Distinguish correlation from causation, identifying confounding variables and the criteria for establishing causation

What this dot point is asking

NESA wants you to distinguish correlation from causation, identify confounding variables, and explain how science establishes causation when randomised trials are not possible. This dot point appears in 4-7 mark questions in every recent paper.

The answer

A correlation is a statistical association. Causation is a directed relationship where one variable produces changes in another. Mistaking correlation for causation is one of the most common errors in scientific reasoning and media reporting.

Correlation

A statistical association between two variables. As variable X changes, variable Y tends to change in a related way.

• Positive correlation. Both variables increase together. Ice cream sales and shark attacks (both higher in summer).
• Negative correlation. One variable increases as the other decreases. Coffee consumption and sleep duration.
• Zero correlation. No statistical association.

Correlation is measured by the correlation coefficient (r), ranging from -1 (perfect negative) through 0 (no correlation) to +1 (perfect positive).

Causation

A directed relationship where changes in X produce changes in Y. Three minimum conditions:

1. X and Y are correlated.
2. X precedes Y in time.
3. No alternative explanation (confounder) accounts for the correlation.

Why correlation does not imply causation

Three common reasons a correlation can exist without causation.

1. Confounding

A third variable causes both. Ice cream sales and drowning deaths are correlated because both are caused by hot weather. Eating ice cream does not cause drowning.

2. Reverse causation

Y causes X, not X causes Y. People with depression sometimes use cannabis to self-medicate. A correlation between cannabis use and depression might reflect depression leading to cannabis use, rather than cannabis causing depression.

3. Chance

Random fluctuations produce statistical associations in large datasets. With 100 random tests, on average 5 will appear "significant" at p < 0.05 by chance alone.

The Bradford Hill criteria

In 1965 the epidemiologist Sir Austin Bradford Hill proposed nine criteria for establishing causation from observational evidence. The criteria are not a checklist but a set of considerations to weigh.

1. Strength of association. Strong associations (relative risk over 5) are less easily explained by confounders.
2. Consistency. The association is reproduced across different populations, places and times.
3. Specificity. The cause is associated with a specific outcome, not a wide range.
4. Temporal sequence. The exposure precedes the outcome.
5. Biological gradient (dose-response). More exposure produces more outcome.
6. Plausibility. A biological mechanism is consistent with current scientific knowledge.
7. Coherence. The relationship fits known facts about the natural history of the disease.
8. Experimental evidence. Where possible, intervention reduces the outcome.
9. Analogy. Similar cause-effect relationships exist elsewhere.

Worked example: smoking and lung cancer

In the 1950s, observational studies (Doll and Hill in the UK, Wynder and Graham in the US) found that smokers had much higher lung cancer rates than non-smokers. Tobacco companies and some scientists argued correlation was not causation.

Application of Bradford Hill criteria:

1. Strength. Smokers had over 10 times the lung cancer risk of non-smokers.
2. Consistency. Replicated in dozens of studies across many countries.
3. Specificity. Smoking strongly linked to lung cancer specifically.
4. Temporal sequence. Smoking decades before cancer onset.
5. Dose-response. Pack-years strongly predicted risk.
6. Plausibility. Tobacco smoke contains over 60 carcinogens that damage DNA.
7. Coherence. Lung pathology consistent with chemical insult.
8. Experimental. Animals exposed to tar developed tumours.
9. Analogy. Other chemical carcinogens behaved similarly.

All nine criteria supported causation. The medical consensus shifted by the late 1960s. Australia's National Tobacco Strategy and the world-first plain-packaging legislation followed.

When randomised trials are not possible

For many important questions (smoking, climate, diet over decades), randomised trials are unethical or impractical. Causal inference relies on:

• Multiple independent observational studies.
• Biological mechanism.
• Dose-response evidence.
• Animal models and in vitro studies.
• Natural experiments. When policy changes (e.g. smoking bans) act like randomisation, the before-and-after comparison strengthens inference.
• Mendelian randomisation. Using genetic variants as natural randomisation for a risk factor (e.g. genetic variants for high cholesterol show that cholesterol causes heart disease).

Worked example: vaping and cardiovascular risk

In 2025, multiple Australian cohorts (45 and Up, Australian Longitudinal Study) reported associations between vaping and elevated heart rate and blood pressure in young adults. The TGA's review applied Bradford Hill criteria:

• Consistency moderate (multiple studies agree).
• Strength moderate (relative risk 1.5 to 2).
• Biological plausibility high (nicotine raises heart rate).
• Dose-response observed.
• Temporal sequence established in longitudinal studies.
• No RCT, but Mendelian randomisation supportive.

The conclusion is that vaping likely causes short-term cardiovascular changes, but long-term cancer or chronic disease causation requires longer observation. The case study illustrates how causal inference is built incrementally.

Spurious correlations

The website Spurious Correlations lists hundreds of statistically significant but absurd correlations:

• US cheese consumption per capita and number of people who died from being entangled in their bedsheets (r = 0.95).
• Maine divorce rate and margarine consumption (r = 0.99).

These illustrate that without mechanism, plausibility and the other Bradford Hill criteria, correlations alone are meaningless. They are useful pedagogical reminders.