Regression Toward the Mean

Regression toward the mean, or regression to the mean, is a statistical phenomenon that is often observed in student assessment and repeated measurements research in different branches of science. Regression toward the mean is present whenever a construct that is being measured is not accessible directly but is estimated by using methods that are not absolutely reliable. This is the case in the vast majority of measurements in social sciences, education, and students’ assessment. Observations with extreme values in the first measurement will tend to be closer to the mean in the second measurement, and extreme observations in the second measurement will tend to be closer to the mean in the first measurement, whenever two variables are not perfectly correlated.

Regression toward the mean must be seriously considered when designing scientific studies and data analysis to avoid making incorrect inferences. This phenomenon is observed both on a subject level and on a group level. It is caused by random fluctuations in the subjects and by nonrandom sampling of a group from the population.

The observed result of a measurement is the sum of unobserved real value and a random error of measurement. A random error influences single observations but does not affect the mean value of the whole set of observations (assuming that the sample was randomly drawn from the population). If the real value did not change between two measurements, it is expected that mean values for those two measurements stay the same. In each measurement, some observations are below the true value and others are above it. The observed value changes due to random error of measurement.

This entry presents basic information about regression toward the mean. After providing background information, it shows how this phenomenon could influence research at the subject level and at the group level and how to deal with this effect.