Regression toward the mean facts for kids

Regression toward the mean is a cool idea that means if something really unusual or extreme happens, the next time it happens, it will probably be closer to average. Imagine someone has an amazing game in basketball, scoring way more points than usual. The next game, they'll probably score fewer points, closer to their average.

This idea was first noticed by a scientist named Francis Galton. He studied how traits like height were passed down in families. He found that very tall parents often had children who were a bit shorter than them, and very short parents often had children who were a bit taller. Galton realized that if things didn't tend to go back to the average, everything would quickly get out of control!

How It Was Discovered

In 1886, Francis Galton wrote a paper called Regression towards mediocrity in hereditary stature. In this paper, he shared his observations. He noticed that very extreme traits in parents, like being super tall, weren't fully passed on to their children. Instead, the children's traits seemed to "regress" or move back towards a more "mediocre" (average) point. Today, we call this average point the mean.

Galton measured the heights of hundreds of people. This helped him figure out how much this "regression to the mean" actually happened. He found that the difference between a child's height and the average height of the population was usually a certain fraction of the difference between their parents' height and the population average. For example, if parents were much taller than average, their child would likely be shorter than the parents, but still taller than the general average.

Understanding the Idea

Galton used the word "regression" to describe something he saw happening with traits that are passed down through many genes, like height. He noticed that children of parents who were at the very ends of the height scale (either very tall or very short) tended to be closer to the middle, or average, height of the population.

His work helped create a big part of modern statistics called linear regression analysis. This is a way to study how different things are related.

Galton's first idea about why this happened wasn't quite right. He thought that children inherited traits not just from their parents, but also from many ancestors further back, which would "average out" their traits. However, we now know that children get their genes directly from their parents. There's no "skipping" generations for genes.

A better way to understand this is to think that traits like height are controlled by many different genes. Very tall people might have many "tall" genes. But when they have children, their children only get half of their genes from each parent. So, the children might not get all the "tall" genes that made their parents so extreme. Also, things like diet and environment can affect height, not just genes. This also helps explain why children often end up closer to the average than their very extreme parents.

Sometimes, "regression to the mean" is also used to describe other situations. For example, if you measure something only a few times and get an unusual result, taking more measurements will likely bring the average closer to the true average. This is because the first few measurements might have been a bit lucky or unlucky.

Images for kids

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  Galton's experimental setup (Fig.8)

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  Francis Galton's 1886 illustration of the connection between the heights of adults and their parents. This showed that children's heights tended to be closer to the average height than their parents, which led to the idea of "regression toward the mean."

See also

In Spanish: Regresión a la media para niños