Regression to the Mean

Regression to the mean is the tendency for an extreme measurement to be followed by one closer to the average, purely because the extreme value was partly the product of chance. It is a property of repeated measurement, not a real change in the thing being measured — and mistaking it for one is among the most common sources of false claims of effect in research that lacks a control group.

Why it produces spurious findings

Any observed value combines a stable underlying quantity with measurement error and short-term variation. Select participants because their first measurement was extreme — the highest blood pressures, the lowest test scores, the worst-performing hospitals — and you have preferentially selected cases where chance pushed the value outward. On re-measurement, that chance component is unlikely to repeat, so the group’s average moves back toward the population mean whether or not anything was done to it.

The practical consequence: an uncontrolled before-and-after study on a group chosen for its extreme baseline will tend to show improvement even if the intervention does nothing. The effect is strongest exactly where interventions are usually targeted, which is what makes it dangerous rather than merely technical.

Where it shows up in practice

• Clinical and screening studies that enrol on a threshold value and report change from baseline.
• Quality-improvement work that targets the worst-performing units and measures them again after an intervention.
• Educational and behavioural research selecting low scorers for remediation.
• Performance management generally — the well-known observation that praising an exceptional result appears to make performance worse, and criticising a poor one appears to help, when both are regression.

What actually controls for it

Regression to the mean cannot be adjusted away after the fact by any amount of analysis; it has to be handled by design.

• A concurrent control group selected on the same criterion. Both arms regress equally, so the difference between them remains interpretable. This is the reason the control group exists, and the reason single-arm before-after designs are weak evidence.
• Randomisation, which ensures the selection effect is shared rather than confined to the treated group.
• Multiple baseline measurements before allocation, averaging out the chance component that drove the extreme value.
• Pre-specifying the analysis — see pre-registration — so a regression-driven improvement cannot be reinterpreted as a treatment effect after the fact.

What it is not

It is not confounding: no third variable is causing the change. It is not selection bias in the usual sense of an unrepresentative sample, though selection on an extreme value is what triggers it. And it is not a small effect — with noisy measures and a strict selection threshold it can account for the entire apparent benefit of an intervention.