Correlation vs Causation: Confounders and Study Designs

Phase 1: Prepare

Step 1 Warm-up recall

From Module 1: what is the strongest claim a correlational study supports, and what does random assignment add?

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

name a confounder and reverse causation and give an example of each (Foundation);
match a design to the question it can answer: within-person change, natural experiment, randomised trial (Core);
say what a design still cannot rule out (Core).

Phase 2: Teach

Step 3 A familiar example

People who earn more also tend to be healthier, better educated and more likely to be in stable relationships. If higher earners report higher satisfaction, income, health or any of the others may be doing the work.

Step 4 Clear explanation

Two problems stand in the way of a causal claim. A confounder is a third factor that influences both things you measured (health may raise both income and satisfaction). Reverse causation means the arrow points the other way (satisfied people may perform better at work and earn more).

Three tools help, each with a limit.

Tool	What it does	What it cannot rule out
Within-person change (panel)	Compares each person with their own earlier level, which removes stable differences between people. Lucas (2007) did this for disability.	Other things that changed at the same time as the event.
Natural experiment	Uses a change that people did not choose, such as a prize drawn by lot, so the change is unrelated to the person’s traits.	Differences between who enters the situation, and whether the change is typical of other changes.
Randomised trial	Assigns the change by chance, so groups are alike on average. Best support for cause.	Short duration, narrow samples and the gap between a trial and real life.

Step 5 Worked example (4 marks)

A survey finds that people with higher incomes report higher life satisfaction. Give two non-causal explanations and one design that would help.

Confounder: health, education or stable relationships may raise both. (1 mark)
Reverse causation: satisfied people may be more productive and earn more. (1 mark)
Design: follow the same people over years and compare each person’s satisfaction before and after a change in income, to remove stable differences between people. (1 mark)
Remaining limit: other changes may coincide with the income change, so cause is still not proved. (1 mark)

Phase 3: Practise

Step 6 Learner practice (instant-marked)

1. People with more friends report higher satisfaction. Which is a confounder explanation?

2. A prize is drawn by lot among ticket buyers. Why is this useful for studying income?

3. A panel compares each person with their own earlier satisfaction. What does that remove?

4. Which design gives the best support for a causal claim?

Phase 4: Close

Step 7 Recap

Confounder: a third factor behind both. Reverse causation: the arrow points the other way.
Within-person change removes stable differences between people.
Natural experiments use changes outside people’s control.
Randomised trials give the best support for cause, with their own limits.

Step 8 Exit ticket (ungraded)

Choose a link you believe in (for example, between sleep and mood). Write one confounder and one reverse-causation story.

Your answer

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Step 9 Go further (Extension)

Look for a published study of a lottery or other chance event and life satisfaction. Note how participants were identified and what the authors say about limits.

Common mistakes

Mistake	Why it fails
Believing a large sample fixes confounding	Size reduces chance error, not systematic bias.
Treating a panel as proof of cause	It removes stable differences; simultaneous changes remain.
Dismissing correlational work as useless	It narrows the options and guides better tests.

Limits. Real studies combine tools and use statistical adjustment. This lesson names the logic, not the full methods.