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Am Nat. 2005 Dec;166(6):700-7. Epub 2005 Oct 4.

Correcting for regression to the mean in behavior and ecology.

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  • 1Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182, USA. colleen.kelly@vuw.ac.nz

Abstract

If two successive trait measurements have a less-than-perfect correlation, individuals or populations will, on average, tend to be closer to the mean on the second measurement (the so-called regression effect). Thus, there is a negative correlation between an individual's state at time 1 and the change in state from time 1 to time 2. In addition, whenever groups differ in their initial mean values, the expected change in the mean value from time 1 to time 2 will differ among the groups. For example, birds feeding nestlings lose weight, but initially heavier birds lose more weight than lighter birds, a result expected from the regression effect. In sexual selection, males who remain unmated in the first year are, on average, less attractive than mated males. The regression effect predicts that these males will increase their attractiveness in the second year more than mated males. In well-designed experiments, changes in the experimental and control groups would be compared. In observational studies, however, no such comparison is available, and expected differential effects must be accounted for before they can be attributed to external causes. We describe methods to correct for the regression effect and assess alternative causal explanations.

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