Regression to the Mean
What is Regression to the Mean?
Regression to the mean is the statistical tendency for extreme measurements to be followed by ones closer to the average, due to chance.
When an outcome partly reflects luck, an unusually high or low reading tends to move back toward the mean on the next measurement, with no real cause needed. In economics this can fool analysts into crediting a policy for improvement that was just a rebound from a bad year. Ignoring it causes the 'we punished the worst performers and they improved' illusion.
Regression to the Mean: a worked example
A chain of 200 stores averages $120,000 in monthly sales, with month-to-month swings driven partly by luck. Management sends the 20 worst performers, averaging $84,000, to a sales training course. The next month those stores average $101,000, a $17,000 gain, and the course is declared a success. But the 20 best stores, averaging $158,000 and given no training at all, fall to $142,000, down $16,000. Both groups drifted toward $120,000. With no untrained comparison group of equally weak stores, none of that $17,000 can be attributed to the course with any confidence.
The mistake students make with regression to the mean
The usual misreading turns regression to the mean into a force that pulls results back, which is the gambler's fallacy wearing a lab coat. A store that had a terrible month is not owed a good one. Nothing pushes it anywhere; it was selected because bad luck and its true level happened to coincide, and the bad luck simply does not repeat. The distinction matters, because the wrong version predicts an overshoot above average while regression predicts only a move partway toward it.
Regression to the Mean questions
What is regression to the mean in simple terms?
Regression to the mean means that when you pick a case because its measurement was extreme, the next measurement of that same case will usually be less extreme. It appears whenever a measurement blends a stable underlying level with random noise. The extreme reading required both an unusual true level and unusual luck, and the luck part rarely repeats, so the second reading lands closer to average.
How does regression to the mean cause false conclusions about policy?
Regression to the mean produces false policy conclusions because programs are normally aimed at the worst performers, exactly the group selected for an extreme reading. Those cases would improve at the next measurement even with no intervention at all, so a simple before-and-after comparison credits the program for a rebound it did not cause. The fix is a control group drawn from the same extreme pool, so the drift appears in both arms.
Does regression to the mean mean everything ends up average?
Regression to the mean does not flatten real differences over time. It applies to the extreme reading you selected on, not to the underlying quality, so a genuinely strong performer still scores above average next time, just below its record. If regression truly erased differences, the spread in the data would shrink every period. It does not, because fresh noise enters each round as the old noise fades.
Related terms
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