Date: 5 June 2021
This is Chapter 2 of the book, The Book of Why. This chapter is an account of the history of statistics and how it departs from understanding causation to only correlation. I personally did not validate the accuracy and completeness of the stories in the Chapter. I feel that the Author holds a strong opinion on current statistics development. I personally treat the stories like serious entertainment.
The Chapter mainly talks about the stories of three men: Francis Galton, for his famous experimental apparatus “Galton Board”; Karl Pearson, who said, “… there was a category broader than causation, namely correlation, of which causation was only the limit..”; And, Sewall Wright, the use of path diagrams.
I believe we all saw some form of Galton board somewhere. But, like myself, you may not know it was the experimental apparatus used by Galton to illustrate the “Typical Laws of Heredity” (Laws of passing characteristics from parents to children). He first discovered that the data collected on the heights of people follows a normal distribution. He believed that the balls in the Galton Board inherit their position in the same way that humans inherit their stature. But there is one problem in this explanation. If we put extra rows of pins (like another generation), the distribution will be more spread out. This contradicts the stable variation of human traits, like height across generations. What explains the stability?
Galton then discovered something called the reversion to the mean. He found that sons of tall men tend to be taller than average but not as tall as their fathers. Sons of short men tend to be shorter than average but not as short as their fathers. Galton put chutes in the Galton Board to move the “second generation” back closer to the centre (third figure).
But what explains regression to the mean? In the process of finding this out, Galton took the first step toward divorcing statistics from causation. He started to collect data of human, height, forearm length, head length, etc. He noticed that when he plotted one against the other, like height against forearm length, he found that tall men usually had longer-than-average forearms but not as far above average as their height — reversion to the mean. In Statistics term, the correlation factor is less than 1. If the correlation factor is greater than 1 (for example, correlation of father and son height), after a few generations, we would start having very tall and very short people. However, he still didn’t solve the question of what explains regression to the mean. But his efforts stopped here after he discovered correlation.
Galton ideas were picked up by Karl Pearson, an extremely important guy in the development of Statistics. In fact, he derived the first number that you will calculate in a statistic class, called correlation coefficient. In the upcoming blog posts, we would present his stories.