Correlation means two variables tend to move together, while causation means a change in one variable directly produces a change in another. This distinction matters because data can show strong patterns that do not prove one thing caused the other. In science, medicine, economics, and daily decision making, confusing correlation with causation can lead to wrong conclusions.
A graph can suggest a relationship, but it cannot by itself prove the reason for that relationship.
A correlation may happen because A causes B, B causes A, a third variable affects both, or the pattern is a coincidence. Lurking and confounding variables are especially important because they can create or hide relationships in observed data. Experiments help establish causation by randomly assigning treatments and controlling other factors.
Good statistical reasoning asks not only whether two variables are related, but why the relationship exists.
Key Facts
- Correlation measures association, not proof of cause and effect.
- Correlation coefficient r ranges from -1 to 1.
- r = 1 means perfect positive linear correlation, r = -1 means perfect negative linear correlation, and r = 0 means no linear correlation.
- Causation means changing X produces a change in Y, often written as X causes Y.
- A confounding variable is related to both X and Y and can make a causal claim misleading.
- Randomized experiments are the strongest common method for testing causation because random assignment helps balance other variables.
Vocabulary
- Correlation
- A statistical relationship in which two variables tend to change together in a consistent pattern.
- Causation
- A cause and effect relationship in which a change in one variable directly produces a change in another variable.
- Confounding variable
- A third variable that is connected to both the possible cause and the outcome, making the relationship harder to interpret.
- Lurking variable
- An unmeasured variable that influences the variables being studied and may explain an observed pattern.
- Reverse causation
- A situation in which the outcome may actually be causing the supposed cause rather than the other way around.
Common Mistakes to Avoid
- Assuming a strong correlation proves causation is wrong because a high r value only shows a pattern between variables, not the mechanism behind it.
- Ignoring a possible confounding variable is wrong because a third factor may be responsible for changes in both variables.
- Treating time order as complete proof is wrong because even if X happens before Y, other explanations may still account for the result.
- Using observational data as if it were a randomized experiment is wrong because observed groups may differ in important ways before any treatment or exposure occurs.
Practice Questions
- 1 A study of 12 cities finds that ice cream sales and drowning incidents have correlation coefficient r = 0.86. Does this number prove that ice cream sales cause drowning incidents? Identify one likely confounding variable.
- 2 A researcher records hours studied and exam score for 20 students and finds r = 0.72. If one student studied 2 hours and scored 68, while another studied 6 hours and scored 88, calculate the change in score per extra study hour between these two students.
- 3 A school finds that students who attend a tutoring program earn higher math grades than students who do not. Explain why this observation alone does not prove the tutoring caused the higher grades, and describe an experiment that would better test causation.