Measurement Error and Regression to the Mean in Matched Samples

This is a treatment of "regression to the mean" in matched samples produced by measurement error in matching variables. An equation expressing the respective contributions of regression and treatment effects to a difference of Y-means for two matched groups is derived, followed by an intuitive picture of regression effects showing their dependence on the variance in error and the normal distribution of error and of X. An illustration of a crude estimate of regression effects produced by measurement error in occupational prestige completes the paper. Analyses of data from matched samples (and panel studies) have long been considered vulnerable to the "regression fallacy" (or regression effects or "regression to the mean") (McNemar, 1940a, 1940b; Rulon, 1941; Thorndike, 1942). The problem is said to arise because groups under study (e.g., matched groups) have been "selected for their extremity" (Campbell and Stanley, 1966:11) on certain variables. (These variables are sometimes considered fallible; at other times considered error-free.) * We are grateful to the following for their helpful comments on earlier drafts of this paper: James Posner, Charles Werts, Robert Linn, H. M. Blalock, and Robert McGinnis. We are also indebted to the following organizations who supported the study which drew our attention to regression effects and which provided the illustrative data discussed in the latter part of this paper: the College Entrance Examination Board, and the Ford, Carnegie, Esso Education, Alfred P. Sloan, New York, Woodrow Wilson National Fellowship, Seth Sprague Education, John Hay Whitney, Field and Roger Williams Straus Memorial Foundations. This content downloaded from 157.55.39.22 on Sat, 16 Jul 2016 04:56:37 UTC All use subject to http://about.jstor.org/terms Measurement Error and Regression / 207 When we match, for example, we attempt to "equalize" the members of two or more experimental or natural groups with respect to one or more characteristics or matching variables.1 In doing this we usually oversample members of each group who are decidedly above or below the average values of each characteristic; because prior to matching, the average characteristics of the respective groups differ. As a result, the values of the matching variables of each matched group "regress" toward different and respectively less extreme population means of Y, a dependent variable or post-test, creating a difference of Y-means which is in part arti-