Correlation Statistics Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
mediumA study finds a strong positive correlation between the number of firefighters at a fire and the damage caused. Does this mean sending more firefighters causes more damage? Explain.
Solution
- 1 Step 1: The confounding variable is the size of the fire — larger fires require more firefighters AND cause more damage.
- 2 Step 2: The correlation exists because both variables are driven by fire size, not because firefighters cause damage.
Answer
No. The lurking variable (fire size) drives both. Correlation does not imply causation.
This classic example illustrates why correlation does not imply causation. A confounding (lurking) variable can create a statistical association between two variables that have no causal link.
About Correlation
Correlation is a statistical relationship between two variables where changes in one are associated with changes in the other. Positive correlation means both increase together; negative correlation means one increases as the other decreases; no correlation means no consistent pattern.
Learn more about Correlation →More Correlation Examples
Example 1 medium
A scatter plot shows that as hours of study increase, test scores tend to increase. Describe the cor
Example 2 mediumClassify each as positive correlation, negative correlation, or no correlation: (a) Temperature and
Example 4 mediumA scatter plot shows that as outside temperature increases, hot chocolate sales decrease. Describe t