# Correlation is Not Causation **The model:** Two variables moving together does not mean one causes the other. The slogan is the most-repeated cautionary note in statistics for a reason: humans are pattern-matching machines, and our pattern-matcher does not natively distinguish "X causes Y" from "X and Y coincidentally co-vary" or "Z causes both." The warning's power comes from the structural reasons correlations appear without causation: 1. **Coincidence.** Pure chance, especially in large datasets where many variable pairs will randomly correlate. 2. **Confounders.** A third variable Z causes both X and Y, producing X-Y correlation without X→Y causation. 3. **Reverse causation.** Y causes X, not the other way around. 4. **Selection effects.** The correlation appears because of how the sample was drawn, not because of any underlying relationship. 5. **Misclassified noise.** The correlation is a measurement artifact. Each of these mechanisms is common in real data. A working statistical mind treats every correlation as suspect until causation has been independently established by experimental design or careful confounder control. ## The Mechanism **Spurious correlations are abundant.** Tyler Vigen's project (*Spurious Correlations*) catalogued joke-worthy examples: U.S. spending on science and suicide-by-hanging are 0.99 correlated; per-capita cheese consumption tracks bedsheet-tangling deaths. With enough variables, pure chance produces apparently-strong correlations that mean nothing causal. The lesson is not that the cheese-bedsheet correlation is interesting; it's that *strong correlations alone do not even weakly evidence causation*. **Confounders dominate observational data.** In any uncontrolled comparison, third variables explain most of what looks like direct relationships. Sample-based studies of education, income, health, and political behavior are all confounded by income, education, age, geography, and a hundred other things. The studies that produce policy-relevant causal claims do extensive work to control these — and the results are still contested. **The selection effect is the silent killer.** When a sample is drawn non-randomly, almost any correlation in the sample can be a selection artifact. Surveys of Twitter users, donations from political activists, employees of any company that hires for political views — all are non-random samples. Generalizing from selection-biased samples produces correlation-as-causation errors at industrial scale. **Reverse causation is harder to spot than confounders.** "Antidepressants are correlated with worse depression in users" — does that mean antidepressants cause depression? Or that depressed people seek antidepressants? Almost certainly the latter. The correlation is real; the implied causal direction is wrong. ## KB Applications ### Crime-and-Diversity Correlations A frequent right-wing claim: "diverse cities have more crime, therefore diversity causes crime." The correlation is real (with significant caveats about how "crime" is measured). The causal claim is unsupported. Confounders: city size (large cities are both more diverse and have more crime), historical poverty (long-poor cities have both more diversity and more crime), reporting differences (cities with more police generate more reported crime), demographic composition by age (urban populations skew younger, and crime is age-correlated). Once these are controlled, the residual effect of diversity is contested and small. The correlation has been treated as causation by activists who don't want to engage the confounders. ### Economic-Policy Causal Claims Both right and left make correlation-as-causation errors in economics. "Tax cuts in 1981 were followed by economic growth, therefore tax cuts caused the growth" — correlation, with extensive confounding (Volcker disinflation, baby-boomer entry into prime working years, the productivity boom from 1970s-era tech, oil-price normalization). "Minimum wage increases were followed by no employment decline, therefore minimum wage increases don't cause unemployment" — correlation, with confounders (booming economy, sectoral shifts, contemporaneous benefits changes). Honest economic analysis (e.g., the David Card / Alan Krueger studies, the synthetic-control methodology) goes to great lengths to identify causal effects; sloganeering on either side ignores that work. ### Vaccine and Autism The cleanest cautionary case: a single 1998 *Lancet* paper claimed an autism-vaccine correlation that turned out to be fraud. But even before the fraud was uncovered, the autism-rate increase coincided with the vaccine-schedule expansion. So the correlation existed (briefly, weakly, in selected data). The causal claim was wrong. Confounders: diagnostic-criteria expansion accounted for most of the apparent autism increase, and timing was simultaneous with many other things. The case is now the canonical example of how a confused correlation hardened into a movement. ### Why "What Is the Cause" is Often the Wrong Question The model's deeper lesson is that "what causes X" is sometimes a confused question. Many things participate in producing X; specifying *the* cause requires choosing which factor in a multi-causal web you want to highlight, and that choice is often political rather than scientific. "What caused the 2008 financial crisis?" — there are 15 viable answers, all partially correct; the choice of which to elevate tracks the analyst's framework. Recognizing this guards against both fake-precision causal claims and against treating the absence of a single cause as evidence that nothing caused anything. ## Practicing the Discipline 1. **Treat every correlation as causally suspect by default.** The burden of proof for causation is on the claimant. 2. **Ask the four questions for each correlation.** Coincidence? Confounder? Reverse causation? Selection? 3. **Look for natural experiments.** When some external event randomly assigns the X variable (different states' policy timing, eligibility cutoffs, lottery outcomes), the resulting comparisons can identify causation more cleanly than observational data. 4. **Be patient.** Causation in complex systems is hard to establish. Confident-sounding causal claims about messy social phenomena are usually wrong. ## See Also - Cause and Effect — the substantive theory - [[Counterfactuals]] — the structural test for whether correlation is causation - [[False Cause]] — the canonical fallacy form (cum hoc / post hoc) - Texas Sharpshooter — the related move of selecting which correlations to highlight