Regression fallacies in the matched groups experiment

This paper is concerned particularly with certain regression effects which appear whenever matched groups are drawn from populations which differ with regard to the characteristics being studied. It is shown that regression will produce systematic differences between specifically matched. The size and direction of these differences depends upon the differences between the parent populations both in the matching and in the experimental variables and upon the correlation between the matching and experimental variables. Formulas are presented for estimating the expected regression effect. Several alternative procedures are suggested for avoiding the erroneous conclusions which the regression effect is likely to suggest.