Regression to the middle

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Regression to the middle is a statistical term ; it describes the phenomenon that after an extremely failed measured value, the subsequent measurement is closer to the average again, if chance has an influence on the measured variable. This always applies if the two measurements correlate , but not 100%.

Since this effect cannot be understood intuitively, it leads to various thinking errors. On the one hand, illusory causal relationships are often seen instead of random regression, and on the other hand, the dampening effect of the regression is not taken into account in forecasts, but the first measured value is simply extrapolated. The sentence "The condition of depressed children who are treated with energy drinks improves significantly over a period of three months" is true, but because of the regression towards the middle, not because of the effects of the drinks. In the US sports world, the "Curse of Sports Illustrated " and the " Madden Curse " are known: an athlete shows poor performance after being featured on the cover of this magazine / game. The reason they grace the title page is often outstanding performance, which is naturally followed by mediocre performance.

history

The term goes back to the research of the British scientist Francis Galton , who demonstrated this phenomenon for the first time at a presentation at the Royal Institution . He called the effect 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 grass pea ( sweet peas ), as they do not tend to self-fertilization and its weight and size are not dependent on the surrounding humidity. After weighing and measuring thousands of peas, he confirmed that weight and height were normal . He divided the peas into seven different size classes and sent a complete set of each to friends asking them to plant them. An experiment he himself carried out failed.

He observed that the offspring were just as normally distributed within each size class as that of each full set and the parent generation. He also observed that the extremes in the offspring generation were closer together than in the previous generation.

Parent and Offspring Generation Diameter (in 1/100 of an inch)
parents 15th 16 17th 18th 19th 20th 21st
Offspring (mean diameter) 15.4 15.7 16.0 16.3 16.6 17.0 17.3

He also found that if he recorded the averages of both generations, he could connect them with a straight line - the first regression line . Galton referred to this relationship as regression or return to the middle: "The return is the tendency of the ideal, middle offspring type to deviate from the parent type and thereby return to what one could roughly and perhaps reasonably describe as the average ancestor type." ( Reversion is the tendency of the ideal mean filial type to depart from the parental type, reverting to what may be roughly and perhaps fairly described as the average ancestral type ).

The regression to the middle is responsible for the fact that, for example, the size distribution of people does not show any outliers up or down, as Galton showed in a study published in 1886 on the measurement of the body length of over 900 adult children and their parents. Even if extremely small or large parents have children, they do not keep getting smaller or bigger. Rather, he demonstrated that very tall parents generally have children whose height is smaller than their own (but which is still taller than average), while the children of very small parents are generally taller than the parents, but are still smaller than average.

Galton later researched geniuses, and especially their descendants. He found that although the children were gifted, their talent was closer to the population average than that of their parents. Ultimately, this work led Galton to develop the concept of correlation .

Economics and finance

In the economics , especially in the financial industry , an exceeding phenomenon negative autocorrelation in connection with partially yield rates , yields and rates observed. It is often referred to as the mean reversion effect .

medicine

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

If we choose, for example, as part of a screening ( screening ) under routine patients, the group of patients with the highest measured values from, for example. B. blood pressure, and examines this group again at a later point in time, the patients will usually have a value that is closer to normal - regardless of whether treatment has taken place in the meantime.

literature

Web links

Individual evidence

  1. ↑ "We will not learn to understand regression from experience." In: D. Kahneman: Thinking, fast and slow. 2011, p. 195.
  2. ↑ Example taken from D. Kahneman: Thinking, fast and slow. 2011, p. 183.
  3. ^ SM Stigler: The History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, Cambridge, Massachusetts 1986, ISBN 0-674-40341-X . (Reprinted 1990)
  4. ^ DW Forrest: Francis Galton: The Life and Work of a Victorian Genius. Taplinger, New York 1974, ISBN 0-8008-2682-5 .
  5. ^ F. Galton: Regression towards mediocrity in hereditary stature . In: Journal of the Anthropological Institute . tape 15 , 1886, p. 246–263 ( galton.org [PDF; 2.6 MB ]).
  6. ↑ P. Kleist: Four effects, phenomena and paradoxes in medicine . In: Switzerland Med Forum . tape 6 , 2006, p. 1023-1027 ( medicalforum.ch [PDF; 228 kB ]).