Correlation and Causation (Higher)
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
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Q1A correlation coefficient of 0.95 is calculated between two variables. What does this value tell you about the strength of the relationship?Show answer
Answer: It shows a very strong positive correlation (close to 1).
Q2State the term used for a variable that affects both variables in a study, potentially producing a correlation without direct causation.Show answer
Answer: A confounding (third) variable.
Q3A study calculates a correlation coefficient of -0.85 between hours of television watched and exam grade. Does this prove watching television causes lower grades? Give a reason.Show answer
Answer: No; correlation does not prove causation, a third variable (e.g. less time spent revising) could explain both.
Q4Two variables have a correlation coefficient of 0.08. What does this suggest about a causal link between them?Show answer
Answer: Very little to no linear relationship, so there is no evidence here to support a causal link.
Q5A correlation coefficient of 0.99 is found between two variables using only 4 data points. Give one reason to be cautious about this result.Show answer
Answer: The sample size is very small, so the strong correlation could be due to chance rather than a real relationship.
Q6Explain why a strong correlation coefficient calculated over a very short time period should be treated with caution when claiming causation.Show answer
Answer: A short time period may not capture enough variation and could reflect a temporary coincidence rather than a genuine, lasting relationship.
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.
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Give two reasons why a strong correlation coefficient between two variables might not indicate that one causes the other.
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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.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the correlation and causation (higher) worksheet pack - 18 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 13 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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