Correlation vs. Causation
Aligned to S-ID.C.9 — Common Core State Standards for Mathematics.
What this lesson teaches
Two variables can be correlated without one causing the other — a hidden third factor or pure coincidence may link them. Only a controlled experiment can establish cause.
Worked examples
Example 1
Ice cream sales and drowning both rise together, so they are correlated. But ice cream does not cause drowning; hot weather is the hidden factor that raises both.
Example 2
Reverse causation is the other trap. Do bigger fire crews cause more damage, or do bigger fires bring more crews?
Example 3
Only a controlled experiment separates them. That is why the treatment is assigned at random rather than chosen.
Practice questions
- Give an example of two correlated things where neither causes the other.
- Shoe size correlates with reading level in children. What hidden factor explains it?
- Why can't correlation alone prove that one variable causes another?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Correlación vs. Causalidad
Dos variables pueden estar correlacionadas sin que una cause la otra: un tercer factor oculto o pura coincidencia puede relacionarlas. Solo un experimento controlado puede establecer la causa.
Ejemplo 1: Las ventas de helado y los ahogamientos suben juntos, así que están correlacionados. Pero el helado no causa ahogamientos; el calor es el factor oculto que aumenta ambos.
Ejemplo 2: La causalidad invertida es la otra trampa. ¿Las cuadrillas grandes causan más daño, o los incendios grandes atraen más cuadrillas?
Ejemplo 3: Solo un experimento controlado los separa. Por eso el tratamiento se asigna al azar en vez de elegirse.
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