Correlation vs. Causation
Distinguish between correlation (a statistical association) and causation (a direct cause-and-effect relationship). Evaluate real-world statistical claims critically and identify confounding variables and lurking variables.
A lesson of Algebra 1, in Data Analysis & Statistics, about 30 minutes.
By the end of this lesson, you will be able to name the four explanations for any correlation, spot a confounding variable, say what an experiment does that observation cannot, and evaluate a statistical claim you meet in the wild.
Two Different Claims
Correlation is a statement about data: two variables move together.
Causation is a statement about mechanism: changing one changes the other.
Correlation is measurable from the data alone. Causation is not, and no amount of extra data of the same kind will supply it.
$$\text{ice cream sales} \uparrow \quad \text{drownings} \uparrow$$
Real, strong, and repeated every year. Banning ice cream would prevent no drownings, because both are caused by hot weather.
This is the most consequential idea in the whole of statistics, and the most frequently ignored. Correlation is evidence that something connects the two variables. Deciding WHAT connects them requires reasoning the data cannot do for you.
Four Explanations, Every Time
When $A$ and $B$ correlate, exactly four possibilities exist. Working through all four is the discipline.
1. $A$ causes $B$. Smoking and lung cancer.
2. $B$ causes $A$. The direction is reversed. Hospitals correlate with illness because sick people go to hospitals, not because hospitals cause illness.
3. A third variable causes both. Ice cream and drownings, both driven by heat. This is confounding, and it is the most common real explanation.
4. Coincidence. With enough variables compared, some will correlate by pure chance.
Never stop at explanation 1. It is the one that comes to mind first and it is the least often correct. Asking "what else could produce this pattern?" before accepting it is the entire skill.
Sort It: Which Explanation
The firefighter one is worth sitting with. More firefighters really do accompany more damage, and sending fewer would not help at all.
Confounding Variables
A confounder is a third variable that influences both of the variables you are looking at, manufacturing a correlation between them.
$$\text{shoe size} \longleftarrow \text{AGE} \longrightarrow \text{reading level}$$
Among children, shoe size correlates strongly with reading ability. Age causes both, and within any single age group the correlation vanishes entirely.
How to hunt for one: ask what could plausibly influence BOTH variables. Age, income, education, location, season and general health account for most of the confounders you will meet.
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