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1Scan for outdated or missing drivers - takes under a minute2Clear out junk files and repair common Windows errors3Fix the driver behind crashes, sound loss and screen glitchesCorrelation means two variables tend to vary together; causation means a change in one variable produces a change in another. A correlation can be a clue worth investigating, but it does not, on its own, show that one thing caused the other.
Correlation vs. causation: what’s the difference?
Correlation describes an association between variables. The commonly used correlation coefficient summarizes the direction and strength of a linear association: a positive value indicates that the variables tend to move in the same direction, while a negative value indicates that they tend to move in opposite directions. Causation is a stronger claim: changing one variable would produce a change in the other, under specified conditions.
Correlation is useful for describing patterns and may help predict one value from another. But the same observed pattern can have multiple explanations, so it is not a causal verdict. A correlation coefficient also does not capture every possible relationship: variables can be related in a nonlinear way even when their linear correlation is small or zero. [UC Berkeley: Correlation and Association]
Does correlation imply causation?
No. The phrase “correlation does not imply causation” is a warning against treating an association as proof, not a claim that correlation and causation can never occur together. A cause can create an association; the association alone does not tell you whether that happened.
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An observed relationship could also arise from chance, a third factor, biased selection of people or cases, inaccurate measurement, or other errors in study design or analysis. Statistical significance can help assess the role of chance, but it does not rule out those alternatives or establish cause and effect. [CDC: Analyzing and Interpreting Data]
A third factor can explain the pattern
Suppose a study finds higher mortality among factory workers than office workers. It would be premature to conclude that factory work caused the difference. If factory workers are substantially older, and age is related to both job category and mortality, age could account for some of the association. That third factor is a potential confounder: it is related to both the exposure being studied and the outcome, and can distort the apparent relationship between them. [CDC: Analyzing and Interpreting Data]
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A shared trend can create an association
Two variables can move together over time without one causing the other. UC Berkeley uses the example of average adult height in the United States increasing while plant species were decreasing. The variables showed a negative correlation, but a direct causal connection is not established by that pattern; the shared time period may help produce the association. [UC Berkeley: Correlation and Association]
A striking example is not a causal explanation
Allan J. Rossman’s statistics-teaching article, “Televisions, Physicians, and Life Expectancy,” compares country-level life expectancy with the number of people per television and per physician. The point is to show how a strong association can be useful to notice without showing that television availability causes longer life expectancy. A variable can help predict another while not being its cause. [Journal of Statistics Education: Televisions, Physicians, and Life Expectancy]
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What a correlation coefficient and scatter plot can—and can’t—tell you
A correlation coefficient compresses a pattern into a summary of linear direction and strength. That summary can be misleading if the relationship is nonlinear or if one unusual observation has a large influence on the result. It also does not establish which variable, if either, affects the other.
A scatter plot can help you inspect the data: look for direction, shape, clusters, and outliers. It can reveal patterns that a single coefficient conceals, but it cannot by itself prove causation. Calling one axis the “independent variable” and the other the “dependent variable” does not establish that the first is causally independent or causes the second. [CDC COVE: Scatter Plot]
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How do you know if one thing causes another?
There is no single checklist item or graph that proves causation. A sound causal argument examines how the evidence was produced, tests plausible alternatives, and considers whether different lines of evidence point in the same direction. Useful questions include:
- Did the proposed cause come first? The exposure must precede the outcome for it to be a cause.
- Were the groups comparable? Consider whether they differed in age or other factors that may affect the outcome.
- Could bias or measurement problems explain the result? Check how people entered the study, how variables were measured, and whether data collection or analysis could distort the comparison.
- Could the pattern be due to chance? Statistical testing addresses chance, but a statistically significant result can still be biased or confounded.
- Does the result fit with other evidence? Consistency, a plausible mechanism, and converging evidence can strengthen a case, while alternative explanations still need attention.
These considerations guide judgment; they do not mechanically convert an association into proof. The CDC lists temporal association, consistency, and biologic plausibility among factors to consider. Berkeley’s guidance likewise emphasizes testing alternatives and looking for multiple converging lines of evidence. [CDC: Analyzing and Interpreting Data] [UC Berkeley: Correlation and Association]
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Why randomized experiments offer stronger causal evidence
In a randomized experiment, researchers use chance to assign participants to a treatment or comparison group. Random assignment makes systematic baseline differences less likely on average, helping the groups provide a fairer comparison of outcomes. It does not guarantee that every difference disappears, but it offers stronger protection against confounding than simply observing who received an exposure. [UC Berkeley: Experiments]
Observational studies do not assign exposure this way. People or circumstances determine who is exposed, so the exposed and unexposed groups may differ in ways that also affect the outcome. Careful design and statistical adjustment can help, but adjustment cannot automatically remove confounding—particularly when important factors were not measured. [CDC: Biases to Consider in Vaccine Effectiveness Studies] [UC Berkeley: Experiments]
Randomized trials are not always practical or ethical. Observational evidence can still inform causal questions, but its interpretation depends on the study’s assumptions, potential confounders and biases, and how well it rules out alternative explanations. [From Association to Causation: Some Remarks on the History of Statistics]
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