Causal relationships (Edexcel GCSE Statistics): Revision Notes
Causal relationships
What is a causal relationship?
A causal relationship exists between two variables when a change in one variable directly causes a change in the other variable. This means there is a genuine cause-and-effect link between them.
Examples of causal relationships:
- The number of hours of sunshine and temperature (more sunshine causes higher temperature)
- The age of a car and its value (as cars get older, their value decreases due to wear and depreciation)
- Hours spent studying and exam performance (more study time typically leads to better results)
Correlation vs causation
This is one of the most important concepts to understand, and it frequently appears in GCSE exams!
Correlation means that two variables appear to be related - when one changes, the other tends to change too. However, correlation does not necessarily imply causation. Just because two things happen together doesn't mean one causes the other.
The key difference explained
When you see a scatter diagram showing a relationship between two variables, you need to ask yourself: "Does one variable actually cause the change in the other, or are they both affected by something else?"
The key question to always ask when examining correlations: Does one variable actually cause the change in the other, or are they both affected by something else?
Example: Temperature, ice cream sales, and sunglasses sales
Imagine you collect data and find that:
- As temperature increases, ice cream sales increase
- As temperature increases, sunglasses sales increase
- Therefore, ice cream sales and sunglasses sales are positively correlated
However, there is no causal relationship between ice cream sales and sunglasses sales. An increase in ice cream sales doesn't cause more sunglasses to be sold. Both are caused by the same third factor: temperature.
This shows correlation without causation - both variables increase together because they're both affected by temperature, but they don't affect each other directly.
Worked example: Umbrellas and road accidents
Worked Example: Analysing Correlation vs Causation
The scenario: A scatter diagram shows data about umbrella sales and road accidents in a town over 12 months. There's a positive correlation between the number of umbrellas sold and the number of road accidents.
The mistake: Someone might think: "Buying umbrellas causes road accidents" - this would be incorrect!
The correct explanation: Both variables are affected by a third factor: weather conditions, particularly rain. During rainy periods:
- More umbrellas are sold (people need protection from rain)
- More road accidents occur (wet roads are more dangerous for driving)
The umbrellas don't cause the accidents - both are caused by the same weather conditions.
Common exam traps and tips
Common Exam Traps to Avoid:
Exam trap 1: Assuming correlation means causation
What examiners look for: Students who can identify when correlation does NOT imply causation How to avoid: Always ask "Could there be a third factor affecting both variables?"
Exam trap 2: Not considering alternative explanations
What examiners look for: Students who can suggest other factors that might explain the correlation How to avoid: Think about what other variables could influence both of the ones being studied
Problem-solving method for causal relationship questions:
- Identify the two variables being compared
- Look at the type of correlation shown
- Ask yourself: "Does one variable directly cause changes in the other?"
- Consider whether there might be a third factor affecting both variables
- Explain your reasoning clearly, mentioning why correlation doesn't necessarily mean causation
Key phrases to use in exams
Essential Exam Phrases:
- "Correlation does not necessarily imply causation"
- "Both variables may be affected by a third factor"
- "There is no direct causal relationship between..."
- "The correlation could be explained by..."
Remember!
Key Points to Remember:
- Causal relationship = one variable directly causes changes in another variable
- Correlation = two variables appear to be related, but this doesn't mean one causes the other
- Always consider third factors - many correlations exist because both variables are influenced by the same external factor
- In exams, be very careful not to assume that correlation automatically means causation
- Look for alternative explanations when you see correlations in data