regression towards the mean

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In statistics, the tendency for the value of a variable predicted probabilistically and with random error to be closer to its mean than predicted. When a predictor variable is used to predict the value of a dependent variable with which it is imperfectly correlated, and then the actual value of the dependent variable is observed and compared with its predicted value, the observed value turns out most often to be somewhere between the predicted value and the mean. To clarify this phenomenon, consider the limiting case of a totally unreliable predictor variable that has a zero correlation with the dependent variable. Suppose a fair coin is tossed ten times, and the number of heads (the predictor variable) is used to predict the number of heads in the following ten tosses (the dependent variable). In this case there is complete regression to the mean, the expected value of the dependent variable being equal to its mean, namely five heads. The higher the correlation between the predictor variable and the dependent variable, the less the regression towards the mean, but unless the correlation is perfectly reliable, the expected value of the dependent variable is always somewhere between its predicted value and its mean. One manifestation of this phenomenon is the fact that when values fluctuate randomly around a mean value, an extreme score is relatively improbable, so that if such a score is observed, then the following observation is likely to be a less extreme score. A familiar instance of regression towards the mean is filial regression. US regression toward the mean. See also non-regressiveness bias, one-group pretest-posttest design, regression fallacy. Compare overdominance. [From Latin regressus a stepping back + Old French moien, from Latin medius middle]

Subjects: Psychology.

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