Summary: In statistics, regression toward the mean refers to the phenomenon that a variable that is extreme on its first measurement will tend to be closer to the center of the distribution on a later measurement. To avoid making wrong inferences, the possibility of regression toward the mean must be considered when designing experiments and interpreting experimental, survey, and other empirical data in the physical, life, behavioral and social sciences.

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Regression Toward the Mean and the Study of Change

Among many threats to the representation and assessment of change in behavioral research are effects associated with the phenomenon of regression toward the mean. This concept has a long history, but its definition and interpretation have remained unclear. In the present article, regression effects in longitudinal sequences of observations are examined by formulating expectations for later observations conditioned on an initial selection score value. The expectations are developed for several variations of classical test theory and autocorrelation models.

From this perspective, expectations based on the general concept of regression are seen not only to depart from those depicted in the psychometric lore but to vary considerably from one underlying model to another, particularly as one moves from the two-occasion to a multiple-occasion measurement framework. In some cases “unrelenting” regression toward the mean occurs. In others, scores may initially regress and then show egression from the mean. Still other patterns are expected for some models. In general, it is important to understand that regression toward the mean is not an ubiquitous phenomenon, nor does it always continue across occasions. It is necessary to specify the characteristics of model assumptions to understand the when, how, and extent of regression toward the mean. Past interpretations have been incomplete and to an extent incorrect because they focused largely on a limited circumstance: two-occasions of measurement and simplexlike correlation matrices.

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Regression Toward the Mean (1 of 6)

A person who scored 750 out of a possible 800 on the quantitative portion of the SAT takes the SAT again (a different form of the test is used). Assuming the second test is the same difficulty as the first and that there was no learning or practice effect, what score would you expect the person to get on the second test? The surprising answer is that the person is more likely to score below 750 than above 750; the best guess is that the person would score about 725. If this surprises you, you are not alone. This phenomenon, called regression to the mean, is counter intuitive and confusing to many professionals as well as students.

The conclusion that the expected score on the second test is below 750 depends on the assumption that scores on the test are, at least in some small part, due to chance or luck. Assume that there is a large number, say 1,000 parallel forms of a test and that (a) someone takes all 1,000 tests and (b) there are no learning, practice, or fatigue effects. Differences in the scores on these tests are therefore due to luck. This luck may be a function of simple guessing or may be a function of knowing more of the answers on some tests than on others.

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