Some Examples for Teaching Regression toward the Mean from a Sampling Viewpoint

The situation that the initial measurements of a high risk group of persons tends to be lower on a subsequent measurement is well established both in theory and practice. Almost every screening operation experiences this phenomenon and its understanding by the persons involved in such operations is extremely desirable. These persons are likely to have nonstatistical backgrounds, and methods to teach the concept of regression to the mean without explicit mathematics are necessary. The derivation of this concept often appears to persons with limited statistical intuition as the result of magic. The general approaches to regression toward the mean usually require the use of an explicit mathematical model containing withinand amongpersons components of variability. The regression toward the mean is obtained from information about the expected values of truncated distributions. However, the purely mathematical approach is not suitable for a basic service course in biostatistics. This paper tries to display an approach which builds understanding from simple concepts with little mathematics required. It is assumed that the students have had enough preparatory work to have some idea of probability and the standard normal distribution.