# Regression to the mean.

Regression to the mean explains that, after an extreme value of a variable, the next time we will obtain a value closer to the mean.

A few days ago I read that it’s believed that there’s a curse on Sports Illustrated Magazine. Some people say that everyone who appears on its cover, all of them are successful athletes, do not take a long time to worsening their athletic performance.

You might think that this believe is another urban legend, like that about the girl on the road, but I reckon that, in this case, there could be some truth. And it’s not because the magazine is cursed, but because of a phenomenon known as regression to the mean.

## Regression to the mean

This phenomenon states that if we measure a variable for the first time in a given individual and we get an extreme value, the next time we measure the same variable we will obtain a value closest to the average value of the variable. We can apply this reasoning to the case of our athletes.

To be on the cover of Sports Illustrated, the athlete in question has to be at the top of his or her career. And from the top you can only go in one direction: down. This would explain the fact that after appearing on the cover, with time it could be a decrease in performance comparing with the level he or she was when on the spot light.

Hasn’t anyone ever told you, after doing something really bad, not to be worried because next time you do it you come out better?. It’s going to happen that there’s some mathematical truth in this.

This phenomenon is used in many aspects of life. Some people even use it to make money in the stock market, although I recommend you not to try, just in case.

But this so nice phenomenon can be the source of many errors in the interpretation of results of scientific experiments. If you think about it, healthy people can only change to illness. On the other hand, sick people can only change (if any) to improve.

As treatments are usually tested on diseases or risk factor with values worse than the ordinary, it may happen that subsequent measurements were less extremes due to the phenomenon of regression to the mean and not due to the beneficial effect of the intervention.

This explains how many times some ineffective interventions seem to be effective. If we suffer from and awful pain we’ll test different treatments. In the meantime, when we reach the worse of our illness, from then on we can only improve. If that moment coincides with any alternative remedy, we will think that this is the responsible of our improvement.

Regression to the mean is even more common when we select individuals with characteristics that vary over time, since the variation we find in the successive measurements may be due to this phenomenon and not to the intervention we’re testing.

Can we get rid of this troublesome phenomenon when we perform our studies?. The answer is no. We cannot make it go away, but we can control it with a suitable control group. As it will occur the same in both control and intervention groups, we can discriminate between the intervention effect and the regression to the mean effect.

## We’re leaving…

Finally, just say that this is not the only effect than can introduce confusion in the interpretation of the efficacy of any intervention. There are other ones like the well-known placebo effect (the effect caused by the fact of being treated with any therapy) and the Hawthorne effect, which consists in improving just by knowing we are being studied. But that’s another story…

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