Correlation and Causation
Correlation and causation are two different ideas: correlation is a statistical relationship where two variables change together, measured by a coefficient between -1 and 1, while causation means one variable directly causes a change in the other. In GCSE Statistics, Higher tier questions often give a correlation coefficient and ask why a strong value still does not prove causation.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the correlation coefficient given (or calculated from Spearman's rank or the PMCC) and describe its strength and direction.
- State that the coefficient only measures how closely the two variables change together, not whether one causes the other.
- Look for a plausible confounding (third) variable that could explain both variables changing together.
- Consider whether the direction of any causal link could be reversed, or whether the relationship could be coincidental.
- Check the sample size and time period the coefficient was calculated from; a coefficient based on very little data is less reliable evidence of a relationship.
- Use the context given in the question to write a specific explanation, rather than a generic statement that correlation is not causation.
Worked example
A researcher calculates a correlation coefficient of 0.92 between the number of libraries and the number of universities in different regions of a country. A politician claims that building more libraries causes more universities to be founded. Explain why this conclusion is not necessarily correct.
- A coefficient of 0.92 shows a very strong positive correlation between the two variables.
- This only shows the two variables tend to increase together across the regions studied, not that one causes the other.
- Identify a plausible third variable: regions with a larger population or greater investment in education are likely to have both more libraries and more universities.
- This third variable (population size or education investment) is a more likely common cause of both increases.
- Final answer: the strong correlation (0.92) does not prove causation; a third variable such as regional population size or education investment is more likely to explain why both figures rise together.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A study calculates a correlation coefficient of 0.78 between the number of police officers and the number of reported crimes in different towns. A councillor claims that employing more police officers causes more crime. Assess this claim.
Give two reasons why a strong correlation coefficient between two variables might not indicate that one causes the other.
A gym chain calculates a correlation coefficient of 0.85 between the number of coffee shops and the number of gym memberships in different towns. The marketing team claims that coffee shops encourage people to join gyms. (a) State what a correlation coefficient of 0.85 indicates about the relationship. (b) Explain whether the marketing team's claim is justified.
Free printable worksheet
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