Two variables moving together is evidence of association, not proof that one causes the other

What it is

Correlation is not causation means that two variables changing together establishes associational evidence; a scatterplot or coefficient alone cannot show that changing one would change the other. Alternatives include reverse causation, common causes, mechanisms selecting observations into the sample, shared time trends, measurement processes, and chance. Even a strong, reproducible association does not identify causal direction, mechanism, or the result of an intervention without design and domain evidence.

Why it happens

A pooled point cloud compresses the data-generating process into a two-dimensional projection. A confounder affecting both axes can create, strengthen, attenuate, or reverse an association. Simpson's paradox describes cases where within-group and pooled trends differ, but stratification alone does not reveal the correct causal answer. Conditioning on how cases enter the sample can also induce association through a collider. Range restriction, missingness, measurement error, unmodeled repeated observations, and common time trends all alter correlations. A regression line summarizes a specified model; it is not a causal arrow.

Studying it

Frame the causal question by specifying treatment, outcome, temporal order, observational unit, and target population. Use a causal diagram or comparable assumptions to distinguish confounders, mediators, colliders, and selection factors. Randomized experiments can, within their implementation and adherence conditions, support intervention effects. Observational research should state an identification strategy such as matching, weighting, a natural experiment, or regression discontinuity, and examine sensitivity to unmeasured confounding and selection bias. Exploratory views may compare pooled data with substantively motivated strata; they should not search many groups after the fact and report only the most dramatic reversal.

Where it stops holding

Correlation remains useful for prediction, quality monitoring, and hypothesis generation, while ethics, feasibility, and external validity limit experiments. Controlling more variables does not necessarily move an estimate closer to causality: controlling a mediator changes the effect being estimated, and controlling a collider can introduce bias. Without identification, “still correlated after adjustment” remains associational. Small samples, outliers, dependent records, and multiple exploration can also make associations unstable; visualization cannot repair incorrect pairing or selective deletion.

Applying it

• Use evidence-matched terms such as “associated” and “change together” in titles, captions, and alternative text. “Causes,” “increases,” and arrows require an explicit causal design and target effect.
• State the observational or experimental design, time window, sample selection, missingness and filtering, transformations, treatment of repeated observations, and intervals for the correlation or model.
• Stratify or adjust only for candidate confounders supported by prior reasoning, and show pooled and key subgroup views together; distinguish composition changes from within-group relations.
• Provide an accessible data summary and structured table; do not use color as the sole distinction between adjusted states or groups.
• Before release, have research, domain, and communication roles check identification assumptions, statistical uncertainty, and wording. If readers restate an unsupported intervention claim, revise the title, annotation, or chart structure.

Related

• Same group: U2.05.1 Scatterplots suit the relation between two continuous variables · U2.05.2 Many points overplot; use transparency or binning
• Nearby: U3.04.1 On dual axes, relative placement is an arbitrary choice · U3.04.2 Dual axes can fabricate correlation that does not exist
• Search terms: correlation · causal inference · confounding · selection bias · Simpson's paradox