Regression toward the mean

Regression toward the mean is the tendency for unusually high or low measurements to be followed by measurements closer to the average, partly because random variation is not repeated.

Correlation: Correlation measures the direction and strength of association between two variables. When repeated measurements are imperfectly correlated, extreme values tend to be followed by less extreme ones.
Francis Galton: Francis Galton was a nineteenth-century English scientist who studied heredity, statistics, and human variation. His analysis of parent and offspring heights established the classic example of regression toward the mean.
Clinical trial: A clinical trial is a prospective study that evaluates health interventions in human participants. Patients selected for unusually severe symptoms may improve even without an effective treatment.
Regression fallacy: The regression fallacy is the mistaken attribution of regression toward the mean to a causal intervention or event. It names the error of treating a return from an extreme as proof that something caused it.
Mean: The arithmetic mean is the sum of observed values divided by their number. Regression toward the mean describes movement toward this average after an extreme measurement.
Variance: Variance measures how widely values in a dataset spread around their mean. Variation between measurements leaves room for an extreme result to be followed by a less extreme one.
Galton board: A device in which falling balls bounce among pins and form an approximately bell-shaped distribution. Its random deflections illustrate how extreme starting positions can yield less extreme outcomes.
Pretest–posttest design: A study design that measures outcomes before and after an intervention. An extreme pretest score can move closer to average at posttest independently of the intervention.
Causal inference: Causal inference is the process of estimating whether one factor produces changes in another. A before-and-after improvement alone cannot show that a treatment caused the change.
Standard deviation: Standard deviation measures the typical distance of observations from their mean. It expresses how unusual an extreme measurement is relative to the distribution.

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