Regression toward the mean

Regression to the mean is a term of statistics; he refers to the phenomenon that after an extremely unusual reading the subsequent measurement is again closer to the average, if the accident has an influence on the measured variable. This always works if the two measurements are correlated, but not 100 %.

Since this effect is not intuitively understand it leads to various errors in reasoning. On the one hand often illusory causal relationships instead of the random regression be seen, on the other hand the dampening effect of the regression is not considered in forecasting, but the first reading simply extrapolated. The sentence " The state of depressed children who are treated with energy drinks, improves significantly over a period of three months. " Is true, but because of regression to the mean, not due to the effect of the drinks. In the sports world, the United States you know the "Pirates of the Sports Illustrated ": An athlete shows deteriorated benefits after he was featured on the cover of this magazine. The reason why they adorn the title page, outstanding achievements, which naturally mediocre performances are often follow.

History

The term goes back to the researches of British scientist Francis Galton, who first demonstrated this phenomenon in a presentation at the Royal Institution. He called the effect of reversion (1877 ) and later regression toward mediocrity (1885 ). Galton used for his experiment on the advice of his cousin Charles Darwin and the botanist Joseph Dalton Hooker fragrance Pea ( sweet peas ), as these do not tend to self-fertilization and its weight and its size does not depend on the moisture surrounding them. He confirmed, after thousands of peas weighed and measured that weight and size were normally distributed. He divided the peas in seven different size classes and sent each a complete set of friends with an invitation to plant them. A project implemented by himself experiment failed.

He observed that the offspring were normally distributed within each size class as well as the complete set of each as well as the parental generation. Furthermore, he observed that the extremes were closer together in the offspring generation than in the previous generation.

He also found out that he, when he recorded the mean values ​​of both generations, this could be connected by a straight line - the first regression line. Galton described this context as regression or return to the center: "The return is the tendency of the ideal, middle junior type deviate from the parental type and thereby return to that one, and perhaps reasonably be described as average ancestor type coarse. " ( Reversion is the tendency of the ideal mean filial type to depart from the parental type, reverting to what may be fairly Perhaps Roughly and Described as the average ancestral type).

The regression to the mean is responsible for ensuring that, for example, the size distribution of the people has no outliers up or down as Galton showed in a 1886 study published to measure the body length of about 900 adult children and their parents. Although extremely small or large parents bring children into the world, they will not ever smaller or larger. Rather, he showed that very large parents in general children with compared to them smaller body length ( which is still larger than the average), while the children of very small parents usually be bigger than the parents, but is still smaller than the average.

Later, Galton explored genius and particularly their descendants. He found that although the children were gifted, her talent closer to the average of the population was as that of their parents. Finally, this study Galton led to the development of the concept of correlation.

Economics and Finance

In economics, particularly in the financial sector, this phenomenon is observed in the context of rates of return, returns and interest and often referred to as mean reversion effect.

Medicine

In medicine, the phenomenon plays an important role in connection with clinical studies.

If one chooses, for example, as part of routine screening (screening) under routine patients, the group of patients with the highest values ​​measured, for example, blood pressure, and investigated this group at a later time, the patient will usually have a value of at closer normal value is - regardless of whether a treatment is done in the meantime.