【Haichuan Teahouse】Brain-teasing Series: The Magic Galton Board

A Galton board is an experimental device used to demonstrate the normal distribution. It consists of 3 parts. The first part, the entrance, is an open V-shaped opening. The second part, barriers – the various obstacles scattered across the central area of the entire board. Part three: vertical grooves. The usage is to insert a small ball from the V-shaped inlet; as it passes through the intermediate barrier area, its path of movement is altered by the various obstacles in that area, resulting in random motion, before it finally falls into one of the vertical slots in the vertical slot area. If a sufficient number of balls are placed, then the balls in the vertical slot area will exhibit a clear normal distribution pattern, that is, they will follow a bell-shaped curve.

If another set of Galton boards is placed beneath a Galton board, a normal distribution curve will still be observed in the vertical slits of the second set of Galton boards; however, statistically speaking, this set of curves has a larger standard deviation. Standard deviation means that there are more extreme cases. When it comes to height, through generations of evolution, there will be an increasing number of people who are either extremely tall or extremely short. But that is not the case. If one observes the right edge of the normal distribution curve, after passing through the second Galton board, the result is a further movement toward the center. To illustrate with a practical example, the first generation had very tall heights, but the second generation was not as tall ； The first generation was great, but the second generation wasn’t as good. Galton called this phenomenon \"the regression to the mean.\" Why is this?

In modern statistics, this phenomenon is referred to as “regression toward the mean.” The reason for returning to the mean is that there is not a causal relationship between the input and output, but rather a correlation. Galton was the first to realize that \"correlation is not causation.\" Success = talent + luck. And luck plays a role in it that is greater than we imagine. In terms of height, tall fathers may reach such heights not only due to genetics but also a bit of luck. As for his son, although genes can be passed down, luck cannot; therefore, it is highly likely that the son will not be as tall as his father. This is what is known as returning to the mean. Its essence is that events with low probability do not occur repeatedly; it is simply a statistical concept. Just like our own performance. It performed well on the first day; on the second day, it is most likely to perform at the **average level, rather than better or worse.

This thing needs to be done with great precision; otherwise, it won’t follow a normal distribution and will deviate……

I checked Taobao; those of good quality cost over 500

I happened to come across this while browsing Douyin yesterday.

It’s amazing, isn’t it? I checked – it’s still an important principle in statistics