The Art of Statistics: Learning from Data

by David Spiegelhalter

Regression-to-the-mean also operates in clinical trials. In the last chapter we saw that randomized trials were needed to evaluate new pharmaceuticals properly, since even people in the control arm showed benefit – the so-called placebo effect. This is often interpreted to mean that just taking a sugar pill (preferably a red one) actually has a beneficial effect on people’s health. But much of the improvement seen in people who do not receive any active treatment may be regression-to-the-mean, since patients are enrolled in trials when they are showing symptoms, and many of these would have resolved anyway. So if we want to know the genuine effect of installing speed cameras in accident black spots, then we should follow the approach used for evaluating pharmaceuticals and take the bold step of randomly allocating speed cameras. When such studies have been conducted, it is estimated that about two-thirds of the apparent benefit from cameras is due to regression-to-the-mean.

Regression to the mean theory in RCTs