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When two things move together, don't assume one is driving the other. A real relationship can be direct causation, causation running the other way, a hidden third factor driving both, or plain coincidence. The job is to work out which one you're looking at before you act on it.
The Dr. Wallace’s Favorite Mental Models is designed to turn useful ways of thinking into reusable tools. Each model gives you a fast visual overview, deeper interactive learning, practical application exercises and an AI-ready Markdown skill you can save for future use.
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When a chart, a study or a dashboard shows two things rising or falling together, that pattern alone doesn't say which one is pushing the other, or whether anything is pushing either one directly. Investigate before you commit budget, policy or trust to the relationship.
Important: both climb every summer. Neither one causes the other. Warm weather drives more swimming and more ice cream buying at the same time.
The model matters most when a chart, report or claim treats a statistical relationship as proof that one thing is causing another.
Correlation is a legitimate starting point for investigation. This model stops the jump from a plotted relationship straight to an action plan.
Notice that two variables move together: both rise, both fall, or one rises as the other falls.
Ask which of four explanations fits: direct causation, reverse causation, a shared third cause, or coincidence.
Look for evidence beyond the correlation itself: which came first, a plausible mechanism, or a controlled comparison.
Act on relationships that survive scrutiny. Keep watching the rest, and say plainly what still isn't known.
Open a use case to see what the model changes.
Check whether the channel is creating purchases or simply reaching people who were already about to buy. A holdout group or a timing check is more convincing than a chart alone before shifting budget toward it.
Support tickets and page load time might rise together because both spike during a traffic surge, not because one causes the other. Look for the shared driver before changing either system.
People who keep a regular journal often report better sleep. That could mean journaling helps, or it could mean disciplined people are more likely to do both. Consider the second explanation before crediting the habit alone.
A school using a new curriculum often also has more funding and smaller classes. Check what else changed at the same time before crediting the program by itself.
Users who discover a feature stick around longer. That could mean the feature drives retention, or it could mean engaged users are simply the ones who find features in the first place. Test it by changing who sees the feature, not by reading the correlation.
A supplement's use correlates with lower reported illness. Income, diet and access to care often move with both. Adjust for those before recommending the supplement broadly.
This is a widely used illustrative example designed to teach the method, not a real policy case.
Expand for where the maxim comes from and the tools statisticians built to test a relationship more rigorously than a chart alone.
The underlying caution is old: logicians have long named the mistake of assuming that because one event follows another, the first must have caused the second (sometimes called “post hoc ergo propter hoc,” Latin for “after this, therefore because of this”). The statistical tool most often involved, the correlation coefficient, was formalized by Karl Pearson in the 1890s. The maxim itself is a widely used statistical principle rather than one person's invention. It is best read as a standing warning about how to interpret that coefficient, not a line Pearson wrote down word for word.
In 1965, epidemiologist Austin Bradford Hill proposed a set of considerations for weighing whether an observed association is likely to be causal: among them, whether the cause happens before the effect (temporality), whether the association shows up consistently across different studies (consistency), whether a stronger exposure produces a stronger effect (biological gradient), and whether there is a believable mechanism (plausibility). Hill was explicit that none of these considerations, on its own, proves causation.
A randomized controlled trial, where researchers decide by chance who receives the intervention and who does not, is the strongest common tool, because randomization spreads unknown third factors evenly across both groups. When a trial isn't possible or ethical, researchers use natural experiments, statistical controls and causal diagrams to approximate the same logic, but each of those remains more fragile than random assignment.
A chart showing two lines tracking each other is a starting point for investigation, not a finding on its own.
If the supposed effect happened before the supposed cause, the causal story is backwards or wrong. Check the timing before the theory.
Two things can rise together because something else is driving both of them, not because either one is driving the other.
A relationship that fits a good narrative isn't automatically real. The story should follow the evidence, not the other way around.
A relationship can be statistically real and still be too small, too indirect or too confounded to justify acting on it.
Some correlations are causal and well understood. Treating every relationship as automatically suspect can be as costly as treating every relationship as automatically causal.
it comes from a randomized experiment, where assignment to each condition was made by chance rather than by choice.
the stakes are low and acting on the correlation costs little even if it turns out to be non-causal.
the decision is expensive, safety-related or affects many people, and deserves a controlled study rather than a quick judgment call.
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Save as Skill converts the model into portable Markdown instructions that teach an AI when and how to check correlation against causation, what questions to ask, what evidence to seek, what mistakes to avoid and how to structure its analysis.
Save the skills you find useful and organize them into your own reusable library. The Markdown is intentionally model-neutral, so it can be used wherever an AI system accepts uploaded files, project knowledge, custom instructions or reusable text context. Platform capabilities differ, so this is a portable skill file rather than a claim of one-click installation.
Yes. The common correlation coefficient mainly captures straight-line relationships. Two variables can have a strong, non-linear causal link (a U-shaped pattern, for example) and still show close to zero linear correlation. Always look at a plot, not just the number.
It settles it far better than an observational correlation, but a poorly designed or too-small experiment can still mislead. Sample size, how people were actually assigned to each group, and whether the experiment measured the real outcome of interest all still matter.
A confounder is a third variable that influences both things being compared and creates a misleading link between them. A mediator sits on the real causal path between two variables (A causes B partly because A causes M, which causes B), so removing a mediator from the analysis can hide a genuine effect instead of correcting a false one. Mixing the two up leads to opposite mistakes.