Correlation vs. Causation
In short: Correlation vs causation separates two measures that rise and fall together in a data set from a real mechanism where one of them forces the other to change.
Algebra 1StatisticsS-ID.C.9
What is Correlation vs. Causation?
Whenever two quantities rise and fall together, the correlation vs causation question appears: did one produce the other, or do they only show up side by side? A strong trend in a scatter plot reveals a link in the numbers and nothing more.
Causation means that changing one variable on purpose, with everything else held fixed, changes the other. Data alone can establish an association. Proving a cause takes a randomized experiment, or strong evidence that rules out a third factor, called a lurking variable.
How to spot it
- A headline says one habit leads to or causes a result after only comparing two columns of survey data.
- A scatter plot shows a tight trend and someone argues that the trend proves one variable drives the other.
- Two quantities that both depend on the season, the weather or the size of a town grow together.
- A study reports a correlation coefficient near 1 or -1 but never assigned people to groups at random.
The method
- Describe the association first: direction, strength and form, using the scatter plot and the value of \(r\).
- Ask whether changing the first variable on purpose could really change the second, and whether the order in time makes sense.
- Hunt for a lurking variable that could drive both quantities, such as temperature, age or income.
- In any correlation vs causation decision, claim a cause only when the data come from a randomized experiment; otherwise write association.
Correlation vs. Causation: solved example
Problem
A coastal county tracks 12 months of ice cream sales and urgent-care visits for sunburn. The correlation coefficient is \(r = 0.94\). A councilor proposes banning ice cream sales to reduce sunburns. Is the plan supported by the data?
Solution
The value \(r = 0.94\) shows a strong positive association, and \(0.94^2 = 0.8836\), so about 88% of the variation in sunburn visits follows the straight-line pattern with sales.
Both quantities peak in July, when highs reach 86°F, and both drop in January. Hot weather is a lurking variable that raises beach trips and ice cream purchases together. Ice cream does not burn skin, so banning it would not change the sunburn counts. Conclusion: strong association, but no evidence of causation.
Try it
Question 1
Cities with more libraries also have more coffee shops, with \(r = 0.81\). Does opening libraries cause new coffee shops? Name a possible lurking variable.
Show the answer
No cause is shown. Population size likely drives both counts: bigger cities hold more libraries and more coffee shops.
Question 2
A researcher randomly assigns 120 students to sleep 6 hours or 9 hours before a quiz and compares scores. Why can this study support a cause claim?
Show the answer
Random assignment spreads other factors evenly across the two groups, so a score difference can be traced to the change in sleep.
Correlation vs. Causation vs. Correlation Coefficient
The correlation coefficient \(r\) is a number between \(-1\) and \(1\) that measures how closely points follow a line. It describes strength and direction of an association only. A value such as \(r = 0.97\) can come from two quantities sharing a hidden driver, so a high \(r\) never settles the cause question by itself.
Keep going
Lessons
Worksheets and quizzes
- Scatter Plots, Lines of Fit and Two-Way Tables – Worksheet
- Scatter Plots, Lines of Fit and Two-Way Tables – Quiz
Related words
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