 Regression toward the mean

Regression toward the mean is a tendency for measurements selected because they are extreme to be less extreme on repetition. A large first reading can combine a persistent signal with unusually positive measurement error; a fresh error need not repeat that contribution. This can change the selected group's mean even when the underlying signal stays fixed and no intervention occurs.

The claim concerns a conditional expectation, not a rule that every individual moves toward the population mean. Some second readings are more extreme. Nor does an observed change establish a causal effect: selection alone can produce it. The following original normal distribution model makes both distinctions quantitative.

Regression toward the mean is a statistical phenomenon that occurs when extreme values or measurements in a dataset tend to be closer to the average on subsequent measurements or observations. This concept is rooted in the idea that extreme events or behaviors are often influenced by a variety of factors, some of which may be random. As a result, when a measurement is taken that is significantly above or below the average, subsequent measurements are likely to be less extreme and move closer to the mean.