Correlation vs Causation Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Correlation vs Causation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Correlation shows two variables move together; causation means one actually makes the other change. Correlation doesn't prove causation.

Ice cream sales and drowning deaths both increase in summer. Are ice creams deadly? No! A third factor (hot weather) causes both. This is why 'correlation \neq causation' - just because things happen together doesn't mean one causes the other.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Correlation only means two variables tend to move together. Causation requires controlled experiments to show that one variable directly produces changes in the other.

Common stuck point: News headlines often phrase correlations as causes ('X causes Y'). Students must ask: was there random assignment? Could a third variable explain both?

Worked Examples

Example 1

easy
A study finds that towns with more ice-cream shops tend to have higher crime rates. Does this mean ice-cream shops cause crime? Explain.

Solution

  1. 1
    Step 1: Identify the correlation: more ice-cream shops is associated with higher crime rates.
  2. 2
    Step 2: Consider a lurking variable: larger towns have both more ice-cream shops and more crime simply because they have more people. Population size is a confounding variable.
  3. 3
    Step 3: Correlation does not imply causation — the relationship between ice-cream shops and crime is explained by a third variable (population), not by a direct cause-and-effect link.

Answer

No, ice-cream shops do not cause crime. Both variables are related to a third factor — population size — which is the actual explanatory variable.
Correlation vs causation is a fundamental concept in statistics. Two variables may be correlated because they are both affected by a confounding variable, not because one causes the other. Establishing causation requires controlled experiments or rigorous study designs.

Example 2

medium
A newspaper headline reads: 'Students who sleep more get higher grades — sleeping longer causes better academic performance!' Critically evaluate this claim.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Data shows that countries with higher chocolate consumption per capita have more Nobel Prize winners. A blogger writes: 'Eating chocolate makes you smarter!' Give two reasons why this conclusion is flawed.

Example 2

hard
A pharmaceutical company observes that patients who take their new supplement have lower rates of heart disease compared to those who don't. The company wants to claim the supplement prevents heart disease. What type of study would provide the strongest evidence, and what conditions must it satisfy?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

correlation introvariables