Correlation vs Causation
Correlation vs causation is a Grade 11 Algebra 1 statistics concept from enVision Chapter 3 distinguishing between two variables that change together versus one actually causing the other. A strong correlation coefficient r near +1 or -1 shows a pattern but does not prove causation. Ice cream sales and drowning incidents correlate strongly (r = 0.85) because both are driven by hot weather — not because ice cream causes drowning. Hours studied and test scores (r = 0.92) likely have causal direction because studying increases knowledge. Correlation can result from coincidence, a hidden third variable, or reverse causation.
Key Concepts
Correlation measures the strength and direction of a linear relationship between two variables, while causation indicates that one variable directly causes changes in another. A strong correlation coefficient $r$ (close to $\pm 1$) does not prove that one variable causes the other to change.
Common Questions
What is the difference between correlation and causation?
Correlation means two variables change together in a pattern. Causation means one variable directly causes changes in the other. Correlation does not imply causation.
Why do ice cream sales correlate with drowning incidents?
Both increase in summer due to hot weather — a confounding variable. Ice cream does not cause drowning; they share a common cause.
Can a correlation coefficient of 0.92 prove causation?
No. Even a near-perfect correlation only shows that two variables move together. Additional evidence (experiment, mechanism, or logic) is needed to establish causation.
What is a confounding variable?
A third variable that influences both measured variables, creating the appearance of a direct relationship between them. Hot weather confounds the ice cream-drowning correlation.
Do hours studied and test scores have a causal relationship?
Likely yes. Studying increases knowledge and preparation, which logically should improve performance. This is supported by both correlation data and a plausible mechanism.
What is reverse causation?
When the assumed cause is actually the effect. For example, hospitals correlate with illness — but hospitals do not cause illness; illness causes hospitalization.