## Regression effects

*June 22, 2019*

When evaluating the effect of a treatment, it may be tempting to perform the treatment on a group of subjects that have scored extremely on some measurement, and then measure the subjects again after the treatment. The difference in the measured values would provide a good estimate of the treatment effect. Or wouldn't it?

The answer is, that if measurement errors and accidental variation affect the measurements randomly, more subjects will be included with too high values than with too low, and at the next measurement they will in general not be as unlucky; their measured values will tend to be less extreme. This statistical phenomenon is known as regression to the mean. The only practically way to properly account for such regression effects is to include a control group selected using the same criteria as the treated group. Treatment effects can then be separated from regression effects in the statistical analysis.