# What does "chi" mean and come from in "chi-squared distribution"?

What does "chi" mean and come from in "chi-squared distribution"? Does "chi" mean a random variable with a standard normal distribution? Thanks!

## 1 Answer

Chi is a Greek letter. The canonical modern history references are Karl Pearson's introduction of the chi-square test in 1900 and R.A. Fisher's work in 1924, but there is ancient history too: F.R. Helmert in 1876 deserves more than a nod.

http://jeff560.tripod.com/c.html is a good start, especially if other historical bits and pieces are of interest. It includes links. Books such as Anders Hald's histories say more.

Chi appears to be just notation that Pearson used.

• +1 A couple of tidbits: Early on, the distribution of the square root of a chi-squared r.v., the chi distribution ($\chi$-) was more widely used than now; useful for standard deviations. E.g. you can occasionally see in old papers or books people writing about the $t$ distribution as the distribution of the ratio of a normal to an independent (scaled) chi. One advantage of it (but not the original motivation for it) was that the normal approximation kicks in much faster (this is pre-Wilson-Hilferty); handy when tables tended to be quite limited. Jun 1, 2013 at 0:35