Correlation and Causation (Foundation)
Correlation is a relationship between two variables, where a change in one variable tends to go with a change in the other, for example taller people often having a bigger shoe size. Causation means that a change in one variable directly causes the change in the other. In GCSE Statistics it is important to remember that correlation between two variables does not, on its own, prove that one causes the other.
Before you start
Make sure you're comfortable with these topics first:
Method
- Look at a scatter graph to see whether the points show a pattern (correlation) or are scattered with no clear pattern.
- Describe the type of correlation: positive (both variables increase together), negative (one increases as the other decreases), or none.
- Describe the strength of the correlation: strong (points close to a line) or weak (points more spread out).
- Remember that correlation only shows the two variables change together, not that one causes the other.
- Consider whether a third variable could be causing both, or whether the link could simply be coincidence, before claiming causation.
- Only conclude causation if there is a plausible mechanism linking the variables, ideally supported by other evidence, not the graph alone.
Worked example
A study finds a strong positive correlation between the number of ice creams sold and the number of people who go swimming each day in summer. A newspaper claims that eating ice cream causes people to go swimming. (a) Describe the correlation. (b) Explain why the newspaper's claim is not justified. (c) Suggest a more likely explanation.
- A strong positive correlation means that as ice cream sales increase, the number of swimmers also tends to increase.
- The claim assumes correlation proves causation, but correlation only shows that the two variables change together.
- There is no direct mechanism by which eating ice cream would cause someone to go swimming.
- A third variable, hot weather, is a more likely cause of both: hot days lead to more ice cream sales and more people swimming.
- Final answer: there is a strong positive correlation, but it does not prove causation; hot weather is a more likely common cause of both ice cream sales and the number of swimmers.
Practice questions
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Q1A scatter graph shows that as temperature increases, the number of hot drinks sold decreases. What type of correlation is this?Show answer
Answer: Negative correlation.
Q2Define correlation in your own words.Show answer
Answer: A relationship where a change in one variable is associated with a change in another variable.
Q3A study finds a positive correlation between shoe size and reading ability in primary school children. Does having big feet cause better reading?Show answer
Answer: No; this is likely due to a third variable, age (older children have bigger feet and better reading skills), not causation.
Q4What word describes a situation where one variable directly causes a change in another?Show answer
Answer: Causation.
Q5Two variables have a correlation coefficient close to 0. What does this suggest?Show answer
Answer: There is very little or no linear correlation between the variables.
Q6A researcher finds that towns with more fire engines have more fire damage, and concludes that fire engines cause fire damage. Identify the flaw in this reasoning and suggest the true common cause.Show answer
Answer: The flaw is assuming correlation proves causation; the true common cause is likely the size of the fire, since bigger fires need more fire engines and cause more damage.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A scatter graph shows a strong positive correlation between a country's number of doctors and its number of hospitals. State what 'strong positive correlation' means, and state whether this proves that having more doctors causes more hospitals to be built.
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A local newspaper reports a positive correlation between the number of umbrellas sold and the number of bus delays in a city, and claims that people buying umbrellas causes buses to be delayed. Explain why this conclusion is flawed, and suggest a more likely common cause.
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A scatter graph of 10 towns shows a positive correlation between the number of cafes and the number of car parking spaces. A student says: 'Building more car parks will cause more cafes to open.' Discuss whether the data supports this claim, referring to correlation, causation and possible other explanations.
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Free printable worksheet
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This topic is chapter 9 of GCSE Statistics Foundation Workbook 2, the whole course as one free printable PDF.
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