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Regression to the mean

If people are chosen because a measurement was unusually high or low, their next measurement will on average be closer to the average, purely because part of the original extremeness was chance.

Why it happens

Any measurement is a stable component plus a fluctuating one: biological variation, measurement error, the day someone happened to have. Selecting the extreme values selects both a genuinely extreme stable component and an unusually large fluctuation. The stable part persists; the fluctuation does not. So the second measurement is lower, on average, with nothing having changed.

What regression to the mean looks like

Regression to the mean. People selected for unusually high first measurements are measured again with nothing done, and their values move back toward the average of everyone.Regression to the mean: an extreme group selected, then measured againMeasured valueAverage of everyoneSelected for a high first valueMeasured again, with nothing doneNoise that helped a value be extreme does not repeat, so the second measurement drifts back toward theaverage without any intervention at all.
Conceptual diagram. It shows the structure of the idea, not data from any study.

Where it shows up

  • Enrolling patients with values above a threshold and reporting the improvement at follow-up.
  • Targeting quality improvement at the worst-performing wards or hospitals, then reporting their gains.
  • Any before-and-after audit that was triggered by a bad result.
  • Speed cameras placed at sites with an unusual cluster of accidents, and their apparent effect.
  • Responder analyses that define response using the same measurement used to select.

How to deal with it

The reliable defence is a concurrent control group selected the same way, since regression to the mean acts equally on both. Failing that: use the average of repeated baseline measurements to select, which reduces the fluctuating component; select on one measurement and analyse a different, later baseline; or model the expected regression explicitly using the measurement's known reliability. Analysing change scores makes it worse, not better.

What to watch out for

This is the mechanism behind most uncontrolled before-and-after improvements, and it is strongest exactly where interventions are usually targeted: at the patients, wards or hospitals selected for having the worst baseline values. The size of the effect grows with the measurement error and with how extreme the selection was, so a programme that recruits the worst 10 percent on a noisy measure will show a large improvement whether or not it does anything.

Clinical example

A clinic offers an intensive programme to patients whose HbA1c was above a threshold at one visit, and reports a large fall at six months. Some of that fall would have occurred with no programme at all, and without a comparison group selected the same way there is no way to say how much.

Recent studies that used this
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Part of the learning path Evaluate a change on your own ward (step 3 of 6).
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Sources & further reading
  1. Regression to the mean: what it is and how to deal with it (opens in a new tab) · Int J Epidemiol · doi 10.1093/ije/dyh299
  2. Statistics notes: Analysing controlled trials with baseline and follow up measurements (opens in a new tab) · BMJ · doi 10.1136/bmj.323.7321.1123
Last source review: 2026-09-06
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