Regression away from the mean: Theory and examples

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Abstract
Using a standard repeated measures model with arbitrary true score distribution and normal error variables, we present some fundamental closed‐form results which explicitly indicate the conditions under which regression effects towards ( RTM ) and away from the mean are expected. Specifically, we show that for skewed and bimodal distributions many or even most cases will show a regression effect that is in expectation away from the mean, or that is not just towards but actually beyond the mean. We illustrate our results in quantitative detail with typical examples from experimental and biometric applications, which exhibit a clear regression away from the mean (‘egression from the mean’) signature. We aim not to repeal cautionary advice against potential RTM effects, but to present a balanced view of regression effects, based on a clear identification of the conditions governing the form that regression effects take in repeated measures designs.
Funding Information
  • Deutsche Forschungsgemeinschaft (DFG Schw 611/3-1)

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