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Surprising Inferences from Unsurprising Observations: Do Conditional Expectations Really Regress to the Mean?
David C. Schmittlein
The American Statistician
Vol. 43, No. 3 (Aug., 1989), pp. 176-183
Stable URL: http://www.jstor.org/stable/2685070
Page Count: 8
You can always find the topics here!Topics: Population mean, Statistical models, Linear regression, Random variables, Regression analysis, Probabilities, Binomials, Property reversion, Test scores, Population distributions
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Most social science descriptions of the statistical regression effect envision the effect as occurring toward the population mean. If individuals that initially had extreme values regress back toward the mean on subsequent observations, then as a corollary individuals who were at the population mean initially are expected to stay at the population mean. Both the regression to the mean statement and its corollary are generally false for models exhibiting a regression effect. For commonly used probability mixture models, conditional expectations of subsequent observations based on previous observations regress not to the mean, but to some other value. Examples are presented using mixtures of normal, Poisson, and binomial random variables.
The American Statistician © 1989 American Statistical Association