between the number of letters in a country's name and its GDP per capita. Explain why this does not prove causation.

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$r = 0.91$ is a strong positive correlation, but correlation only shows association, not cause-and-effect.
No matter how high the r value, correlation alone never establishes causation.
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6

Apply causal reasoning

Classify claims and revisit the opening example.

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Activity, causation or correlation?

For each scenario, state whether it is an example of causation or correlation (or both), and identify any confounding variable:

  1. A study finds that students who own more books score higher on tests. ($r = 0.78$)
  2. A medical trial randomly assigns half of 500 patients to a new drug and half to a placebo. The drug group recovers faster.
  3. In a city, neighbourhoods with more green space have lower rates of depression. ($r = -0.65$)
  4. Sunscreen sales and skin cancer rates both increase in summer.
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Revisit your thinking

At the start you identified that temperature (hot weather) explains why both ice cream sales and drowning rates rise in summer, temperature is the confounding variable. Ice cream does not cause drowning. Both are driven by the same third variable. This is exactly the reasoning you need for HSC questions that ask you to explain why a correlation does not prove causation.

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7

Answer causation questions

Explain confounding and evaluate causal claims in context.

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Short answer
AnalyseBand 43 marks

Q1. A dataset shows that cities with more fast food restaurants have higher rates of obesity ($r = 0.83$). (a) What does $r = 0.83$ tell us about the relationship? (b) Does this prove that fast food causes obesity? Explain. (c) Identify a possible confounding variable. (3 marks)

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UnderstandBand 32 marks

Q2. Explain the difference between causation and correlation in your own words, using an example. (2 marks)

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Answers (click to reveal)

Activity: (1) Correlation, confounder: socio-economic status (wealthier families buy more books AND have better educational resources). (2) Causation, this is a controlled trial; random assignment controls for confounders. (3) Correlation, confounder: socio-economic status (wealthier areas have more green space AND better mental health services). (4) Correlation, confounder: hot weather (drives both sunscreen purchases and sun exposure leading to cancer).

Q1 (3 marks): (a) $r = 0.83$ indicates a strong positive linear correlation, cities with more fast food restaurants tend to have higher obesity rates [1]. (b) No, this is observational data, not an experiment. A confounding variable could explain the pattern [1]. (c) Possible confounder: socio-economic disadvantage. Poorer areas tend to have more fast food restaurants (cheaper food) AND higher obesity rates due to limited access to fresh food and exercise facilities [1].

Q2 (2 marks): Correlation means two variables tend to move together (association), but does not tell us why [1]. Causation means one variable directly produces a change in another. Example: smoking (x) causes lung cancer (y) is causation established by controlled studies, not just because smokers have higher lung cancer rates [1].